Prokon manual

Installing PROKON 1-1

Chapter

Installing PROKON

This explains the procedures for installing PROKON. step-by-step to help new users avoid pitfalls. The minimum and recommended system requirements are also given.

Installing PROKON 1-2

Quick Reference

System Requirements 3

Program Installation 5

Precautionary measures 18

System Requirements 1-3

System Requirements

The minimum system requirements and recommended specification to run the 32-bit Windows version of PROKON are:

Required Recommended

PC with Pentium II or higher processor running Windows 98 second edition, Windows 2000 or Windows XP

Pentium IV or higher

128 MB RAM, 100 MB free disk space 256 MB RAM or more

CD-Rom drive or access to one over a network

VGA adapter displaying 800x600 resolution in 256 colours

Super VGA adapter displaying 1024x768 resolution in High Colour

The suite often needs to save temporary information on your hard disk. For this purpose, the Windows temporary folder, typically ’C:\Windows\Temp’ or C:\WinNT\Temp’, is used. Especially when analysing large structures, a significant amount of error-free disk space may be required.

Tip: To check your hard disk for errors, it is recommended that you use Scandisk, or similar program, on a regular basis.

System Requirements 1-4

Program Installation 1-5

Program Installation

Wait for the auto-run function or browse your CD’s content for the SETUP.EXE file. Run the SETUP.EXE file and the following window will appear. Welcome to PROKON Structural Analysis and Design!


Installed folders

Before installing PROKON, we recommend you take a moment to study the folder tree that will be created during installation. The main components are:

• The main suite folder: This is the folder enclosing all program folders and is always called ’Prokon’.

• The main program folder: The folder that contains all the executable programs and other files that make up the system. The folder has a child folder where the Dos components of the suite reside.

• The default data folder: This is the folder used for data storage. Directly after installation, the working folder is set to ’\Prokon\Data\Demo’. When you start to use the suite, you will be creating new working folders where input and output data will be stored. Working folders can be created anywhere on your computer, or even on your network.

• User folders: Each user’s preferences, e.g. favourite design codes and on-screen layout of each program, are automatically stored in a dedicated folder.

Note: The default data folder, ’\Prokon\Data\Demo’, is the only data folder created during installation. Other data folders are created only when you define new working folders while using PROKON.

The installation procedure is discussed in the following text. Please follow all instructions carefully to ensure error-free installation.


Installing on a standalone computer

The procedure to install and activate PROKON on a stand-alone PC can be broken into two steps:

1. Installing the programs to your hard disk.

2. Activating the programs for use.

Installing the program files to your hard disk. To copy the program files, follow the steps below:

• Check the PC’s date and time and adjust if necessary. To adjust the date or time, double-click the clock displayed on the Task Bar. Alternatively open the Control Panel and double-click Date/Time.

• Insert the CD-Rom and wait for the PROKON Structural Analysis and Design Setup utility to start. If the utility does not start automatically, then run ’Setup.exe’ on the CD-Rom. You can read the latest Newsletter by selecting the Release Notes button. Click next to proceed.

• The location of the Destination Folder where the PROKON suite will reside, i.e. the main suite folder will default to ‘C:\Prokon’. Optionally use ‘Browse’ to choose a parent folder. If you browse to 'C:\Program Files', for example, the suite will be installed in 'C:\Program Files\Prokon'. The ‘Disk Usage’ button will show you a summary of the available space on all your local and mapped physical drives. Use the Reset button only if you want to go back to the default settings. Click ‘Next’ to proceed.

• Click Install to begin installation. If you want to review or change any of your installation settings, press ‘Back’. Click ‘Cancel’ to exit the installation wizard at any time.

• Click ‘Finish’ to complete the installation process.


Activating the programs The above installation procedure copies all necessary program files to your PC. You will, however, be unable to use the programs until you activate them.

The licensing method of PROKON has changed from the pervious versions. Terminology:

License (Seat): A collection of PROKON modules installed on a stand alone or network computer. A user can have more than one license installed to enable network users to access more than one PROKON package at the same time. One license can be split into two sets, i.e. collection of steel and a collection of concrete modules. Two network users can run one license of PROKON if it is split into two sets.

Sets: One license of PROKON can be ordered in two different sets. In this case two users can each access one set of PROKON. It is important to note that both users will then be limited to the modules within their own set. Sets can be exchanged by selecting the relevant setting on the ‘Settings’ Æ ‘User name’ menu in Calcpad.

To activate the programs:

After completing the above installation steps, run the PROKON for the first time. The following window will appear:

You can also find this window at the ‘Tools’ menu in Calcpad under ‘Activate programs’ .

Various activation options are available for the user.

• Activate through internet: Make sure that your computer is connected to the internet. The activation program will use the following ports to access the PROKON web server: Port 80, 20 and 21. (Normal browsing and FTP ports). The local PROKON software will then communicate with the remote PROKON web server. The following information will appear in the Activate stations’ window:

• Number of sets: This indicates the number of sets ordered.

• Number available: The number of sets available for the user to activate.

• Number to activate: The user can specify the number


of sets (Set1 and Set2) to be activated.

• Activate through E-mail: PROKON will use the default e-mail program; such as Microsoft Outlook to generate an encrypted e-mail. The user has to enter the number of sets to activate on Set 1 or/and Set 2. Click on ‘Send E-mail’ and the default e-mail program will open with a new e-mail window. It is very important to note that the user shouldn’ t change the contents of the e-mail. The web server at PROKON will reply within minutes (depending on the user’ s e-mail poll interval time) with the return code. Click on the ‘Enter Return code' button and type in the user specific random return code.

• Activate by phoning PROKON: If the above mentioned methods fails or is unavailable, the user can contact the nearest PROKON dealer.

• Run PROKON in demo mode: This mode will allow the user to evaluate the software. All the modules will run in a restricted mode until activation. The activation window is located under the ‘Tools’ menu in PROKON Calcpad.

Note: You can install PROKON on any number of PCs. Activation of the suite will however be limited to the number of available workstations. You can however at any time deactivate an active workstation to restore the set on the web server, and then activate the suite on another PC.

Deactivating an active workstation You can at any time deactivate an active workstation, e.g. to move it to another PC:

• Check the PC's date and time and adjust if necessary.

• Click on the tools menu in PROKON ‘calcpad’ .

• Select deactivate programs form the ‘Tools’ menu:

• Deactivate through internet: As discussed above, use this option only if you have an active internet connection. Select the amount of licences to deactivate from the window. The active licenses will be clearly indicated in the number available row. Click on the ‘Ok’ button, and all your modules will return to demo mode.


• Deactivate through E-mail: Type in the number of licenses to deactivate. Click on ‘Send E-mail’ and PROKON will generate an encrypted e-mail message with your default e-mail program. Send the message and the PROKON web server will credit you your licenses.

• Deactivate by phoning PROKON: If the above mentioned methods fails or is unavailable, the user can contact the nearest PROKON dealer.

Note: Deactivating does not delete any files. Instead, all program and data files are left in position to enable you to later activate the workstation again. To completely remove PROKON from a PC, use the Uninstall procedure described on page 1-17


Activating a deactivated workstation To reactivate a deactivated workstation:

• Check the PC’s date and time and adjust if necessary.

• Run PROKON Structural analysis and design software.

• Click on the ‘Tools’ dropdown menu, and select Activate programs. Follow the same procedure discussed on page 1-8.


Installing on a network

PROKON can be installed on a network for simultaneous use by more than one person. The number of simultaneous users will be limited to the number of sets ordered, i.e. number of licences.

The network installation procedure has three steps:

1. Copying the program files to the server.

2. Activating the programs for simultaneous use.

3. Configuring each workstation that will use PROKON.

Note: You do not need a dedicated file server to be able to install PROKON on your network. Any PC on the network, even an ordinary PC connected to a peer-to-peer network, can be identified as the ’server’ for the purpose of sharing PROKON.

In the explanation of the network installation procedure that follows below, the following terminology is used:

• Server: The computer on to which the suite will be installed.

• Local PC: The computer where you are seated when you install the suite.

• Workstation: A computer that will access PROKON over the network.

Note: To install PROKON on a server running Windows NT Server software, you may need to first log in as an administrator.

Copying the program files to the server The network installation procedure may be performed from any of the connected network PCs, i.e. a workstation or the server itself. You may however find it easiest to perform the procedure while seated at the server itself:

• Check the server PC’s date, time and time zone settings and adjust if necessary. To adjust the date, time or time zone, double-click the clock displayed on the Task Bar. Alternatively open the Control Panel and double-click Date/Time.

• Insert the CD-Rom and wait for the PROKON Setup Wizard utility to start. If the utility does not start automatically, then run ’Setup.exe’ on the CD-Rom.

• The location of the Destination Folder where the PROKON suite will reside, i.e. the main suite folder will default to ‘C:\Prokon’ . Optionally use Browse to choose a parent folder. You are free to also browse the Network Neighbourhood for an appropriate folder. If you browse to '\\Server\Shared Applications', for example, the suite will be installed in '\\Server\Shared Applications\Prokon'. The ‘Disk Usage’ button will show you a summary


of the available space on all your local and mapped physical drives. Use the Reset button only if you want to go back to the default settings. Click ‘Next’ to proceed.

• Click ‘Install’ to begin installation. If you want to review or change any of your installation settings, press ‘Back’ . Click ‘Cancel’ to exit the installation wizard at any time.

• Click ‘Finish’ to complete the installation process.

Activating the programs for simultaneous use over the network The above installation steps will have copied all the necessary files to the server. You will, however, be unable to use the programs until you activate them.

To allow simultaneous use of PROKON on your network, you only need to activate the programs on the server. All connected workstations will then automatically be allowed access to the system.

To activate the programs on the server:

• After completing the above steps and still seated at the same computer, i.e. workstation or server, run PROKON for the first time. The following window will appear:

You can also find this window at the tools menu in PROKON Calcad under Activate programs.

Various activation options are available for the user.

• Activate through internet: Make sure that your computer is connected to the internet. The activation program will use the following ports to access the PROKON web server: Port 80, 20 and 21. (Normal browsing and FTP ports). The local PROKON software will then communicate with the remote PROKON web server. The following information will appear in the Activate stations’ window:


• Number available: The number of sets available for the user to activate.


• Number to activate: The user can specify the number of sets (Set1 and Set2) to be activated.

• Activate through E-mail: PROKON will use the default e-mail program; such as Microsoft Outlook to generate an encrypted e-mail. The user has to enter the number of sets to activate on Set 1 or/and Set 2. Click on ‘Send E-mail’ and the default e-mail program will open with a new e-mail window. It is very important to note that the user shouldn’ t change the contents of the e-mail. The web server at PROKON will reply within minuets (depending on the user’ s e-mail poll interval time) with the return code. Click on ‘Enter Return code’ button and type in the user specific random return code.

• Activate by phoning PROKON: If the above mentioned methods fails or is unavailable, the user can contact the nearest PROKON dealer.

• Run PROKON in demo mode: This mode will allow the user to evaluate the software. All the modules will run in a restricted mode until activation. The activation window is located under the tools menu in PROKON calcpad.

Note: The number of simultaneous network users will be limited to the number of sets selected when you activate the suite.

Assigning network user privileges User permissions on your server need be configured correctly to ensure error-free performance. All installed folders may have read-only access except for the following folders that require full control:

• User folder and sub-folders where each user's preferences are saved.

• The Prolock folder contains the PROKON installation status and keeps a log of users accessing the system.

• The Dos folder under the main program folder, Bin, contains configuration files for the Dos modules. Read-only access is sufficient for the Bin folder itself.

• Data folder with sub-folders for different jobs.

Refer to page 6 for more details regarding the installed folders.


Configuring the network workstations to use PROKON After successfully installing and activating PROKON on your server, configuring the workstations is a simple case of creating a shortcut on each station.

To prevent unnecessary copy-protection errors and for the sake of accurate record keeping on your network, it is essential that the date and time of each workstation should be correct. Because Windows intelligently manages file creation times on networks across different time zone, each workstation should also be using the correct time zone setting.

To check or adjust a PC’s date, time and time zone settings double-click the clock displayed on the Task Bar. Alternatively open the Control Panel and double-click Date/Time. If you change the PC’s time zone, you need to restart the PC to make the change take effect.

To create a shortcut on a workstation:

• Seated at the workstation, browse the Network Neighbourhood to the main program folder on the server, e.g. \\server\prokon\bin

• Locate the file, ‘Prokon32.exe’ within the main program folder.

• Single click on the file to select it. Single click the right mouse button on the file and select send to from the menu. Another menu will appear. Select Desktop (create shortcut). The icon displayed on the Desktop of the workstation will run the PROKON package.

Note: For a network installation it is not necessary to install the PROKON CD on each individual workstation.

If you are using multiple sets

More than one set of programs can be activated on the server using the procedure described on the previous page. On running PROKON, a user can select the set to use when setting his User name.

The set selected is saved as part of the user preferences. In other words, using the example of separate steel design and concrete design sets, a steel designer needs to select the steel design set only the first time he uses PROKON.


The next time he uses the system, he will automatically be presented with the steel design set. More details regarding the setting of a user name are in given in Chapter 2.

Deactivating a network installation You can deactivate a network installation:

• Check the server PC’s date and time and adjust if necessary.

• Click on the ‘Tools’ Æ ‘Deactivate’ menu in Calcpad.

• Deactivate through internet: Make sure that your computer is connected to the internet. The deactivation program will use the following ports to access the PROKON web server: Port 80, 20 and 21. (Normal browsing and FTP ports). The local PROKON software will then communicate with the remote PROKON web server. The following information will appear in the deactivate stations’ window:


• Number active: The number of sets available for deactivation.

• Number to deactivate: The user can specify the number of sets (Set1 and Set2) to be deactivated.

• Deactivate through E-mail: PROKON will use the default e-mail program; such as Microsoft Outlook to generate an encrypted e-mail. The user has to enter the number of sets to activate on Set 1 or/and Set 2. Click on ‘Send E-mail’ and the default e-mail program will open with a new e-mail window. It is very important to note that the user shouldn’ t change the contents of the e-mail. The web server at PROKON will then credit your account with the relevant amount of licences.

• Deactivate by phoning PROKON: If the above-mentioned methods fails or is unavailable, the user can contact the nearest PROKON dealer.


Uninstalling PROKON

To remove PROKON from a PC or network, follow the steps below:

• Seated at the PC where PROKON is installed or at the server in the case of a network installation:

• Insert the CD-Rom and wait for the Setup utility to start. If the utility does not start automatically, then run ’Setup.exe’ on the CD-Rom.

• Click Remove to remove the program files.

Note: Some files or folders may not be removed during the uninstall procedure. Folders containing data, for example, will not be removed automatically and will need to deleted manually. Remember to deactivate the software first as discussed on page 1-9.

Precautionary measures 1-18

Precautionary measures

The activation status of your PROKON programs may be damaged in some instances. The following situations require the programs to be deactivated first and activated again afterwards:

• Moving the programs to another folder on a local or network drive. Unlike the DOS version of PROKON, you are free to move or copy data folders.

• Compacting the hard disk using Drivespace or similar disk compression utility.

• Converting the hard disk file structure to FAT32 under Windows 98.

• Upgrading of hardware, e.g. replacement of the hard disk.

Note: Disk defragmenting utilities such as Defrag can be used safely with PROKON.

To deactivate the PROKON suite, follow the procedures described on the previous pages.

The importance of dates and times Dates are recorded as part of the suite’s copy protection system. To prevent unnecessary errors, it is important that all relevant computers should have the correct date and time. Windows has a built-in feature that intelligently adjusts the date and time on networks spanning across different time zones. This means that you should also ensure that all computers use the correct time zone settings.

To check or adjust a PC’s date, time or time zone settings, double-click the clock displayed on the Task Bar. Alternatively open the Control Panel and double-click Date/Time. If you change the PC’s time zone, you need to restart the PC for the change to take effect.

The PROKON Basics 2-1

Chapter

The PROKON Basics

The basic principles of using PROKON are discussed in this chapter. Starting with the issues you need to address when using the program for the first time, e.g. setting up a working folder, the text progresses to everyday tasks like running analysis and design modules. The chapter ends with explaining advanced procedures like creating an equation library and customising the page layout for your projects.

The PROKON Basics 2-2

Quick Reference

Using PROKON for the First Time 3 Using the Analysis and Design Modules 11 Using the Table Editor 19 Using the PROKON Calculator 27 Working with Pictures 29 Adding Text and Graphics 35 Working with Equations 41 Customising the Page Layout 51 Configuring the Section Database 57 Configuring the Material Database 60

Using PROKON for the First Time 2-3

Using PROKON for the First Time

Depending on the shortcut options chosen during the installation procedure, you will be able to run PROKON by double-clicking the shortcut on the Desktop or selecting it from the Start Menu.


Configuring PROKON

On launching PROKON, the main program, called Calcpad, is displayed. From here, you are able to launch the individual analysis and design modules. Calcpad is also the application that you will use to collect analysis and design results and save them in project files.

Some aspects are best attended to immediately when using PROKON for the first time:

• Creating a user folder.

• Setting the preferred design codes, design parameters and units of measurement.

• Setting up a working folder.

• Selecting a wallpaper.

• Customising your project’s appearance.

Note: When running PROKON for the very first time, the default design codes and units of measurement are automatically set to match your current Windows Regional Settings. To check or change your settings, open Control Panel and double-click Regional Settings.

Once you start using the PROKON analysis and design modules, you will want to progress to working with project files:

• Entering a header for a project.

• Working with more than one project at a time.

• File management.

Setting your user name The PROKON suite can be made to adapt to your style of working by automatically saving your preferences in a user folder. Information recorded include:

• Preferences: Design codes, units of measurement and custom sections.

• Display properties: Size and position of each module on the screen.

To select your user folder or create a new one, open the Settings menu and choose User. The user folder resides under the main PROKON program folder. If you use the system on a network, you will be able to select your user folder regardless of which workstation on the network you use.


If you are using multiple sets on a network

If more than one set of programs has can be activated on your network, e.g. a set with mainly steel design modules and another with mainly concrete design modules, each user can select a set to use. The sets are identified by the relevant Key Disk numbers.

The set selected is saved as part of the user preferences. In other words, using the example of separate steel design and concrete design sets, a steel designer needs to select the steel design set only the first time he uses PROKON. The next time he uses the system, he will automatically be presented with the steel design set. More details regarding the setting of a user name are in given in Chapter 2.

Selecting your preferences During program installation, the default design codes and units of measurement are automatically set according to your PC’s regional settings, i.e. the information recorded in the Regional settings function of the Windows Control Panel.

To change your preferred design code and parameters, use the General preferences command on the Settings menu.

The design modules use the selected preferences to determine the default values for design codes and relevant design parameters. You can however temporarily override these setting using the Design code, Units or Preferences command on a design module’s File menu.

If a particular preference is not available in module, e.g. the preferred design code is not supported, the module will automatically make a next-best selection.

Note: The preferences for the Dos modules are set separately using the Design codes (Dos) command. Refer to page 2-15 for detail.


Setting up a working folder By default, all input and output data is saved in the working folder. The first time you use PROKON, the working folder will be set to ’. . .\Prokon\Data\Demo’. Once you get accustomed to using the suite, it is recommended that you create a new working folder for each project you are working on. Working folders can be created in any convenient location, be it on you own hard disk or on the network.

To create a new working folder or select another existing folder, open the Settings menu and choose Working Folder. When naming a new working folder, you should use a valid Windows folder name:

• A folder name may contain up to 255 characters, including spaces.

• A folder name cannot contain the following characters: \ / : * ? " < > |.

Note: The Dos modules also use the working folder to save data files. This effectively removes the eight plus three character limitation imposed by Dos.

Selecting a wallpaper To personalise your PROKON workstation, you may want to display a wallpaper in Calcpad. To load a wallpaper, open the Settings menu and choose Wallpaper. The following limitations apply to wallpapers:

• Supported graphics formats include: Windows Bitmap (.bmp), Icon (.ico), Metafile (.wmf) and Enhanced Metafile (.emf).

• The wallpaper image is scaled to fit the Calcpad working area. Therefore, not all images will necessarily look well.

Customising your project’s appearance Once you get accustomed to using PROKON, it is recommended that you use the procedures explained from page 2-51 to load another page template or create your own template.


Working with project files

Apart from acting as a launch platform for the analysis and design modules, you can use Calcpad to group analysis results and design calculations and then save all the information in a project file.

You can use project files to keep a complete record of all your analysis and design calculations:

• In an analysis or design module, the input data and results are typically collected on the module’s Calcsheets page from where you send it to Calcpad. For an explanation of the procedure, refer to page 2-13 and 2-17.

• Results obtained from the various analysis and design modules are then saved together in a project file.

• You can then use Calcpad to supplement the results from the analysis and design modules with additional design notes and pictures. Refer to page 2-35 for more detail.

• Links are retained with each individual analysis via data file objects. These objects are visible in the right-hand margin as yellow folders. Double-clicking a data file object recalls the original input data in the relevant analysis or design module.

• To perform calculations not covered in the scope of the design modules, you can use equations – a feature built into Calcpad. The use of the Equation Editor is explained on page 2-41.

Entering a header for a project The information at the top each page should be completed to reflect the designers name, the date etc. To edit the header information:

• Select the Header command from the Edit menu or double-click the header in Calcpad.

• Type the information for each field.

• To insert the current date, click Insert date.

If you use similar headers for your different projects, you can save retyping information by saving the header information. Click Save as default to save the information and Load default to retrieve it.


Click OK to apply the new header to the active project. The new header will apply to the current and following pages. This allows you, for example, to use different people’s names in the Designed by field if more than one person is working on the same project file.

The composition of the header can be changed to suit your own needs by customising the page template. For more details, refer to the customisation procedures explained from page 2-51.

Working with more than one project at a time You can open more than one project in Calcpad at a time. The current selected project is referred to as the active project. All results sent to Calcpad from the analysis and design modules are placed in the active project.

To select an open project and make it the active project, click its tab with the mouse.

File management Use the File menu commands to open and save project files in the working folder or any other location on your own computer or on a network drive that you have write access to:

• To create a new project file, select New Project.

• To open an existing project file, use the Open Project command.

• Use Save Project to save the active project.

• To save a new, unnamed project file, use Save Project as.

• To close the active projects or all open projects, use Close Project or Close All.

• To open a recently used project file, click the file name at the bottom of the File menu.

PROKON Project files as saved with the extension ’.PPF’ for easy recognition.

To open a project file on your hard disk or network

1. On the File menu, click Open Project.

2. In the Look in box, click the drive and folder that contains the document.

3. In the folder list, double-click folders until you locate the folder that contains the document you want.

By default, the file list is filtered to show only project files created by Calcpad. You can change this by selecting All files in the Files of type box, e.g. when wanting to open a text file. You can also type a filter File name box; for example, type ’p*.*’ to find all files starting with the letter p.

4. To change the appearance of the file list, click List or Details. With Details selected, you can click a column heading to sort the data files by name, size, date or type.


5. Double-click the document you want to open.

Saving a new, unnamed project file

1. On the File menu, click Save Project.

2. To save the project in a different folder, click a different drive in the Save Project in box, or double-click a different folder in the folder list.

3. To save the document in a new folder, click Create New Folder.

4. In the File name box, type a name for the document. You can use long, descriptive file names if you want. The program will automatically add an appropriate file extension.

5. Click Save.


Using the Analysis and Design Modules 2-11

Using the Analysis and Design Modules

To run a PROKON analysis or design module, click its icon on the shortcut bar or select it from the Program Menu. If a particular module’s shortcut icon or menu item is dimmed, it means that the module is not included in your workstation.

When you run a module by clicking its icon or choosing it from the Programs menu, the best available version of that module is launched. If the Windows version of a module is not available, the Dos version will be launched instead.

Where available, the Dos version of each module is also included in the suite. To run the Dos version of a module, right-click its icon on the shortcut bar.


Using the Windows modules

The analysis and design modules follow a similar pattern. By familiarising yourself with a few concepts, you should find using the PROKON suite relatively simple and intuitive.

Setting the preferred design codes Use the General preferences command on the Settings menu to select the design codes and parameters to use. More detail of the procedure is given on page 2-5.

Similar layout All modules present you with a number of tabbed pages or menus:

• The File menu: Standard Windows commands are provided for opening and saving data files. The commands are similar to those described on page 2-8.

• The Input page: All input data is entered on this page. In the case of some of the larger analysis modules, e.g. the frame analysis modules, this page will itself contain a number of tabbed input pages. Some modules also allow specialised input trough a separate Settings page or button.

• The Analysis or Design page: Selecting this page typically starts the analysis and displays the results.

• The Calcsheets page: Analysis and design results can be accumulated in a single calcsheet. You can choose between printing or sending the information to Calcpad.

• The Drawings or Bending Schedules page: Most design modules are capable of generating a detailed drawing or bending schedule of the designed element. Drawings and bending schedules can be edited and printed using Padds.

• The Help menu: Access is provided to on-line Help topics and built-in Examples.

To display a particular page or menu, click it with the mouse. Alternatively use F11 and F12 to move forward and back between the pages.


Data input Except when using Padds for graphical input, e.g. for frames, all data is entered in tables. Data is normally evaluated immediately as entered. If invalid input is detected, a list of errors is normally displayed.

Entered data is typically shown in Pictures that interact with the Table Editor to automatically update with every entry in the tables. Pictures can be zoomed and panned for more detail. Some pictures have visible zoom buttons, others not. However, all pictures can be zoomed by right-clicking it and using the pop-up menu. Pictures can also be saved as drawings.

The use of the Table Editor is explained in detail on page 2-19 and the manipulation of Pictures on page 2-29.

Sending analysis results to Calcpad After a successful analysis or design, you can group the results in a calcsheet. You can then choose to print or send the information to Calcpad. To send results to Calcpad:

• Access the relevant module’s Calcsheets page.

• Use the Settings function to select the components to include in the calcsheet. You can optionally select the Data File to have the input data saved as part of the Calcpad project.

Note: In the case of some of the larger modules, e.g. the frame analysis modules, you need to first view the results and select individual components to be included in the calcsheet.

• Click Send to Calcpad to append the results to the active project in Calcpad.

Saving input You can use the File menu of a module to save and open input data files. However, if you enable the Data File option before sending a calcsheet to Calcpad, you can later recall the input data by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and does not need to be saved in the relevant module as well.

If you do save a data file in an analysis or design module, the file name extension will automatically be set to the program number for easy recognition, e.g. ’.A03’ for Frame Analysis.


Using the online help You can access context-sensitive help by pressing F1. Alternatively use the Help menu to display an overview of the program.

It is easier to update electronic information than printed manuals. Therefore, you may occasionally find that the on-line help is more up to date that the manual.

Updated help files are published regularly on the PROKON Support Web. Additional information not given in either the manual or Help, e.g. answers to frequently asked questions and details of program revisions, is also available on the PROKON Support Web. Refer to the introduction of this manual to read more about support service included with your purchase of PROKON software.


Using the Dos modules

The Dos modules all have a similar look and feel, making their use relatively simple. A few important topics are briefly explained in the following text. For a more detailed explanation, consult the Dos Version User’s Guide.

Setting your preference Use the following commands on the Settings menu to select your preferences:

• Colour screen prints (Dos): If selected, all screens sent to Calcpad will be in colour. If you are using black-and-white printer, you will get better printing results if you de-select the option.

• Design codes (Dos): Display the Dos version’s configuration utility. Change the design codes and parameters to suit your requirements.

Note: The Dos modules support British Standards and equivalent SABS design codes only.

The design codes and parameters can be saved for later re-use, e.g. for projects requiring special design parameters.


Data input Input is done on a module’s main screen or on a series of input screens that are typically accessed by pressing I. Data entry is done using a table editor, as explained in Chapter 2 of the Dos Version User’s Guide.

All input screens display the input data graphically and the graphics are updated automatically as you enter data. Some input screens also allow sketches to be zoomed for more detail.

Saving input data Input data is normally saved using F2 and existing files retrieved using F3. In addition, the current input data is saved automatically to a last file whenever you leave a program. To allow you to continue where you ended your last session, the last file is automatically read the next time you run a program. Last files are named after the respective applications, e.g. Continuous Beam and Slab Design saves a file called ’LASTCB’.

Note: The last files get saved independently from files saved using F2:Save. Since the last files get overwritten from time to time, the F2:Save option should be used to name files and save them permanently.


Analysis and design The buttons to analyse, design or generate a bending schedule or drawing are always easily recognisable.

Sending design output to Calcpad Output can be viewed graphically or in tabular format. Output is normally displayed directly after an analysis or by pressing V or L. Output can be sent to Calcpad and used together with the output from the Windows modules:

• To send the current screen images to Calcpad, press PrtSc. You can also send more than one screen image by pressing PrtSc while each of the screens is displayed. Screens can be captured in colour or black-and-white. Refer to page 2-15 for detail on setting your preference.

• Use the normal Print functions to display input tables and output files in the PROKON Preview utility. From here you can either print the information or send it to Calcpad.

Using on-line help Context-sensitive help is always available by pressing F1. The help facilities are typically organised to include a table of contents at the top, followed by the various topics. More information is given in Chapter 2 of the Dos Version User’s Guide.


Using the Table Editor 2-19

Using the Table Editor

You can edit text in tables using the standard Windows functions, i.e. as employed by most spreadsheet applications. The standard Windows functions are supplemented with a number of special functions that speed up table editing.

For information on tabular input in the Dos modules, refer to Chapter 2 of the Dos Version User’s Guide.


Moving around and editing text

You can move around in tables and edit cells in very much the same way as you do in your favourite spreadsheet program.

Moving the cursor in a table Use the arrow keys to move between cells. Press Enter to jump to the left-most cell in the next row. Pressing Tab moves one cell to the right and Shift+Tab one cell to the left. If you press Tab at the end of a row, the cursor will jump to the left-most cell in the next row.

Home jumps to the first cell in the row and End to the last. PgUp and PgDn moves one screen up or down. To jump to the top left or bottom right corner of the table, press Ctrl+Home or Ctrl+End.

Tip: Click a cell with the mouse to quickly move the cursor to that cell.

Entering and editing text To enter text into a cell, position the cursor on the cell and start typing. Press Enter or one of the arrow keys to accept the new text and move to a next cell. Depending on the key pressed, the cursor will move to a specific cell:

• Pressing Enter accepts the entry and moves the cursor to the left-most cell in the next row.

• If you press the right, up or down arrow key, the cursor will move one cell right, up or down.

• If you wish to move one cell to the left, use Shift+Tab.

Note: Some cells have special drop-down lists for selecting values. Depending on the specific application, you may be able to select common values from the list or optionally type values.

While entering or editing text, you can move left and right using the left and right arrow keys. To jump to the left-most or right-most positions, press Home or End. To move one word to the left or right, use Ctrl with the left and right arrows.

To edit text in a cell, move the cursor to the cell and press F2 or double-click it. If you want to replace the text in the cell rather than change it, simply retype the text without first pressing F2.


Deleting text

Press Del or Backspace to clear the current cell’s contents. While entering or editing text in a cell, Del and Backspace will delete one character to the right or left respectively.

Inserting lines

Press Enter to move to the first cell on the next line. To insert a blank line at the cursor, press Ctrl+I.

Finding and replacing text You can search for and replace text in a table by pressing Ctrl+F. This feature can be especially handy when working with large tables, e.g. when entering nodes for a frame analysis.

To repeat the last search without first opening the dialog box, press F3.


Working with blocks

You can copy, move or delete cells using the block commands. These actions typically require two steps:

• Marking a cell or block of cells – you can choose between using the normal Windows methods of selecting cells or the extended PROKON functions.

• Using a block command to manipulate the block.

Marking blocks When marking blocks, you can choose between using the standard Windows functions and the extended PROKON block functions – the behaviour of the resulting blocks are different.

Using the standard Windows functions

To select a cell or block of cells using standard Windows commands, use any of the following procedures:

• Click and drag the mouse to select a rectangular block of cells.

• Position the cursor on one of the corner cells. Press and hold Shift and then use the arrow keys to move to the opposite corner.

Note: When marking a block this way, moving the cursor will undo the selection.

Marking persistent blocks

The extended functions allow you to mark persistent blocks, i.e. blocks that remain selected even if you move the cursor. Persistent blocks are marked as follows:

• To select one or more rows, move the cursor to the first row and press Ctrl+L. Then move to the last row and press Ctrl+L again.

• To select one or more columns, move the cursor to the first column and press Ctrl+K and then move to the last column and press Ctrl+K again.

• To mark a rectangular block of cells, position the cursor on the top left cell and then press Ctrl+B. To end the selection, move to the bottom right cell and press Ctrl+E.

Note: A persistent selection will remain active until unmarked with Ctrl+U. While the cells are selected, you are free to move the cursor without the block being de-selected.


Copying, moving or deleting cells A selected cell or group of cells can be copied, moved or deleted using the standard Windows functions or the extended PROKON block functions.

Using the Windows clipboard functions

You can use the normal Windows clipboard Cut, Copy and Paste functions:

• To copy a cell or block to the clipboard, press Ctrl+C. Alternatively right-click it and choose Copy.

• To cut a block, i.e. remove it from the table and copy it to the clipboard, press Ctrl+X. Alternatively right-click it and choose Cut.

• To paste the clipboard contents into the table at the cursor position, press Ctrl+V. alternatively right-click and choose Paste. If you are pasting a block of cells, the current cursor position will be taken as the top left corner of the block.

Examples:

• To copy cells in the table, first select the cell or block of cells and Copy the information to the clipboard. Then position the cursor to the new position and Paste the text.

• To move one or more selected cells, Cut them to the clipboard and Paste them at the new position.

• To delete one or more selected cells, select and Cut them. Alternatively press Del to delete the selected cells.

Copying, moving and deleting cells using persistent blocks

You can use the extended functions to mark persistent blocks and then copy and move text without using the Windows clipboard.

• To copy one or more cells, first mark a persistent block, move to the new position and then press Ctrl+V.

• To move a persistent block, use Ctrl+M.

• To delete a persistent block selection, use Ctrl+D.


Advantages of using persistent blocks The normal block selection functionality offered by Windows allows you to quickly mark an area with the mouse or keyboard. However, the selection is cancelled as soon as you move the cursor. In contrast, persistent blocks offer the following advantages:

• You are allowed to move the cursor while defining the selection, without cancelling the selection. You could, for example, move up or down in the table without undoing the selection.

• You do not need to first Copy or Cut information to the Windows clipboard - while a persistent block is selected, you can Paste or Move it directly.

• You can quickly mark persistent blocks using the keyboard.

Copying text from another program You may sometimes find it easier to generate tables of values using another application, e.g. your favourite spreadsheet program. Relevant information can then be copied to a PROKON table (or from PROKON to the other program) using the Windows clipboard:

• Select relevant text and Copy it to the clipboard.

• Press Alt-Tab to swap to the destination program or click it on the Windows Task Bar.

• Position the cursor and Paste the information from the clipboard.


Summary of commands

Moving around:

Arrows : Move one cell up, down, left or right.

Enter : Jump to the first cell in the next row.

Tab : Move one cell right.

Shift+Tab : Move one cell left.

Home : Jump to the first cell of the current row.

End : Jump to the last cell of the current row.

Ctrl+Home : Jump to the top left corner of the table.

Ctrl+End : Jump to the bottom left corner of the table.

Del : Delete the cell at the cursor.

Ctrl+Y : Delete the line at the cursor (irrespective of any block selected).

Backspace : Delete the cell at the cursor and open it for editing.

Ctrl+I : Insert a blank line.

Ctrl+F : Find or replace text

Editing cells:

F2 : Edit the cell at the cursor.

Left/right : Move the cursor inside the text.

Ctrl+left/right : Move the cursor left or right one word.

Up/down : Accept the changed text and moves to the adjacent cell.

Enter : Accept the changed text and jumps to the first cell in the next row.

Del : Delete the character to the right.

Backspace : Delete the character to the left.

Marking persistent blocks:

Ctrl+A : Select all cells.

Ctrl+B : Mark the top left corner of a rectangular block.

Ctrl+E : Mark the bottom right corner of a rectangular block.

Ctrl+K : Mark the first or last column of a block.


Ctrl+L : Mark the first or last line of a block.

Ctrl+U : Unmark the current block.

Clipboard commands

Ctrl+C : Copy the block to the clipboard.

Ctrl+X : Cut the block to the clipboard.

Ctrl+V : Paste the clipboard to the cursor position.

Persistent block commands

Ctrl+V : Copy the persistent block to the cursor position

Ctrl+M : Move the persistent block to the cursor position.

Ctrl+D : Delete the block.

Using the PROKON Calculator 2-27

Using the PROKON Calculator

Use the PROKON calculator for basic calculations. You can copy a result to the Windows clipboard and then paste it into Calcpad or an input table of a design module.

Using the PROKON Calculator 2-28

Using the Calculator

Use the PROKON calculator for basic calculations. You can copy a result to the Windows clipboard and then paste it into Calcpad or an input table of a design module.

During installation, the calculator can be configured to automatically load when Windows starts. If so, the calculator will be visible in the Windows system tray that is typically located in the bottom right corner of the screen, i.e. next to the clock.

Clicking its icon or pressing Ctrl+1 can display the calculator. To close the calculator, click Exit or press Esc. On closing, the calculator will return to its idle status in the system tray.

To close the calculator and remove it from memory, right-click its icon and choose Close.

Doing calculations Operation is similar to a conventional hand-held calculator:

• Enter an equation using the normal mathematical operators.

• To enter a mathematical function, click the relevant button or write out the function.

• Simplify complex equations by enclosing portions in brackets.

• Press Enter to display the result.

• To remove the displayed equation and continue working with the result, press Clear left.

Sending calculation results to other programs The result of a calculation can be copied to the Windows clipboard for reuse in another program:

• Click Copy or press Alt-C to copy the result to the clipboard and close the calculator.

• In the relevant application, e.g. Calcpad or an input table of a design module, use the Paste command or press Ctrl+V to paste the value.

Tip: When using a Dos module, press Ctrl+Z to display a calculator. Use F10 to send the result back to the module’s input table.

Working with Pictures 2-29

Working with Pictures

The analysis and design modules often have pictures linked to the input tables to make data entry interactive and more intuitive. Pictures are also often used to present analysis results.


Zooming and panning pictures

You can ’zoom in’ to get a close-up view of a picture. Some pictures have Zoom buttons for this purpose. If a picture does not have such buttons, you can still zoom it by right-clicking the picture and choosing a command from the pup-up menu. The following zoom commands are normally available for all pictures:

• Window: Indicate a rectangular area to zoom into.

• All: Display the whole picture, based on the size defined internally for the background.

• Last: Revert to the last zoom setting.

• Extents: Display the whole picture, based on the drawn entities.

• In: Zoom in by 50%.

• Out: Zoom out by 50%.

• Pan: Drag the project in any direction to view an adjoining portion.

• Print: Send the picture to the printer.

Saving pictures

In addition to the Zoom button commands, the right-click pop-up menu also allows you to save the picture in the following file formats:

• PAD: Fully editable Padds drawing.

• PIC: Prokon picture file.

• EMF: Enhanced Windows metafile, readable by many graphics and presentation packages.

• DXF: 2D or 3D DXF drawings for use in other CAD systems.

In some modules, e.g. the frame analysis modules, a special button may is available for adding a picture to the Calcsheets.


Working with 3D pictures

Because of their nature, some analysis and design modules need to display 3D pictures. The commands available for 3D pictures are:


• All: Display the visible portion of structure from the current view point.


• Extents: Display the complete structure, moving forward or back if necessary.




• Print: Print the current view of the structure.

• Viewpoint: Display the View Point Control dialog box for defining the view point and other view characteristics.

• View plane: Display the View Plane Control dialog box for defining a view plane.

• Rotate left: Rotate the structure to the left about the Y-axis. The rotation angle is defined in the View Point Control dialog box.

• Rotate right: Rotate the structure to the right about the Y-axis.

• Rotate up: Rotate the structure backward.

• Rotate down: Rotate the structure forward.

Detailed settings

Some modules allow detailed configuration of pictures. In the frame analysis modules, for example, you can access the Graphics Options to enable or disable display of node numbers, global axes etc. Pictures can also be rendered in 3D or shown as simple line diagrams.


View point control Use the view Point Control Dialog function to define the viewpoint and other view properties:

• View point: Imagine viewing the structure through a camera lens. The view point is then defined as the position of the camera. Enter the view point coordinates or use the Walk function to move the camera by the distance defined as the Step size.

• View direction: The direction in which the camera is aimed. The default position is the centre of the structure. Enter the view direction or use the Turn function to rotate the camera through the angle defined as the Turn angle.

• View angle: The lens angle. A larger angle will show more of the structure in a close-up situation.

• Projection: Choose between using an orthogonal or perspective projection. The latter gives a more realistic view of the structure. However, you may get a distorted picture when using a large view angle in a close-up situation.

• Elevations: For a quick view from the top or one of the sides, choose a positive or negative X, Y or Z-elevation.

Tip: The default view angle of 50° works well with perspective projections of structures. If you cannot see the complete structure, the view point is probably to near to the structure. Use the Zoom extents function to move back far enough to view the complete structure.

The View Point Control dialog box can be left open while you work in the program. You can also use the zoom and pan functions while the dialog box is open.


View plane control When viewing a complicated 3D structure, you may often find it difficult to identify points in the structure. Use the View Plane Control function to define only certain planes to be viewed. View planes can be defined in three ways:

• Nodes: Enter or use the mouse to indicate three nodes that describe a plane. The plane does not need to vertical or horizontal.

• Axis: Define a view plane perpendicular to the X, Y, or Z-axis. Enter the position along the indicated axis.

• Coordinates: Enter three 3D coordinates to describe a plane.

• Enter a view plane thickness to define how much of the structure should be visible.

Click Clear to restore the settings to displaying the whole structure. Click Apply to make the entered view plane take effect. Click Close to close the dialog box

The View Plane Control dialog box can be left open while you work in the program. You can also use the zoom and pan functions and the View Point Control while the dialog box is open.

Tip: If your PC’s screen resolution permits, you may move the View Point Control and View Plane Control dialog boxes to one side so as not to clutter the display of the underlying program.


Saving and recalling views You can use viewpoints and view planes to display the whole structure or portions of it in convenient ways, e.g. a plan view of a floor of a multi-storey building. You can save each combination of view point and view plane as a view for later re-use.

Some pictures display the name of the current view and allow you to select another saved view by clicking the view name.

Adding Text and Graphics 2-35

Adding Text and Graphics

The analysis output generated by the various analysis and design modules will provide normally sufficient detail of your designs. However, you may want to enhance your project files by adding additional design notes, pictures and even additional calculations.

The procedure to write and edit text and to insert and manipulate pictures in Calcpad is described in the following text. Equation writing is explained from page 2-41.


Writing and editing text

You can use Calcpad as a simple word processor to write and edit text. You may possibly find that you can use the exact same or similar editing and formatting commands as in your favourite word processor.

Typing text

Type text as you would in any other word processor or text editor.

Typing over existing text

Press the Ins key to toggle between overtype and insert modes. In overtype mode, you will replace existing text as you type, one character at a time.

Replacing selected text

Select the text to be replaced and start typing to replace it.

Inserting symbols or special characters

You can insert Greek symbols and other special characters using the Symbol command on the Insert menu. You can also insert a character or symbol by typing the character code on the numeric keypad, e.g. ’Alt-225' inserts the ß character.

Insert the date and time in a project

You can insert the current date or time in a project using the Date command on the Insert menu.

Insert a text file

To insert a complete text file, use the Text File command on the Insert menu. To insert only a portion of a text file instead:

1. Open the text file using the Open Project command on the File menu. Change the Files of type field to 'All files' and select the file.

2. Select and copy the relevant text using the procedures described on page 2-39.

Deleting text

Use Del and Backspace to delete a character to the left or right. To delete words or paragraphs, select the text and press Del.


Changing the appearance of text To change the appearance of text, e.g. underline text or numbers:

1. Select the text you want to change.

2. On the formatting toolbar, select a font or click a style or point size.

The change will be applied to the selected text only or, if you did not select any text, to new text from the cursor position and further.

You can also use the keyboard shortcuts Ctrl+B, Ctrl+I and Ctrl+U to make text bold, italic or underlined.

When changing font style of text with mixed style, the style will toggle between normal, formatted and mixed, e.g. all normal, all bold and mixed normal and bold.

Moving around in a project You can scroll through a project by using the mouse or shortcut keys.

To scroll through a project by using the mouse:

• Scroll up one line: Click the up arrow on the scroll bar.

• Scroll down one line: Click the down arrow on the scroll bar.

• Scroll up one screen: Click above the scroll box.

• Scroll down one screen: Click below the scroll box.

• Scroll left: Click the left arrow on the horizontal scroll bar (if displayed).

• Scroll right: Click the right arrow on the horizontal scroll bar (if displayed).

After scrolling, click where you want to start typing. To move the cursor using the keyboard:

• Move up or down one line: Press the Up or Down arrow.

• Move up or down one screen: Press PgUp or PgDn.

• Move left or right one word: Press Ctrl+Left or Ctrl+Right.

• To jump to the beginning or end of the current line: Press Home or End.

• To jump to the first or last lines in the project: Press Ctrl+Home or Ctrl+End.

• To move to the reference column on the far right: Press Ctrl+Tab.


Using graphics in your project

Graphics can be used to supplement text and serve to enhance your projects. Inserted graphics can be moved, copied and resized.

Inserting a graphic Use the commands on the Insert menu to insert graphics:

• To insert a Windows Bitmap or Metafile: Click Picture and select the file.

• To insert a Padds drawing: Click Drawing and select the file.

Moving and resizing graphics

To move a graphic:

1. Select the graphic by clicking it.

2. Drag it to the new position.

To resize a graphic:

1. Select the graphic.

2. Drag the graphic’s edge to change its horizontal or vertical size.

3. Drag one of the graphic’s corners to proportionally change its horizontal or vertical size.


Moving and copying text and graphics

You can move or copy text and graphics within a project, between projects, or between Calcpad and another program.

Selecting text and graphics to move or copy You can select text and graphics by using the mouse or shortcut keys. To select text and graphics using the mouse:

• To select any amount of text, drag over the text.

• To select a graphic, click it.

• To select a whole word, double-click the word.

Using the keyboard, select text by holding down Shift and pressing the same key that moves the cursor. To extend a selection:

• One character to the left or right: Shift+Left or Right arrow.

• To the beginning or end of a word: Ctrl+Shift+Left or Right arrow.

• To the beginning or end of a line: Shift+Home or End.

• One line up or down: Shift+Up or Down arrow.

• One screen up or down: Shift+PgUp or PgDn.

• To the beginning or end of the project: Ctrl+Shift+Home or End.

• To select all the words in a line: Ctrl+L.

• To select the entire project: Ctrl+A.

Moving or copying text and graphics To move or copy text and graphics:

1. Select the text or graphics you want to move or copy.

2. To move the selection, click Cut or press Ctrl+X.

3. To copy the selection, click Copy or enter Ctrl+V.

4. If you want to move or copy the text or graphics to another document, switch to it.

5. Click where you want your text or graphics to appear.

6. Click Paste or press Ctrl+V.


Zooming a text and graphics

You can ’zoom in’ to get a close-up view of a project or ’zoom out’ to see more of the page at a reduced size. Use the Zoom buttons or right-click the project for a pop-up menu with zoom commands:


• Margin: Display the whole page width between the left and right margins.

• Page: Display the whole page.





• Page up: Scroll one page up. Same as pressing PgUp.

• Page down: Scroll one page down. Same as pressing PgDn.

Working with Equations 2-41

Working with Equations

You can use the Equation Editor to create your own equations in Calcpad. The Equation Editor is also used to edit existing equations or save equation objects for re-use in future, e.g. create a library of equations


Inserting and editing equations

To open the Equation Editor for inserting or editing an existing equation:

• To insert a new equation: Choose Equation from the Insert menu.

• To edit an existing equation: Select and right-click the equation. Then choose Edit from the pop-up menu.

To create or edit an equation, work through the different pages to create an equation object:

• Equations: Use one or more lines to enter equations. When creating a new equation, this page is displayed first.

• Variables: Assign a value to each variable used on the Equations page. When editing an exiting equation, this page is displayed by default.

• Settings: Choose how the equations should be displayed and optionally attach a picture.

Note: When sending a series of equations to Calcpad, the equations are grouped together as a unit, called an equation object.


Entering equations

Enter one or more lines of equations on the Equations page. Equations are written in ’normal English’ and then automatically displayed in the correct mathematical format.

Writing equations A few simple rules apply when writing equations:

• Like when using a simple calculator, use ’normal English’ to write an equation – the equation is automatically formatted for you. For example, if you want to enter the equation y = a · x2 + b · x + c, enter ’y=a∗x^2+b∗x+c’.

• The mathematical operators that can be used include +, –, /, ∗ and ^.

• Use parenthesis to simplify an equation, e.g. for ( )( )dc

ba++

enter 'y=(a+b)/(c+d)'.Use

multiple lines for a sequence of equations. Variable values are inherited by equations that follow. Refer to page 2-48 for more detail on using a series of equations.


Defining variables A variable can be a single letter or several letters and/or numbers, e.g. a, a2 and ab. The program intelligently takes care of formatting variables with sub-scripting and italic characters.

The following simple rules apply:

• Enter numbers using normal or scientific notation. Example, ’0.002’ and ’2E-3’ has the same meaning.

• When entering a variable, the second and following characters are used as sub-scripts, e.g. enter ’abc’ to get abc.

• Variables are case sensitive, e.g. ’a’ and ’A’ are seen as two different variables.

• A variable cannot start with a number. Using ’1’ and ’a’ separately yields a valid number and variable respectively, but entering ’1a’ is not allowed.

Using Greek symbols Greek symbols are treated exactly like normal letters. To create a Greek symbol, enter a hash before the equivalent Roman letter, e.g. enter ’#S’ and ’#s’ to get and respectively.

The following rules apply:

• Greek symbols are case sensitive, e.g. and are seen as two different variables.

• You may mix Greek symbols with normal characters.

Note: The Greek symbols �and �are reserved and cannot be used as variable. Their values are fixed at 3.141593 etc. You may however use the symbol e as a normal variable.

Entering normal text Normal text entries, e.g. headings and comments, are distinguished from equations by enclosing or preceding them in double quotes, e.g. "Comments" or "Comments without a trailing quote.


Using mathematical functions

You can use the built-in mathematical functions as necessary, e.g. ’sqrt(...)’ to determine the square root of an expression. Built-in functions include:

Trigonometry

Normal functions

Arc functions

sin, cos, tan

asin, acos, atan

Logarithmic functions

ln, log

Other functions

Square root

Absolute value

sqrt

abs

Additional functions can be derived using the standard mathematical operators and functions. A few simple examples include:

• Instead of using the built-in square root function, you may determine the square root and

other roots as follows: cba += can be entered as ’a=sqrt(b+c)’ or ’a=(b+c)^(1/2)’

• If a = log(b), then b = 10a, which is entered as ’b=10^a’.

• Trigonometric functions are inter-dependent, e.g. ( ) ( )θθ

tan1

cot = . To enter the equation

a = FRW� ��W\SH�a=1/tan(#h)’ or ’a=(tan(#h))^(-1)’.


Assigning values to variables

Assign values to variables on the Variables page. A list of all variables used on the Equations page is displayed:

• Assigned variables: Variables that are not calculated but require values to be assigned to them are listed first.

• Calculated variables: Variables denoting equation results are listed last. The values for these items are typically shown as ’EqX:Y’, where X is the relevant row number in the table on the Equations page and Y is the equation result.

• To explain the symbols, an image can be displayed alongside the list of variables. Refer to page 2-46 for more information on using images with equations.


Equation settings

The Settings page is used to configure the display properties of an equation object:

• Title: You can enter a title for an equation object. When inserting the equation in Calcpad, the title can optionally be displayed above it.

• Image: An image can be loaded and optionally displayed when inserting the equation in Calcpad. The image is also displayed on the Variables page.

• Numeric format: You can choose to display equation results in decimal, scientific or engineering format.

• Font: Select a font, style and height to use for the equation.


Advanced techniques

Once you have mastered the basic functions of the Equation Editor, you may want to proceed to creating more sophisticated equation objects.

Using units of measurement You may enhance your equations by adding units of measurement. Units are designated by enclosing them in curly brackets.

The following rules apply:

• The unit should be written in curly brackets immediately after the variable.

• You may use a mathematical operator to create derivatives of units, e.g. use ’m^2’ for m2.

• You may use either Metric or Imperial units.

Examples:

• To determine the circumference of a circle in feet, you may enter ’Circ{ft}=#p*r{ft}’. The result in Calcpad will be:

• To calculate the area of a circle in square meter, you may enter ’A{m^2}=#p*r{m}^2’. The result will be:

r = 2.5m

=A π r2. = 19.635 m2

Note: The program does not evaluate the consistancy of units within equations.

Using a series of equations When entering multiple lines of equations, all assigned and calculated values of variables are carried over to equations down the list – a characteristic referred to as inheritance. This allows you to break complex equations into smaller pieces, making them a lot easier to write and verify. It also allows you to use multiple inter-dependent equations in a complex calculation.


Conditional branching You can use the inheritance characteristic of equations to your further advantage. By combining inheritance with conditional branching, you can create equation objects that can intelligently adjust for different values of the variables.

To create a conditional branch:

• Define the condition using the ’if’ statement, e.g. ’if a>b’ will do something only if a is greater than b. For comparison, you may use the operators <, >, =, >= and <=.

• In the lines following the ’if’ statement, enter one or more equations to be evaluated if the condition is met. Use the ’end’ or ’else’ statement to terminate such a series of equations and continue with the normal flow.

• If a condition is not met, an alternative series of equations can be entered after an ’else’ statement. Terminate the series of equations with an ’end’.

In the following example, taken from the Help menu of the Equation Editor, the area of reinforcement in a rectangular beam is calculated using the formulae in BS 8110 - 1997:

#bb=(100-%RD)/100 if %RD<10 then (first conditional branch) K’=0.156 else (if condition is not met) K’=0.402*(#bb-0.4) - 0.18*(#bb-0.4)^2 end (end of first branch) K=M{kNm}*1e6/(b{mm}*d{mm}^2*fcu{MPa}) if K<=K’ then (second conditional branch) "Compression reinforcement not required because K<=K’" z=d*(0.5+sqrt(0.25-K/0.9)) x=(d-z)/0.45 As{mm^2}=M*1e6/(0.95*fy{MPa}*z) else (if condition is not met) "Compression reinforcement required because K>K’" z=d*(0.5+sqrt(0.25-K’/0.9)) x=(d-z)/0.45 A’s{mm^2}=(K-K’)*fcu*b*d^2/(0.95*fy*(d-d’{mm}) As{mm^2}=(K’*fcu*b*d^2)/(0.95*fy*z) + A’s (end of second branch)

In the example, the first conditional branch causes K’ to determined differently for different values of the percentage of redistribution, %RD. Further, by comparing the values of K and K’, additional compression reinforcement is calculated when necessary.


Creating an equation library You can use the File menu commands to save and recall all useful equations.

The advantages of saving equation objects in a library will become obvious once you have created a number of intelligent equation objects comprising multiple equations and conditional branching.

You are free to save your equations in any folder on your PC or on the network. Using a dedicated and well-structured folder is recommended to ensure easy access to a large library of equations.

Use the Open command on the File menu to retrieve an equation object from disk. When working with an existing equation, the Variables page is displayed automatically, i.e. the program assumes that you want to reuse the equations with new values.

The usability of an equation library can be greatly enhanced by using titles and pictures with equations, even if you do plan on displaying them when inserting equations in Calcpad. Equation objects with descriptive titles and explanatory pictures are easier to use, especially in a multi-user environment. Refer to page 2-46 for information on equation titles and pictures.

Customising the Page Layout 2-51

Customising the Page Layout

By default, projects are displayed on a framed page with the PROKON logo. The top portion of the page, called the header, also includes a number of pre-defined fields like ’Designed by’, ’Date’ etc. The page layout and header items are collectively referred to as a template.


Selecting another template or creating a new template

You can select one of the other pre-defined templates or create your own using the Page Setup command on the File menu:

• To select a template, click Select template.

• To modify an existing template or create a new one, click Edit template.

• Click OK to close the Page Setup dialog box.

The following templates are available when you run PROKON for the first time:

• Default: The default template with frame and PROKON logo. For a start, you may want to replace the PROKON logo and contact details with your own.

• Frame: No-frills template with a frame only. This template offers a larger workspace.

• Nothing: A blank template, in case you prefer printing on blank sheets.


Creating your own template A template is defined using a simple scripting language that has been derived from the Padds macro language. In essence, the script is a series of two-letter commands similar to the keyboard shortcuts used in Padds. Several new commands have been introduced to for special effects like setting margins.

To create a new template, it may be easiest to modify an existing template:

1. Click Edit template to open the template script in the Text Editor.

2. Use the Save As command on the File menu to save the template with a new name.

3. Edit the script as necessary.

4. Choose Save on the File menu to save the script.

5. To preview your new template, press Alt-Tab to swap back to the Page Setup dialog box or select it from the task bar.

6. Click Select template and open the new template.

7. To make further modifications, swap back to the Text Editor.

Repeat steps 3 to 7 until you are satisfied with the new template.

8. Finally close the Text Editor and the Page Setup dialog box to return to Calcpad.

Script commands A number of script commands are available to draw lnes, write text and define special items. All commands use parameters, i.e. values, to define certain entities. Parameters are separated with spaces or commas.

The template script commands can be categorised as follows:

Global page layout:

• XO Xleft and YO Ybot : Define the origin, or reference point, from where all entities are measured, e.g. ’XO 5’ and ’YO 7.5’ . The position of the origin is measured from the bottom left corner of the page. In fact, if you do not enter an origin the bottom left corner of the page will be used. You may repeatedly redefine the origin – the last definition is used for subsequent lines in the script.

• MA Mleft,Mbot,Mright,Mtop : Set the left, bottom, right and top margins in millimetres, e.g. ’MA 15,15,285,195'. The margins define the workspace in Calcpad and the values are measured from the origin rather than the edges of the page. The margin command does not draw any lines.


• RT colpos : Right column tab stop, measured in millimetres from the origin, e.g. ’RT 170’. The design modules use the right column for code references and other comments.

Graphics:

• BM Xleft,Ybot,Xright,Ytop,filename : Insert a Bitmap image and stretch it between the coordinates Xleft,Ybot and Xright,Ytop , e.g. ’BM 5,261,34.6.5,2779.5,LOGO.BMP’. The Bitmap is assumed to reside in the same folder as the template file. For the best printing results, the bitmap should be sized so that it can be placed at true size, e.g. an image of 700 pixels wide by 300 pixels high, placed 29.6mm wide by 12.7mm high should print well at 600 dpi.

Line drawing:

• LT thickness: Set the line thickness in millimetres, e.g. ’LT 0.25’.

• LL X1,Y1,X2,Y2: Draw a line from the coordinate X1,Y1 to X2,Y2, e.g. ’LL 5,10,5,110’ to draw a vertical line 100mm long.

Text:

• TF font,style: Set the font and style, e.g.’TF Times New Roman, Normal’

• TS size: Set the text height in points, e.g. ’TS 11’.

• TT Xleft,Ybot,text: Write text at the coordinate Xleft,Ybot , e.g. ’TT 5,10,Project No’.

Header items:

• HI Xleft,Ybot,Xright,Ytop,description: Insert a header item in the rectangle defined by the coordinates Xleft,Ybot and Xright,Ytop, e.g. ’HI 150,270,Designed by’. In Calcpad, the header item is later referenced by its description. See page 2-7 for details on entering header information.

Other:

• Comments can be written after two slashes, e.g. ’//comment’.


Example

Below is an abstract from the Default template script:

XO 15 // X Origin YO 15 // Y Origin BM 1,260, 41,267 PROKON.BMP // Load Bitmap x1,y1,x2,y2 LT 0.3 // Line Thickness mm LL 0, 0,186, 0 // Line x1,y1,x2,y2 LL 0,248,186,248 LL 0,268,186,268 LL 0, 0, 0,268 . . . . . . . . . LL 166, 0,166,248 TF Arial Italic // Text Font TS 8 // Text Size Points TT 156.5,267.8, Sheet // Text x,y,text TT 42.5,267.8, Job Number TT 42.5,262.8, Job Title TT 42.5,257.8, Client TT 42.5,252.8, Calcs by TT 90.5,252.8, Checked by TT 138.5,252.8, Date TT 3,259 , Software Consultants Pty Ltd TT 3,255.5, Internet: http://www.prokon.com TT 3,252 , E-Mail : [email protected] MA 1, 1, 185, 247 // Margins left, b, r, t RT 166.5 // Right column tab stop TS 10 // Text Size Points HI 165.0,267.2, First Sheet No // Header Item HI 60.0,267.2, Job Number // x,y,Description HI 55.0,262.2, Job Title HI 55.0,257.2, Client HI 55.0,252.2, Calcs by HI 106.0,252.2, Checked by HI 150.0,252.2, Date


Configuring the Section Database 2-57

Configuring the Section Database

The Section Database utility is a base component for all steel member and connection design modules. The module contains several listings international section databases and can be expanded to include custom sections.

Use the Section database command on the Tools menu to edit the database or select another international database.


Using the section database

The section database is accessible from all the steel member and connection design modules. Before using any of these modules, you may wish to first configure the database to your requirements.

Selecting a database Depending on the Windows Regional Settings, PROKON will automatically select an appropriate section database when you run it for the first time. You can load another country’s database using at any time using F3:

• Australia and New Zealand: Load ’Sectable.aus’.

• United States: Choose ’Sectable.us’.

• Southern Africa: Choose ’’Sectable.za’.

• United Kingdom: Choose ’’Sectable.uk’.

Once you have localised the database by added some additional sections using the procedure below, you may wish to backup your work using F2.

Adding your own sections The database may be expanded to include welded and other non-standard sections. If a section conforms to the basic definition of one of the standard shapes, it may be added as a standard section. Non-standard shapes can be added to the ’user-defined’ group of sections.

Adding a standard section

To add a new I-section, for example, press I to access the current list of I-sections. Enter the section dimensions and then press F2 to have the section properties calculated and added to the database.

Typical examples include:

• I-shaped plate girders can be added with the other standard I-sections.

• Older steel structures built with imperial sections can be checked after first adding the relevant sections to the database.

• A haunch in a portal can be conservatively modelled as an I-section with an increased depth.

Tip: The normal text editing commands apply when entering sections. Refer to Chapter 2 for detail on copying, deleting and inserting lines.


Adding a non-standard section

Sections with non-standard shapes should be entered as ’User-defined’ sections. Press U to enter the section’s properties. These properties can be calculated manually or using Prosec.

Tip: Some modules, e.g. Steel Member Design for Combined Stress, support certain section types only. Therefore, it may in some cases be better to simplify a non-standard section and then add it as a standard shape. That way, the simplified version of the section will be available to the relevant design modules.


Configuring the Material Database

Use the Material database command on the Tools menu to edit the database. The Material Database utility is a base component for all frame analysis modules. The database initially lists the properties of a number of typical building materials. These can be expanded to include more materials.


Using the material database

The material database is accessible from all the frame analysis modules. Before using any uncommon materials, you may wish to first configure the database to your requirements.

Adding your own materials Materials in the database are organised in categories for steel, concrete aluminium and all other types. If you frequently use material that are not listed, you can add them to the database for easy reference from the frame analysis modules.

The following properties are required for all material types:

• Grade: Strength classification.

• E: Modulus of elasticity.

• Poisson: Poisson’s ratio.

• Density: Unit weight.

• Expansion coefficient: Thermal expansion coefficient

Additional properties for steel and aluminium:

• fy: Yield strength

• fu: Ultimate strength.

Special properties for concrete:

• fcu/f’ci: Concrete cube strength or, in the case of ACI 318-95, cylinder strength.

Copying and deleting materials

The normal table editor functions apply. You can thus mark blocks of materials to copy and delete. Refer to the beginning of Chapter 2 for detail.

Opening and saving the material database Use the File menu commands (refer to beginning of Chapter 2 for detail) to save your changes to the database or open another database. The default database is called ’Defaults.mtl’ and resides in the User folder.

3-1

Chapter

Structural Analysis

The structural analysis collection includes frame analysis and also some specialised finite element and beam analysis modules.

Structural Analysis using PROKON 3-2

Quick Reference

Structural Analysis using PROKON 3-3 Frame Analysis 3-5 Plane Stress/Strain Analysis 3-78 Single Span Beam Analysis 3-78 Beam on Elastic Support Analysis 3-78

3-3

Structural Analysis using PROKON

The accent of the analysis modules falls on user friendliness, speed and efficiency. The frame analysis module is ideally suited for the analysis of small to medium sized structures, not to say that the analyses of large structures are not possible. Frame has a comprehensive array of static and dynamic analysis modes.

Extensive use is made of interactive graphic representations during both the input and output phases. The input modules incorporate error checking to help eliminate input errors as they occur.

Frame analysis Frame can take account of own weight, temperature changes, prescribed displacements and elastic supports. Loads are entered as load cases and grouped in load combinations at ultimate and serviceability limit states.

The following static analysis modes are available:

• Linear analysis: Normal elastic frame analysis.

• Second order analysis: Models sway behaviour by incorporating P-delta effects. The solution is obtained by iterative analysis, thereby allowing for options like tension elements.

• Non – linear analysis. This takes the second order analysis a bit further. The load is applied in steps and the deflected structure at the end of each step is used to apply the next step. Material non – linearity is not yet supported.

• Buckling analysis: For calculating safety factors for structural instability due to buckling.

• Dynamic analysis modes available include:

• Modal analysis: Calculation of a frame’s natural modes of vibration.

• Harmonic analysis: For determining a frame’s response to harmonic loading.

• Earthquake analysis: Quasi-dynamic analysis of a frame subjected to ground acceleration.

Structural Analysis using PROKON 3-4

Finite element analysis Frame allows you to use finite shell elements and solid elements alongside normal beam elements. The shell elements enables you to model the combination of plate bending and membrane action in 3D. To model plate bending in concrete slabs, you may prefer using the Finite Element Slab Design – see Chapter 6 for details.

You can also use the Plane Stress/Strain Analysis module to perform a finite element analysis of any general plane geometry subjected to plane stress or strain. The module features an automated element grid generation facility to help speed up the input and analysis processes.

Beam analysis Modules are available for the analysis of simple beams and beams on elastic supports.

Post-processing of analysis results Linear and second-order analysis output can be post-processed by the steel member design modules, Strut and Com, to evaluate and optimise section profiles. The Space Frame Analysis module can also design finite shell elements as reinforced concrete members.

3-5

Frame Analysis

Frame can be used for the analysis of the following types of structures by selecting a domain on the ‘General’ input tab:

• Plane Frames: Analysis of a frames in a vertical (X-Y) plane.

• Grillages: Analysis of a structure in a horizontal (X-Z) plane.

• Space Frames: Analysis of three-dimensional structures made up of beam and/or shell elements and design of concrete shells.

• Space Trusses: Analysis of three-dimensional trusses where only axial forces are considered.

Frame analysis results can be post-processed using the steel member design modules for axial and combined stress, namely Strut and Com.

Frame Analysis 3-6

3-7

Theory and application

The following text explains the sign conventions used and gives a brief background of the analysis techniques.

Sign conventions Frame input and output uses a mixture of global axis and local axes values.

Global axes

The global axis system is nearly exclusively used when entering frame geometry and loading. Global axes are also used in the analysis output for deflections and reactions.

The global axes are defined as follows:

• For the sake of this definition, the X-axis is chosen to the right.

• The Y-axis always points vertically upward.

• Using a right-hand rule, the Z-axis points out of the screen.

Note: Unlike some other 3D programs that put the Z-axis vertical, Frame take the Y-axis as being vertical.

Beam element local axes

Local axes are used in the output for element forces. You can also apply loads in the direction of a beam element’s local y-axis.

Frame Analysis 3-8

The local axes for beam elements are defined as follows:

• The local z-axis and axial force is chosen in the direction from the smaller node number to the larger node number.

• The y-axis is taken in a vertical plane perpendicular to the z-axis. The y and z-axes thus describe a vertical plane with the y-axis pointing vertically or diagonally upward.

• The x-axis is taken perpendicular to the y and z-axes, using a left-hand rule.

• One special case exists:

• In the case of a vertical member, the z-axis is taken parallel to the global Y-axis. A unique definition of the y-axis is obtained by taking it parallel to the global X-axis.

Shell element local axes

For shell elements, the local axes are defined as follows:

• The local x and y-axes are chosen in the plane of the shell in such a way that the x-axis is horizontal and the y-axis lies perpendicular to and upward from the x-axis.

• Using a right-hand rule the z-axis is taken perpendicular to the shell element to point diagonally upward.

• Two special cases exist:

• Horizontal elements: The local x is chosen parallel to the global X-axis and the y-axis parallel to the negative Z-axis. The z-axis is then taken parallel to the Y-axis.

• Vertical elements: The y-axis is taken vertically upward, i.e. parallel to the global Y-axis. The x-axis is taken horizontal in the plane of the shell and z-axis is taken horizontal perpendicular to the shell. The z-axis points towards you if the shell’s nodes are defined in an anti-clockwise direction and away if defined clockwise.

To simplify the analysis output, the orientation of the local shell axes can sometimes be manipulated by slight rotation of the shell elements. In the case of horizontal slab, for example, the local x and y-axes (and stresses) are taken parallel to the global X and Z-axes. In the case of a circular slab, radial and concentric stresses may often be more desirable. By generating the shell elements at a slight slope towards the centre, they will not be considered as horizontal

3-9

anymore. As a result, local y-axes will point (upward) towards the centre and the x-axes taken perpendicular to that, i.e. radial and concentric respectively. The small inclination will normally have no significant effect on the analysis.

Note: Rotating elements (for the sake of manipulating the local axes) can induce additional support conditions in some cases. Such manipulation should thus be performed with great care.

Beam element forcesThe sign conventions are as follows:

• The axial force, Pz, is taken in the z-direction.

• The shear forces, Vx and Vy, are given in the x and y-directions respectively.

• Torsional moment, T, is taken about the z-axis using a right-hand rule.

• The moments, Mxx and Myy, are about the x and y-axes respectively.

Note: In this manual, the global and local axes are written in uppercase and lowercase respectively.

Shell element stresses

Shell element stresses are given using the local axes:

• Bending stresses: The entities Mx and My are moment per unit width about the local x and y-axes. Mxy represents a torsional moment in the local x-y plane. The principal bending moments per unit width are represented as Mmax and Mmin.

• Plane stresses: The stresses in the plane of a shell, Sx and Sy, are given in the directions of the local x- and y-axes. Sxy represents the shear stress in the plane of the element. Values are also given for the principal plane stresses, Smax and Smin.

Note: To assist you in evaluating shell element stresses, stress contour diagrams show orientation lines at the centre of each shell element. An orientation line indicates the direction (not axis) of bending or plane stress. In a concrete shell, the orientation line would indicate the direction of reinforcement resisting the particular stress.

Frame Analysis 3-10

Shell reinforcement axes

Reinforcement is calculated in the user-defined x’ and y’-directions. Refer to page 3-64 for detail.

Solid element stresses

Shell element stresses are given using the global axes:

Direct stresses, Sx , Sy and Sz, are given in the directions of the global X-, Y- and Z-axes. Sxy represents the shear stress in the XY-plane of the element. Sxz represents the shear stress in the XZ-plane of the element. Syz represents the shear stress in the YZ-plane of the element. Values are also given for the principal plane stresses, S1, S2, and S3. Von Mises stresses are also calculated.

Units of measurement The following units of measurement are supported:

Units Metric Imperial

Distance mm, m ft, inch

Force N, kN lb, kip

Use the Convert Units button on the Settings page to change the units for the current analysis:

• Convert Units: Changes the units and converts all numeric data from the old to the new units of measurement.

Analysis modes The following types of analysis are possible:

• Linear analysis: Basic linear elastic analysis. A linear analysis is normally sufficient for the static analysis of a frame or truss with negligible sway.

• Second order analysis: Choose this mode to include p-delta effects in the analysis. This option is recommended for structures where sway may have a marked effect on the member forces, e.g. portal frames. The second order analysis is an iterative procedure. The total strain energy of the frame is calculated after each iteration. The analysis is deemed to have converged once the total strain energy of two sequential iterations differs by less than the specified tolerance. If convergence was not possible, e.g. structural instability due to buckling of critical members, a message to that effect will be displayed.

• Non Linear analysis: Choose this mode where non-linear effects and large deflections may be expected or where second order analysis might not provide sufficient accuracy.

3-11

Loading is applied in a series of steps and an iterative analysis is carried out at each step so that the forces in the deflected structure at that point balance with the applied loading.

• Modal analysis: For calculating the natural modes of vibration. The modal analysis is an iterative procedure during which several sets of trial vectors are selected and evaluated. The process takes relatively long to complete and it is therefore recommended that the structure size be limited to a few hundred nodes. You can specify the number of mode shapes to be calculated and other dynamic analysis parameters.

• Harmonic analysis: Choose harmonic analysis to determine the response of the frame to harmonic loading. Load amplitudes are entered exactly like static nodal and element loads. You can enter a load frequency and phase angle for each harmonic load case. The first step of a harmonic analysis is the calculation of the frame’s natural modes of vibration. Therefore, if preceded by a modal analysis, the results of that analysis are re-used and only the harmonic response calculated. The harmonic response is taken as the sum of the square (SSRS) of the maximum modal responses, a method that is considered fundamentally sound when modal frequencies are well separated. When frequencies of major contributing modes are very close together, the SSRS method can give poor results.

• Earthquake analysis: Use this option to calculate the response of the frame to the specified a seismic acceleration parameters. Nodal and element loads entered are treated as static loads. The analysis procedure starts by calculating the frame’s natural modes of vibration. Therefore, if preceded by a modal analysis, the results of the modal analysis are re-used and only the seismic response calculated.

• Buckling analysis: Use this option to determine the buckling load factors and mode shapes for each load case or combination. Being the critical case, the first buckling mode shape is normally the only one of interest.

Finite element shells Frame allows you to use finite shell elements alongside normal beam elements. For this purpose the program uses four-node quadrilateral and three-node triangular isoparametric shell elements with plate bending and membrane behaviour.

Element formulation

The bending formulation of the quadrilateral shell element was derived from the Discrete Kirchoff-Midlin Quadrilateral. The membrane behaviour of the element was improved by introducing the drilling degree of freedom using an interpolation technique by Alman. The result is a shell finite element that shows good plate and membrane performance characteristics.

Accuracy of triangular elements

Both the quadrilateral and triangular elements yield accurate stiffness modelling. However, stress recovery from the triangular elements is not as accurate as is the case for quadrilateral

Frame Analysis 3-12

elements. This means that deflections calculated using triangular elements are generally quite accurate, but moments may be less accurate.

Stress smoothing

A reduced integration technique is used to calculate the element stiffness matrices. The stresses are calculated at the Gaussian integration points and subsequently extrapolated bi-linearly to the corner point and centre point of each element. Taking the average of all contributing stress components smooths stresses at common nodes.

Element layout

Consider a typical continuous flat concrete slab supported on columns or walls. To ensure accurate modelling of curvature, a minimum of about four elements should be used between bending moment inflection points. This translates to a minimum of about eight elements per span in both directions.

Using more elements per span often does not yield a significant improvement in analysis accuracy. In addition, the particular finite element formulation yields its most accurate results when the element thickness does not greatly exceed its plan dimensions.

For a typical concrete slab with a thickness of about one-tenth or one-fifteenth of the span length, a reasonable rule of thumb is to make the plan dimensions of the shell elements no smaller than the thickness of the slab. In other words, use a maximum of about ten to fifteen elements per span.

Finite element solids Frame also provides 8-noded hexahedral and 4-noded tetrahedral solid finite elements. The elements have 3 rotational degrees of freedom per node and are generally more accurate than more commonly used solid elements that do not have rotational degrees of freedom.

Accuracy of tetrahedral elements

Both the hexahedral and tetrahedral elements yield accurate stiffness modelling. However, stress recovery from the tetrahedral elements is not as accurate as is the case for hexahedral elements. This means that deflections calculated using tetrahedral elements are generally quite accurate, but stresses may be less accurate.

Stress smoothing

A reduced integration technique is used to calculate the element stiffness matrices. The stresses are calculated at the Gaussian integration points and subsequently extrapolated to the corner nodes of each element. Taking the average of all contributing stress components smooths stresses at common nodes.

Element layout

3-13

To ensure accurate modelling of curvature, a minimum of about four elements should be used between bending moment inflection points. This translates to a minimum of about eight elements per span direction in a continuous slab.

Concrete design Frame can perform reinforced concrete design for shell elements. The Wood and Armer equations are used to transform the bending and torsional stresses to effective bending moments in the user-defined x’ and y’-directions.

To allow for the effect of in-plane forces, bending moments Mx, My and Mxy are increased to include the effects of these forces. The moments are increased by conservatively taking the in-plane forces to act with a lever arm of a quarter of the section depth. The Wood and Armer equations are then evaluated in same manner as described above.

Codes of practice

The following concrete design codes are supported:

• ACI 318 - 1995.

• BS 8110 - 1997.

• CSA A23.3 - 1993.

• Eurocode 2 - 1992.

• SABS 0100 - 1992.

Steel member design Frame analysis results can be opened in the steel member design modules for design. The available options are:

• Steel Member Design for Axial Stress, Strut: Can design steel trusses.

• Steel Member Design for Combined Stress, Com: Can design beam members.

Frame Analysis 3-14

Settings

Settings are done on the ‘Settings’ tab:

Analysis type

• Linear analysis: Normal linear elastic frame analysis. A linear analysis is normally sufficient for the static analysis of a frame or truss with negligible sway. The linear analysis procedure is performed faster than any other type of analysis. If you need to perform a second order, buckling or dynamic analysis, it will be wise to first verify the basic integrity of the frame input by performing a linear analysis.

• Second order analysis: Models sway behaviour by incorporating P-delta effects. The solution is obtained by iterative analysis, thereby allowing for options like tension elements.

3-15

• Non-linear analysis: This analysis is used when large deflections or non-linear behaviour are expected. Only geometric non-linearity is supported a this stage. Material non-linearity will be added in the near future. The solution is obtained by a stepped iterative analysis. Loads are added in steps. The analysis is iterated to convergence for each step so that the reactions and forces are in balance with the applied loads after each step. The deflected structure at the end of each step is then used to apply the next load step and the process is repeated until the total load has been applied.

• Modal analysis: Calculation of a frame’ s natural modes of vibration. The process takes relatively long to complete and it therefore recommended that the structure size be limited to a few hundred nodes. You can specify the number of mode shapes to be calculated and other dynamic analysis parameters.

• Harmonic analysis: For determining a frame’ s response to harmonic loading.

• Earthquake analysis: Quasi-dynamic analysis of a frame subjected to ground acceleration.

• Buckling analysis: For calculating safety factors for structural instability due to buckling. You can specify the number of mode shapes to be calculated.

Analysis parameters

Depending on the selected analysis type, you may need to specify additional analysis parameters:

• Concrete design parameters: Concrete and reinforcement properties. Details are given on page 3-64.

• Second order and buckling parameters: Required analysis tolerance and number of buckling mode shapes. Refer to page 3-65 for detail.

• Dynamic parameters: Values influencing modal, seismic and harmonic analysis. A detailed discussion is given on page 3-67.

• Non linear parameters: Values influencing the non-linear analysis. A detailed discussion is given on page 3-67.

Own weight

The own weight of the frame can be calculated using the entered cross-sectional areas and member lengths. If you specify a load case, the own weight is calculated and added to the other loads of that case.

The following are points of importance:

• By default, the own weight of the frame is set to not be included in the analysis. Be sure to select the appropriate load case for own weight or, alternatively, to include the frame's own weight in the values of the loads entered.

Frame Analysis 3-16

• The list of load cases from which you can select is based on the load cases defined on the Nodal loads, Beam loads, and Shell loads input pages. You may thus prefer to specify the own weight load case only after completing all other input for the frame. However, you can also enter the own weight load case at the start of the frame input process in which case you may ignore the warning message (that the load case does not exist).

Tip: If you wish to use own weight in its own separate load case, you can do so by defining an empty load case. You can enter a zero load at any node number, for example, and then select that load case as the one to use for own weight.

The own weight or beam elements are modelled as uniformly distributed loads along the lengths of the beams. In the case of a vertical beam element, own weight is modelled as two equal point loads at the ends of the beam, yielding a constant axial force equal to half the own weight. In the case of shell elements, own weight is modelled as point loads at the corner nodes. In the case of solids, the weight is added as point loads at the nodes.

Graphics Options

Click on the graphics options button to have the graphics options dialog displayed.

• Select whether you want items like node numbers and supports to be displayed.

• Choose whether you want all beam elements or only a certain type to be displayed.

• Display the structure with full 3D rendering, e.g. to verify section orientations. 3D rendering is automatically suppressed when viewing output.

• Choose quick or detailed rendering. Quick rendering is faster than the detailed method, but you may find that some surfaces are drawn incorrectly.

All surfaces are drawn as polygons. You can choose to make the surfaces transparent or have them filled and outlined.

Tip: The Graphics options and 3D rendering function can also be accessed using the buttons next to the displayed picture.

3-17

• Views: You can save the current viewpoint and view plane. The current view’s name is displayed on the picture. To re-use a saved view, click the view name on the picture to drop down a list of saved views.

The functions described above can also be used when viewing output. Contour diagrams, for example, are drawn as polygons. You can therefore use the Graphics options setting for polygons to change their appearance. Views defined during input are also available when viewing output and vice versa.

Frame Analysis 3-18

Input

Work through the relevant Input pages to enter the frame geometry and loading:

• General input: Select the domain (Plane frame, grillage etc.) The input wizards can also be selected here. More about these wizards later.

• Nodes input: Frame coordinates.

• Beams input: Join nodes with beam elements.

• Beam sections input: Enter properties or read sections from the database.

• Shells input: Define shell elements.

• Solids input: Define 4- or 8- noded solid elements

• Spring elements input: For special effects, optionally enter spring elements.

• Supports input: External supports.

• Nodal loads input: Point loads and moments.

• Beam element loads input: Uniform distributed, triangular, trapezium and point loads on beams.

• Shell loads input: Apply uniform distributed loads to shells.

• Load combinations input: Group dead, live and wind loads in load combinations.

Alternative methods of generating frame analysis input are discussed on page 3-61.

Viewing the structure You may want to enlarge portions of the picture of the structure or rotate it on the screen. Several zoom and rotate functions, all of which are described in detail in Chapter 2, are available to help you using pictures of the structure:

• Use the Zoom buttons to zoom into a part of the structure or view it from another angle.

• Use the View Point Control to set a new viewpoint or camera position.

• Use the View Planes Control to view a slice of the structure.

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General input

Wizards

The wizards are suitable for the rapid generation of complete input files for some typical structures. Because the resulting input data is presented in the normal way on the input pages, you are free to edit and append to the data as necessary.

Input generated this way can optionally be appended to existing data – you can therefore repeatedly use the wizards to generate complicated structures.

Note: The frame analysis modules are not limited to modelling only those frames generated by the wizards. Any general two or three-dimensional frame can be collectively built up. The wizards merely serve to simplify input of typical frames.

Adding input data to the Calcsheets

You can append the input tables (as they appear on the screen) to the Calcsheets by clicking the Add input tables to Calcsheets button.

You can add a picture from any input pages to the Calcsheets by clicking the Add to Calcsheets button next to the picture in question.

Title

Enter a descriptive name for the frame. It should not be confused with the file name you use when you save the input data.

Frame Analysis 3-20

Nodes input Use as many lines as necessary to enter the nodes defining the frame. A unique number must be assigned to each node. The node number is entered in the No column, followed by the X, Y and Z-coordinates in the X, Y and Z columns. If you leave X, Y or Z blank, a value of zero is used.

You are allowed to skip node numbers to simplify the definition of the frame. You may also leave blank lines in the input to improve readability. If a node number is defined more than once, the last definition will be used.

Note: Most of the examples given in this section show 3D co-ordinates as would be applicable if the domain is set to Space Frame or Space Truss. If the domain is set to Plane Frame or Grillage use the X-Y and X-Z planes respectively.

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Error checking

The program checks for nodes lying at the same position. If a potential error is detected, an Error list button will appear.

Generating additional nodes

When defining a node, you can have additional nodes generated at regular intervals. Example:

• The Y-coordinate of node 4 is left blank. Therefore, node 4 is put at the coordinate (0.805,0,14.614).

• The No of is set to ’2’, meaning that two additional nodes must be generated.

• Setting Increment to ’7’ means that the node numbers are incremented by seven. Therefore, node 4 is copied to node 11 and node 11 is copied to node 18.

• The values in the X-inc, Y-inc and Z-inc columns set the distance between copied nodes. The coordinates 4 to 18 are horizontally spaced at 1.140 m and 0.472 m along the X and negative Z-axis respectively. The coordinates of the additional nodes are thus (1.945,0,14.142) and (3.085,0,13.670).

An alternative method to generate equally spaced nodes is to use the Inc to End option. This method allows you to define two nodes and then generate a number of nodes in-between:

• Use the same procedure as above to define the first node’s coordinates.

• Set the values of X-inc, Y-inc and Z-inc to the total coordinate difference to the last node and enable the Inc to End option. The last node’s coordinates are then first calculated and the specified number of intermediate nodes then generated.

Second order generation

Once you have defined one or more nodes in the table, you can copy that relevant line’ s nodes by entering a '–' character in the No column of the next line. Then enter the number of additional sets of nodes to be generated in the No of column and the coordinate increments in the X-inc, Y-inc and Z-inc columns.

Frame Analysis 3-22

Second order generation example:

The following nodes are generated:

No X Y Z 15 0.00 5.12 0.00 16 2.00 5.12 0.10 17 4.00 5.12 0.20 18 0.00 5.62 1.00 19 2.00 5.62 1.10 20 4.00 5.62 1.20

Block generation

A group of nodes can be repeated by entering a ’B’ in the No column followed by the first and last table line numbers in which the nodes were defined. Separate the line numbers with a ’–'.

Block generation example:

The nodes defined in lines 11 to 26 are copied twice. Node numbers are incremented by thirty for each copy. The X, Y and Z-coordinate increments are 10 m, zero and zero respectively.

To copy one line only, simply omit the end line number, e.g. 'B10' to copy line 10 only.

Tip: The current line number is displayed in the status bar at the bottom left of the program's window.

The block generation function may be used recursively. That means that the lines specified may themselves contain further block generation statements.

Moving nodes

To move a group of nodes to a new location without generating any new nodes, use the block generation function and set No-of to '1' and Inc to '0'.

Arc generation

A group of nodes can be repeated on an arc by entering an 'A' in the No column, followed by the start and end line numbers. Enter the centre of the arc in the X, Y and Z columns and use the X-inc, Y-inc or Z-inc column to specify the angle increment about the X, Y or Z-axis respectively. If the program domain is set to Plane Frame or Grillage, the angle increment should be entered in the last column. Rotation will be about the Z and Y-axis respectively.

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Example:

All nodes defined in lines 5 to 9 of the table will be repeated eleven times on an imaginary horizontal arc. The centre point of the arc is located at the coordinate (10,0,1.5). The node number increment is set to 5, i.e. node number 3 becomes node 8, etc. The rotation angle between the generated groups of nodes is 30 degrees about the Y-axis, i.e. anti-clockwise using a right-hand rule.

To copy one line only, simply omit the end line numbers, e.g. ’A12’ to copy line 12 only.

Note: The arc generation function may be used recursively.

Rotating nodes

To rotate a group of existing nodes without generating any new nodes, use the arc generation function and set the No-of to ’1’ and Increment to ’0’.

Deleting nodes

Nodes can be deleted by entering ’Delete’ in the Inc to end column. This can be especially handy if you have generated a large group of nodes and then need to remove some of them again.

Example:

Nodes 15 and the additional nodes 18 and 21 are deleted.

Graphical input

The following graphical input functions are available on the left hand side of the screen. The toolbar containing the graphics options buttons can also be dragged and docked on any side of the picture.

To delete nodes click the ‘Delete nodes’ button and then select the nodes to be deleted on the screen using the mouse. Click ‘Done’ when finished. Clicking ‘Undo’ will undo the deletions in reverse order.

To block delete nodes click the ‘Block delete nodes’ button. Select a

Frame Analysis 3-24

rectangle on the screen with the mouse. All nodes inside the rectangle will be deleted. Press ‘Done’ when finished. Pressing ‘Undo’ will undo the deletions in reverse order, one by one. Pressing ‘Undo All’ will undo all deletions done with this function.

Click the ‘Explode nodes’ button to explode the node input. This results in the list of nodes being written, each on a separate line without block & arc generations etc. Once done, it cannot be reversed.

Click the ‘Join loos structure segments’ button to have all duplicate nodes (having the same co-ordinates) that are not connected by spring elements, deleted. This will ensure that loose pieces of the structure become connected. The function is not reversible.

Click on ‘Delete loose nodes’ to have all nodes not connected to elements deleted. The program will ignore loose nodes in the analysis, but the input is neater and easier to interpret if unwanted nodes are removed. The function is not reversible. Deleted nodes can however be undeleted if the bottom of the input table is edited and the nodes entered as ‘deleted’ are removed.

Beam elements input A beam or frame element is defined by entering the node numbers at each end, separated with a '–'. For example, '3–9' is the element linking nodes 3 and 9. The elements themselves are not numbered.

A series if elements can be input in a string, e.g. '2-6-10-14-18-22-24'. If the node number increment of a series is constant, you can replace intermediate nodes with two '–' characters. In the string above, nodes 2 to 22 have a constant increment of four. Therefore, the string can be rewritten as '2-6- - 22-24'. The node increment of four is derived from '2-6'.

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An element definition must include a section number entered in the Section Name column. The section name is used to identify the relevant section. The actual section properties for each section number defined on the Beam Sections input page.

Section orientation in a 3D analysis

In 3D analysis, the local y-z plane of an element is taken as vertical by default. The principle can be illustrated by considering an I-section in its normal orientation. For this case, the web will always be considered to be in a vertical plane.

If the element is aligned vertically, i.e. a column, the web will be in a vertical plane anyway. For this special case, the local y-axis is aligned with the global X-axis, i.e. the web is taken in the global X-Y plane.

Frame Analysis 3-26

An element can be rotated about its axis by entering a beta angle. The beta angle is measured about the z-axis, taking the default orientation as 0°. Instead of entering a beta angle, you may also enter a reference node – the beta angle is then taken in the plane described by the element's nodes and the reference point. To use a reference point, first define a node with the relevant coordinate and then enter 'N' followed by the node number in the Beta column

Tip: Enable full 3D rendering in the Graphics options to view the true beam orientation.

Section orientation in a 2D analysis

In the case of a 2D analysis, the local y-z plane of an element is taken in the global X-Y plane. The principle can be illustrated by considering an I-section in its normal orientation. For this case, the web will always be considered to be in a vertical plane.


A section can be rotated through ninety degrees by selecting the alternative orientation when reading it from the section database.

Note: In a space truss analysis the section orientation is of no importance. The analysis results are influenced by the section area and not by it's second moment of inertia.

End fixity

The fixity at each end of an element, i.e. continuous or pinned, must also be defined in the Fixity columns. Pins are modelled on the element itself and not on the node. External pinned supports should be defined on the supports input table. External supports are described in the next section.

The following types of end fixities can be specified:

• Fixed: Specify 'F' to provide full rotational continuity. If you leave the field blank, 'F' is assumed.

• Pinned: Use 'P' to for no rotational restraint, i.e. a ball-joint.

• Torsional fixity: Use 'T' to provide restraint for rotation about the element axis only. This option is only available in the Grillage domain and the Space Frame domain.

Note: To retain compatibility with the Dos version, you may also use '0', '1' or '2' instead of 'F', 'P' or 'T' respectively.

Entered fixities are applied at an element's lower node number (designated as the 'left' end) and higher node number (the 'right' end). The order of the node numbers entered in the first column of the table has no bearing on the application of the fixity codes.

To define a pin only at the two remote ends of a group of elements, enable the Group fix option by entering a 'Y'. In this case, the normal convention of smaller and larger node

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numbers does not apply. Instead, pins are put at the remote ends in the same order that the nodes have been entered.

Example:

The group of elements from node 42 to 24 is continuous except for the pins used at nodes 42 and 24.

Note: Do not use an internal pin on an element to model an external support that allows free rotation. Rather allow the beam to be fixed to the node and define a simple support on the Support input page.

If the Group fix is left blank or ’N’ is entered, the normal individual element fixity mode is assumed.

Tip: Element fixity can be displayed graphically on the screen. For this, edit the Graphics options to disable the Elements Continuous option.

When using pins, especially in the Space Frame domain, you should take care to ensure overall stability of the frame. Consider two elements on a straight line with pins at all three relevant nodes, for example. The centre node will be unrestrained for rotation about the element axis, resulting in instability during the analysis.

Note: When performing a second order analysis, you can use tension elements to model bracing, for example. For this, special settings need be made on the Beam Sections input page. Refer to page 3-33 for detail.

Tapered beams

A beam can be made to taper between by entering two or three section names, separated with commas:

• Use two sections, e.g. ’Rafter,Haunch’ or ’1,2’, to make the program vary the section properties linearly along the length of the beam element. The first and second sections are taken at the lower and higher node numbers respectively.

• For a more accurate non-linear variation, enter three section names, e.g. ’Rafter,Middle,Haunch’. The first, second and third sections are taken at the at the lower node number, the centre of the element and at higher node number respectively.

The procedure the enter haunches is described on page 3-32.

Frame Analysis 3-28

Rigid links

You can use rigid links to rigidly offset sub-structures, e.g. slabs with downstand beams. To define a rigid link, enter ’R’ in the Section Name column.

Rigid links are modelled as very stiff beams. The stiffness of a rigid link is determined by multiplying the maximum area and bending stiffness of the other beams with a factor, typically one thousand. The rigid multiplication factors can be adjusted using the Advanced option on the Beam sections input page. Refer to page 3-33 for detail.

Rigid link example:

Rigid links are defined between nodes 12 and 24, 14 and 26 and 16 and 26.

Generating additional elements

You can generate additional elements with the same section and fixity code values using the No of extra and Node No Inc columns. Example:

The elements between nodes 251 and 266 are copied ten times with the node numbers decrementing by five with each copy.

Block generation

A group of elements can be repeated by entering a ’B’ in the No column. Then enter the first and last table line numbers in which the elements were defined, separated with a ’–'.

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All elements defined in lines 11 to 26 will be copied twice with a node number increment of thirty. The copied elements will use the same section number and fixity codes as the original elements.

To copy one line only, simply omit the end line number, e.g. ’B11’ to copy line 11 only.

Tip: The current line number is displayed in the status bar at the bottom left of the program’s window.

The block generation function may be used recursively. The group of lines referenced may thus contain block generation statements.

Tip: When entering a complicated structure it may help to leave a few blank lines between groups of elements. Not only will it improve readability, but it will also allow you to insert additional nodes at a later stage without upsetting block and arc generations.

Deleting elements

Beam elements can be deleted by entering a special section name ’Delete’. This can be especially handy if you have generated a large group of elements at regular increments and need to remove some of them again.

Example:

Elements 25-27-29 and 35-37-39 are deleted.

Note: The display of selected beam element groups can be activated or suppressed by editing the Graphics options.

Error checking

The program checks for duplicate elements and elements with zero length. It also checks that a section number is assigned to each element. If an error is detected, an Error list button will be displayed.

Frame Analysis 3-30

Graphical input


To add beams click the ‘Add beams’ button. Enter the section name, ß angle and fixities for the beams. By clicking two successive nodes, a beam will be inserted between them. If ‘follow on’ is checked, the last node of the previous beam is taken as the first node of the next beam. If ‘Link end nodes only’ is checked, only one beam is placed between the last two nodes entered. If not, all nodes between the last two nodes are also added into the beam string. The nodes must lie within a certain tolerance from the straight line between the end nodes to be included. This tolerance can be entered in the Tolerance (%) field. If e.g. 1% is entered, any node closer than 1% of the distance between the end nodes from the line joining them is included. Pressing ‘Undo’ will delete the beams in reverse order, in which they were entered, one by one.

To delete beams click the ‘Delete beams’ button and then select the beams to be deleted on the screen using the mouse. Click ‘Done’ when finished. Clicking ‘Undo’ will undo the deletions in reverse order.

To block delete beams click the ‘Block delete beam elements’ button. Select a rectangle on the screen with the mouse. All beams inside the rectangle will be deleted. Press ‘Done’ when finished. Pressing ‘Undo’ will undo the deletions in reverse order one by one beam. Pressing ‘Undo All’ will undo all deletions done with this function.

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Click the ‘Change beam properties’ button to change beam properties. Enter the desired properties for the beam(s) on the dialog. One can also use the ‘Get properties’ button to do this. Click the button and then click on a beam. The beam’ s properties will then be transferred to the dialog. Clicking on beams will now change their properties to those specified on the dialog. The ‘Undo’ button will undo the changes in reverse order.

Click the ‘Explode beams’ button to explode the beam input. This results in the list of beams being written, each on a separate line without block generations etc. Once done, it cannot be reversed.

On the beams input page one can also delete nodes and groups of nodes in the same way as on the nodes input page. Refer to page 3-24 for details

Beam sections input Section properties should be assigned to all section names used on the Beam elements input page. The following properties are required for all sections:

• Cross sectional area, A.

• Second moment of area about the local x-axis, Ix (not required for Space Truss analysis).

• Second moment of area about the local y-axis, Iy (Space Frame domain only).

• Torsional moment of inertia, J (Grillage and Space Frame domain only).

Frame Analysis 3-32

Each section should also have an associated material selected. If no section or material properties are entered, the values applicable to the previous line in the table are used.

Reading sections from the database

Use the Section database function to display and select sections from database. You can add your own sections, e.g. plate girders, to the database using the procedures described in Chapter 2.

Entering haunches

Haunches are entered by appending the haunch depth to the section designation. To add a haunch of 180 mm to a ’305x102x66’ BS taper flange I-section, enter ’305x102x66 (0.280h)’. The overall depth is then taken to be 305 mm + 280 mm = 585 mm.

Tip: You can verify your definition of haunches by enabling 3D rendering. Refer to page for 3-18 more detail.

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Tension members

When performing a second order analysis, you can designate members to have tension stiffness only, e.g. slender bracing members. To make a member be ignored during the analysis when it would act in compression:

1. Enter the member’s section properties in the usual manner.

2. Edit the value for the cross sectional area and change its sign to negative.

Note: The program uses the absolute value of the cross sectional area. The negative sign entered merely enables the tension-only behaviour for beams of the given section group.

Own weight

If a material’s definition includes a density value, the own weight of a member is calculated automatically and added to the load case specified on the Settings page.

Selecting materials

Each section should have an associated material.

To add one or more materials to a frame analysis data file, click Materials. Open the relevant material type screen and select the materials that are required for the current frame input.

After adding the selected materials to the input, you can select them by clicking the Material column to drop down a list.

Adding materials to the global database

The procedure to permanently add more materials to the database is described in Chapter 2.

Frame Analysis 3-34

Advanced section options

Clicking the Advanced button allows you to configure the behaviour of rigid links. A rigid link is modelled as a very stiff beam of which the area, second moment of inertia and modulus of elasticity are taken as the maximum corresponding properties all other beams multiplied with the specified factors.

Refer to page 3-27 for detail on defining rigid links.

graphical input


Click the ‘Change beam properties’ button to change beam properties. Enter the desired properties for the beam(s) on the dialog. One can also use the ‘Get properties’ button to do this. Click the button and then click on a beam. The beam’ s properties will then be transferred to the dialog. Clicking on beams will now change their properties to those specified on the dialog. The ‘Undo’ button will undo the changes in reverse order.

Shell elements input You can use finite shell elements alongside beam elements, except in the Space truss domain. Shell elements can be optionally designed as reinforced concrete members.

Elements are defined by referring to corner nodes, four in the case of quadrilaterals and three for triangles. You should enter the node numbers in sequence around the perimeter, either clockwise or anti-clockwise, in the Node 1 to Node 4 columns. Leave Node 4 blank to define a triangular element.

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Note: Quadrilateral elements generally yield more accurate analysis results than triangular elements. Refer to page 3-11 for more detail.

An element definition must include a thickness and material type. Refer to page 3-33 for more detail on using materials.

Own weight


Tip: When entering a complicated slab, it may help to leave a few blank lines between groups of elements. Not only will it improve readability, but it will also allow you to insert additional elements at a later stage without upsetting block and arc generations.

Error checking

Frame Analysis 3-36

The program checks for duplicate elements and nodes not connected to elements. It also checks that a group number is assigned to each element. If an error is detected, an Error list button will be displayed.


You can generate additional elements with the same group number using the Number of Extra and Node no Inc columns.

Block generation

You can use the block generation to copy shells you defined earlier in the table. A group of shells can be repeated by entering a ’B’ in the Node 1 column followed by the first and last table line numbers in which the nodes were defined. Separate the line numbers with a ’–'.

To copy a single line only, simply omit the end line number, e.g. 'B11' to copy line 11 only.



Deleting elements

Shell elements can be deleted by entering 'Delete' in the Material column. This can be useful if you have generated a large group of elements and need to remove some of them again. Example:

The element 15-16-26-25 and the generated element 18-19-29-28 are deleted.

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Graphical input


To add shells click the ‘Add shell elements’ button. Enter the material, thickness and shell type (triangular or quadrilateral). The easiest way to enter shells is to define a plane in which they lie. Click 3 nodes to indicate the plane. The three node numbers can also be typed directly into the dialog. Also enter the thickness of the plane. Only the nodes lying in the plane and half of the thickness on either side are now displayed. If one now moves the mouse across the picture, possible shells are shown in purple. Click the mouse to have each shell entered into the input table. If you do not want to use a plane in this way, click ‘Don’ t use plane’ . Pressing ‘Undo’ will delete the shells in the reverse order in which they were entered, one by one.

To delete shells click the ‘Delete shells’ button and then select the shells to be deleted on the screen using the mouse. Click ‘Done’ when finished. Clicking ‘Undo’ will undo the deletions in reverse order.

To block delete shells click the ‘Block delete shell elements’ button. Select a rectangle on the screen with the mouse. All shells inside the rectangle will be deleted. Press ‘Done’ when finished. Pressing ‘Undo’ will undo the deletions in reverse order one by one. Pressing ‘Undo All’ will undo all deletions done with this function.

Frame Analysis 3-38

Click the ‘Change shell element properties’ button to change shell properties. Enter the desired properties for the shell(s) on the dialog. One can also use the ‘Get properties’ button to do this. Click the button and then click on a shell. The shell’ s properties will then be transferred to the dialog. Clicking on shells will now change their properties to those specified on the dialog. The ‘Undo’ button will undo the changes in reverse order.

Click the ‘Explode shells’ button to explode the shell input. This results in the list of shells being written, each on a separate line without block generations etc. Once done, it cannot be reversed.

On the shells input page one can also delete nodes and groups of nodes in the same way as on the nodes input page. Refer to page 3-24 for details

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Solid elements input You can use solid elements alongside beam and shell elements, if the domain is set as Space frame.

Elements are defined by referring to corner nodes, eight in the case of hexahedrons and four for tetrahedrons. You should enter the node numbers in sequence around the perimeter, either clockwise or anti-clockwise, in the Node 1 to Node 8 columns. First define the back face going either clockwise or anti-clockwise in the node 1 to node 4 columns. Next define the front face starting with node 5 above the node defined as node 1 and moving around in the same direction as nodes 1 to 4. For tetrahedrons the four nodes can be entered in any order in columns 1 to 4.

Note: Hexahedral elements generally yield very accurate analysis results. The tetrahedrons should only be used as filler elements where it is not possible to use hexahedrons.

An element definition must include a material type. Refer to page 3-33 for more detail on using materials.

Frame Analysis 3-40

Own weight


Tip: When entering a complicated model, it may help to leave a few blank lines between groups of elements. Not only will it improve readability, but it will also allow you to insert additional elements at a later stage without upsetting block and arc generations.

Error checking



You can generate additional elements with the same group number using the Number of Extra and Node no Inc columns.

Block generation

You can use the block generation to copy shells you defined earlier in the table. A group of solids can be repeated by entering a ’B’ in the Node 1 column followed by the first and last table line numbers in which the nodes were defined. Separate the line numbers with a ’–'.

To copy a single line only, simply omit the end line number, e.g. 'B11' to copy line 11 only.



Deleting elements

Solid elements can be deleted by entering 'Delete' in the Material column. This can be useful if you have generated a large group of elements and need to remove some of them again. Example:

The element 201-202-152-151-226-227-177-176 and the generated element 251-252-201-201-276-277-227-226 are deleted.

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Graphical input


To add solids click the ‘Add solids elements’ button. Enter the material and solid type (tetrahedral, wedges or hexahedra). At the time of writing only hexahedra were available for this function. The easiest way to enter solids is to define a plane in which they lie. Click the ‘set up plane’ button to do this. Click three nodes to indicate the plane. The three node numbers can also be typed directly into the dialog. Also enter the thickness of the plane. Only the nodes lying in the plane and half of the thickness on either side are now displayed. If one now moves the mouse across the picture, possible solids are shown in purple. Click the mouse to have each solid entered into the input table. If you do not want to use a plane in this way anymore, click ‘Clear Plane’ . Pressing ‘Undo’ will delete the solids in the reverse order in which they were entered, one by one.

To delete solids click the ‘Delete solid elements’ button and then select the solids to be deleted on the screen using the mouse. Click ‘Done’ when finished. Clicking ‘Undo’ will undo the deletions in reverse order.

To block delete solids click the ‘Block delete solid elements’ button. Select a rectangle on the screen with the mouse. All solids inside the rectangle will be deleted. Press ‘Done’ when finished. Pressing ‘Undo’ will undo the deletions in reverse order one by one. Pressing ‘Undo All’ will undo all deletions done with this function.

Frame Analysis 3-42

Click the ‘Change solid element properties’ button to change solid element properties. Enter the desired material for the solid(s) on the dialog. One can also use the ‘Get properties’ button to do this. Click the button and then click on a solid. The solid’ s material property will then be transferred to the dialog. Clicking on solids will now change their material to that specified on the dialog. The ‘Undo’ button will undo the changes in reverse order.

Click the ‘Explode solids’ button to explode the solids input. This results in the list of solids being written, each on a separate line without block generations etc. Once done, it cannot be reversed.

On the solids input page one can also delete nodes and groups of nodes in the same way as on the nodes input page. Refer to page 3-24 for details

Spring elements input You can use spring elements to provide elastic links between sub-structures, e.g. to model elastomeric bearings between a slab and supporting walls. In theory, two nodes connected with a spring element should have the same coordinates. The program will warn if this is not the case and still allow you to continue.

Enter linear spring constants in the Kx, Ky and Kz columns and rotational spring constants in the Rx, Ry and Rz columns.

The orientation of a spring element is defined by entering a bearing between any two nodes that do not necessarily need to be connected to the same or other spring elements as well. The directions of the axes are defined as followed:

• A spring element's x-axis is taken in the direction of the orientating nodes.

• The y-axis defined in the same way as for a normal beam element, i.e. perpendicular to spring element in a vertical plane.

• The z-axis is taken perpendicular to the x and y-axes using aright-hand rule.

Spring element example:

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Spring elements are defined between nodes 16 and 116, 17 and 117 up to 19 and 119. The spring elements are aligned parallel to the imaginary line joining nodes 3 and 4.

Tip: Spring elements can also be made "rigid" to force two nodes to have the same translation and/or rotation. In the above example, a very large value for Kx would cause nodes 16 and 116 to have identical displacements in the direction described by nodes 3 and 4.

Graphical input


To add springs click the ‘Add spring elements’ button. Enter the spring stiffnesses and orientation nodes on the dialog.. Now click the mouse on nodes to have springs entered into the input table. Pressing ‘Undo’ will delete the springs in the reverse order in which they were entered, one by one.

To delete springs click the ‘Delete spring elements’ button and then select the springs to be deleted on the screen using the mouse. Click ‘Done’ when finished. Clicking ‘Undo’ will undo the deletions in reverse order.

To block delete springs click the ‘Block delete spring elements’ button. Select a rectangle on the screen with the mouse. All springs inside the rectangle will be deleted.

Frame Analysis 3-44

Press the ‘Done’ button when finished. Pressing ‘Undo’ will undo the deletions in reverse order, one by one. Pressing ‘Undo All’ will undo all deletions done with this function.

Click the ‘Change spring element properties’ button to change spring element properties. Enter the desired spring stiffnesses and orientation on the dialog. One can also use the ‘Get properties’ button to do this. Click the button and then click on a spring. The spring’ s properties will then be transferred to the dialog. Clicking on springs will now change their properties to those specified on the dialog. The ‘Undo’ button will undo the changes in reverse order.

Click the ‘Explode springs’ button to explode the spring input. This results in the list of springs being written, each on a separate line without block generations etc. Once done, it cannot be reversed.

On the springs input page one can also delete nodes and groups of nodes in the same way as on the nodes input page. Refer to page 3-24 for details

Supports input Frames require external supports to ensure global stability. Supports can be entered to prevent any of the six degrees of freedom at a node, i.e. translation in the X Y and Z-directions and rotation about the X, Y and Z-axes. You can also define elastic supports, e.g. an elastic soil support, and prescribed displacements, e.g. foundation settlement.

Enter the node number to be supported in the Node No column. In the next column a combination of the letters 'X', 'Y' and 'Z' can be entered to indicate the direction of fixity. Use capitals and lowercase to define restraint of translation and rotation respectively, e.g. 'XYZy' means fixed against movement in the X, Y and Z-direction and rotation about the Y-axis.

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Note: The use of lowercase for rotational restraints should not be confused with the convention of using lowercase for local element axes.

Tip: To enter a simple support with no moment restraint, one would typically enter a ’XYZ’ or ’Y’. Avoid using a pin on an element to model an external hinge.

If you want to repeat the supports defined on the previous line of the table, you need only enter the node number, i.e. you may leave the Fixity column blank. If the XYZxyz column is left blank, the supports applicable to the previous line will be used automatically.

Prescribed displacements and elastic supports

Use the X, Y, Z, Rx, Ry and Rz columns to enter prescribed displacements and rotations in the direction of and about the X, Y and Z-axes. Being a global support condition, the effect of the prescribed displacement is not considered to be a separate load case. Instead, the effect

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of prescribed displacements is added once only to the analysis results of each load case and load combination.

Elastic supports, or springs, are defined by entering spring constants in the X, Y, Z, x, y and z columns. The spring constant is defined as the force or moment that will cause a unit displace-ment or rotation in the relevant direction. Enter an ’S’ in the P/S column to indicate that an entered value is a spring constant rather than a prescribed displacement. If you leave the P/S column blank, the entered values are taken as prescribed displacements.

Note: The display of supports can be activated or suppressed by editing the Graphics options.

Error Checking

The program does a basic check on the structural stability of the frame. If a potential error is detected, an Error list button will appear.

Note: You cannot define an elastic support and a prescribed displacement at the same node because it will be a contradiction of principles.

Generating additional supports

Additional supports and prescribed displacements can be generated using the Number of extra and Node number inc columns. The procedure is similar to that described on page 3-21 for generating additional nodes.

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Graphical input


To add supports click the ‘Add supports’ button. Enter the fixities, prescribed displacements, spring constants and fixity type on the dialog. Now click the mouse on nodes to have supports entered into the input table. Pressing ‘Undo’ will delete the supports in the reverse order in which they were entered, one by one.

To delete supports click the ‘Delete supports’ button and then select the supports to be deleted on the screen using the mouse. Click ‘Done’ when finished. Clicking ‘Undo’ will undo the deletions in reverse order.

To block delete supports click the ‘Block delete supports’ button. Select a rectangle on the screen with the mouse. All supports inside the rectangle will be deleted. Press the ‘Done’ button when finished. Pressing ‘Undo’ will undo the deletions in reverse order, one by one. Pressing ‘Undo All’ will undo all deletions done with this function.

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Click the ‘Change support properties’ button to change support properties. Enter the desired support fixities, type, prescribed displacements and spring constants on the dialog. One can also use the ‘Get properties’ button to do this. Click the button and then click on a support. The support’ s properties will then be transferred to the dialog. Clicking on supports will now change their properties to those specified on the dialog. The ‘Undo’ button will undo the changes in reverse order.

Click the ‘Explode supports’ button to explode the support input. This results in the list of supports being written, each on a separate line without block generations etc. Once done, it cannot be reversed.

On the supports input page one can also delete nodes and groups of nodes in the same way as on the nodes input page. Refer to page 3-24 for details

Nodal loads input Loads on beam elements are categorised as nodal loads, i.e. loads at node points, and element loads, i.e. loads between nodes. Uniform distributed loads can be applied to shell elements.

All loads are organised in load cases, e.g. 'DL' for own weight, 'ADL' for additional dead loads, 'LL' for live load, etc. Load cases apply equally to the various load input screens, meaning that you can build up a load case using different types of loads.

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To define a load case, type a descriptive name for each load case in the Load Case column. Use up to six characters to describe each load case. If the load case name is not entered, the load case applicable to the previous line in the table is used.

The load case at the cursor position is displayed graphically. Press Enter or Display to update the picture.

A nodal load can, as its name implies, only be applied at a node. If a point load is required on an element, use the Beam loads input table instead.

Sign conventions

Nodal loads are applied parallel to the global axes – an explanation of the sign conventions are given on page 3-7.

Tip: For a typical steel or timber frame or roof truss, it may be easiest to define a node at each purlin position. Roof loads transferred via the purlins can then be entered as nodal loads.

Error checking

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The program checks that specified nodes have indeed been defined in the Nodes input table. If an error is detected, an Error list button will appear.

Generating additional nodal loads

Additional nodal loads can be generated using the Number of extra and Node number inc columns respectively.

Block generation of nodal loads

You can use the block function to copy blocks of nodal loads. The procedure is similar to that for generating additional nodes – see page 3-22 for more detail.

Graphical input


To add nodal loads click the ‘Add nodal loads’ button. Enter the forces, moments and the load case on the dialog. Now click the mouse on nodes to have nodal loads entered into the input table. Pressing ‘Undo’ will delete the nodal loads in the reverse order in which they were entered, one by one.

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To block add nodal loads click the ‘Block add nodal loads’ button. Enter the forces, moments and the load case on the dialog. Select a rectangle on the screen with the mouse. All nodes inside the rectangle will have a nodal load added. Pressing ‘Undo’ will delete the nodal loads in the reverse order in which they were entered, one by one.

To delete nodal loads click the ‘Delete nodal loads’ button and then select the nodal loads to be deleted on the screen using the mouse. The load case for which loads are to be deleted should also be entered on the dialog. Click ‘Done’ when finished. Clicking ‘Undo’ will undo the deletions in reverse order.

To block delete nodal loads click the ‘Block delete nodal loads’ button. Select a rectangle on the screen with the mouse. All nodal loads inside the rectangle will be deleted. Press the ‘Done’ button when finished. Pressing ‘Undo’ will undo the deletions in reverse order, one by one.

Click the ‘Explode nodal loads’ button to explode the nodal loads input. This results in the list of nodal loads being written, each on a separate line without block generations etc. Once done, it cannot be reversed.

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Beam element loads input Distributed loads and point loads on beam elements are all referred to as element loads. The Nodal loads input page provides the easiest way of applying point loads and moments at nodes.

Use up to six characters to enter a descriptive name for each load case in the Load Case column. Then enter the element string of nodes in the Beam element definition column. Entering the beam element definition follows the same convention used as for the Elements input table – see page 3-24 for detail.

Sign conventions

Depending on the selected load direction, beam loads are applied parallel to the global axes or parallel to the local y-axis – the definitions of the global and local axes are given on page 3-7 and 7 respectively.

The load direction is entered in the Direction column. Enter a global direction 'X', 'Y' or 'Z'. Element loads are applied to the relevant projected length of the elements. Therefore, if a 'Y' load is entered for a vertical element, for example, the resulting load will therefore be zero.

You can also load a beam element parallel to its local y-axis by setting the load direction to 'L' – refer to page 3-7 for an explanation of the local axis convention used.

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Types of beam loads

The following loads can be entered:

• A point load’s magnitude is entered in the P column and its position from the smaller node number in the a column.

• For a distributed load, entered in the load intensity at the smaller and larger node numbers in the W-begin and W-end columns respectively. If the load is constant over the length of the element, W-end may be left blank.

• To define a temperature load, enter the temperature difference in the dT column. A temperature change is used with the temperature expansion coefficient of the relevant material used.

Note: Positive vertical loads act upward and negative loads act downward.

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Error checking

The program checks that element definitions match previously defined elements. If an error is detected, an Error list button will appear.

Generating additional element loads

The No of extra and Node number Inc columns can also be used to generate additional element loads.

Block generation of beam loads

You can use the block function to copy blocks of beam loads. The procedure is similar to that used to generating additional beam elements – see page 3-28 for detail.

Graphical input


To add beam loads click the ‘Add beam loads’ button. Enter the loads, direction and temperature change on the dialog. The load case also needs to be entered. Now click the mouse on beams to have beam loads entered into the input table. Pressing ‘Undo’ will delete the beam loads in the reverse order in which they were entered, one by one.

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To block add beam loads click the ‘Block add beam loads’ button. Enter the loads, direction and temperature change on the dialog. The load case also needs to be entered. Select a rectangle on the screen with the mouse. All beams inside the rectangle will have a beam load added. Pressing ‘Undo’ will delete the beam loads in the reverse order in which they were entered, one by one.

To delete beam loads click the ‘Delete beam loads’ button and then select the beam loads to be deleted on the screen using the mouse. The load case for which loads are to be deleted should also be entered on the dialog. Click ‘Done’ when finished. Clicking ‘Undo’ will undo the deletions in reverse order.

To block delete beam loads click the ‘Block delete beam loads’ button. Select a rectangle on the screen with the mouse. All beam loads inside the rectangle will be deleted. Press the ‘Done’ button when finished. Pressing ‘Undo’ will undo the deletions in reverse order, one by one.

Click the ‘Explode beam loads’ button to explode the beam loads input. This results in the list of beam loads being written, each on a separate line without block generations etc. Once done, it cannot be reversed.

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Shell loads Distributed loads can be applied on shell elements. Enter a load case description in the Load case column followed by the relevant element numbers in the Shell numbers column. The program automatically assigns numbers to all shell elements in the sequence they are defined on the Shells input page.

A series of elements can be entered by separating the first and last element numbers by a ’–' character, e.g. '1–6' to define elements 1 up to 6.

Tip: If the shell element numbers are not visible in the picture, edit the graphics options to enable detailed rendering and disable the full 3D view. Refer to page 3-18 for detail on changing the graphics options.

Sign conventions

Shell loads are applied parallel to the element's local z-axes – an explanation of the local axes of shell elements are given on page 3-7.

Types of shell loads

The following shell loads can be entered:

• For a distributed load, entered in the load intensity in the UDL column.

• To define a temperature load, enter the temperature difference in the dT column. A temperature change is used with the temperature expansion coefficient of the relevant material used.


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Error checking

The program checks that the entered element numbers are valid. If an error is detected, an Error list button will appear.


The No of extra and Node number Inc columns can also be used to generate additional shell loads.

Block generation of shell loads

You can use the block function to copy blocks of beam loads. The procedure is similar to that used to generating additional shell elements – see page 3-36 for detail.

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Graphical input


To add shell loads click the ‘Add shell loads’ button. Enter the UDL, direction and temperature change on the dialog. The load case also needs to be entered. Now click the mouse on shells to have shell loads entered into the input table. Pressing ‘Undo’ will delete the shell loads in the reverse order in which they were entered, one by one.

To block add shell loads click the ‘Block add shell loads’ button. Enter the UDL, direction and temperature change on the dialog. The load case also needs to be entered. Select a rectangle on the screen with the mouse. All shells inside the rectangle will have a shell load added. Pressing ‘Undo’ will delete the shell loads in the reverse order in which they were entered, one by one.

To delete shell loads click the ‘Delete shell loads’ button and then select the shell loads to be deleted on the screen using the mouse. The load case for which loads are to be deleted should also be entered on the dialog. Click ‘Done’ when finished. Clicking ‘Undo’ will undo the deletions in reverse order.

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To block delete shell loads click the ‘Block delete shell loads’ button. Select a rectangle on the screen with the mouse. All shell loads inside the rectangle will be deleted. Press the ‘Done’ button when finished. Pressing ‘Undo’ will undo the deletions in reverse order, one by one.

Click the ‘Explode shell loads’ button to explode the shell loads input. This results in the list of shell loads being written, each on a separate line without block generations etc. Once done, it cannot be reversed.

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Load combinations input

You can model practical scenarios by grouping load cases together in load combinations. Enter the load combination name in the Load comb column; followed by the load case name and relevant load factors.

If the Load comb column is left blank, the load combination is taken to be the same as for the previous line of the table. The load cases to consider in a load combination are entered one per line in the Load case column. Enter the relevant ultimate and serviceability limit state load factors in the ULS factor and SLS factor columns.

Tip: You may leave one or more blank lines between load combination definitions to improve readability.

The ultimate and serviceability limit states are used as follows:

• Deflections are calculated using the entered SLS loads. A set of reactions is also calculated at SLS for the purposes of evaluating support stability and bearing pressures.

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• Element forces and a second set of reactions are determined using the entered ULS forces.

Tip: If you plan to use a working stress method to design the frame members, e.g. steel design according to SABS 0162 - 1984, you may use the same load factors at ULS and SLS.

Error checking

The program only checks that valid load cases are specified. It has no knowledge of the design code that will be used in the member design and therefore does not check the validity of the entered load factors.

Alternative frame input methods Alternative means of frame input are available:

• Input Wizards: Modules are available for the rapid generation of input for typical frame structures.

• External Graphical input: Structures can be drawn in Padds or another CAD system and converted to frame analysis input.

Input Wizards A number of typical frames can be input by entering a number of parameters. The Input Wizards do most of the data input. See page 3-19 for more detail on the Input wizards.

Note: The frame analysis modules are not limited to modelling only those frames generated by the input wizards modules. Instead, the input wizards merely serve to simplify input of some typical frames.

External Graphical input In some situations, it may be easier to define a frame’s geometry graphically. With Padds you can draw a frame and then generate a frame analysis input file.

Using Dos Padds for frame input

To use Dos Padds to define a frame’s geometry:

1. Use Padds to draw the frame. Alternatively, import a drawing from another CAD system.

2. The frame should be drawn to scale using millimetres as unit. Identify different beam sections by using different pen numbers.

3. Use the Generate input command on the Macro to display the drawing conversion options. Choose the target frame analysis module and press OK to start the conversion procedure.

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The resultant frame analysis input file will be compatible with both the Dos and Windows versions of the frame analysis modules. The file is saved in the working folder as a last file, e.g. ’Lastsf.a03’ for Frame Analysis.

4. Close Dos Padds.

Tip: To see a graphical input example, open ’..\prokon\data\demo\inputgen.pad’ in Padds.

Importing drawings

You can also use your favourite CAD system to save a frame’s geometry in a 2D or 3D Dxf/Dwg format drawing and then use the Import -> Dxf/Dwg files command on the File menu to convert it to frame input.

The same basic rules apply as given above:

• The drawing should be to scale.

• You should use millimetre units.

• Different pen numbers should be used for different beam sections.

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When importing 3D .Dxf & .Dwg drawings, you can optionally interchange the Z- and Y-axes. This option is given to correctly import a drawing where the Z-axis is taken as vertical, into Frame Analysis where the Y-axis is vertical.

Typical problems experienced include the following:

• Polylines may not be recognised correctly. Break or explode polylines into single lines before saving the .Dxf file.

• Blocks may not import correctly and may need to be broken or exploded into individual entities.

• Using AutoCAD, lines colours set ’by layer’ translates to the default pen number. Rather set colours using pen numbers to ensure correct section numbering.

• If you experience problems importing a DXF file saved using a brand new version of your CAD system, it may help saving the file as an older DXF file version, e.g. version 12.

CIMsteel The Space Frame Analysis module can import complete frame models, including geometrical and loading data, defined in the CIMsteel (Computer Integrated Manufacturing for Constructional Steelwork) integration standard. Modelling packages that can create CIMsteel files include Intergraph Frameworks and Microstation Structural Triforma. Note that at the time of writing this feature had not been fully developed.

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Settings

The Settings page allows you to set the parameters relevant to the analysis method.

Analysis type Select the type of analysis to be performed. Refer to page 3-14 for a description of the various analysis modes.

Concrete design parameters input It is generally impractical to design reinforcement to resist torsional moments in slabs. Reinforcement is usually fixed in two directions approximately, but not necessarily, perpendicular to each other. This justifies the use of transformed moments to calculate reinforcement.

Frame uses the Wood and Armer theory to convert calculated bending and torsional moments to transformed bending moments. More detail is given on page 3-13. Please note that these parameters only apply to shell elements and not to beams or solids.

The required concrete design parameters are:

• Enter the concrete and reinforcement material characteristics, fcu and fy.

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• Define the orientation for the ’main’ and ’secondary’ reinforcement, i.e. the x’ and y’-axis. Looking from the top, the x’-axis is measured anti-clockwise from the local x-axis to the reinforcement x’-axis. The y’-axis is in turn measured anti-clockwise from the local x’-axis. The direction of the local x-axis of a shell element is explained on page 3-7.

• Define the reinforcement levels in the slab by entering the concrete cover values for the top and bottom reinforcement in both directions.

• Optionally incorporate membrane behaviour by including the effect of in-plane stresses.

Reinforcement contours can be displayed on the Reinforcement tab under the View Output age. Values are calculated for reinforcement at the top and bottom of shell elements. In this context, top and bottom are defined as follows:

• The top of a shell element is taken on the side towards which its local z-axis points.

• For a non-vertical element, the top side is the visible side when looking down on the element.

• For a vertical element, the top side is the visible side if the nodes (as entered on the Shell elements input page) defining the element are orientated anti-clockwise.

Second order parameters input If you want to perform a second order analysis of the frame, you need to set the relevant analysis parameters:

• Second order analysis tolerance: The second order analysis is an iterative procedure. The analysis is deemed to have converged once the total strain energies of two sequential iterations differ by less than the specified tolerance

Buckling parameters input

• Number of buckling mode shapes: Set the number of buckling mode shapes to be calculated when determining the load factor for buckling for each load case or combination. The first mode shape is often critical since it represents the most likely buckling failure mechanism. For practical reasons, only the first mode shape would normally be of interest. However, the accuracy of the analysis improves with the number of mode shapes analysed. It is therefore suggested that you allow at least four mode shapes to be calculated. The program supports a maximum number of forty mode shapes. Note that internally the program actually

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calculates quite a few more mode shapes than specified to improve the accuracy of the output for the modes that are specified. Because of this, the model should not contain too few nodes. If no convergence is obtained, split the members into smaller portions by adding extra nodes.

Non-linear analysis parameters input Number of load steps:

Each load case is applied to the structure in a number of steps. The accuracy increases with the number of steps entered. Ten steps should be adequate for most problems.

One must be aware that for each step, the structure is completely analysed a number of times for each load case to obtain convergence for that step. The analysis time can therefore become very long if a high number of steps are specified on a large structure with many load cases. It is suggested that one use say 3-5 steps initially, to ensure that the solution progresses properly, before increasing the number of steps for a final analysis.

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Dynamic analysis parameters input Edit the dynamic analysis parameters if you will be performing a modal, harmonic or earthquake analysis. Some parameters should be entered in all cases while others are specific to harmonic or earthquake analysis. The graphic below shows all the possible input fields, although some of them might not be visible, depending on the type of dynamic analysis selected.

Number of mode shapes

Enter the number of natural modes of vibration to be calculated. You can use the following guidelines when deciding on the number of mode shapes to be calculated:

• The number of mode shapes should preferably not exceed the number of degrees of freedom in the structure divided by twelve.

• In a harmonic analysis, use enough mode shapes so that the highest natural frequency is at least 50% higher than the applied loading frequency.

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• For an earthquake analysis, the first three or four mode shapes are normally sufficient to obtain the probable maximum combined effects.

• Do not use too few nodes. If convergence is not obtained when calculating the natural frequencies, add more nodes and split the elements. See also the first point above.

Add axial force effects to stiffness

Compression forces in a frame’s members reduce the effective stiffness of the frame. The frequencies of vibration are therefore reduced with corresponding changes in the mode shapes.

If the option is enabled, the effect of axial force is incorporated as follows:

• A static analysis is first performed with the mass of the structure, i.e. own weight and the Y-components of the specified load cases, being the only load case.

• The resulting axial forces are then incorporated when calculating the modified geometric stiffness matrix of the structure. The geometric stiffness matrix is subsequently used to modify the global stiffness matrix to account for the axial force effects.

Include torsional modelling

This applies to beam elements. If included, the torsional modes of the beams will also be included.

Include load cases as mass

A frame’s frequencies of vibration and mode shapes depend on its inertia or mass distribution in relation to its stiffness distribution. Any loads on the structure will therefore influence the natural frequencies and therefore its response to dynamic loadings. The user must select the loads to be included as mass in the right hand side list. Only the Y-components (vertical) of the loads are added as mass.

The program uses the following components for compiling the mass matrix:

• The own weight of the frame, calculated using the density values entered in the Section properties input table.

• The loads cases entered by the user.

Note: In a harmonic or seismic analysis, all dead and live load that move with the structure during its dynamic response will influence the dynamic response of the structure. Such loads should be considered as masses for the purpose of determining the mode shapes.

Own weight and distributed vertical loads are added using the consistent mass matrix formulation. Point loads are added as lumped masses at the relevant nodes.

Note: In a seismic analysis all loads not selected as masses will be excluded from the analysis.

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Average damping ratio

The dynamic response of a frame will include some viscous effects. The average damping ratio depends on the type and condition of the structure. Typical values, taken from TMH7 - Part 2, are tabled below:

Stress level Type and condition of structure Damping ratio O

Welded steel. Prestressed concrete, well

reinforced concrete (slight cracking) 2%

Working stress no more than about

half of yield stress

Reinforced concrete with considerable cracking 3% to 5%

Bolted and riveted steel 5% to 7%

Welded steel, prestressed concrete under

full pre-stress (slight cracking) 5%

Working stress near yield point Prestressed concrete in cracked state 7%

Reinforced concrete 7% to 10%

Bolted and/or riveted steel 10% to 15%

Design ground acceleration (seismic analysis only)

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For an earthquake analysis, specify the maximum ground accelerations. TMH7 - Part 2 gives the following typical values according to a modified Mercalli classification:

Modified Mercalli intensity at epicentre

Design ground acceleration

ii – iii 0.003 g

iv – v 0.01 g

Vi 0.03 g

vii – viii 0.1 g

Ix 0.3 g

x – xi 1.0 g

Note: Refer to local seismic data for relevant acceleration data.

TMH 7 - Part 2, when considering the influence of seismic disturbances, gives the following guidelines:

• Symmetrical structures: The influence of seismic disturbances should be considered along both principal axes of symmetry.

• Non-symmetrical structures: It would normally be sufficient to consider the seismic effects along any two arbitrarily chosen orthogonal axes.

• For structures, symmetrical and non-symmetrical, the seismic effects along two orthogonal axes may normally be considered independently of each other.

Design load factor (seismic analysis only)

Seismic action is normally not considered in combination with other secondary loads. For this reason, the following approach is used:

• The vertical components of selected load cases are included as masses when determining the mode shapes. Refer to page 3-68 for detail.

• All other effects of all load cases and combinations are ignored.

• The dynamic response of the structure to the applied ground accelerations is amplified with the specified design load factor.

The design load factor for forces and moments should be chosen in accordance with the relevant loading code. At ultimate limit state, an average factor between 1.3 and 1.5 is normally applied.

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Spectrum reduction factor for vertical direction (seismic analysis only)

The relevant resonance frequencies of a structure in the vertical direction are generally quite different from those in the horizontal direction. If it is deemed necessary to consider the effects of vertical seismic motions, the average vertical design spectrum can often be reduced.

For typical bridge structures, TMH7 - Part 2 allows the average vertical design spectrum to be taken as two-thirds the average horizontal seismic response spectrum.

Ductility P (seismic analysis only)

The ductility of a structure is a function of the type and arrangement of the elements resisting lateral forces. A unity value corresponds to perfect elastic behaviour and a value greater than unity elastic-plastic behaviour.

Typical ductility values, taken from TMH7 - Part 2, are given below.

Type or arrangement of resisting elements Structural ductility factor P

Un-braced structural steel structures with elements adequately designed to resist the total lateral forces in bending

4

Structures with braced flexural vertical members of structural steel

Slender reinforced columns carrying superstructure of braced structural steel, reinforced concrete or prestressed concrete designed to resist the total lateral force

3

Vertical elements of shear wall proportions with superstructure in monolithic reinforced or prestressed concrete designed to resist the total lateral force

2

If you enter a value greater than one, the elastic response spectrum will be adjusted to obtain an appropriate inelastic response spectrum. The program allows you to adjust the design response spectrum as required.

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Foundation soil type (seismic analysis only)

Additional factors not covered above can be accounted for by adjusting this load factor. TMH7 - Part2, for example, gives an additional factor relating to the type of founding material.

Description of founding material Foundation factor f

Rock, dense and very dense coarse-grained soils, very stiff and hard fine-grained soils

Compact coarse-grained soils, and firm and stiff fine-grained soils from 0 to 15 m deep

1.0

Compact coarse-grained soils, firm and stiff fine grained soils with a depth greater than 15 m

Very loose and loose coarse-grained soils and very soft and soft fine-grained soils from 0 to 15 m deep

1.2

Very loose and loose coarse-grained soils and very soft and soft fine-grained soils with depths greater than 15 m 1.5

Acceleration response spectrum (seismic analysis only)

Acceleration response spectra are empirically derived definitions for typical responses of structures to a range of ground accelerations. Choose an applicable response spectrum:

• SABS 0160 - 1989.

• TMH7 - Part2.

• UBC 1194.

Alternatively, define a custom response spectrum by entering the ground acceleration for damping ratios of 0.5%, 3%, 5% and 10% for nine different periods. Any period values can be entered, including those for the acceleration/velocity and velocity/displacement bound regions dividing points.

If the ductility value greater than unity is specified, the elastic response spectrum is adjusted to obtain an inelastic response spectrum. The elastic spectrum, for any given damping ratio, is modified along the displacement bound region by multiplying it with a factor 1/µ. Along the acceleration bound region the elastic spectrum is multiplied by a factor 1/(2µ−1)½.

.

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Analysis

To analyse the structure, open the Analysis page and press Start Analysis:

The analysis progress is displayed to help you judge the time remaining to complete the analysis.

After a successful analysis, the deflected shape is displayed for the first load case or load combination or, in the case of modal or buckling analysis, the first mode shape.

Error checking during analysis

During the input phase, the frame geometry and loading data is checked for errors. Not all reported errors are necessarily serious. To define duplicate elements between two nodes, for example, could be an accidental error on your side. However, the program can deal with a situation like this and will allow the analysis procedure to continue.

Other input errors could be serious enough to prevent an analysis from being completed successfully. Nodes with no elements, for example, have no restraints and will cause numeric instability during the analysis.

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The first step of any analysis is the final verification of the input data. In the case of critical errors still present, a warning message will be displayed. If you then choose to not proceed with the analysis, you will be taken to the input table with the error. However, choosing to proceed and ignore the warning will have an unpredictable result.

Fixing errors that occurred during the analysis Even if all input data seems valid, numeric errors may still occur during an analysis. For example, if you entered incorrect section properties, such as a very small E-value, the mistake may go by unnoticed. However, the analysis will then yield an invalid value in the stiffness matrix or extremely large deflections. The same applies to the stability of the frame. Although the frame may appear stable, some combinations of internal hinges may result in some nodes being unstable.

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If an error was detected during the analysis, a warning will be displayed. The cause of the error should become clear when studying the output file:

• The text at the end of the output file normally gives the reason for the error.

• If the output file seems complete, the problem will require more careful attention. Scan all output tables for excessively large or small values.

Second order and buckling analysis problems

The following points should be kept in mind when trouble-shooting a second order analysis:

• During a second-order analysis, an element is removed from the frame as soon as its axial force exceeds its Euler buckling load. If one or more elements have been removed from the frame in this way, structural stability cannot necessarily be guaranteed any more. The removal of a single element may cause a chain reaction of elements failing. If the remaining members do not constitute a stable structure, the structure will fail. All member forces in the output file will then be shown as ’∗∗∗∗∗∗∗∗’.

• A second order analysis fails in instability can be verified using a buckling analysis. You can examine the buckling mode shapes to easily locate problem areas in the structure that may require stiffening.

• Slender non-structural elements often buckle before major structural members, distorting analysis results. Such elements should preferably be excluded from the model.

• If the linear and second order analysis results show negligible differences, the structure is likely not sensitive to p-delta effects for the given loading. This is often true for truss-type frames.

Tip: Perform a buckling analysis to get an indication of the general stability of the frame under the entered loads. A frame with a buckling load factor less than unity normally experiences the same local or global stability problems during a second order analysis.

Frame Analysis 3-76

Design Links

Once the analysis is complete, Frame can link up with other Prokon modules for further post-processing and design. This is done on the ‘Design links’ tab:

Selecting a design link The following links are available:

• Steel connections: Select this option on the left hand side of the screen. Now click on any node in the structure. A dialog with possible connections will appear as shown above. The program will look at the types of members meeting at the node. These members must be steel members selected from the Prokon database. There should also be at least two members meeting at the node. If for example, there are no hollow sections at the node, the ‘Hollow section connection’ option will remain greyed. For the ‘Apex connection’ the members must be I- or H-sections. Check the type of connection that you want. Sometimes there is more than one possible connection of the chosen type at the node. The desired connection can be chosen from the drop-down(s) to the right of the connection type

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chosen. Pressing ‘OK’ will convert the output data and transfer it to the relevant connection design module.

• Concrete columns: Select ‘rectangular’ or ‘circular’ column on the left hand side of the screen. Now select a member on the screen with the mouse. The data will be transferred from Frame and the relevant column design module will be opened.

• Concrete base: Select ‘Concrete base’ on the left hand side of the screen. Now select a support node on the screen with the mouse. The data will be transferred from Frame and the base design module will be opened. Note that only support nodes can be selected.

• Member design modules: Separate buttons are provided to call up ‘Member design for axial stress’ , ‘Member design for combined stress’ and ‘Timber member design’ . Each of these modules will open with the current structure and output, ready for further processing.

• Important note regarding load combinations: If the analysis was a linear analysis, the load combinations are broken up using the load factors entered in Frame. In the case of a second-order analysis, the results of a combination are not necessarily equal to the sum of the load cases times their load factors, due to the secondary effects taken into account. The program will calculate appropriate load factors, which will be similar to the ones entered, but adjusted so that the sum of load case forces times load factors gives the final forces calculated by Frame.

Frame Analysis 3-78

Viewing output

The analysis results can be viewed graphically or in tabular format. Output data, including graphics and tabled values, can be selectively appended to the Calcsheets using the Add to Calcsheets function on each output page.

Viewing output graphics Diagrams can be displayed for deflection, member forces and stress and shell reinforcement of any load case:

• Deflections: Deflections are generally small in relation to dimensions of the structure. To improve the visibility of the deflection diagram, you can enter a screen magnification factor. You can optionally display the deflected shape without the original geometry.

• Mode shapes: In the case of a dynamic or buckling analysis, you can display the mode shapes one-by-one. Use the Animate function to bring a mode shape to life. If you tick the ‘record animation’ box, the animation is stored as an animated .gif file as shown below.

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Note: Mode shapes should not be confused with deflections. Mode shapes represent the natural dynamic characteristics of a structure. Values are normalised with the maximum "displacement" given as one thousand.

• Reactions: The reactions forces and moments at all supported nodes are displayed. The arrowheads points in the direction of each reaction.

• Beam element forces:

• Axial forces: The force is shown as expanded red and blue lines. Compression forces

are shown in red and tension forces in blue. The distance of a line from the element centre line is in proportion to the size of the axial force.

• Moments: Bending moments about the local x and y-axes. A plot factor can also be entered to enlarge or reduce the bending moment diagram on the frame.

• Shear: Shear force diagrams are drawn for the local y and x-directions. A beam element’s shear force diagram is constructed by viewing it with its local z-axis pointing to the right. Since the direction of the z-axis depends on the node numbers, irregular numbering of nodes can result in apparent irregular signs used in the shear

Frame Analysis 3-80

force diagrams. Refer to page 3-8 for detail on the sign conventions used for beam element forces.

• Torsion: The torsional moment about the z-axis, i.e. element axis.

• Beam element force envelopes:

• Envelopes: Enter a series of elements and select the load case and combinations to include in the envelopes. Envelopes are drawn using the values as tabulated from the output file. Positive moments, for example, are drawn below the line and negative above. Because members of different orientations can be included in the same envelope, no simple distinction is made between tension and compression faces of members.

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• In-plane stresses in shells:

• Stresses in x, y and xy directions: Display contours of the membrane stresses in the

local x and y-directions and the shear stresses. Refer to page 3-7 for detail on the local axis convention for shell elements.

• Maximum and minimum stresses: These correspond to the largest tensile and compression stresses respectively. Positive values indicate compression and negative values tension.

• Von Mises stresses: The Von Mises stresses give a graphical indication of a yield criterion, i.e. a general indication of the combined effect of all stresses. The Von Mises stresses takes into account in-plane stresses as well as bending stresses and is presented for both the top and bottom faces of the shell elements..

Frame Analysis 3-82

• Bending moments and shear forces in shells:

• The x, y and xy bending moments: The bending moments about the local x and y-

axes and the torsional moment. The direction (not axis) of bending is shown as a small line on each shell element.

• Maximum and minimum bending moments: The principal bending moments.

• The x, y and maximum shear forces: The shear forces are in local x and y-axes. The maximum shear stress is also given and is obtained by dividing the maximum shear force by the thickness of the element.

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• Reinforcement in shells:

Contours of the required reinforcement in the top and bottom faces in the x’ and y’-directions are given. The corresponding ‘Wood & Armer’ moments from which the reinforcement was calculated is also given. The reinforcement direction is shown as a small line on each shell. Refer to page 3-64 for the definition of the reinforcement directions.

Tip: If the lines indicating the direction of bending or of the reinforcement is not clearly visible, enable detailed rendering under the graphics options. Refer to page 3-18 for instructions.

Tip: Shell element stress contours are drawn on the deflected shape of the structure. Careful choice of the deflection magnification factor can enhance contour diagrams.

Frame Analysis 3-84

• Stresses in solids:

The stresses presented are the direct stresses in the X, Y and Z directions, the shear stresses in the XY, XZ and YZ planes, the 3 principal stresses 1,2 and 3 as well as the maximum shear stress and the von Mises stress. For solids all the stresses are plotted in the global co-ordinates.

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Viewing output tables

Open the Output file page for a tabular display of the frame analysis output file. You can filter the information sent to the calcsheets by enabling or disabling the relevant sections.

The Find heading function allows you to quickly locate any main section of the output file.

If you right click on the output, various editing functions are available. For example, you can search for any string by pressing Ctrl and F.

Frame Analysis 3-86

Calcsheets

Frame analysis output can be grouped on a calcsheet for printing or sending to Calcpad. To include a particular component of the output in the calcsheets, view the relevant output information and then click Add to Calcsheets.

Recalling a data file The Data File is automatically included in the calcsheet sent to Calcpad. You can later recall the frame by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the frame analysis module as well.

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Plane Stress/Strain Analysis 3-88

Plane Stress/Strain Analysis

The Plane Stress/Strain Analysis module can be used to perform a finite element analysis of a membrane of any general geometry subjected to plane stress or strain. An automated element grid generation facility helps speeding up the input and analysis processes.

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The following text gives an overview of the finite element analysis theory and its application.

Scope The program analyses membrane structures of any general shape, including openings. The cases of plane stress and plane strain are both supported. Element grids are automatically generated with a customisable grid size.

Plane strain and plane stress The conditions of plane stress and plane strain are two similar two-dimensional states of stress and are subsequently often confused. However, their definitions set them apart as two very distinct conditions.

When forces are applied to a thin two-dimensional plate in its own plane, the state of stress and deformation in the plate is called plane stress. A typical example would be a shear wall that, due to it being a thin plate, will experience mainly in-plane stresses. No restraint is provided for out-of-plane deformation.

On the other hand, a prismatic solid subjected to a constant loading normal to its axis can be analysed as an infinite length of two-dimensional slices of unit thickness experiencing plane strain. A dam wall, for example, would typically be subjected to hydrostatic and soil pressures normal to its surface. A slice is taken from the wall will be restrained from deforming out-of-plane.

Finite element modelling The program uses eight-noded quadrilateral and six-noded triangular isoparametric finite elements formulated for plane stress and plane strain.

A mesh of isoparametric quadrilateral or triangular is automatically generated and optimised during analysis. You can specify the grid spacing in the X and Y-directions as part of the analysis parameters. A finer grid will often improve accuracy. However, the time taken to perform an analysis is a function of the number of finite elements – the finer the grid, the longer the analysis time.


Sign conventions When entering coordinates and forces, the following sign convention is used:

• Positive Y-coordinates and vertical forces are taken upward, i.e. parallel to the Y-axis.

• Positive X-coordinates and horizontal forces are taken to the right, i.e. parallel to the X-axis.

In the analysis results, deflections are measured along the Y-axis. A positive deflection therefore denotes an upward movement.

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Input

Use the four input tables, i.e. Nodes, Supports, Material properties and Loads, to define the structure’s geometry and loading.

Nodes input A structure is defined by entering one or more shapes. A shape may comprise straight lines and arcs. When more than one shape is entered, the shapes will accumulate and form one structure. Often, a complicated section is easier defined using more than one shape.

Note: Shapes must be entered in an anti-clockwise order.

An explanation of the node input table is given below:

• The Mat. No. column is used for categorise the data that follows in the next columns:

1 to 9 : The start of a new polygon with the specified material property. An absolute reference coordinate must be entered in the X and Y columns. If you leave X or Y blank, a value of zero is used.

0 : Start of an opening. An absolute reference coordinate must be entered in the X and Y columns.

R : If you enter an ’R’ or leave the Mat. No. column blank, a line is drawn using relative coordinates, i.e. measured from the previous coordinate.

A : Enter an ’A’ in the Mat. No. column blank to make the coordinate absolute.

• The X and Y columns are used for entering coordinates:

X : Absolute or relative X coordinate. Values are taken positive to the right and negative to the left.

Y : Absolute or relative Y coordinate. Values are taken positive upward and negative downward.

• Use the Bulge column to define an arc of a specified radius. Consider an imaginary line joining the previous coordinate and the coordinate entered in the X and Y columns. A bulge greater than zero then defines an arc to the right of the line. Similarly, a negative bulge draws an arc to the left of the line. If no bulge is specified, a zero value is used, i.e. a straight line.

You do need to close the polygon defining a shape – the starting coordinate is automatically used as the ending coordinate. If two polygons intersect, the geometry of the last polygon takes preference and the previous polygon is clipped. A hole in a structure can, for example, be entered on top of previously entered shapes.


Nodes are automatically numbered as they are input. You can later use the node numbers to position supports and loads.

Supports input You can define point supports, distributed support and prescribed displacements anywhere along the edges of the structure. Supports are entered as follows:

Nodes : Enter a single node number for a point support or a range of nodes for a distributed support, e.g. ’2’ for node 2 only and ’2-5’ for the zone described by the straight line joining nodes 2 and 5.

XY support : Enter ’X’ and/or ’Y’ for horizontal and/or vertical support.

Displ. : Specify the value of any horizontal or vertical prescribed displacement in the relevant column (m).

Note: Point supports invariably result in localised stress concentrations, with the effect increasing for smaller element grids. It is therefore recommended to avoid point supports and rather distribute each support over as large a width as possible.

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Material properties The following material properties must be input for every material property code used in the Code column of the Nodes input table:

t : Thickness (m).

E : Modulus of elasticity (kN/m3). If left blank, the value for the preceding material type is used. Typical values are tabled below.

Poisson : Poisson ratio. If left blank, the value for entered in the previous row is used. Typical values are tabled below.

Dens : Density on (kN/m3). Typical values are tabled below.

Material E modulus (kPa)

Poison’s ratio

Density (kN/m3)

Masonry 10E6 0.20 20 - 25

Concrete (normal strength) 25E6 to 35E6 0.20 ± 24

Aluminium ± 70E6 0.16 ± 27

Structural steel ± 205E6 0.30 ± 78

Loads input Point loads and distributed loads can be defined anywhere along the edges of the structure. Use as many lines as necessary to define the loads.

Loads are entered as follows:

Nodes : Enter a single node number for a point load or a range of nodes for a distributed load, e.g. '2' for node 2 only and '2-5' for the zone described by the straight line joining nodes 2 and 5.

X : The load direction can be either 'X' or 'Y' for horizontal or vertical respectively.

Wleft : Distributed load intensity at the smaller node number (kN/m).

Wright : Distributed load intensity at the larger node number (kN/m).


a : Distance from first node to beginning of distributed load (m). A value of zero is used if field is left blank.

b : Length in m, of distributed load. The load is taken up to the ending node if this field is left blank.

Note: Positive forces are taken to work upward and to the right.

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Analysis

On completing the input, go to the Analyse page to analyse the structure. Following a successful analysis, use the View page the display the analysis results.

The following text describes the analysis options that are available and gives information on finding and fixing analysis problems.

Analysis options During the analysis, the program generates a rectangular grid of nodes in which rectangular and, where necessary, triangular finite elements are placed. The grid spacing can be set independently in the horizontal and vertical directions.

Choose Settings to set the grid spacing and other analysis options:

• Finite element size: Horizontal and vertical grid spacings (m).

• Type of analysis: Enter ’E’ for plane stress or ’A’ for plane strain.

• Angle increment: The program models arcs as straight lines at the specified angle increment. Although a smaller angle would yield a smoother modelling of an arc, the resulting increase in modes will mean that more elements will be used. Generally, an angle increment between 5° and 15° would yield good results.


Analysis results The analysis results can be viewed and printed in tabular or graphical format:

• Elastic deflections.

• Maximum principal stresses, i.e. the largest tensile stresses. Positive values indicate tension and negative values compression.

• Minimum principal stresses, i.e. the largest possible compression stresses. Negative values indicate compression.

• The Von Mises yield condition if often used to determine whether a material is behaving elastically under combined stress. According to the Von Mises theory, the total elastic energy comprises volumetric changes and shearing distortions. By considering only the shearing distortion at yield in simple tension in relation to that under combined stress, the yield criterion can be established. The Von Mises theory assumes a ductile isotropic material.

• Principal stress vectors, with compression stresses in red and tension stresses in blue.

• You can also inspect the results in tabular format by displaying the output file, named PS.OUT

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Fixing errors that occurred during the analysis Some common problems during plane stress and plain strain analyses are:

• If the program is unable to analyse the structure, there may be errors in the input. A common mistake is the definition of shapes in a clockwise direction – the program expects anti-clockwise input.

• Stress concentrations will be present at positions of point loads and point supports. Such concentrations are further exaggerated when using finer element grids. In practice, loads and supports rarely act at points, but rather on small areas. It is likewise recommended to spread all point loads and supports over small lengths.


Calcsheets

The finite element analysis output can be grouped on a calcsheet for printing or sending to Calcpad. Various settings can be made with regards to the inclusion of design results and pictures.

Tip: You can embed the Data File in the calcsheet for easy recalling from Calcpad.

Recalling a data file If you enable the Data File option before sending a calcsheet to Calcpad, you can later recall its design by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the analysis module as well.

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Single Span Beam Analysis 3-100

Single Span Beam Analysis

The Single Span Beam Analysis module can be used to quickly analyse a beam. The beam can be a single span beam or a single span taken from a continuous beam with the appropriate end conditions. The analysis results of steels beams can be post-processed with the steel member design module for combined stress, Com.

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Sign conventions

When entering forces and moments, the following sign convention is used:

• Positive vertical forces act downward, i.e. parallel to the negative Y-axis.

• Positive moments work anti-clockwise.

• In the analysis results, the following applies:

• Deflections are measured along the Y-axis. A positive deflection indicates uplift and negative deflection a downward movement.

• Shear forces are measured along the Y-axis. A positive shear force at the left edge of the beam, for example, represents an upward vertical reaction.

• Moments are drawn on the tension face of the beam.


Input

The beam definition has two main input components:

• Geometry and material properties.

• Loads.

Beam input The following values must be entered:

Length : The overall length of the beam (m).

M Left : The applied moment at the left-hand end (kNm). If you leave the field blank, a zero moment is used, e.g. the beam is simply supported. You can also fix an end by entering an ’F’ or make it a free cantilever end with a ’C’.

M Right : The applied moment at the right-hand end (kNm).

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I : The second moment of inertia of beam (m4).

E : Young’s modulus of the beam (kPa). A value of 205x106 kPa, i.e. steel, is used if this field is left blank. Typical values are:


Timber 5E6 to 15E6

Concrete (normal strength) 25E6 to 35E6

Aluminium ± 70E6

Structural steel ± 205E6

Section input

The moment of inertia of a standard steel section can be selected from the section database. You can also define your own sections or remove sections from the database.

Own weight

On selecting a steel section form the database, the own weight is automatically entered as a uniform distributed load.

Loads input Use as many lines as needed to enter any general loading on the beam in the Loads input table:

W Left : Distributed load intensity (kN/m) applied at the left-hand starting position of the load. If you do not enter a value, the program will use a value of zero.

W Right : Distributed load intensity (kN/m) applied on the right-hand ending position of the load. If you leave this field blank, the value is made equal to Wleft, i.e. a uniformly distributed load is assumed.

P : Point load (kN).

M : Moment (kNm).


a : The start position of the distributed load, position of the point load or position of the moment (m). The distance is measured from the left-hand edge of the beam. If you leave this field blank, a value of zero is used, i.e. the load is taken to start at the left-hand edge of the beam.

b : The end extent of the distributed load, measured from the start position of the load (m). Leave this field blank if you want the load to extend up to the right-hand edge of the beam.

Note: Positive forces and moments are taken to work downward and taken anti-clockwise respectively.

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Analysis

Press Analyse to display the analysis results:

• Elastic short-term deflections.

• Bending moment diagram.

• Shear force diagram.


Calcsheet

The beam analysis results can be grouped on a calcsheet for printing or sending to Calcpad. Various settings can be made with regards to the inclusion of design results and pictures.


Recalling a data file If you enable the Data File option before sending a calcsheet to Calcpad, you can later recall the beam analysis by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the beam analysis module as well.

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Beam on Elastic Support Analysis 3-108

Beam on Elastic Support Analysis

The Beam on Elastic Support Analysis module can be used to quickly analyse a beam or slab on an elastic foundation. The beam cross-section may vary along its length and the elastic foundation can include gaps and rigid supports.

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The following text gives a background into the analysis technique used.

Sign conventions and units of measurement When entering forces and moments, the following sign convention is used:

• Positive vertical forces act downward, i.e. parallel to the negative Y-axis.

• Positive moments work anti-clockwise.

In the analysis results, the following applies:

• Deflections are measured along the Y-axis. A positive deflection indicates uplift and negative deflection a downward movement.

• Bearing pressure is also measured along the Y-axis. A positive bearing pressure denotes an upward reaction.

• Shear forces are measured along the Y-axis. A positive shear force at the left edge of the beam, for example, represents an upward vertical reaction.

• Moments are drawn on the tension face of the beam.

Analysis procedure The program performs a linear analysis in which the beam is modelled as a two-dimensional frame on a series of least fifty closely spaced springs. Rigid supports are put at the specified positions and gaps in the elastic support where the supporting width is set to zero. Nodes are taken at close intervals along the length of the beam. A node is also introduced at every support and load position.

If negative soil pressures are not allowed, i.e. uplift is allowed, springs with negative reactions are removed and the analysis repeated. Likewise, previously removed springs are restored if downward deflections are calculated at the points concerned. The analysis procedure is repeated until the iteration converges to a stable solution.

A beam is considered unstable, i.e. to overturn under the applied load, if the analysis yields less than two springs with compressive forces.


Input

The beam definition has several input components:


• Supports input

• Loads.

Beam input The beam is defined as one or more segments, each with its own properties. The following values must be entered:

Lsec : The length of a beam segment with a specified stiffness and support width (m). You may enter more than one segment to define a beam varying section or an elastic medium of varying stiffness. Each additional beam segment entered is added to the right-hand side of beam.

Isec : The stiffness of the beam segment, express as the second moment of inertia of the relevant cross section (m). The value of Young’s modulus, applicable to the whole beam, is entered under the analysis settings.

Bsec : The support width of the beam segment (m). This beam width is multiplied by the foundation modulus of the soil, Km, to obtain the support stiffness per unit length of the beam. Enter a zero value for no foundation stiffness, i.e. a gap in the elastic medium.

Supports input Use the Support input columns to enter rigid supports in the elastic medium:

Position : A rigid support position, measured from the left-hand side (m).

Support : You can set the support type to vertical and/or rotational:

Support Description

Y Vertical support, e.g. a solid rock intrusion in the elastic medium

R Rotational support, e.g. a rigid column above built into the beam

YR Vertical and rotational support, e.g. a rigid pile below that is built into the beam.

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Loads input Use as many lines as needed to enter any general loading on the beam in the Loads input table:

W Left : Distributed load intensity (kN/m) applied at the left-hand starting position of the load. If you do not enter a value, the program will use a value of zero.

W Right : Distributed load intensity (kN/m) applied on the right-hand ending position of the load. If you leave this field blank, the value is made equal to Wleft, i.e. a uniformly distributed load is assumed.


M : Moment (kNm).


b : The end position of the distributed load, measured from the start position of the load (m). Leave this field blank if you want the load to extend up to the right-hand edge of the beam.

Note: Positive forces and moments are taken to work downward and taken anti-clockwise respectively.

Analysis settings Press Settings to edit the material constants and other parameters to be used in the analysis:

• E modulus: Young’s modulus for the beam (kPa). Values for typical building materials are tabled below:


Timber 5E6 to 15E6

Concrete (normal strength) 25E6 to 35E6

Aluminium ± 70E6

Structural steel ± 205E6


• K modulus: Foundation modulus or modulus of subgrade reaction (kN/m3). Typical empirical values derived suggested by Bowles

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are given below:

Soil type K modulus (kN/m3)

Loose sand

Medium dense sand

Dense sand

Clayey medium dense sand

Silty medium dense sand

Clayey soil:

qa ≤ 200 kPa

200 kPa ≤ qa ≤ 800 kPa

qa > 800 kPa

4 800 to 16 000

9 600 to 80 000

64 000 to 128 000

32 000 to 80 000

24 000 to 48 000

12 000 to 24 000

24 000 to 48 000

> 48 000

The foundation modulus, K, is a conceptual relationship between the soil pressure and deflection of the beam. Because the beam stiffness is usually ten or more times as great as the soil stiffness as defined by K, the bending moments in the beam and calculated soil pressures are normally not very sensitive to the value used for K. Recognizing this, Bowles suggests that the value of K can be approximated from the serviceability limit state bearing capacity, qa, as being 40 × qa (kN/m3) or 12 × qa (k/ft3).

• Allow negative pressure: Enter 'Y' to enable full adhesion between beam and elastic medium. Enter 'N' to allow uplift, i.e. zero adhesion between beam and elastic medium.

Note: The foundation modulus, Km, is multiplied with the support width to obtain the support stiffness per unit length of the beam. Enter a zero value for no foundation stiffness, i.e. a gap in the elastic medium.

∗ 'Foundation Analysis and Design, Fifth Edition', by Joseph E. Bowles, published by McGraw Hill

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Example The sketch shows an 800 mm wide by 300 mm deep beam is modelled on an elastic foundation:

• The first fourteen meters of its length is supported on very stiff clay. The foundation modulus is set to 40 000 kN/m3.

• The beam crosses a rock intrusion ten meters from the left that provides vertical support.

• The beam then spans four meters over a ditch, i.e. no support. This is modelled by entering a zero section width.

• On the other side support is provided on a strip of hard clay, two meter wide. The hard clay is modelled by increasing the support width to 1.2 m. The resulting effective foundation modulus is then given by 1.2/0.8 x 40 000 = 60 000 kN/m3.

• The beam is loaded with a long trapezoidal distributed load, twelve meters long, a point load and a moment at its right-hand end.


Analysis

Press Analyse to display the analysis results:

• Bearing pressure.

• Bending moment.

• Shear force diagram.

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Calcsheet

The beam analysis results can be grouped on a calcsheet for printing or sending to Calcpad. Various settings can be made with regards to the inclusion of design results and pictures.


Recalling a data file If you enable the Data File option before sending a calcsheet to Calcpad, you can later recall the beam analysis by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the beam analysis module as well.

Steel Member Design

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Chapter

Steel Member Design

The steel member design modules can be used for elastic and plastic design of structural steel members. Several modules act as post-processors for the frame analysis modules, facilitating integrated frame analysis and design.

Steel Member Design 4-2

Quick Reference

Steel Member Design using PROKON 33 Steel Member Design for Axial or Combined Stress 45 Plastic Frame Design Error! Bookmark not defined. Crane Gantry Girder Design Error! Bookmark not defined.6 Plate Girder Design 4-89

Steel Member Design using PROKON 4-3

Steel Member Design using PROKON

A variety of steel member design modules are included in the PROKON suite. These are considered useful tools when designing members using either elastic or plastic methods.

Elastic member design When designing struts and ties, you can post-process frame analysis results using the member design module for axial stress, Strut. Similarly, the member design module for combined stress, Com, can be used to design members subjected to both axial force and moment, or beam-columns.

Plastic frame design The Plastic Frame Design module can be used to design steel frames using plastic design methods. The same module can also optimise sections for better economy.

Girder design Specialised modules are available for designing crane gantry girders and plate girders.


Steel Member Design for Axial or Combined Stress The steel member design modules are suitable for the following design tasks:

• Use Strut for checking and optimising steel members subjected to axial stress only, e.g. truss members.

• Com is used for checking and optimising steel members subjected to a combination of axial and uniaxial or biaxial bending stresses, e.g. beams and columns in frames.

The steel member design modules primarily act as post-processors for the frame analysis modules. Both modules also have an interactive mode for the quick design or checking of individual members without needing to perform a frame analysis.



A brief background is given below regarding the application of the design codes.

Design scope The steel member design modules can design hot-rolled sections subjected to axial stress or a combination of axial and bending stresses.

• Strut can be used to design any hot-rolled section for axial stress. Because the design procedure is relatively simple, design results are presented in tabular format. This feature makes the program especially useful when designing of a large number of struts and ties.

• Com can design hot-rolled double symmetric sections and channels subjected to axial and bending stress. Non-symmetric sections like angles are not supported. More design checks need to be performed for each member requiring more detailed output.

Strut and Com use a similar design approach. Although there may seem to be a degree of overlapping in their design features, the two modules rather complement each other with specialised individual design functions. You will typically use them to design the different components of the same structure, e.g. design a roof truss in Strut and its supporting columns in Com.

Note: Support for cold-formed sections is not provided. However, hot-rolled hollow circular and rectangular sections may be designed with the programs if such sections are deemed to have relatively thick walls with a resulting low risk of local buckling.

Tapered sections

The current versions of Strut nor Com cannot design tapered sections, e.g. haunches in portal frames. When evaluating members with varying sections, the section type at the first node is used over the whole length of the member.

Design codes The program designs axially loaded steel members according to the following design codes:

• AISC - 1993 LRFD (Strut only).

• BS 5950 - 1990.

• CSA S16.1 - M89.

• Eurocode 3 - 1992 (Strut only).

• SABS 0162 - 1984 (allowable stress design).

• SABS 0162 - 1993 (limit state design).


Units of measurement The steel design modules support the following units of measurement:

• Metric.

• Imperial (Strut only).

The preferred unit of measurement can be selected using the Units command on the File menu.

Symbols Where possible, the same symbols are used as in the design codes:

Ane/Ag : Effective area factor with which the gross sectional area must be multiplied to obtain the effective sectional area, reduced for fasteners holes. The factor applies to elements subjected to tensile axial stress only.

Ke : Factor with which the member length is multiplied to obtain the effective length for lateral torsional buckling (Com only).

Kv : Factor with which the member length is multiplied to obtain the effective length for buckling about the v-v (weakest) axis of the member (Strut only).

Kx : Factor with which the member length is multiplied to obtain the effective length for buckling about the x-x axis of the member.

Ky : Factor with which the member length must be multiplied to obtain the effective length for buckling about the local y-y axis of the member.

AISC - 1993 LRFD (Strut only):

F : Applied axial force (kN or kip).

Fy : Specified minimum yield strength of steel (MPa or ksi).

Fu : Specified minimum tensile strength of steel (MPa or ksi). L/r : Slenderness ratio.

Pu : Ultimate axial stress (MPa or ksi).

Pn : Allowable axial stress based on the slenderness ratio (MPa or ksi).

Sc : Actual axial stress in member (MPa or ksi).

BS 5950 - 1990:


F : Applied axial force (kN or kip). L/r : Slenderness ratio.

M : Applied moment (kNm or kipft).

Ma : Maximum buckling moment in presence of axial load (kNm or kipft).

Mb : Lateral torsional buckling resistance moment (kNm or kipft).

Mc : Moment resistance in the absence of axial force (kNm or kipft).

m : Equivalent uniform moment factor.

n : Slenderness correction factor.

Pc : Allowable axial stress based on the slenderness ratio (MPa or ksi).

Py : Design strength of steel (MPa or ksi).


Z : Elastic modulus (mm³ or in³).

CSA S16.1 - M89:

Ce : Euler buckling strength (kN or kip).

Cr : Factored compression resistance (kN or kip).

Cu : Ultimate compression force (kN or kip). L/r : Slenderness ratio.

Fu : Ultimate strength of steel (MPa or ksi).

Fy : Design yield strength of steel (MPa or ksi).

Mcr : Elastic buckling moment (kNm or kipft).

Mr : Factored moment resistance (kNm or kipft).

Mu : Ultimate bending moment (kNm or kipft).

Tr : Factored tensile resistance (kN or kip).

Tu : Ultimate tensile force (kN or kip).

U1 : Capacity factor to account for moment gradient and second-order effects.

Zpl : Plastic modulus (mm³ or in³).

ω1 : Equivalent uniform bending moment factor.

ω2 : Moment gradient factor giving increased moment resistance of laterally unsupported members.

Eurocode 3 - 1992 (Strut only):


F : Applied axial force (kN or kip).

fy : Design yield strength of steel (MPa or ksi). L/i : Slenderness ratio.



SABS 0162 - 1984:

f ’cr : 0.6 times the Euler buckling stress (MPa or ksi).

fy : Design yield strength of steel (MPa or ksi). L/r : Slenderness ratio.

fy : Design yield strength of steel (MPa or ksi).


Pmc : Allowable compressive bending stress (MPa or ksi).

Pmt : Allowable tensile bending stress (MPa or ksi).


St : Average axial tensile stress (MPa or ksi).

Smc : Maximum compressive bending stress (MPa or ksi).

Smt : Maximum tensile bending stress (MPa or ksi).

ω : Coefficient allowing for varying bending moment.

SABS 0162 - 1993:

Ce : Euler buckling strength (kN or kip).

Cr : Factored compression resistance (kN or kip).

Cu : Ultimate compression force (kN or kip). L/r : Slenderness ratio.

fu : Ultimate strength of steel (MPa or ksi).

fy : Design yield strength of steel (MPa or ksi).

Mcr : Elastic buckling moment (kNm or kipft).

Mr : Factored moment resistance (kNm or kipft).

Mu : Ultimate bending moment (kNm or kipft).

Tr : Factored tensile resistance (kN or kip).


Tu : Ultimate tensile force (kN or kip).

U1 : Capacity factor to account for moment gradient and second-order effects.

Zpl : Plastic modulus (mm³ or in³).



Sign conventions Member design is done in the local element axes. Bending about the x-x axis generally corresponds to strong axis bending and bending about the y-y axis to weak axis bending. For non-symmetric sections like angles, the x-x and y-y axes are horizontal and vertical with the v-v axis representing the weakest axis.

Tip: The exact orientation of the v-v axis of a mono-symmetric section can be determined using the Section Properties Calculation module, Prosec.

Axial force and moment

The local axes system and force directions are defined as follows:

• Axial force: The local z-axis and axial force is chosen in the direction from the smaller node number to the larger node number. A positive axial force indicates compression and a negative force tension.

• Bending: Moments about the x and y-axes represent bending about the section's strong and weak axes respectively. Positive moments are taken anticlockwise in all diagrams.

P-delta effects Design codes generally allow stability effects to be taken into account in buckling checks by reducing design capacities or amplifying design moments or axial forces. Trusses are normally not sensitive to sway. However, in any structure, if you judge P-delta effects to be an important part of the analysis, you should perform a second order frame analysis.


Second order analyses

The desirability of a second order analysis is echoed in the various design codes:

• AISC - 1993 LRFD: Section C1 states that an analysis of second order effects is required for frames. This is done by second order elastic analysis or first order analysis with amplification factors B1 and B2.

• BS 5950 - 1990: Accounts for stability effects by amplification of design moments by suggesting a ’more exact approach’ in clause 4.8.3.3.2.

• CSA S16.1 - M89: Desirability is expressed in clause 8.6.1.

• Eurocode 3 - 1992: See clause 5.2.1.2.

• SABS 0162 - 1984: Encourages second order analysis of frames with sway by limiting the coefficient for variable bending moment, ω, to no less than 0.85 in the absence of second order analysis.

• SABS 0162 - 1993: Same as CSA S16.1 - M89.

The programs do not make automatic adjustments to take account of stability effects. If deemed necessary, you should conduct a second order analysis using the Plane Frame Analysis or Space Frame Analysis modules.

When post-processing a second order frame analysis, Com also performs a second order analysis for each member. This generally results in more economic design of sections.

Design parameters Different design parameters can be set for each group of elements designed:

Effective area factor

When an element is subjected to a tensile axial force, allowance should be made for the reduction in sectional area due to fastener holes.

The various design codes follow similar approaches for calculating the effective area factor:

• AISC: Guidance is given in section B3.

• BS 5950 - 1990: See clauses 3.3 and 3.4.

• CSA S16.1 - M89: When calculating the allowable tensile force, allowance is made for reduction of the effective net area for shear lag (clause 12.3). The effective area is thus effectively a function of the yield strength and ultimate strength of the steel (clause 13.2).

• Eurocode 3 - 1992: See clause 5.4.2.2.

• SABS 0162 - 1984: See clauses 5.3 and 9.2.


• SABS 0162 - 1993: The same clauses apply as for CSA S16.1 - M89.

Effective length factors for struts and ties

The effective length factors depend on the degree of restraint to be expected at each end of compression members. Guidelines are given in the codes:

• AISC: See section E1.

• BS 5950 - 1990: Refer to clause 4.7.2 and Appendix D.

• CSA S16.1 - M89: See clause 9.3 and Annex C.

• Eurocode 3 - 1992: See clause 5.8.2.

• SABS 0162 - 1984: See clause 8.2.1 and Appendix E.

• SABS 0162 - 1993: The same clauses apply as for CSA S16.1 - M89.

Considering a plane truss, the effective length Lx relates to in-plane buckling. For struts where rotational fixity is provided by the connection, e.g. two or more fasteners or a welded connection, a value between 0.70 and 0.85 is usually appropriate. Where rotation at the joints are possible, e.g. single bolted connection, a value of 1.0 would normally be applicable.

The effective length Ly relates to buckling out of the vertical plane. This phenomenon can often govern the design of the top and bottom chords of a truss that can buckle in a snakelike ’S’ pattern, giving an effective length equal to unrestrained length. Lateral restraints are normally provided to reduce this effective length. For example, with braced purlins connected to the top flange of the truss, the effective length could be taken equal to the purlin spacing.

The effective length Lv relates to buckling about the v-v axis, i.e. the weakest axis, and requires special attention. Because movement about the v-v axis requires movement about both the x-x and y-y axes, Lv is usually set equal to the least of Lx and Ly.

Effective length factors for beam-columns

The codes give similar guidelines:

• AISC: See section E1.

• BS 5950 - 1990: Refer to clause 4.3.5 guidance on factors to use for members in bending. Refer to clause 4.7.2 and Appendix D for members in compression.

• CSA S16.1 - M89: Refer to clauses 9.1 to 9.4 and Annexes B and C.

• Eurocode 3 - 1992: See clause 5.8.2.

• SABS 0162 - 1984: See clause 7.2.2 for flexural members. Refer to clause 8.2.1 and Appendix E for compression members.

• SABS 0162 - 1993: Same as for CSA S16.1 - M89.


Note: CSA S16.1 - M89 and SABS 0162 - 1993 clause 9.3.2 allows the effective length factor for compression members to be reduced to 1.0 if a second-order frame analysis has been performed. A second order analysis will therefore normally yield a more economic design.

Consider a typical portal frame subjected to dead and live load. The effective length Lx relates to buckling in the plane of the portal, i.e. about the strong axis of each member. The length Ly relates to out-of plane buckling, i.e. weak axis buckling. This value is typically set equal to the distance between restraining purlins and sheeting rails.

The effective length Le relates to lateral torsional buckling of a member’s compression flange about its weak axis. The length depends on the distance between restraints of the compression flange. For rafters with purlins restraining the top flange, Le can therefore be set equal to Ly in zones of sagging moment. However, if the rafter is relatively deep and no special precautions are taken, the purlins could possibly have no effective restraint on the bottom flange. Therefore, where the bottom flange is in compression, i.e. zones of hogging moment, longer effective lengths for lateral torsional buckling will apply.

Note: The current versions of Strut and Com cannot design tapered sections. The use of haunches in the sketch is merely for the sake of explaining the effective lengths. See page 5 for more detail.


Slenderness limits

The different codes specify similar slenderness ratios for members in compression, typically 200. For tension members, a maximum slenderness ratio of 300 is generally used. When launching Strut or Com, the slenderness limits given by the selected design code will be used by default.

You are free to alter the maximum slenderness ratio for each individual load case or combination if required. For example, in the case where uplift due to wind is dominant, the maximum slenderness ratio may possibly be increased, e.g. SABS 0162 - 1984 clause 8.4 and BS 5950 -1990 clause 4.7.3.2 allows a slenderness ratio of 250.


Member design techniques

The programs have two basic modes of operation:

• Read and post-process the frame analysis results.

• Alternatively, you can do an independent interactive design of one or more members.

Uses and limitations of the member design modules

Strut considers only axial forces during the design – any prevailing bending moments are ignored. This means that you should use the program for the design of trusses and truss-type sub-structures of frames only, i.e. where members experience predominantly axial forces.

Use Com when working with members that have significant bending moments. This program can however not design non-symmetrical sections like angles. Such members are typically used for constructing trusses or bracing frames and often have negligible bending moments, making Strut the appropriate design tool.

Reading and post-processing frame analysis results Given the nature of the different frame analysis modules, selective compatibility exists between the various frame analysis and the steel member design modules:

• Strut designs members for axial stress only and can therefore read the results of Plane Frame Analysis, Space Frame Analysis and Space Truss Analysis. The Grillage Analysis and Single Span Beam Analysis modules are used to analyse beams and are therefore excluded.

• Com designs members for combined axial and bending stress can therefore read the results of Plane Frame Analysis, Grillage Analysis, Space Frame Analysis and Single Span Beam Analysis. The Space Truss Analysis is used to analyse trusses with axial forces only and is therefore supported by Strut instead.

Design steps

Working through the input and design pages, the frame design procedure can be broken up into the following steps:

• The Input page: Defining design tasks by choosing a design approach, selecting members to be designed, setting the design parameters and selecting load cases and slenderness limits. The concept of tasks is described in detail on page 17.

• The Members page (Com only): Define internal nodes and enter effective lengths. Refer to page 17 for detail.

• The Design page (Com only): Evaluating the design results. See page 17 for detail.

• The Calcsheet page: Accumulate design results. See page 17 for detail.


Re-analysis of the frame

Having evaluated the various member sizes, you may find it necessary to return to the original frame analysis and make some changes to section sizes. Before exiting the member design module, first save the task list using the Save command on the File menu. After re-analysing the frame, you can return to the member design module and recall the task list to have the modified structure re-checked without delay.

Note: For a task list to be re-used with a modified frame, a reasonable degree of compatibility is required. Tasks that reference specific laterally supported nodes, for example, will require modification if relevant node numbers have changed.

Interactive design of members As an alternative to the above procedure, individual members can be designed without needing to perform a frame analysis. To enable the interactive design mode:

• In Strut, select the Interactive page.

• In Com, select ’Interactive input of data’ on the Input page.

Design steps

Working through the input and design pages, the interactive design procedure can be broken up into the following steps:

• The Interactive page (Strut) or Input page (Com): Choose a design approach, set the design parameters and enter the element loads. In Strut, results are displayed interactively on the same page. Refer to page 17 for a detailed explanation.

• The Design page (Com): Evaluate the design results. More detail is given on page 17.

• The Calcsheet page: Accumulate design results to print or send to Calcpad. See page 17 for detail.


Tasks input

On entering Strut or Com, it defaults to reading the last compatible frame analysis for post-processing. You can then choose to:

• Read and post-process the frame analysis results: Define one or more design tasks by grouping members with relevant design parameters.

• Interactive design: Ignore the frame analysis and interactively input and design members.

The pages that follow describe the use of the programs for reading and post-processing frame analysis results. Information regarding interactive design is given on page 1725.

Choosing the data input and design mode

In Com, the appearance of the Input page determined by your selection of the mode of operation:

• If you choose to read and post-process the results of the frame analysis modules, you will use the Input page to define design tasks.

• However, if you opt for interactive design of members, the Input page displays a table for entering member geometry and loading.

The appearance and behaviour of Strut is slightly different:

• The Input page is used to manage design tasks for post-processing frame analysis output.

• The Interactive page is used for entering data pertaining to interactive design of members.

Reading frame analysis output files You can select another frame output file or view the current file:

• Read data from: Use this option to load the output of a different frame module than the one displayed. Click the box and select the relevant file from the list or enter a file name.

• View output: To display the current frame analysis output file.

Defining design tasks Central to the process of post-processing frame analysis results, are design tasks. By grouping selective members with their relevant design parameters into one or more design tasks, you should find it easy to manage the vast amount of frame analysis data generated for larger frames.


The design of a frame should be simplified by breaking it into one or more manageable tasks. Each task then defines a group of members to be designed together with the relevant design parameters to be used.

Once you have defined one or more design tasks, the Calcsheet page (Strut) or Design page (Com) is enabled – viewing that page automatically performs all design tasks.

After having carefully defined a number of tasks, you can save the task list to disk for later re-use. This means that you can return to the relevant frame analysis module, make some changes to the structure, re-analyse it and then repeat the previous design tasks by simply reloading the task list.

Defining tasks

To define design tasks, you have to select or enter the following information:

1. Select a design approach.

2. If you choose to select the lightest section, then also choose a profile to use.

3. Select the members to be designed.

4. Enter the design parameters.

5. Select the load cases to be considered.

To save a task, enter a Task title and click Add task. Once added to the task list, a task will be automatically performed when you go to the Calcsheet page. Define as many tasks as necessary to design the frame in the required detail.


Modifying design tasks

To modify an exiting task:

1. Click Task title to display a list of defined tasks.

2. Select the task you want to modify.

3. Make the necessary changes to the selected members, design parameters etc.

4. Click Update task to save the changes.

Deleting tasks

To remove a task from the list, first select the task and then click Delete task. To save the complete task list to disk, use the Save commands on the File menu.

Note: In Com, saving the task list with File | Save also saves the intermediate nodes and effective lengths entered in the Members page.


Selecting a design code The current selected design code is displayed in the status bar. To select a different design code, use the Code of Practice command on the File menu or click the design code on the status bar.

Choosing a design approach Depending on what you would like to achieve, e.g. preliminary sizing or final design checks, you can choose between the following design approaches:

• Select lightest sections: Elements are optimised for economy using mass as the criterion. Specify the type of section to be used, e.g. equal leg angles, using Profile (F5). If you are unsure about the section sizes to use or want to do some preliminary sizing, this is the probably best approach to follow.

• Evaluate current sections: The sections specified in the original frame analysis are checked. This approach is best suited for final design checks.

Note: The section type selected under Profile (F5) is used when the design approach is set to ’Select lightest section’. However, the selected section type has no bearing on the design when the approach is set to ’Evaluate current sections’.

Selecting members for design in Strut Use the Element groups (F6) function to select one or more element groups from the list or by clicking members in the picture. Lateral supports are assumed at all nodes. If certain nodes are not laterally supported, you can indicate them as follows:

• Use the Laterally unsupported (F7) function to indicate those nodes that are supported –all other nodes are then assumed to by unsupported. The program uses the shortest path between the specified nodes to identify the relevant elements. Leave a blank line to end a series of supported nodes or use the New group function to start a new series of laterally supported nodes. You can manually enter node numbers or click them on the picture.


The following apply to the calculation of effective lengths when you indicate laterally unsupported members:

• Ly is based on the cumulative length between the specified supported nodes.

• Lx and Lv remain a function of the individual element lengths between adjacent nodes.

Tip: To keep the design of a large truss manageable, consider using more tasks and specifying fewer nodes at a time.

Selecting members for design in Com Use the Element groups (F6) function to select one or more element groups from the list or by clicking members in the picture. A lateral supports is assumed at each node. If certain internal nodes are not laterally supported, you can indicate them on the Members page. Refer to page 17-29 for detail.

Setting the design parameters Use the Design parameters (F8) function to enter appropriate design parameters and material properties. You can select a different set of design parameters with each task.

Note: In Com, effective length factors are entered on the Members page. Refer to page 1730 for details on entering effective lengths in Com.

Selecting load cases and limiting slenderness ratios When loading the last frame analysis results, the program automatically displays a list of all load cases and combinations that can be designed and also the default slenderness limits for struts and ties.

In the Maximum L/r ratios (F9) table, you can exclude any load case or combination from the current design task by clicking its right-most column. A cross next to a load case means that the particular load case will be included.

Tip: In the frame analysis modules you can also select to analyse load combinations only. The analysis output will then be more compact due to the omission of individual load case results.

You are free to modify the slenderness limit for each individual load case or combination as required. In the case where uplift due to wind is dominant, for example, you may be able to set a higher slenderness limit. The code requirements regarding slenderness limits are discussed on page 14.


Controlling design output The amount of information that will be added to the Calcsheet page can be controlled using the Settings function on the Input page:

• In Strut, you can select whether all members should be added to the Calcsheet or only a number of most critical members.

• In Com, you can choose between showing detailed calculation with or without diagrams or a summary of results.


Interactive input

The interactive design mode offers an alternative method of designing members. Instead of performing a frame analysis and then and post-processing the results, you can enter member length and forces and design them interactively.

To enable the interactive design mode:

• In Strut, select the Interactive page.

• In Com, select ’Interactive input of data’ on the Input page.

The pages that follow describe the use of the programs for interactive member design. The procedure to reading and post-processing frame analysis results is explained on page 15



• Select lightest sections: Using mass as the criterion, the most economical section size will be determined for each member. The type of section that will be selected will be as specified above. Specify the type of section to be used, e.g. equal leg angles, using Profile (F5). This approach is very useful for if one is unsure about the section sizes to use or if one wants to do some preliminary sizing.

• Evaluate current sections: This approach allows you to specify a section size for each member. Use the Profile (F5) function to select a section.

Setting the design parameters In Com, use the Effective lengths (F6) function to enter effective length factors. Use Design parameters (F8) to enter appropriate design parameters. All members designed in a particular interactive session use the same set of design parameters.


Specifying slenderness limits Use the Maximum L/r ratios (F9) function to enter appropriate maximum allowable slenderness ratios for compression and tension.

Entering member lengths and forces in Strut Use as many lines as necessary to enter member lengths and axial forces:

• L: Length of the member (m or ft).

• F: Axial force (compression positive) (kN or kip).

• Designation: Profile or section chosen using Profile (F5). With ’select lightest section’ enabled, you only need to choose the type of profile. With ’Evaluating current section’ selected, you should select a section for evaluation.

Note: All entered forces and moments are ULS design values. For allowable stress design with SABS 0162 - 1984, you should enter working loads.


Entering member lengths and forces in Com One or more lines of information can be entered for each member. The program automatically accumulates multiple lines of loads for the same member. The following input data is required:

• Name: A descriptive name for each member.

• L: Length of the member (m or ft).

• F: Axial force with compression being positive (kN or kip).

• X/Y: Axis of bending relating to the values that follow next. Use as many lines as necessary to define the loading on the member about the x-x and y-y axes.

• M1: Moment applied at the left end (anti-clockwise positive) about the X or Y axis (kNm or kipft).

• M2: Moment at the right end (anti-clockwise positive) (kNm or kipft).

• W1: Distributed load at the left end. The load works over the whole length of the member load and varies linearly between the left and right ends (downward positive) (kN/m or kip/ft).


• W2: Value of distributed load on right side (kN/m or kip/ft).

• P: Point load applied on the member (downward positive) (kN or kip).

• A: Position of the point load, measured from the left end (m or ft).

Note: All entered forces and moments are ULS design values. For allowable stress design with SABS 0162 - 1984, you should enter working loads.

The profile of the members to evaluate is chosen using the Profile (F5) function. On opening the Design page, the lightest section will be chosen for each member. Lighter or heavier sections of the same profile can then be browsed as required.

Viewing design results Similar design criteria are applied in Strut and Com. The presentation of the design results are however done quite differently. Refer to page 17 for detail.


Beam-column member definition

In Com, internal nodes and effective lengths are defined on the Members page. The data entered on the Members page is applicable to all design tasks defined on the Input page. To use different effective lengths for different design tasks lateral support group tasks with identical effective lengths and save them in separate files.

Defining internal nodes An internal node is defined as a node in-between the end nodes of a member. When you add internal nodes, the program joins relevant members to allow for easy input of effective lengths

Adding an internal node

You can add internal as follows:

• Enter internal node numbers in the table or click them with the mouse.

• Use the Auto Select function to let the program detect all internal nodes.

Removing an internal node

You can remove an internal node by deleting it form the list or by clicking it again in the picture.

Consolidation of members

With the addition of each internal node, the relevant node is ’removed’ by joining the two adjacent members into a single member. The table of members is continuously updated to show the new member layout.

The program uses the following guidelines to decide which members to join at an internal node:

• For the automatic selection of internal nodes, adjoining members must have the same section.

• Only members with an included angle greater than 100° (where 180° corresponds to a perfectly straight member) are joined.

• Where members of different sections intersect, the larger section defines the main member that should be joined.

• Where two or more members intersect, the internal node is taken to belong to one of the intersecting members only. The chosen member will be the straightest member or, if the same, the first in the table of members.


Entering effective lengths Enter effective length factors as follows:

• Apply the same value of Kx, Ky or Ke to all members by clicking the Kx, Ky en Ke buttons in the table heading.

• Enter the effective length factors for individual elements.

Note: The list of internal nodes and effective length factors are automatically saved when you save the task list. See page 17 for detail.

Tip: You can quickly find a member in the table by pressing Ctrl+F. Enter the member name by referring to one or both of its end node numbers.


Design results

In Strut the design results are shown on the Calcsheet page. In Com, select the Design page to perform all design tasks and display the design results. All specified load cases and combinations are considered for each member designed. Unless a very large number of elements and load cases are involved, the design procedure will normally be completed almost instantaneously.

By default, the results for the design task active on the Input page are displayed. The results of any other design task can be displayed by selecting the task from the list (see description below). If an interactive member design was performed, the displayed results will be for the interactive design task instead.

The design criteria The following criteria are used in the design:

• The interaction formulae given by the relevant design code are used to evaluate the effect of axial stress or combined effect of axial stress and bending stress. In calculating the allowable stresses, the program takes account of the member slenderness and effective tension area.

• The slenderness ratio checked against the specified maximum allowable slenderness ratio for compression and tension.

Note: Strut designs members for axial stress only and ignores any bending stresses.

Viewing design results in Strut The design results are given in tabular format with ’OK’ and ’FAIL’ remarks to indicate success or failure. The mass of each group of elements is summarised below the relevant table. The results of each new design are appended to the bottom of the existing output.

Viewing results in Com The complete interaction formulae are displayed for the critical load case of the first member of the first design task. Individual calculations have ’OK’ and ’FAIL’ remarks to indicate success or failure.

To view the results of another task, member, section or load case:

• Use the Up and Down buttons to move up or down the list of available options. Tasks and load cases are listed in the order of definition. Sections are ordered by mass. Alternatively click the item, i.e. sections, and use the Up and Down arrow keys.

• Alternatively click the relevant input box and select an item from the list that drops down.


Adding results to the Calcsheet page In Strut, the design results are automatically displayed on the Calcsheet page.

In Com, the following options are available when adding design results to the Calcsheet page:

• Member to Calcsheet: Add the current displayed member only.

• Task to Calcsheet: Add the design results of all members in the current task, including those members not currently displayed.

• All tasks to Calcsheet: Add all members of all tasks.

Note: The level of detail of the information added to the Calcsheet can be set using the Settings function on the Input page. Refer to page 17 for detail.


Calcsheet

The design results of all tasks are grouped on the Calcsheet page for sending to Calcpad or immediate printing.

Use the Output settings function on the Calcsheets page and Settings function on the Input page for the following:

• Embed the Data File in the calcsheet for easy recalling from Calcpad.

• Clear the Calcsheet page.

Recalling a data file If you enable the Data File option before sending a calcsheet to Calcpad, you can later recall the design by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the member design module as well.


Plastic Frame Design

The Plastic Frame Design module can perform a linear elasto-plastic analysis of any general two-dimensional framed structure. The program can be used in the following plastic design modes:

• The plastic collapse mechanism and load factors can be determined for a series of load combinations.

• The frame’s plastic behaviour can be optimised to achieve more economical sections.

Elastic design of a steel frames can be done using the Plane frame Analysis or Space Frame Analysis modules in conjunction with the steel member design modules axial and combined stress, Strut and Com. See Chapter 4 for detail.




Design scope The use of plastic design methods is normally limited to the design of continuous beams and single storey frames with rigid joints, e.g. portal frames. It may also be acceptable to use plastic methods for designing some braced multi-storey planar frames.

Determining plastic mechanisms

The program performs an elasto-plastic analysis of plane frames. A rational analysis approach is followed to obtain a true collapse mechanism for each load case or combination:

1. A linear elastic analysis is performed to determine the position of the first plastic hinge.

2. The bending moment at that position is then limited to the relevant plastic moment while the position of the next hinge is calculated.

3. The procedure is repeated to obtain more plastic hinges.

4. If the formation of further plastic hinges results in the bending moment at one of the existing hinges to decrease, that hinge is removed and elastic behaviour re-instated at that position.

5. The procedure is repeated until a collapse mechanism forms.

Analysis modes Depending on the analysis module used, the following types of analysis can be performed:

• Linear analysis: Basic linear elastic analysis. A linear analysis procedure is typically performed markedly faster than a plastic analysis. It therefore is recommended that you verify the basic integrity of the frame input by performing a linear analysis prior to attempting a plastic analysis.

• Plastic analysis: Choose between evaluating the adequacy of the frame as entered or optimising the section sizes. When optimising, the program will search for a more economic configuration of sections. The plastic modulus, Zpl, is used as the criterion for section economy.

Two design modes are available during plastic analysis:

• No optimisation: Evaluate the frame with sections as entered and calculate the adequacy against collapse for each load combination.


• Optimise sections: Optimise the frame’s plastic behaviour by determining more economical sections.

Design codes The program uses general plastic theory. Working within their scope, the program can be considered to support the following design codes:

• BS 5950 - 1990.

• CSA S16.1 - M89.


• SABS 0162 - 1984.

• SABS 0162 - 1993.

Note: SABS 0162 - 1984 use an allowable stress design method for elastic design. For plastic design, however, it adopts an ultimate limit state design method.

Sign conventions Frame input and output uses a mixture of global axis and local axes values.

Global axes

The global axis system is nearly exclusively used when entering frame geometry and loading. Global axes are also used in the analysis output for deflections and reactions.


• The X-axis is chosen to the right.

• The Y-axis points vertically upward. A positive vertical load thus works up and a negative load down.


Local axes


Local axes are used in the output for element forces. You can also apply loads in the direction of a beam element’s local y-axis. The local axis system is defined as follows for beam elements:

• The local z-axis and axial force is chosen in the direction from the smaller node number to the larger node number.

• The x-axis is taken parallel to the global Z-axis, i.e. pointing towards you. A rotation about the x-axis is thus always anti-clockwise.

• The y-axis is taken perpendicular to the x and z-axes, using a right-hand rule.

Beam element forces

The element forces are given in the local element axis system. The following conventions apply to beam elements:

• The axial force, Pz, is taken in the z-direction.

• The shear force, Vy, is taken in the y-direction.

• The moment, Mxx, is taken about the x-axis, i.e. anti-clockwise.

Note: In this manual the global and local axes are written in uppercase and lowercase respectively.



Distance mm, m ft, inch

Force N, kN lb, kip

Use the Units commands on the Options menu to change the units for the current analysis:

• Set Units: Changes the units of measurement without altering the input data.

• Convert Units: Changes the units and converts all numeric data from the old to the new units of measurement.


Input

Work through the relevant Input pages to enter the frame geometry and loading:

• General input: Select the analysis type and special analysis parameters.

• Nodes input: Frame coordinates.

• Beams input: Join nodes with beam elements.

• Beam sections input: Enter properties or read sections from the database.

• Spring elements input: For special effects, optionally enter spring elements.


• Nodal loads input: Point loads and moments.

• Beam element loads input: Uniform distributed, triangular and trapezium loads on beams.

• Load combinations input: Group dead, live and wind loads in load combinations.

Alternative methods of generating frame analysis input are discussed on page 17.

Viewing the frame You may want to enlarge portions of the picture of the structure or rotate it on the screen. Several functions, all of which are described in detail in Chapter 2, are available to help you using pictures of the frame:


• Use the View Point Control to set a new view point or camera position.

The Options menu makes the following additional functions available:

• Graphics:


• Choose whether you want all beam elements or only a certain type to be displayed.


• Display the structure with full 3D rendering, e.g. to verify section orientations. 3D rendering is automatically suppressed when viewing output.


• All surfaces are drawn as polygons. You can choose to make the surfaces transparent or have them filled and outlined.


• Views: You can save the current view point and view plane. The current view’s name is displayed on the picture. To re-use a saved view, click the view name on the picture to drop down a list of saved views.



Saving and printing pictures

Any picture can be saved or printed using the relevant buttons next the picture. Pictures on the Input and Output pages can also be added to the Calcsheets.

Tip: You can zoom into a picture and print, save or add the picture to the Calcsheets.

General input The General input page handles several important analysis parameters.

Analysis type

Choose between performing a simple linear elastic analysis or a plastic analysis. Refer to page 17 for an explanation of the analysis modes.

Plastic design parameters

You need to set the following analysis parameters when performing a plastic analysis:

• Plastic analysis tolerance: The plastic analysis is an iterative procedure. The analysis is deemed to have converged once the total strain energies of two sequential iterations differ by less than the specified tolerance.

• Maximum number of iterations: The analysis procedure calculates as many hinges as necessary to form a plastic mechanism. You can terminate the analysis at an earlier stage. A complex analysis that takes a very long time to converge can also be forced terminate earlier. To force the analysis to end before the formation of the final collapse mechanism, you can limit the maximum number of iterations to be performed.

Own weight



• By default the own weight of the frame is set to not be included in the analysis. Be sure to select the appropriate load case for own weight or, alternatively, to include the frame’s own weight in the values of the loads entered.

• The list of load cases from which you can select is based on the load cases defined on the Nodal loads and Beam loads input pages. You may thus prefer to specify the own weight load case only after completing all other input for the frame. However, you can also enter


the own weight load case at the start of the frame input process in which case you may ignore the warning message (that the load case does not exist).


Parametrics

The parametric plastic frame input modules are suitable for the rapid generation of complete input files for some typical structures. Because the resulting input data is presented in the normal way on the input pages, you are free to edit and append to the data as necessary.

Input generated this way can optionally be appended to existing data – you can therefore repeatedly use the parametric input modules to generate complicated structures.

Note: Plasdes is not limited to analysing only those frames generated by the parametric modules. The program can treat any general two-dimensional frame. The parametric modules merely serve to simplify input of typical frames.




Title

A descriptive name for the frame. It should not be confused with the file name you use when you save the input data.


Nodes input Use as many lines as necessary to enter the nodes defining the frame. A unique number must be assigned to each node. The node number is entered in the No column, followed by the X and Y-coordinates in the X and Y columns. If you leave X or Y blank, a value of zero is used.

You are allowed to skip node numbers to simplify the definition of the frame. You may also leave blank lines in the input to improve readability. If a node number is defined more than once, the last definition will be used.

Error checking

The program checks for nodes lying at the same coordinate. If a potential error is detected, an Error list button will appear.




• The Y-coordinate of node 4 is left blank. Therefore, node 4 is put at the coordinate (0.805,0).

• The No of is set to ’2’, meaning that two additional nodes are generated.


• The values in the X-inc and Y-inc columns set the distance between copied nodes. The coordinates 4 to 18 are horizontally spaced at 1.140 m to the right at 0.472 m downward, i.e. along the X and negative Y-axis respectively. The coordinates of the additional nodes are thus (1.945,-0.472) and (3.085,-0.944).



• Set the values of X-inc, Y-inc and Z-inc to the total coordinate difference to the last node and enable the Inc to End option. The last node’s coordinates are then first calculated and the specified number of intermediate nodes then generated.


Once you have defined one or more nodes in the table, you can copy that relevant line’s nodes by entering a '–' character in the No column of the next line. Then enter the number of additional sets of nodes to be generated in the No of column and the coordinate increments in the X-inc and Y-inc columns.




No X Y 15 0.00 5.12 16 2.00 5.12 17 4.00 5.12 20 0.00 5.62 21 2.00 5.62 22 4.00 5.62

Block generation

A group of nodes can be repeated by entering a ’B’ in the No column followed by the first and last table line numbers in which the nodes were defined. Separate the line numbers with a ’–'.


The nodes defined in lines 11 to 26 are copied twice. Node numbers are incremented by thirty for each copy. The X and Y-coordinate increments are 10 m and zero respectively.



The block generation function may be used recursively. That means that the lines specified may themselves contain further block generation statements.

Moving nodes

To move a group of nodes to a new location without generating any new nodes, use the block generation function and set No-of to '1' and Inc to '0'.

Arc generation

A group of nodes can be repeated on an arc by entering an 'A' in the No column, followed by the start and end line numbers. Enter the centre of the arc in the X and Y columns and use the X-inc column to specify the angle increment about the Z-axis.

Example:

All nodes defined in lines 5 to 9 of the table will be repeated eleven times on an imaginary horizontal arc. The centre point of the arc is located at the coordinate (10.0,1.5). The node


number increment is set to 5, i.e. node number 3 becomes node 8, etc. The rotation angle between the generated groups of nodes is 30 degrees about the Z-axis, i.e. anti-clockwise on the screen using a right-hand rule.

To copy one line only, simply omit the end line numbers, e.g. ’A12’ to copy line 12 only.


Rotating nodes


Mirror

Nodes of a plane frame or grillage can be mirrored horizontally or vertically by entering an ’M’ in the No column, followed by the start and end line numbers.

Mirror example:

All nodes defined in lines 5 to 9 are mirrored about a vertical (horizontal for a grillage) line through X=10 m. Node numbers are incremented with 5. By specifying a Y or Z-value instead of an X-value, nodes can be mirrored about a horizontal line passing through the specified Y or Z-value.

Deleting nodes

Nodes can be deleted by entering ’Delete’ in the Inc to end column. This can be especially handy if you have generated a large group of nodes and then need to remove some of them again.

Example:



Beam elements input A beam or frame element is defined by entering the node numbers at each end, separated with a ’–'. For example, '3–9' is the element linking nodes 3 and 9. The elements themselves are not numbered.

A series if elements can be input in a string, e.g. '2-6-10-14-18-22-24'. If the node number increment of a series is constant, you can replace intermediate nodes with two '–' characters. In the string above, nodes 2 to 22 has a constant increment of four. Therefore, the string can be rewritten as '2-6- - 22-24'. The node increment of four is derived from '2-6'.

An element definition must include a section number entered in the Section Name column. The section name is used to identify the relevant section. The actual section properties for each section number defined on the Beam Sections input page.


Section orientation

The local y-z plane of an element is taken in the global X-Y plane. The principle can be illustrated by considering an I-section in its normal orientation. For this case, the web will always be considered to be in a vertical plane.

A section can be rotated through ninety degrees by selecting the alternative orientation when reading it from the section database.


End fixity

The fixity at each end of an element, i.e. continuous or pinned, must also be defined in the Fixity columns. Pins are modelled on the element itself and not on the node. External pinned supports should be defined on the Supports input table. External supports are described in the next section.

The following types of end fixities can be specified:

• Fixed: Specify ’F’ to provide full rotational continuity. If you leave the field blank, ’F’ is assumed.

• Pinned: Use ’P’ to for no rotational restraint, i.e. a pin.

Note: To retain compatibility with the Dos version, you may also use ’0’ or’1’ instead of ’F’ and ’P’ respectively.

Entered fixities are applied at an element’s lower node number (designated as the ’left’ end) and higher node number (the ’right’ end). The order of the node numbers entered in the first column of the table has no bearing on the application of the fixity codes.

To define a pin only at the two remote ends of a group of elements, enable the Group fix option by entering a ’Y’. In this case the normal convention of smaller and larger node numbers does not apply. Instead, pins are put at the remote ends in the same order that the nodes have been entered.


Example:

The group of elements from node 42 to 24 is continuous except for the pins used at nodes 42 and 24.

If the Group fix is left blank or ’N’ is entered, the normal individual element fixity mode is assumed.

Tip: Element fixity can be displayed graphically on the screen. For this, edit the Graphics options to disable the Elements Continuous option.

When using pins, you should take care to ensure overall stability of the frame. Consider two elements on a straight line with pins at all three relevant nodes, for example. The centre node will be unrestrained for rotation about the element axis, resulting in instability during the analysis.

Note: Do not use an internal pin on an element to model an external support that allows free rotation. Rather allow the beam to be fixed to the node and define a simple support on the Support input page.

Tapered beams

The current version of Plasdes does not support tapered sections.

Rigid links

You can use rigid links to rigidly fix sub-structures to each other. To define a rigid link, enter ’R’ in the Section Name column.

Rigid links are modelled as very stiff beams. The stiffness of a rigid link is determined by multiplying the maximum stiffnesses of the other beams with a factor, typically one thousand.

Rigid link example:

Rigid links are defined between nodes 12 and 24, 14 and 26 and 16 and 26.



You can generate additional elements with the same section and fixity code values using the No of extra and Node No Inc columns. Example:

The elements between nodes 251 and 266 are copied ten times with the node numbers decrementing by five with each copy.

Block generation

A group of elements can be repeated by entering a ’B’ in the No column. Then enter the first and last table line numbers in which the elements were defined, separated with a ’–'.


All elements defined in lines 11 to 26 will be copied twice with a node number increment of thirty. The copied elements will use the same section number and fixity codes as the original elements.




Tip: When entering a complicated structure it may help to leave a few blank lines between groups of elements. Not only will it improve readability, but it will also allow you to insert additional nodes at a later stage without upsetting block and arc generations.

Deleting beams

Beam elements can be deleted by entering a special section name 'Delete'. This can be especially handy if you have generated a large group of elements at regular increments and need to remove some of them again.


Example:

Elements 25-27-29 and 35-37-39 are deleted.

Note: The display of selected beam element groups can be activated or suppressed by editing the Graphic options.

Error checking

The program checks for duplicate elements and elements with zero length. It also checks that a section number is assigned to each element. If an error is detected, an Error list button will be displayed.

Beam sections input Section properties should be assigned to all section names used on the Beam elements input page. The following properties are required for all sections:

• Cross sectional area, A.

• Second moment of area about the local x-axis, Ixx.

• Plastic modulus about the local x-axis, Zxx.

Each section should also have an associated material selected. If no section or material properties are entered, the values applicable to the previous line in the table are used.

Reading sections from the database

Use the Section database function to display and select sections from database. You can add your own sections, e.g. plate girders, to the database using the procedures described in Chapter 2.

Entering haunches

Haunched sections are entered by appending the haunch depth to the section designation. To add a haunch of 280 mm to a ’305x102x66’ BS taper flange I-section, enter ’305x102x66 (0.280h)’. The overall depth is then taken to be 305 mm + 280 mm = 585 mm.

Tip: You can verify your definition of haunches by enabling 3D rendering. Refer to page for 15 more detail.


Note: Although haunched sections can be entered, Plasdes does not support analysis of members with tapered sections. A tapered haunch in a typical portal frame, for example, should be modelled by entering one or more members that approximate the stiffness of the actual haunch.

Own weight

If a material’s definition includes a density value, the own weight of a member is calculated automatically and added to the load case specified on the General input page.


Selecting materials

Each section should have an associated material. To add one or more materials to a frame analysis data file, click Materials. Open the relevant material type screen and select the materials that are required for the current frame input.




Spring elements input You can use spring elements to provide elastic links between sub-structures. In theory, two nodes connected with a spring element should have the same coordinates. The program will warn if this is not the case and still allow you to continue.

Note: By default the Spring elements input page is not visible. This behaviour can be changed using the Advanced command on the Options menu.

Enter linear spring constants in the Kx, Ky and Kz columns and rotational spring constants in the Rx, Ry and Rz columns.

The orientation of a spring element is defined by entering a bearing between any two nodes that do not necessarily need to be connected to the same or other spring elements as well. The directions of the axes are defined as followed:

• A spring element’s x-axis is taken in the direction of the orientating nodes.

• The y-axis defined in the same way as for a normal beam element, i.e. perpendicular to spring element in a vertical plane.

• The z-axis is taken perpendicular to the x and y-axes using aright-hand rule.

Spring element example:

Spring elements are defined between nodes 16 and 116, 17 and 117 up to 19 and 119. The spring elements are aligned parallel to the imaginary line joining nodes 3 and 4.


Tip: Spring elements can also be made "rigid" so as to force two nodes to have the same translation and/or rotation. In the above example, a very large value for Kx would cause nodes 16 and 116 to have identical displacements in the direction described by nodes 3 and 4.

Supports input Frames require external supports to ensure global stability. Supports can be entered to prevent any of the three degrees of freedom at a node, i.e. translation in the X and Y-directions and rotation about the Z-axes. You can also define elastic supports, e.g. an elastic soil support, and prescribed displacements, e.g. foundation settlement.

Enter the node number to be supported in the Node No column. In the next column a combination of the letters ’X’, ’Y’ and ’z’ can be entered to indicate the direction of fixity. Use capitals and lowercase to define restraint of translation and rotation respectively, e.g. ’XYz’ means fixed against movement in the X and Y-direction and rotation about the Z-axis.



Tip: To enter a simple support with no moment restraint, you should enter ’XY’ or ’Y’.

If you want to repeat the supports defined on the previous line of the table, you need only enter the node number, i.e. you may leave the Fixity column blank. If the XYZxyz column is left blank, the supports applicable to the previous line will be used automatically.

Prescribed displacements and elastic supports

Use the X, Y and Rz columns to enter prescribed displacements and rotations in the direction of the X or Y-axis or about the Z-axis. Being a global support condition, the effect of the prescribed displacement is not considered to be a separate load case. Instead, the effect of prescribed displacements is added once only to the analysis results of each load case and load combination.

Elastic supports, or springs, are defined by entering spring constants in the X, Y and z columns. The spring constant is defined as the force or moment that will cause a unit displacement or rotation in the relevant direction. Enter an ’S’ in the P/S column to indicate that an entered value is a spring constant rather than a prescribed displacement. If you leave the P/S column blank, the entered values are taken as prescribed displacements.

Note: The display of supports can be activated or suppressed by editing the Graphic options.

Error Checking

The program does a basic check on the structural stability of the frame. If a potential error is detected, an Error list button will appear.



Additional supports and prescribed displacements can be generated using the Number of extra and Node number inc columns. The procedure is similar to that described on page 17 for generating additional nodes.


Nodal loads input Loads on beam elements are categorised as nodal loads, i.e. loads at node points, and element loads, i.e. loads between nodes. Uniform distributed loads can be applied to shell elements.

All loads are organised in load cases, e.g. ’DL’ for own weight, ’ADL’ for additional dead loads, ’LL’ for live load, etc. Load cases apply equally to the various load input screens, meaning that you can build up a load case using different types of loads.

To define a load case, type a descriptive name for each load case in the Load Case column. Use up to six characters to describe each load case. If the load case name is not entered, the load case applicable to the previous line in the table is used.

The load case at the cursor position is displayed graphically. Press Enter or Display to update the picture.

A nodal load can, as its name implies, only be applied at a node. If a point load is required on an element, use the Beam loads input table instead.

Sign conventions


Nodal loads are applied parallel to the global axes – an explanation of the sign conventions are given on page 17.

Tip: For a typical steel frame or roof truss, it may be easiest to define a node at each purlin position. Roof loads transferred via the purlins can then be entered as nodal loads.

Error checking


Generating additional nodal loads

Additional nodal loads can be generated using the Number of extra and Node number inc columns respectively.

Block generation of nodal loads

You can use the block function to copy blocks of nodal loads. The procedure is similar to that for generating additional nodes – see page 17 for more detail.

Beam element loads input Distributed loads and point loads on beam elements are all referred to as element loads. The Nodal loads input page provides the easiest way of applying point loads and moments at nodes.

Use up to six characters to enter a descriptive name for each load case in the Load Case column. Then enter the element string of nodes in the Beam element definition column. Entering the beam element definition follows the same convention used as for the Elements input table – see page 17 for detail.

Sign conventions

Depending on the selected load direction, beam loads are applied parallel to the global axes or parallel to the local y-axis – the definitions of the global and local axes are given on page 17 and 17 respectively.

The load direction is entered in the Direction column. Enter a global direction 'X' or 'Y'. Element loads are applied to the relevant projected length of the elements. Therefore, if a 'Y' load is entered for a vertical element, for example, the resulting load will therefore be zero.



For a distributed load, entered in the load intensity at the smaller and larger node numbers in the W-begin and W-end columns respectively. If the load is constant over the length of the element, W-end may be left blank.

Error checking

The program checks that element definitions match previously defined elements. If an error is detected, an Error list button will appear.


The No of extra and Node number Inc columns can also be used to generate additional element loads.

Block generation of beam loads

You can use the block function to copy blocks of beam loads. The procedure is similar to that used to generating additional beam elements – see page 17 for detail.


Load combinations input You can model practical scenarios by grouping load cases together in load combinations. Enter the load combination name in the Load comb column, followed by the load case name and relevant load factors. Use up to six characters for a descriptive load combination name.

If the Load comb column is left blank, the load combination is taken to be the same as for the previous line of the table. The load cases to consider in a load combination are entered one per line in the Load case column. Enter the relevant ultimate and serviceability limit state load factors in the ULS factor and SLS factor columns.



• Deflections are calculated using the entered SLS loads. A set of reactions is also calculated at SLS for the purposes of evaluating support stability and bearing pressures.

• A second set of reactions and all element forces are determined using the entered ULS forces.


Note: Unlike elastic design, which is done using an allowable stress design technique, plastic design to SABS 0162 - 1984 is done at ultimate limit state. Refer to clause 12.2 and Table 30 for guidance on load factors to be used.

Error checking



Alternative frame input methods

Alternative means of frame input are available:

• Parametric input: Modules are available for the rapid generation of input for typical frame structures.

• Graphical input: Structures can be drawn in Padds or another CAD system and converted to frame analysis input.

Parametric input A number of typical frames can be input by entering a number of parameters. The Parametrics input modules do most of the data input. See page 17 for more detail on the Parametrics.

Note: Plasdes is not limited to modelling only those frames generated by the parametric modules. Instead, the parametric modules merely serve to simplify input of some typical frames.

Graphical input In some situations it may be easier to define a frame’s geometry graphically. With Padds you can draw a frame and then generate a frame analysis input file.

Using Padds for frame input

To use Padds to define a frame’s geometry:

1. Use Padds to draw the frame. Alternatively import a DXF drawing from another CAD system.

2. The frame should be drawn to scale using millimetres as unit. Identify different beam sections by using different pen numbers.

3. Use the Generate input command on the Macro to display the drawing conversion options. Choose the Plasdes as the target frame analysis module and press OK to start the conversion procedure.

The resultant frame analysis input file will be compatible with both the Dos and Windows versions of Plasdes. The file is saved in the working folder as a last plastic analysis file, e.g. ’Lastpl.s04’.

4. Close Padds.

Tip: To see a graphical input example, open ’..\prokon\data\demo\inputgen.pad’ in Padds.

Importing DXF drawings


You can also use your favourite CAD system to save a frame’s geometry in a 2D drawing and then use the Import DXF file command on the File menu to convert it to frame input.

The same basic rules apply as given above:

• The drawing should be to scale.

• You should use millimetre units.

• Different pen numbers should be used for different beam sections.

Typical problems experienced include the following:

• Polylines may not be recognised correctly. Break or explode polylines into single lines before saving the DXF file.

• Blocks may not import correctly and may need to be broken or exploded into individual entities.

• Using AutoCAD, lines colours set ’by layer’ translates to the default pen number. Rather set colours using pen numbers to ensure correct section numbering.

• If you experience problems importing a DXF file saved using a brand new version of your CAD system, it may help saving the file as an older DXF file version, e.g. version 12.


Analysis

On completing the frame input, you should set the analysis options before commencing the actual analysis.

Analysis options Use the General input page to select the analysis mode:

• Linear analysis: Basic linear elastic analysis. A linear analysis procedure is typically performed markedly faster than a plastic analysis. It therefore is recommended that you verify the basic integrity of the frame input by performing a linear analysis prior to attempting a plastic analysis.

• Plastic analysis: Choose between evaluating the adequacy of the frame as entered or optimising the section sizes. When optimising, the program will search for a more economic configuration of sections. The plastic modulus, Zpl, is used as the criterion for section economy.

Note: The results of an optimising plastic analysis should not be regarded as a final solution. You should return to the input data and enter the suggested or other preferred sections and then re-analyse the frame as a final check.

On the Analysis page, select the following:

• Output file: Enter an output file name or accept the default file name, e.g. ’Pasdes.out’.

• Analyse load combinations only: Enable this option if the results of only the load combinations are required. Generally one would require results for the load combinations only. How-ever, you may have a special need to view the results of specific load cases as well. Disable this option to include the results for the individual load cases as well.


Analysing the structure To analyse the structure, open the Analysis page and press Start Analysis. The analysis progress of displayed to help you judge the time remaining to complete the analysis.

After a successful analysis, the deflected shape is displayed for the first load case or load combination.


During the input phase, the frame geometry and loading data is checked for errors. Not all reported errors are necessarily serious. To define duplicate elements between two nodes, for example, could be an accidental error on your side. However, the program is quite capable of dealing with a situation like this and will therefore allow the analysis procedure to continue.


The first step of any analysis is the final verification of the input data. In the case of critical errors still present, a warning message will be displayed. If you then choose to not proceed with the analysis, you will be taken to the input table with the error. However, choosing to proceed and ignore the warning, will have an unpredictable result.

Fixing errors that occurred during the analysis Even if all input data seems valid, numeric errors may still occur during an analysis. For example, if you entered incorrect section properties, such as a very small E-value, the mistake may go by unnoticed. However, the analysis will then yield an invalid value in the stiffness matrix or extremely large deflections. The same applies to the stability of the frame. Although the frame may appear stable, some combinations of internal hinges may result in some nodes being unstable.





Viewing output

The analysis results can be viewed graphically or in tabular format. Output data, including graphics and tabled values, can be selectively appended to the Calcsheets using the Add to Calcsheets function on each output page.

Viewing output graphics Diagram can be displayed for the following:

• Deflections: Deflections are generally small in relation to dimensions of the structure, especially in the case of linear analyses. To improve the visibility of the deflection diagram, you can enter a screen magnification factor. You can optionally display the deflected shape without the original geometry.

• Beam element forces:

• Axial forces: The force is shown as expanded red and blue lines. Compression forces are shown in red and tension forces in blue. The distance of a line from the element centre line is in proportion to the size of the axial force.

• Moments: Bending moments about the local x and y-axes. A plot factor can also be entered to enlarge or reduce the bending moment diagram on the frame.

• Shear: Shear force diagrams are drawn for the local y and x-directions. A beam element’s shear force diagram is constructed by viewing it with its local z-axis pointing to the right. Since the direction of the z-axis depends on the node numbers, irregular numbering of nodes can


result in apparent inconsistent signs used in the shear force diagrams. Refer to page 1736 for detail on the sign conventions used for beam element forces.

• Envelopes: Enter a series of elements and select the load case and combinations to include in the envelopes. Envelopes are drawn using the values as tabulated from the output file. Positive moments, for example, are drawn below the line and negative above. Because members of different orientations can be included in the same envelope, no simple distinction is made between tension and compression faces of members.

Tip: When working with complicated frames, you may prefer adding one or more zoomed pictures to the Calcsheets instead of a single cluttered picture. To do this, simply into a picture and then use the Add to Calcsheets function.

Viewing output tables Open the Output file page for a tabular display of the frame analysis output file. You can filter the information appended to the Calcsheets by enabling or disabling the relevant sections.

The Find output function allows you to quickly locate any section of the output file.


Calcsheets

Frame analysis output can be grouped on a calcsheet for printing or sending to Calcpad. To include a particular component of the output in the calcsheets, view the relevant output information and then click Add to Calcsheets.

Recalling a data file The Data File is automatically included in the calcsheet sent to Calcpad. You can later recall the frame by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the frame analysis module as well.



Crane Gantry Girder Design The Crane Gantry Girder Design module can be used to design and optimise multi-span crane gantry girders with one or two cranes. Girders may be continuous or simply supported. The program supports multiple combinations of main beams and capping beams, including standard I-sections, plate girders and box girders.



A brief background is given below regarding the application of the theory and principles given by the design codes.

Design scope Crane gantry girders are generally constructed from rolled I-beams or welded plate girder. Channel capping beams are often used to stiffen top flanges. The program can check and optimise crane gantry girders made of rolled or welded I-sections or box sections with or without capping beams. One or two simultaneous cranes can be specified.

The design procedure for crane gantry girders is similar to that used for statically loaded girders. The various loading codes recognise the varying degree of duty of different types of crane and give parameters for horizontal transverse effects. Especially in the case of heavier duty cranes, certain aspects of the design and construction may require special consideration.

Design codes The program designs plate girders according to the following design codes:

• BS 5950 - 1990.

• CSA S16.1 - M89.



Symbols Where possible, the same symbols are used as in the design codes. A list is given below.

A : Cross-sectional area (mm2).

b : Width of capping beam top flange (mm).

bbot : Width of main beam bottom flange (mm).

btop : Width of main beam top flange (mm).

Cw : Warping torsional constant (mm4).

h : Height of section (mm).

Ixx : Second moment of area about major axis (mm4).

Iyt : Second moment of area top flange only (mm4).

Iyy : Second moment of area about minor axis (mm4).


J : St. Venant’s torsional constant (mm4).

r1 : Radius between flange and web (mm).

r2 : Outside radius at end of taper flange in (mm).

ry : Radius of gyration about minor axis (mm).

tf bot : Main beam bottom flange thickness (mm).

tf top : Main beam top flange thickness (mm).

tw : Web thickness (mm).

Zpl : Plastic section modulus about major axis (mm3).

Zpt : Top flange plastic modulus about minor axis (mm3).

Zyt : Top flange section modulus about minor axis (mm3).

ß : Angle between web and inside taper flange surface (°).

Stresses, forces and related entities

BS 5950 - 1990:

F : Applied axial load (kN).

M : Applied moment (kNm).

Ma : Maximum buckling moment in presence of axial load (kNm).

Mb : Lateral torsional buckling resistance moment (kNm).

Mc : Moment resistance in absence of axial load (kNm).



Pc : Compression resistance (kN).

py : Design strength of steel (MPa).

CSA S16.1 - M89.:

Cr : Factored compression resistance (kN).

Cu : Ultimate compression force (kN).

fy : Yield strength (MPa).

Mr : Factored moment resistance (kNm).

Mu : Ultimate bending moment (kNm).

U1 : Capacity factor to account for moment gradient and second-order effects. The value depends on the bending moment diagram and the member stability.


Vr : Factored shear resistance (kN).

Vu : Ultimate shear force moment (kN).

1 : Equivalent uniform bending moment factor.

2 : Moment gradient factor giving increased moment resistance of laterally unsupported members.

SABS 0162 - 1984:

f’cr : 0.6 times the Euler buckling stress (MPa).


Pc : Allowable axial compressive stress (MPa).

Pco : Maximum allowable axial compressive stress (MPa).

Pmc : Allowable compressive bending stress (MPa).

Pmco : Maximum allowable compressive bending stress (MPa).

c : Average axial compressive stress (MPa).

mc : Maximum compressive bending stress (MPa)

: Coefficient allowing for varying bending moment.

SABS 0162 - 1993:









1 : Equivalent uniform bending moment factor.

2 : Moment gradient factor giving increased moment resistance of laterally unsupported members.


Design parameters Various design parameters need to be set when designing a crane gantry girder:

Effective lengths

The codes give guidelines for determining effective length factors for flexural members:






Input

Design input comprises five categories:

• General parameters: Design parameters including general characteristics of the girder, load factors, support conditions.

• Main beam sections: Dimensions and material properties of main beams sections.

• Capping beam sections: Dimensions and material properties of optional capping beams.

• Spans: Section composition and lengths along the length of the girder.

• Crane data: Capacity, weight and dimensions of each crane.

General parameters Various design parameters, some of which depend on the code used, should be entered.

General design parameters

• Spans can be made continuous or simply supported. If this entry is left blank, full continuity at supports is assumed.

• Modulus of elasticity. The entered value is used for all main beam and capping beam sections.

• The rail height is used as eccentricity when applying horizontal crane loads.

• The effective length factor for a typical span relates to effective length for lateral torsional buckling. This will depend on the degree of fixity at the supports and the de-stabilizing effect of applied loads.

• During the analysis each crane is moved step-wise across the beam to determine the force and deflection envelopes. A larger step can be used for an initial analysis and a smaller step for the final design. A smaller step size will yield a more accurate analysis and smoother output diagrams but will result in a longer analysis time.

• ULS load factors:

• Dead load factor: Factor by which the dead load, i.e. the self-weight of the girder, bridge and crab, is to be multiplied to obtain the ultimate limit state design load.

• Live load factor: Factor by which the live loads are to be multiplied

• Combined live load factor: Factor by which both the horizontal and vertical live loads must be multiplied if they are considered as acting together. This factor is usually smaller than the normal live load factor.

• When designing a girder for two cranes, enter the minimum spacing between the cranes.


• You can choose to make either end of the girder pinned (simply supported), fixed (built-in) or free (cantilevered).

Dynamic load factors and deflection limits

By default, the tabled values are set to those given by the selected design code:

• Vertical: Amplification factor for vertical loading per wheel, including the effect of impact.

• Horizontal surge: Factor for transverse force due to acceleration and braking of the crab. The program assumes that surge forces are transmitted via the wheel flanges. The full effects of such forces are applied perpendicular to the crane track.

• Misalignment: For the effects of misalignment of the bridge’s wheels or the crane tracks. The misalignment forces are applied as two equal opposing forces.

• Skewing: Allows for skewing of the bridge. Skewing forces are applied as two equal opposing forces.

• L/D vertical: Vertical deflection limit, given as a ration of the span length.

• L/D horizontal: Horizontal deflection limit.

Note: The program does not include the effects of horizontal force due to acceleration, braking or force exerted on end stops.

Design options

Two design approaches are available:

• You can choose to evaluate the capacity of entered beam sections to carry the specified loads.

• The main beams and capping beam sections can be optimised to obtain the lightest sections capable of resisting the design loads.

Main beam sections Enter the properties for all the main beam sections that will be used in the analysis. You can read the properties of any standard I, H, square or rectangular hollow section from the database.

Plate girder and box girder sections can also be used as main beams. The properties for these should be entered manually. Only fields relevant to the type of section need be completed:

• The designation column is optional and is used to describe a section.

• For square and rectangular hollow sections only h, b-top and tf-top are required.


• The value for r2 and ß applies to sections with tapered flanges only.

Each main beam section must be given a unique number for easy reference when defining the girder.

Capping beams section data Main beam sections may optionally have channels or flat plates as capping beams. Enter each section that will be used during the analysis. Standard channels can be read from the database and flat plates can be defined by entering values for h and b.

Each capping beam section must be given a unique number for easy reference when defining the girder. Main and capping beam sections are numbered independently. The various sections are combined when defining the girder geometry.

Spans The data for a typical span comprises a span number, span length, main beam section number and, if required, capping beam section number.

Information required for each span:


Length : The length of a segment (m). Segment lengths are added to get the total length of the girder.

Section M : Main beam section number.

Section C : Capping beam section number. Leave blank if no capping beam is used.

Any combination of previously defined main and capping beams may be used. However, you should take care that the capping beam will correctly fit over the main beam.

Crane data Enter the loading and dimensional data for the cranes. In the case of a single crane analysis, simply leave the information for the second crane blank.

Capacity : The rated lifting capacity of crane (T, i.e. 10 kN units).

Class : The crane class designates it’s type of use:

Class Type of use

• 1 • Light duty and hand operated cranes

• 2 • Medium duty cranes

• 3 • Heavy duty cranes

• 4 • Extra heavy duty cranes

Weight bridge : Weight of the bridge assembly (kN).

Weight crab : Weight of the crab assembly (kN). The crab is defined as the portion that can move across the bridge.

Tip: If the exact value of the crab weight is not known, a value of 15% of the capacity of the crane will usually be a reasonable estimate.

Wheel spacing : Spacing between the bridge wheel assemblies (m).

Wheel load : For web buckling and crippling checks, the maximum load that any single wheel will exert on the girder is required. This value should be obtained from the manufacturer's technical data.


Viewing analysis output

The analysis output is displayed graphically. To view the detailed design calculation, select the Calcsheets page.

You can view the following results and use the mouse to read values from the diagrams:

• The vertical and horizontal deflected shape of the crane gantry girder.

• Ultimate limit state bending moment diagrams about the X-X (horizontal) and Y-Y (vertical) axes. Bending moment diagrams are drawn on the tension face of the girder.

• Vertical and horizontal shear force diagrams.

To append a deflection, moment or shear force diagram to design results on the Calcsheets page, first display the diagram and then click Add to Calcsheets.


Calcsheet

The design results of all tasks are grouped on a calcsheet for printing or sending to Calcpad. The design calculations include the following:

• Section properties for each combination of main beam and capping beam sections used.

• Web buckling and crippling checks for each section.

• Design checks for each span, including checks for the critical section and overall member strength.

The design output shows the complete interaction formulae, with the zero values for axial force. If required, the output equations can be edited to include bending about the minor axis. To edit an equation, select it in the calcsheet, right-click it and choose Edit.

Recalling a data file You can later recall the design by double-clicking the Data File object in Calcpad. Because a data file is embedded in the calcsheets sent Calcpad and saved as part of a project, you normally will not need to explicitly save your plate girder input using the Save command on the File menu as well.


Plate Girder Design 4-77

Plate Girder Design

The Plate Girder Design module can be used to design I-shaped welded plate girders. The program checks the behaviour of girders under specified loading and gives guidance regarding bearing and intermediate stiffeners.



A brief background is given below regarding the application of the theory and principles given by the design codes.

Design scope Welded plate girders can often be effectively and economically used as flexural sections. Modern mechanised manufacturing and automated welding techniques have simplified the production of plate girders greatly, boosting their popularity.

The program is capable is designing I-shaped sections with identical or different top and bottom flanges. You can also make the section properties vary along the length of the girder to model a tapered element.

Tapered sections

CSA S16.1 - M89 and SABS 0162 - 1993 do not cover the design of tapered sections. You can however choose to use the approach given by BS 5950 - 1990 to design tapered elements.

Bi-axial bending moment

Plate girders are normally used to resist high bending moments and/or vertical shear forces. The program correspondingly assumes that these effects would govern the design and does not explicitly perform the checks for bi-axial bending moment.

The design output shows the complete interaction formulae, with the zero values for bending moments about the minor axis. If required, the output formulae can be manually adjusted to include bending about the minor axis.

Buckling under axial compression

The program assumes that the effect of axial compression is small and therefore uses the full moment capacity for bending about the major axis. No capacity reduction is made on account of buckling about the major axis.

Design codes The program designs plate girders according to the following design codes:

• BS 5950 - 1990.

• CSA S16.1 - M89.




Symbols Where possible, the same symbols are used as in the design codes. A list is given below.


A : Cross-sectional area (mm2).

Bbot : Width of bottom flange (mm).

Btop : Width of top flange (mm).

Cw : Warping torsional constant (mm4).

fyf : Yield strength of flange (MPa).

fyw : Yield strength of web (MPa).

h : Total height of section (mm).

Ix : Second moment of area about major axis (mm4).

Iy : Second moment of area about minor axis (mm4).

J : St. Venant torsional constant (mm4).

ry : Radius of gyration about minor axis (mm).

Tb : Bottom flange thickness (mm).

Tt : Top flange thickness (mm).

Tw : Web thickness (mm).

Zcx : Compression flange section modulus about major axis (mm3).

Ztx : Tension flange section modulus about major axis (mm3).

Zplx : Plastic section modulus about major axis (mm3).

Zply : Plastic section modulus about minor axis (mm3).

Zy : Section modulus of entire section about minor axis (mm3).


BS 5950 - 1990:

Ag : Gross sectional area (mm2).

F : Applied axial load (kN).

M : Applied moment (kNm).

Ma : Maximum buckling moment in presence of axial load (kNm).

Mb : Lateral torsional buckling resistance moment (kNm).


Mc : Moment resistance in absence of axial load (kNm).



Pc : Compression resistance (kN).

py : Design strength of steel (MPa).

CSA S16.1 - M89.:










SABS 0162 - 1984:

f’cr : 0.6 times the Euler buckling stress (MPa).

Pc : Allowable axial compressive stress (MPa).

Pco : Maximum allowable axial compressive stress (MPa).

Pmc : Allowable compressive bending stress (MPa).

Pmco : Maximum allowable compressive bending stress (MPa).

σc : Average axial compressive stress (MPa).

σmc : Maximum compressive bending stress (MPa)

ω : Coefficient allowing for varying bending moment.

SABS 0162 - 1993:











Design parameters Various design parameters need to be set when designing a plate girder:

Effective lengths

The effective length of a member depends on the degree of restraint to be expected at each end of the member. The program assumes that the effect of axial compression is relatively small and hence uses the full bending capacity for bending about the major axis.

However, the program allows you to specify positions of restraints for lateral torsional buckling of the compression flange. You can apply a different effective length factor to each unsupported length, e.g. different factors for a cantilever end and internal continuous lengths.

Guidelines given in the codes include:






Bending moment factors

A flexural member’s lateral torsional behaviour is influenced by the shape of its bending moment diagram. This phenomenon is acknowledged by the design codes through their introduction of special design factors:

• BS 5950-1990: The equivalent uniform moment and slenderness correction factors, m and n, may not be less than 0.43 and 0.65 respectively.

• CSA S16.1 - M89: The equivalent uniform bending moment, ω1, may not be less than 0.4 and the moment gradient factor, ω2, may not be higher than 2.5.

• SABS 0162-1984: The values of the coefficient for varying bending moment, ω, may not be less than 0.4. For members subjected to sway, ω should not be taken less than 0.85.


The program automatically calculates the above factors and restrict their values to the minimum and maximum values specified.


Input

Design input comprises five categories:

• General: Design parameters, supports and axial load.

• Sections: Dimensions and material properties of section webs and flanges.

• Spans: Section variations and lengths along the length of the girder.

• Loads: Ultimate loads.

• Lateral supports: Compression flange supports.

General parameters Various design parameters, some of which depend on the code used, should be entered:

• The shape of a flexural member’s bending moment diagram influences its lateral torsional stability. The design codes use different design factors to accommodate this phenomenon. See page 17 for more details.

• The entered support width is used to calculate local buckling and crushing of the girder’s web at every support.

• Specify whether the program should calculate and add the girder’s own weight in the analysis.

• You can choose to make either end of the girder pinned (simply supported), fixed (built-in) or free (cantilevered).

• Enter an axial force, with a positive force denoting compression (kN or kip).

Note: Although the program allows you to enter an axial force, it does not check for buckling under axial load. The effect of axial compression is assumed to be so small as not to cause a reduction in the moment capacity for bending about the major axis.

Sections You can define a variety if I-section by entering the dimensions for the web and top and bottom flanges. If different grades of steel are used for the flanges and web, you should enter the appropriate yield strengths for each. Each section should be given a unique number for easy reference when defining the girder.


Spans The plate girder is entered as one more continuous segments. Up to twenty segments may be defined by entering the following values in the Section Lengths input table:

• Length: The length of a segment (m or ft). Segment lengths are added to the right hand side of the girder.

• Section Left/Right: Section numbers to be used at left and right ends of a segment. You can define a tapered section by specifying different section numbers for the left and right ends.

Note: CSA S16.1 - M89 and SABS 0162 - 1993 do not cover the design of tapered sections. When designing such elements, the program gives the option to use the weakest portion of such elements or to design of them using the approach given by BS 5950 - 1990.

Loads Applied loads may comprise distributed loads, point loads and moments. Positive forces and moments are taken to work downward and anti-clockwise respectively:

Wleft : Distributed load intensity (kN/m or kip/ft) applied at the left-hand starting position of the load. If you do not enter a value, the program will use a value of zero.

Wright : Distributed load intensity (kN/m or kip/ft) applied on the right-hand ending position of the load. If you leave this field blank, the value is made equal to Wleft, i.e. a uniformly distributed load is assumed.

P : Point load (kN or kip).

M : Moment (kNm or kipft).

a : The start position of the distributed load, position of the point load or position of the moment (m or ft). The distance is measured from the left-hand edge of the girder. If you leave this field blank, a value of zero is used, i.e. the load is taken to start at the left-hand edge of the beam.

b : The end position of the distributed load, measured from the start position of the load (m or ft). Leave this field blank if you want the load to extend up to the right-hand edge of the girder.


Note: Applied forces are taken to be design loads at ultimate limit state. For allowable stress design according to SABS 0162 - 1984, you should enter working loads.

Lateral supports Specify the positions of lateral support by entering the unsupported lengths. A unique effective length factor can also be entered for each length. Refer to page 174 for more details.

Note: The program always draws the specified lateral supports on the top flange. During the analysis, however, these positions are taken to define lateral supports of the compression flange, whether it is the top or bottom flange that is actually in compression.


Viewing analysis output

The analysis output can be viewed graphically. To view the detailed design calculation, select the Calcsheets page.

You can view the following results and use the mouse to read values from the diagrams:

• The deflected shape of the plate girder.

• Ultimate limit state bending moment diagram. The bending moment diagram is drawn on the tension face of the girder.

• Ultimate limit state shear force diagrams.

• Bending stresses at ultimate limit state. The stresses in the top and bottom flanges are shown in red and yellow respectively.

• The shear stresses at ultimate limit state together with the shear capacity for various web stiffener spacings. The actual stresses are shown in red and the shear capacities in blue.


Calcsheet

The design results of all tasks are grouped on a calcsheet for printing or sending to Calcpad. The calcsheets include a Data File for easy recalling of the analysis from Calcpad.

The design output shows the complete interaction formulae, with the zero values for bending moments about the minor axis. If required, the output equations can be edited to include bending about the minor axis. To edit an equation, select it in the calcsheet, right-click it and choose Edit.

Recalling a data file You can later recall the design by double-clicking the Data File object in Calcpad. Because a data file is embedded in the calcsheets sent Calcpad and saved as part of a project, you normally will not need to explicitly save your plate girder input using the Save command on the File menu as well.


Steel Connection Design 5-1

Chapter

Steel Connection Design

The steel connection design modules can be used for design of common welded and bolted steel connection.

Steel Connection Design 5-2

Quick Reference

Steel Connection Design using PROKON 5-3 Base Plate Design 5-5 Moment Connection Design 5-15 Hollow Section Connection Design 5-24 Shear Connection Design 5-Error! Bookmark not defined. Simple Connection Design 5-43

Steel Connection Design using PROKON 5-3

Steel Connection Design using PROKON

The PROKON suite includes several design modules for typical steel connections.

Shear connections Bolt groups and weld groups can be designed for eccentric in-plane shear.

Moment connections The following types of moment transmitting connections can be designed:

• Stiffened and unstiffened column base plates.

• Bolted and welded beam-column connections with or without haunches.

• Bolted or welded apex connections with or without haunches.

Axial force connections Welded hollow section connections can be designed for typical trusses, included triangulated space trusses.

Simple connections Simple beam to column connections that do not transmit moments:

• Web angle cleat connections.

• Flexible end plate connections.

• Fin plate connections.

Steel Connection Design using PROKON 5-4

Base Plate Design 5-5

Base Plate Design

The Base Plate Design module designs column base plates subjected to axial force and bi-axial moment. Both stiffened or unstiffened base plates can be designed. Base plates can bear on concrete or grout or can be supported on studs. Detailed drawings can be generated for editing and printing using the PROKON Drawing and Detailing System, Padds.



A brief discussion of the application of the theory is given below.

Design scope and assumptions The program can analyse column base plates that carry axial force and bi-axial moment. The following assumptions are made:

• The effective applied column force and moment is applied to the base plate as a point load in the flanges and a uniform distributed load in the webs of the approximated section.

• The application of the axial force as uniform distributed load in the webs serves as a mechanism to model the stiffening effect of the webs on the base plate.

• The case of bi-axial bending is simplified by transforming the moments to an effective design moment about one axis. Given the interaction between the base plate and the concrete bearing surface, the clauses of the concrete design codes for bi-axially bent concrete columns are deemed reasonable for this purpose.

• The base plate is analysed as a beam on an elastic support. The resulting concrete bearing stresses or stud forces are applied to the base plate during its analysis.

• Unstiffened base plates are analysed using elastic theory. A rectangular perimeter that encloses the column cross-section is considered and the bending stress in the base plate evaluated on each of its four sides. The required base plate thickness is calculated by limiting the bending stress on each of the lines that extend from edge to edge and passing over a side of the rectangle.

• Stiffened base plates are analysed using yield line theory. Since this is an upper bound method, allowable stresses are reduced by 20%.

• The interaction between the base plate and supporting concrete or grout layer is taken in accordance with the relevant code. When using BS 5950 - 1990, the parabolic stress-strain relationship given in BS 8110 - 1997 is used. Similarly, the parabolic relationship given by SABS 0100 - 1992 is used when designing the base plate using SABS 0162 - 1993 and CSA A23.3 – M89 for CSA S16.1 - 1989. In the case of allowable stress design to SAB 0162 - 1984, a linear stress-strain relationship is assumed.


Design codes The program designs axially loaded steel members according to the following design codes:

• BS 5950 - 1990.

• CSA S16.1 - M89.





a1 : Distance from the left edge of the base plate to the centre line of the bolts (mm).

a2 : Distance from the right edge of the base plate to the centre line of the bolts (mm).

a3 : Distance from the bottom edge of base plate, as shown on the screen, to the centre line of the bolts (mm).

a4 : Distance from the top edge of base plate, as shown on the screen, to the centre line of the bolts (mm)

bg : Bolt grade, e.g. 4.8.

B : Width of the column flange (mm).

D : Overall depth of the column (mm).

fcu : Cube strength of bedding concrete or grout (MPa).

L : Length of the base plate (mm).

L1 : Distance from the left edge of the base plate to the column flange (mm).

Studs : Enter ’Y’ if the bolts are used as studs, i.e. the base plate transmits all tension and compressions forces to the bolts. Enter ’N’ to transmit compression forces to the bedding concrete or grout.

W : Width of the base plate (mm).

W1 : Distance from the top edge of the base plate, as shown on the screen, to the corner of the column flange (mm).



C : Design compression force in the connection (kN).

T : Design tensile force in the connection (kN).

BS 5950-1990:

Pu : Ultimate design axial force in the column (kN). A positive value is taken as a downward force and negative value as an uplift force.

Mux : Ultimate design column moment applied about the X-axis (kNm).

Mux : Ultimate design column moment applied about the Y-axis (kNm).

Ys : Yield strength of steel (MPa).

Us : Ultimate strength of weld (MPa).

SABS 0162 - 1984:

P : Working design axial force in the column (kN). A positive value is taken as a downward force and negative value as an uplift force.

Mx : Working design column moment about the X-axis (kNm).

My : Working design column moment about the Y-axis (kNm).

fy : Yield strength of steel (MPa).

fw : Strength of weld (MPa).

CSA S16.1 - M89 and SABS 0162 - 1993:

Pu : Ultimate design axial force in the column (kN). A positive value is taken as a downward force and negative value as an uplift force.

Mux : Ultimate design column moment applied about the X-axis (kNm).

Mux : Ultimate design column moment applied about the Y-axis (kNm).

fy : Yield strength of steel (MPa).

fuw : Ultimate strength of weld (MPa).


Input

Define the beam and column connection geometry by entering the relevant information in the input table.

Column dimensions To read a column section from the section database, select the section type and choose a profile. For non-standard sections such as plate girders, you can enter the relevant dimensions.

Tip: To move the column to the centre of the base plate, use the Centralise Column function.

Forces acting on the connection Enter the forces transmitted from the column to the base plate using the sign conventions given in the list of symbols. The entered forces are multiplied by the entered load factors to obtain the design forces.


Special configurations You can model some special configurations:

• The bolts can be moved inside the column flanges by sufficiently increasing the values of a1 and a2.

• Use a negative column load to model an uplift force.

• The input table allows you to change the bolts to studs, i.e. transfer the column loads in the bolts rather than support the plate on the bedding concrete.


Design

The base plate connection is designed twice, with and without plate stiffeners.

Calculation of design forces acting on the connection The entered column moments are converted to an effective moment about one axis. The moment and axial force is then applied to the base plate via the column flanges. For a design moment about the X-axis, a point load is applied at each of the two column flanges. If the design moment works about the Y-axis, a trapezium-shaped distributed force is applied over the width of the flanges.

Analysis of the base plate In the case of the base plate bearing on concrete or grout, the plate is analysed as a beam on elastic foundation. The resulting bearing stresses are then used to calculate the moment in the base plate and the base plate thickness. This approach is slightly conservative due to stiffening effect of the column web being neglected.


The unstiffened base plate thickness is calculated using normal elastic theory. For a stiffened base plate, however, the required plate thickness is determined using yield line theory. If tensile forces are dominant, the number of bolts used also influences the plate thickness.

Analysis of the bolts In the case of the base plate bearing on the concrete or grout, the bolts are designed to resist tensile forces only. For the case where the bolts are used as studs, the bolts are designed to resist the full compressions and tension forces. It is then assumed that there is no bearing stress on the concrete or grout.


Calcsheets

The base plate connection design output can be grouped on a calcsheet for printing or sending to Calcpad. Various settings can be made with regards to the inclusion of design results and pictures.


Recalling a data file If you enable the Data File option before sending a calcsheet to Calcpad, you can later recall it by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the connection design module as well.


Drawing

Detailed drawings can be generated for designed connections. Drawings can be edited and printed using Padds.

Generating a drawing Based on your initial input and the design results, initial values are chosen for the dimensions. Change the values to suite your special requirements.

Required information:

• Drawing file name: Name of the Padds drawing file.

• Drawing scale to use.

• Connection properties:

• Plate thickness.

• Stiffener size.

• Weld sizes.

• Bolt and hole sizes and quantities.

Press Generate to create a Padds drawing with the entered settings.

Moment Connection Design 5-15

Moment Connection Design

The moment connection design modules are suitable for the design of the following connections:

• Beam-column connection, BeamCol: Beam connected to the flange of a column.

• Apex connection, Apex: Symmetrical beam apex with end plates.

The connections incorporate beams and columns made of I and H-sections.



The following text gives a brief background of the application of the design codes.

Design scope The moment connection design modules can analyse connections that transmit shear, moment and axial force. Only forces in the plane of the connection are considered, i.e. vertical shear, axial compression or tension and in-plane moment. The connections may be bolted or welded.

The following assumptions are made:

• The centre lines of the connecting beams or beam and column are in the same plane.

• All bolt holes are normal clearance holes.

• Bolts have threads in their shear plane.

• Connections are deep enough for each section’s flanges to resist the prevailing compressive and tensile forces.

• Compressive forces in the flanges and stiffeners are transmitted through the welds and not through bearing.

The following additional assumptions apply to BeamCol:

• Any axial force in the column is ignored.

• Longitudinal and transverse welds in the web plates are full size butt welds.

Codes of practice The following codes are supported:

• AISC - 1993 LRFD.

• BS5950 - 1990.

• CSA S16.1 - M89.


• SABS0162 - 1984 (allowable stress design).

• SABS0162 - 1993 (limit state design).

Units of measurement Both Metric and Imperial units of measurement are supported.


Sign conventions The loads are defined as the forces transmitted by the right-hand side beam onto the connection:

• A positive axial force is taken as a compression force.

• A positive moment corresponds to a tensile force in the top flange of the beam.

• Downward shear is taken as positive.

Tip: Positive loads on the connection correspond to the directions of forces in a typical single bay portal frame subjected to dead and live load.

List of symbols Where possible the same symbols are used as in the design codes. The meanings of the symbols are clear from their use in the design output.

Analysis of bolted moments connections When moments are transferred by bolted connections the bolts are loaded in tension (and shear). The programs allow you to use an elastic or plastic method of analysis for determining the bolt forces:

• With an elastic analysis, the bolt furthest from the compression flange will have the largest tensile force. Forces load will reduce linearly in bolts closer to the compression flange.

• In the case of a plastic analysis, all the bolts have the same force.

Prying action

In moment connection, prying action can be prevalent. The prying forces and method of failure depend on the layout of the design, the thickness of the plate or flange in question and the strength of the bolts.

A yield line analysis method is used to calculate three resistance values for each relevant portion of the connection:

• Plate yielding at the web and the bolts.

• Plate yielding at the web and bolt failure.

• Bolt failure only.

The smallest of the three resistance values is taken to be the ultimate resistance.


Input

The moment connection design modules use a similar procedure for data entry:

• Members: Set the connection type and properties of the beams or beam and column.

• Setting: Select the connection type and main design parameters.

• Loads: Enter the loads applied to the connection.

Members Define the type of connection and the design parameters:

• Define the connection type by selecting an end plate configuration, e.g. no end plate, end plate flush at the top and bottom of the beam or extending at the tope and/or bottom.

• Beam and column designations.

• Inclination of the beam.

• Haunch depth and length. If either value is zero, no haunch is used.

Settings

Use Settings to set the bolt, weld and member material properties:

• Select between elastic and plastic analysis of bolts in tension. The analysis mode determines the distribution of the bolt forces. See page 5-17 for detail.

• Enter a bolt type, grade and diameter. For high strength friction grip bolts, additional information needs to be supplied with regards to the analysis method.

• Enter the strength properties of the beam, column and connection members.

• Specify the weld strength.

Note: If you need to modify the available bolt grades or bolt sizes, edit the General Preferences from the Settings menu in Calcpad.


Loads Enter any number of load cases. For each load case:

• Use a maximum of six characters to enter a descriptive load case name or load case number, e.g. ’Dead’, ’DL + LL’ or ’1’.

• Specify the axial force, shear force and moment that the right-hand side beam exerts on the connection.

• The SLS factor is divided into the entered ULS loads to obtain service loads.

Note: All entered loads should be ULS loads. The corresponding SLS loads are obtained by dividing the entered ULS loads by the SLS factor. The SLS factor should thus be set equal to the relevant ULS load factor divided by the SLS load factor.


Design

The design table lists all variable dimensions and parameters of the connection. A value for any property in the table can be calculated using the Optimise function. You can also selectively fix values for any individual properties to suite your preferences:

• Select values for all properties that should have specific values. To obtain a specific bolt layout, for example, enter preferred values for the bolt offsets.

• Set the values of all other properties to "Optimise".

• Click Optimise to calculate values for the latter.

Tip: For a table summarising the design results, go to the Calcsheet page.


After optimisation, you should evaluate each of the values calculated by the program. You are then free to refine the results by selectively entering more appropriate values. After adjusting some values, you may wish to optimise some of the other values again.

Note: Several valid design solutions are possible for any particular connection. The optimised results calculated by the programs should be regarded as one such solution.


Calcsheet

Open the Calcsheet page to view the detailed design calculation. The information on the can be printed or sending to Calcpad. Various settings can be made to include input data, tabular design summaries and the complete design calculations.


Recalling a data file The Data File can be included when sending a calcsheet to Calcpad. You can later recall the data file by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the connection design module as well.


Drawing

Detailed drawings can be generated for designed connections. Drawings can be edited and printed using Padds.

Printing or saving a drawing A drawing is displayed using the dimensions of the final design. To save or print the drawing to disk, use the buttons next to picture. Drawings can be saved a variety of formats, including Padds and DXF formats.

Hollow Section Connection Design 5-24

Hollow Section Connection Design

The Hollow Section Connection Design module does a complete design of welded structural hollow section connections. The connecting members may transmit axial force and can be circular, square or rectangular hollow sections. I-sections and H-sections can also be used for the main chord.



The program designs structural hollow section connections that transmit axial forces. Various connection layouts can be designed. These include K, T, N, X, and Y joints and combinations thereof.

Design codes The program designs according to recommendations given in Annex K of Eurocode 3 - 1992.

Symbols Where possible, the same symbols and sign conventions are used as in the design codes:

Section dimensions

bi : Width of a section (mm or inches).

hi : Height of a section (mm or inches).

hw : Web height of an I-section or H-section (mm or inches).

i : Section number. The main chord is identified by i = 0 and the left, right and centre chords by i = 1 to 3 respectively.

ro : Radius between the web and flange of an I-section or H-section (mm or inches).

ti : Thickness of a section, i.e. wall thickness of a hollow section or flange thickness of an I-section or H-section (mm or inches).

tw : Web thickness of an I-section or H-section (mm or inches).

Joint geometry

g : The clear gap between bracing as measured member on the chord surface (mm or inches). A negative value denotes an overlap.

Symmetry : Enter ’Y’ to make an X-joint symmetric, i.e. mirrored about the main chord. If you enter ’N’, bracing members continue along their axes to the other side of the main chord.

X-joint : Enter ’Y’ to put bracing elements on both sides of the main chord, i.e. an X-joint. This option can only be used in combination with K, N and T joints where a circular hollow section is used as the main chord. Enter ’N’ for bracing members on one side of the main chord only.


φ : Out-of-plane separation angle between two sets of bracing members (°). The angle must lie between 60° and 90°. This option is useful when modelling joints in triangulated trusses. If this option is used, all setting relating to X-joints are ignored. Leave this field blank if you do not want to use this option. The option can only be enabled when a circular hollow section is used as main chord.

θ1 : Angle between the main chord and the left bracing member (°). The angle must be between 30° and 90°.

θ2 : Angle between the main chord and the right bracing member (°). The angle must be between 30° and 90°.

θ3 : Angle between the main chord and the centre bracing member (°). The angle must be between 30° and 150°. The angle must also by greater than θ1 and smaller than (180° - θ3).

Forces and stresses

Es : Modules of elasticity of steel (GPa or Mpsi).

fy : Yield strength of main chord or bracing members (MPa or ksi).

N0 : Ultimate axial force in the main chord (kN or kip). A positive value denotes a compression force.

N1 : Ultimate axial force in the left bracing member (kN or kip). A positive value denotes a compression force.

N2 : Ultimate axial force in the right bracing member (kN or kip). A positive value denotes a compression force.

N3 : Ultimate axial force in the centre bracing member (kN or kip). A positive value denotes a tensile force.

Units of measurement Both Metric and Imperial units of measurement are supported. When changing from one system of units to another, the program automatically converts all input data.


Input

The definition of the connection requires you to enter geometrical and loading data.

Chord and bracing sections Click Section Database to read a chord or bracing section from the section database. The main chord can be an I-section, H-section or a circular, square or rectangular hollow section. You can use circular, square or rectangular hollow sections as bracing members.

The following general guidelines apply when defining bracing members:

• You should define at least one bracing member.

• A single bracing member should be entered as either the left or right bracing member.

• The centre bracing member can be defined only after defining both the left and right bracing members.

• X-joints can be defined only if the main chord is a circular hollow section.

• X-joints can be made symmetric by enabling the relevant option in the table.

• A separation angle for a 3D joint can only be used if the main chord is a circular hollow section.

Tip: Use the 3D rendering option to view and rotate the connection in 3D.


Forces acting on the connection Enter the forces in each member using the sign conventions displayed in the picture. With the exception of the right bracing member, positive forces work in compression towards the centre of the connection.


Design

The design checks are performed as prescribed in the code, including the following:

• Geometrical evaluation of the connection to ensure compliance with the design codes.

• Checking the main chord for plastification.

• Checking punching shear of the main chord.

• Design of welds.


Calcsheet

The connection design output is given on a calcsheet. You can choose to print the information immediately or rather send it to Calcpad.

Tip: The Data File embedded in the calcsheet can be used for easy recalling of the design from Calcpad.

Recalling a data file The Data File is automatically included when sending a calcsheet to Calcpad. You can later recall the data file by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the connection design module as well.

Shear Connection Design 5-31

Shear Connection Design

The shear connection design modules are suitable for the design of the following connections:

• Bolt Group Design, Boltgr: Eccentrically loaded bolt groups.

• Weld Group Design, Weldgr: Eccentrically loaded weld groups.



When a bolt group or weld group is loaded in its plane and the load does not work through the centroid of the group, additional shear forces are caused in the bolts or welds. The shear connection design modules calculate the maximum resistance of bolt and weld groups.

The modules also determine the smallest bolt or weld size that can be used to resist an in-plane force with arbitrary orientation. In the case of bolt groups, both the cases of single and double shear can be considered.

The groups are analysed using either linear or non-linear strength relationships.

Design codes The programs support the following design codes:

• BS 5950 - 1990.

• CSA S16.1 - M89.





Bolt group geometry

d : Bolt Size.

a1 : Horizontal bolt spacing

a2 : Vertical bolt spacing

nr : Number of rows of bolts in the group.

nc : Number of columns.

Material properties

fu : Ultimate strength of steel or weld.

fy : Yield strength of steel.


Applied loads

F : Force.

x : Force horizontal eccentricity

y : Force vertical eccentricity

β : Force angle

Units of measurement Both Metric and Imperial units of measurement are supported. In addition, you can also choose between units within the selected system, e.g. between mm and cm.

Analysis principles The program designs bolt groups and fillet weld groups subjected to eccentric shear using either linear or non-linear strength relationships.

Linear analysis

Eccentrically loaded fastener groups are usually analysed by considering the group areas as an elastic cross-section subjected to direct shear and torsion. Assuming elastic behaviour, the group’s centre of rotation is taken as the group’s centroid. The deformation of each fastener is then assumed proportional to its distance from the assumed centre of rotation.

The elastic method has been popular because of its simplicity and has been found conservative. Salmon and Johnson1 quotes the ratio between actual strength and service loads to be in the range of 2.5 to 3.0.

Non-linear analysis

The non-linear method, also called plastic analysis or instantaneous centre of rotation method, assumes that the eccentric load causes a rotation as well as a translation effect on the fastener group. The translation and rotation is reduced to a pure rotation about a point defined as the instantaneous centre of rotation.

Similar to the linear method, the deformation of each fastener is taken proportional to its distance from the instantaneous centre of rotation. The load in each fastener is however

1 C. G. Salmon and J. E. Johnson, "Steel Structures, Design and Behaviour", Third Edition (1990), Harper Collins Publishers.


determined using the non-linear strength expression proposed by Fisher2 and used by Crawford and Kulak3:

( ) 55.0101 ∆−−= eRR ulti

The relationship assumes a bearing-type connection and ignores slip. The coefficients 10 and 0.55 were experimentally determined. For the given experimental setup, the maximum deformation, ∆, at failure was about 0.34 inches (8.6 mm).

Salmon and Johnson1 conclude that the plastic analysis method is the most rational approach to obtain the strength of eccentric shear connections.

Application of the non-linear strength relationship

For the purpose of its application in the connection design modules, the strength relationship has been normalised and rewritten:

( ) 55.04.31018.1 ∆−−= eRnorm

The capacity of a fastener group is governed by the yield of the fastener furthest from the instantaneous centre of rotation.

Taking the deformation at that point as unity, the normalised deformations for the other fasteners are determined using linear variance. The force of each fastener is calculated using the strength relationship.

Non-linear analysis of weld groups

Although the load-deformations characteristics of fillet welds depend on the direction of loading, current design codes generally use a lower bound approach based on the longitudinal strength, irrespective the actual loading direction. An expression developed by Lesik and

2 J. W. Fisher, "Behaviour of Fasteners and Plates with Holes", Journal of the Structural Division, ASCE, 91, STD6 (December 1965). 3 S. F. Crawford and G. L. Kulak, "Eccentrically Loaded Bolted Connections", Journal of the Structural Division, ASCE, 97, ST3 (March 1971).


Kennedy4 can be used to determine the ultimate strength of fillet welds loaded in any direction.

Assuming that the resistance for compression and tension-induced shear is the same, the resistance of a weld element for the calculated angle of loading is given by:

( )( )0.1sin5.0 5.1 += θθ uRR

where

Ru = Ultimate strength of a fillet weld loaded with longitudinal shear

Rθ = Resistance of a fillet weld when the loading angle equals θ.

The relationship was determined empirically and implies the resistance in a weld element will vary between 1.0⋅Ru for longitudinal shear and 1.5⋅Ru for transverse shear.

Application of non-linear method

The program divides the weld group into a discrete number of finite weld elements. When performing a non-linear analysis, the instantaneous centre of rotation is determined through iteration. The following criteria are used:

• The Lesik and Kenedy equation is used to determine the resistance of each weld element for the relevant load direction.

• The deformation in an element is taken to vary linearly with the distance from the instantaneous centre of rotation. At ultimate limit state, the element furthest from the centre of rotation is assumed to experience the maximum deformation.

• The ultimate resistance of each element for longitudinal shear is determined using the non-linear strength relationship explained above.

4 D. F. Lesik and D. J. L. Kennedy, "Ultimate Strength of Eccentrically Loaded Fillet Welded Connections", Structural Engineering Report 159, Department of Civil Engineering, University of Alberta


Input

The definition of bolt groups and weld groups follow the same basic pattern. However, the geometry of weld groups is entered using a slightly more complex method of polygon definition.

Defining bolt groups A bolt group analysis requires the following input:

• Analysis method.

• Number of shear planes, i.e. single or double shear.

• Number of rows and columns of bolts.

• Horizontal and vertical spacing of the bolts.

• Applied force, its orientation and offsets.

Defining weld groups A weld group definition has the following components:

• Analysis method.

• Material strengths.

• In-plane force, angle and offsets.

• Weld geometry.

The weld group input table

A weld group’s geometry is defined by entering one or more shapes in the input table. A shape may comprise straight lines and arcs or may be a circle. When more than one shape is entered, the shapes will accumulate and form one weld group.

To be able to enter a weld, you should understand the use of the input table:

• The Code column is used for categorise the data that follows in the next columns:

’+’ : The start of a new weld. An absolute reference coordinate must be entered in the X/Radius and Y/Angle columns.

Blank : Indicates a line drawn with relative coordinates.

’L’ : Indicates a line drawn using polar coordinates.


’A’ : An arc that continues from the last line or arc. The arc radius and angle are entered in the X/Radius and Y/Angle columns respectively. The angle is measured anti-clockwise from the previous line or arc end point.

’B’ : Sets the bearing, or starting angle, for the next entity, likely an arc.

’C’ : A circle with the radius entered in the X/Radius column.

Note: If the Code column is left blank, relative coordinates are used.

• The X/Radius and Y/Angle columns are used for entering coordinates, radii and angles:

X : Absolute or relative X-coordinate. Values are taken positive to the right and negative to the left.

Radius : Radius of a circle or an arc.

Y : Absolute or relative Y coordinate. Values are taken positive upward and negative downward.

Angle : Angle that an arc is extending through.

Note: If the X/Radius or Y/Angle column is left blank, a zero value is used.


Weld group definition

The definition of each portion of a weld group has three basic components:

• A reference coordinate which gives the starting point of a weld or the centre of a circle. In the Code column, enter a ’+’ to indicate the start of a new weld.

• One or more entries defining the weld's coordinates of lines and arcs or a circle’s radius.:

• Enter the absolute values of the reference coordinate in the X/Radius and Y/Angle columns.

• If the Code column is left blank, the coordinate is taken relative from the last point entered.

• Set the Code to '+' if you want to enter an absolute coordinate.

• The coordinate values are entered in the X/Radius and Y/Angle columns. A negative X or Y coordinate must be preceded by a minus sign. The plus sign before a positive X or Y coordinate is optional.

• A circular arc is defined by setting the Code to 'A' and entering the radius in the X/Radius column. The arc is then taken to extend from the end point of the last line or arc, starting at the angle that the previous line or arc ended and extending through the angle specified in the Y/Angle column. To set the bearing, or starting angle, of an arc use a 'B' in the Code column followed by the angle in the Y/Angle column.

• Define a circle by setting the centre point using the Code '+' described above. On the next line enter the Code to 'C' and the radius in the X/Radius column.

• The weld size.

Weld generation

Click the 'standard' shapes for quick generation of welds. Enter the required dimensions and orientation angle. Press Add to input to append the shape to the bottom of the table. The default values of X, Y and ß are set to the ending values of the last weld segment.


Design

Shear distribution in bolt groups and weld groups are calculated in similar ways:

Calculation of design shear forces in bolt groups A simple procedure is followed during linear analysis:

• The applied force causes an equal force in each of the bolts parallel to the force.

• The rotational shear force in each bolt is taken proportional to the distance to the centroid.

Non-linear analysis requires an iterative procedure:

• An arbitrary rotational centre is chosen.

• The strain of each bolt is proportional to its distance from the centre.

• The force on each bolt is calculated assuming the non-linear strength model explained form page 5-33.


• Equilibrium of external and internal forces is considered and the rotational centre adjusted.

• This procedure is repeated until convergence is achieved.

Calculation of design shear stresses in weld groups Assuming linear variation, rotational shear stresses in a weld group is calculated as follows:

• The centroid of the weld group is calculated.

• The rotational shear force in each segment of a weld is taken proportional to its distance from the centroid.

Non-linear analysis requires an iterative procedure:

• An arbitrary rotational centre is chosen.

• The strain in each segment of the weld is taken proportional to its distance from the centre of rotation.

• The force on each segment is calculated assuming the non-linear strength relationship explained from page 5-33.

• External and internal forces are compared and the centre of rotation adjusted to improve equilibrium.

• This procedure is repeated until convergence is achieved.


Calcsheet

The connection design output can be grouped on a calcsheet for printing or sending to Calcpad. Various settings can be made to include input data, tabular design summaries etc.


Recalling a data file The Data File is automatically included when sending a calcsheet to Calcpad. You can later recall the data file by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the connection design module as well.


Simple Connection Design 5-43

Simple Connection Design

The simple connection design modules are suitable for the design of the following connections:

• Double Angle Cleat Connection Design, Cleat: Web cleat connections.

• End Plate Connection Design, Endplate: Flexible end plate connections.

• Fin Plate Connection Design, Finplate: Fin plate connections.



The following text gives a brief background of the application of the design codes.

Design scope The simple connection design modules can analyse connections that transmit end shear and axial force only. A designed connection has negligible resistance to rotation and is thus incapable of transmitting significant moments at ultimate limit state.

The following assumptions are made:

• The centre lines of the beam and column are in the same plane.

• The connection transmits end shear only.

• Bolts have normal clearance holes.

• All bolts have threads in their shear planes.


• AISC - 1993 LRFD.

• BS5950 - 1990.

• CSA S16.1 - M89.


• SABS0162 - 1984 (allowable stress design).

• SABS0162 - 1993 (limit state design).


Sign conventions All applied shear forces are entered as loads in the beam’s local axes:

• A positive axial force is taken as a compression force.

• A downward shear force is taken as positive.


List of symbols Where possible the same symbols are used as in the design codes. The meaning of the symbols should be clear from their use in the design output.

Analysis of bolts in shear Bolt groups in shear can be analysed using a linear or non-linear strength relationship. Refer to page 5-33 for a detailed explanation of the analysis methods.


Input

The simple connection design modules use a similar procedure for data entry:

• Settings: Select the connection type and main design parameters.

• Members: Specify the properties for the beam and column.

• Connection: Define the layout of the fasteners.

• Loads: Enter the loads applied to the connection.

Members Define the connection orientation and profile to use for each member:

• Select a connection type by clicking the Member orientation buttons.

• The column and the beam can be set to I or H-sections.

• The definition of the connecting member depends on the type of connection:

• Double angle cleat connection: Select an angle section and enter the cleat length.

• Fin plate and end plate connections: Enter a plate height, width and thickness.

• Define the relative element positions by entering the spacing between the column and beam and the vertical position of the cleat or connecting plate.

Tip: Click the Auto size and Auto spacing buttons for quick input of workable dimensions.

Design parameters Select the connection shear analysis method and define the fastener and member material properties:

• Select between linear and non-linear analysis of bolts in shear. For a detailed explanation of the analysis methods, refer to page 5-33.

• Enter a bolt type, grade and diameter. For high strength friction grip bolts, additio-nal information needs to be


supplied with regards to the analysis method.

• Enter the strength properties of the beam, column and connection members.

Connections The layout of the bolts on the connecting member is defined by entering their number and spacing.

In the case of angle cleats, the connections to the beam and column are defined indepen-dently.

Tip: Click the Auto size and Auto spacing buttons to quickly input a workable bolt layout.

View connection To verify that you have defined the connection geometry as you intended, you can view it from several angles:

• Dimensioned elevations are an easy way to check bolt spacings and the spacing between the members.

• Use the 3D view to verify the overall layout and check that bolts are far enough from webs and flanges. You can rotate a 3D view and use the View point and View plane controls as described in Chapter 2.


Loads Enter any number of load cases. For each load case:

• Use a maximum of six characters to enter a descriptive load case name or load case number, e.g. ’Dead’, ’DL + LL’ or ’1’.

• Specify the end shear forces by entering the axial force and shear force in the beam.

• When designing high strength friction grip bolts at serviceability limit state, also enter the relevant service loads.


Calcsheet

Open the Calcsheet page to design the connection. The design output is grouped on a calcsheet for printing or sending to Calcpad. Various settings can be made to include input data, tabular design summaries and the complete design calculations.

To view the individual bolt forces, open the Bolt forces page.


Recalling a data file The Data File can be included when sending a calcsheet to Calcpad. You can later recall the data file by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the connection design module as well.


Concrete Design 6-1

Chapter

Concrete Design

The concrete design modules can be used for the design of reinforced and pre-stressed concrete beams and slabs, columns, column bases and retaining walls.

Concrete Design 6-2

Quick Reference

Concrete Design using PROKON 6-3 Continuous Beam and Slab Design 6-5 Pre-stressed Beam and Slab Design 6-9 Finite Element Slab Analysis 6-9 Rectangular Slab Panel Design 6-9 Column Design 6-9 Retaining Wall Design 6-9 Column Base Design 6-9 Section Design for Crack width 6-9 Concrete Section Design 6-9 Punching Shear Design 6-9

Concrete Design using PROKON 6-3

Concrete Design using PROKON

Several concrete design modules are included in the PROKON suite. These are useful tools for the design and detailing typical reinforced and pre-stressed concrete members.

Beam and slab design The Continuous Beam and Slab Design and Pre-stressed Beam and Slab Design modules are used to design and detail reinforced and pre-stressed beams and slabs. Simplified design of flat slab panels is available through the Rectangular Slab Panel Design module. In contrast, the Finite Element Slab Design module is better suited for the design of slabs with more complicated geometries. Punching shear in flat reinforced concrete slabs can be checked with the Punching Shear Design module.

Column design Rectangular Column Design and Circular Column Design offer rapid design and detailing of simple short and slender columns. Columns with complicated shapes can be designed using the General Column Design module.

Substructure design Use the Column Base Design and Retaining Wall design to design and detail typical bases and soil retaining walls.

Section design Two modules, Concrete Section Design and Section Design for Crack width, are available for the quick design of sections for strength and crack width requirements.

Concrete Design using PROKON 6-4

Continuous Beam and Slab Design 6-5

Continuous Beam and Slab Design

The Continuous Beam and Slab Design module is used to design and detail reinforced concrete beams and slabs as encountered in typical building projects. The design incorporates automated pattern loading and moment redistribution.

Complete bending schedules can be generated for editing and printing using Padds.



The following text gives an overview of the theory and application of the design codes.

Design scope The program designs and details continuous concrete beams and slabs. You can design structures ranging from simply supported single span to twenty-span continuous beams and slabs. Cross-sections can include a mixture rectangular, I, T and L-sections. Spans can have constant or tapered sections.

Entered dead and live loads are automatically applied as pattern loads during the analysis. At ultimate limit state, moments and shears are redistributed to a specified percentage.

Reinforcement can be generated for various types of beams and slabs, edited and saved as Padds compatible bending schedules.

Design codes The following codes are supported:

• BS 8110 - 1985.

• BS 8110 - 1997.

• SABS 0100 - 1992.

Reinforcement bending schedules are generated in accordance to the guidelines given by the following publications:

• General principles: BS 4466 and SABS 082.

• Guidelines for detailing: ’Standard Method of Detailing Structural Concrete’ published by the British Institute of Structural Engineers.

Sub-frame analysis A two-dimensional frame model is constructed from the input data. Section properties are based on the gross un-cracked concrete sections. Columns can optionally be specified below and above the beam/slab and can be made pinned or fixed at their remote ends.

Note: No checks are made for the slenderness limits of columns or beam flanges.


Pattern loading At ultimate limit state, the dead and live loads are multiplied by the specified ULS load factors (see page 6-9). Unity load factors are used at serviceability limit state. The following load cases are considered (the sketch uses the load factors applicable to BS8110):

• All spans are loaded with the maximum design load.

• Equal spans are loaded with the maximum design ultimate load and unequal spans with the minimum design dead load.

• Unequal spans are loaded with the maximum design load and equal spans loaded with the minimum design dead load.Note: The case

where any two adjacent spans are loaded with maximum load

and all other spans with minimum load, as was the case with CP 110 - 1972 and SABS 0100 - 1980, is not considered.

The following are special considerations with pertaining to design using SABS 0100 - 1992:

• SABS 0100 - 1992 suggests a constant ULS dead load factor of 1.2 for all pattern load cases. In contrast, the BS 8110 codes suggest a minimum ULS dead load factor of 1.0 for calculating the minimum ultimate dead load. The program uses the more approach given by the BS 8110 codes at all times, i.e. a ULS load factor of 1.0 for minimum dead load and the maximum load factor specified for maximum dead load.

• The South African loading code, SABS 0162 - 1989, prescribes an additional load case of 1.5×DL. This load case is not considered during the analysis – if required, you should adjustment the applied loads manually. In cases where the dead load is large in comparison with the live load, e.g. lightly loaded roof slabs, this load case can be incorporated by increasing the entered dead load or increasing the ULS dead load factor. This adjustment applies to cases where 1.5×DL > 1.2×DL + 1.6×LL or, in other words, LL < 19%. Using an increased dead load factor of 1.4 instead of the normal 1.2 will satisfy all cases except where 1.5×DL > 1.4×DL + 1.6×LL or, in other words, LL < 6%×DL.


Moment redistribution Ultimate limit state bending moments are redistributed for each span by adjusting the support moments downward with the specified percentage. If the method of moment redistribution is set to ’optimised’, the design moments are further minimised by redistributing span moments upward as well.

Note: No moment redistribution is done for serviceability limit state calculations.

The moment envelopes are calculated for pattern loading and then redistributed using the procedures explained in the following text.

Downwards redistribution

The downward distribution method aims to reduce the hogging moments at the columns without increasing the sagging moments at midspan. The redistribution of moments and shear forces procedure is performed as follows:

1. The maximum hogging moment at each column or internal support is adjusted downward by the specified maximum percentage.

2. The corresponding span moments are adjusted downward to maintain static equilibrium. The downward adjustment of hogging moments above is limited to prevent any increase in the maximum span moments of end spans.

3. The shear forces for the same load cases are adjusted to maintain static equilibrium.


Optimised redistribution:

The optimised distribution procedure takes the above procedure a step further by upward distribution of the span moments. The envelopes for the three pattern load cases are redistributed as follows:

1. The maximum hogging moment at each internal support is adjusted downward by the specified percentage. This adjustment affects the moment diagram for the load case where the maximum design load is applied to all spans.

2. The relevant span moments are adjusted accordingly to maintain static equilibrium.

3. The minimum hogging moment at each internal support is subsequently adjusted upward to as close as possible to the reduced maximum support moment, whilst remaining in the permissible redistribution range. A second load case is thus affected for each span.

4. The relevant span moments are adjusted in line with this redistribution of the column moments to maintain static equilibrium.

5. For each span, the moment diagram for the remaining third load case is adjusted to as near as possible to the span moments obtained in the previous step. The adjustment is made in such a way that it remains within the permissible redistribution range.

6. Finally, the shear force envelope is adjusted to maintain static equilibrium.

7. The following general principles are applied when redistributing moments:

8. Equilibrium is maintained between internal and external forces for all relevant combinations of design ultimate load.

9. The neutral axis depth is checked at all cross sections where moments are redistributed. If, for the specified percentage of moment redistribution, the neutral axis depth is greater than the limiting value of (ßb−0.4)⋅d, compression reinforcement is added to the section to sufficiently reduce the neutral axis depth.

10. The amount of moment redistribution is limited to the specified percentage. The maximum amount of redistribution allowed by the codes is 30%.

Note: The exact amount of moment redistribution specified is always applied, irrespective of the degree of ductility of the relevant sections. Where necessary, ductility is improved by limiting the neutral axis depth. This is achieved by adding additional compression reinforcement.


Deflection calculation Both short-term and long-term deflections are calculated. No moment redistribution is done at serviceability limit state.

Elastic deflections

Short-term elastic deflections are calculated using un-factored SLS pattern loading. Gross un-cracked concrete sections are used.

Long-term deflections

Long-term deflections are determined by first calculating the cracked transformed sections:

1. The full SLS design load is applied to all spans to obtain the elastic moment diagram.

2. The cracked transformed sections are then calculated at 250 mm intervals along the length of the beam. The results of these calculations are tabled in the Crack files on the View output pages.

Note: The calculation of the cracked transformed section properties is initially based on the amount of reinforcement required at ULS. However, once reinforcement is generated for beams, the actual entered reinforcement is used instead. You can thus control deflections by manipulating reinforcement quantities.

Next, the long-term deflection components are calculated by numerically integrating the curvature diagrams:

1. Shrinkage deflection is calculated by applying the specified shrinkage strain. Unsymmetrical beams and unsymmetrical reinforcement layouts will cause a curvature in the beam.

2. The creep deflection is calculated by applying the total dead load and the permanent portion of the live load on the beam. The modulus of elasticity of the concrete is reduced in accordance with the relevant design code.

3. The instantaneous deflection is calculated by applying the transient portion of the live load on the transformed crack section.

4. The long-term deflection components are summed to yield the total long-term deflection.

Note: When calculating the curvatures for integration, elastic moments are used together with cracked transformed sections, which implies plastic behaviour. Although this procedure is performed in accordance with the design codes, the use of elastic moments together with cracked sections in the same calculation is a contradiction of principles. As a result of this, long-term deflection diagrams may show slight slope discontinuities at supports, especially in cases of severe cracking.


Calculation of flexural reinforcement The normal code formulae apply when calculating flexural reinforcement for rectangular sections and for flanged sections where the neutral axis falls inside the flange.

If the neutral axis falls outside the flange, the section is designed by considering it as two sub-sections. The first sub-section consists of the flange without the central web part of the section and the remaining central portion defines the second sub-section. The reinforcement calculation is then performed as follows:

1. Considering the total section, the moment required to put the flange portion in compression can be calculated using the normal code formulae. This moment is then applied to the flange sub-section and the required reinforcement calculated using the effective depth of the total section.

2. The same moment is then subtracted from the total applied moment. The resulting moment is then applied to the central sub-section and the reinforcement calculated.

3. The tension reinforcement for the actual section is then taken as the sum of the calculated reinforcement for the two sub-sections. If compression reinforcement is required for the central sub-section, it is used as the required compression reinforcement for the actual section.

Design and detailing of flat slabs When entering the input data for a flat slab, you should use its whole width, i.e. the transverse column spacing (half the spacing to the left plus half the spacing to the right). The program will then calculate bending moments and shear forces for the whole panel width.

When generating reinforcement, however, the program considers the column and middle strips separately. The program does the column and middle strip subdivision as suggested by the design codes. The procedure is taken a step further by narrowing the column strip and widening the middle strip to achieve a simpler reinforcement layout – a procedure allowed by the codes.

Initial column and middle strip subdivision

The flat slab panel is divided into a column strip and middle strip of equal widths and then adjusted to simplify reinforcement detailing:

1. The width of the column strip is initially taken as half the panel width. The total design moment is then distributed between the column and middle strips as follows:

Moment position Column strip Middle strip

Moment over columns 75% 25%

Moments at midspan 55% 45%


2. Reinforcement is calculated for each of the column and middle strips.

Adjusted column and middle strip subdivision

The design codes require that two-thirds of the column strip reinforcement be concentrated in its middle half. The codes also state that a column strip may not be taken wider than half the panel width, thereby implying that it would be acceptable to make the column strip narrower than the half the panel width.

To simplify the reinforcement layout and still comply with the code provisions, the program narrows the column strip and widens the middle strip. The widening of the middle strip is done as follows:

1. The middle strip is widened by fifty percent from half the panel width to three-quarters of the panel width.

2. The reinforcement in the middle strip is accordingly increased by fifty percent. Reinforcement added to the middle strip is taken from the column strip.

The column strip is subsequently narrowed as follows:

1. The column strip is narrowed to a quarter of the panel width.

2. As explained above, rein-forcement is taken from the column strip and put into the widened middle strip.

3. The remaining reinforcement is checked and additional rein-forcement added where necessary. This is done to ensure that the amount of reinforcement resisting hogging moment is greater than or equal to two-thirds of the reinforcement required for the original column strip.


Designing the slab for shear

The program considers the column strip like a normal beam when doing shear calculations. A possible approach to the shear design of the slab is:

• Consider the column strip like a beam and provide stirrups equal to or exceeding the calculated required shear steel.

• In addition to the above, perform a punching shear check at all columns.

Implications of modifying the column and middle strips

In applying the above modifications, the moment capacity is not reduced. The generated reinforcement will be equal to, or slightly greater, than the amount that would be calculated using the normal middle and column strip layout.

The above technique gives simplified reinforcement details:

• A narrower column strip is obtained with a uniform transverse distribution of main bars and a narrow zone of shear links.

• Detailing of the adjoining middle strips is also simplified by the usage of uniform reinforcement distributions.

The design procedures for flat slabs and coffer slabs are described in more detail on page 6-9.


Input

The beam/slab definition has several input components:

• Parameters: Material properties, load factors and general design parameters.

• Sections: Enter cross-sectional dimensions.

• Spans: Define spans and span segments.

• Supports: Define columns, simple supports and cantilevers.

• Loads: Enter dead and live loads.

Parameters input Enter the following design parameters:

fcu : Characteristic strength of concrete (MPa).

fy : Characteristic strength of main reinforcement (MPa).

fyv : Characteristic strength of shear reinforcement (MPa).

Redistr : Percentage of moment redistribution to be applied.

Method : Method of moment redistribution, i.e. downward or optimised. Refer to page 6-8 for detail.

Cover top : Distance from the top surface of the concrete to the centre of the top steel.

Cover bottom: Distance from the soffit to the centre of the bottom steel.

DL factor : Maximum ULS dead load factor.

LL factor : Maximum ULS live load factor.

Note: The ULS dead and live load factors are used to calculate the ULS design loads. The ULS dead and live loads are then automatically patterned during analysis. Refer to page 6-7 for more information.

Density : Concrete density used for calculation of own weight. If the density filed is left blank, the self-weight of the beam/slab should be included in the entered dead loads.

LL perm : Portion of live load to be considered as permanent when calculating the creep components of the long-term deflection.

φ : The thirty-year creep factor used for calculating the final concrete creep strain.

εcs : Thirty-year drying shrinkage of plain concrete.


The graphs displayed on-screen give typical values for the creep factor and drying shrinkage strain. In both graphs, the effective section thickness is defined for uniform sections as twice the cross-sectional area divided by the exposed perimeter. If drying is prevented by immersion in water or by sealing, the effective section thickness may be taken as 600 mm.

Note: Creep and shrinkage of plain concrete are primarily dependent on the relative humidity of the air surrounding the concrete. Where detailed calculations are being made, stresses and relative humidity may vary considerably during the lifetime of the structure and appropriate judgements should be made.

Sections input You can define rectangular, I, T, L and inverted T and L-sections. Every section comprises a basic rectangular web area with optional top and bottom flanges.

The top levels of all sections are aligned vertically by default and they are placed with their webs symmetrically around the vertical beam/slab centre line. The web and/or flanges can be move horizontally to obtain eccentric sections, for example L-sections. Whole sections can also be moved up or down to obtain vertical eccentricity.


Note: In the sub-frame analysis, the centroids all beam segments are assumed to be on a straight line. Vertical and horizontal offsets of sections are use used for presentation and detailing purposes only and has no effect on the design results.

Section definitions are displayed graphically as they are entered. Section cross-sections are displayed as seen from the left end of the beam/slab.

The following dimensions should be defined for each section:

Sec no : The section number is used on the Spans input page to identify specific sections.

Bw : Width of the web (mm).

D : Overall section depth, including any flanges (mm).

Bf-top : Width of optional top flange (mm).

Hf-top : Depth of optional top flange (mm).

Bf-bot : Width of optional bottom flange (mm).

Hf-bot : Depth of optional bottom flange (mm).


Y-offset : Vertical offset the section (mm). If zero or left blank, the top surface is aligned with the datum line. A positive value means the section is moved up.

Web offset : Horizontal offset of the web portion (mm). If zero or left blank, the web is taken symmetrical about the beam/slab centre line. A positive value means the web is moved to the right.

Flange offset : Horizontal offset of both the top and bottom flanges (mm). If zero or left blank, the flanges are taken symmetrical about the beam/slab centre line. A positive value means the flanges are moved to the right.

Note: There is more than one way of entering a T-section. The recommended method is to enter a thin web with a wide top flange. You can also enter wide web (actual top flange) with a thin bottom flange (actual web). The shear steel design procedure works with the entered web area, i.e. Bw × D, as the effective shear area. Although the two methods produce similar pictures, their shear modelling is vastly different.

Spans input Sections specified on the Sections input page are used here with segment lengths to define spans of constant or varying sections.


Spans are defined by specifying one or more span segments, each with a unique set of section properties. The following data should be input for each span:

Span no : Span number between 1 and 20. If left blank, the span number as was applicable to the previous row is used, i.e. another segment for the current span.

Section length : Length of span or span segment (m).

Sec No Left : Section number to use at the left end of the span segment.

Sec No Right : Section number to use at the right end of the span segment. If left blank, the section number at the left end is used, i.e. a prismatic section is assumed. If the entered section number differs from the one at the left end, the section dimensions are varied linearly along the length of the segment.

Tip: When using varying cross sections on a span segment, the section definitions are interpreted literally. If a rectangular section should taper to an L-section, for example, the flange will taper from zero thickness at the rectangular section to the actual thickness at the L-section. If the flange thickness should remain constant, a dummy flange should be defined for the rectangular section. The flange should be defined marginally wider, say 0.1mm, than the web and its depth made equal to the desired flange depth.

Supports input You can specify simple supports, columns below and above, fixed ends and cantilever ends. To allow a complete sub-frame analysis, columns can be specified below and above the beam/slab. If no column data is entered, simple supports are assumed.

The following input is required:

Sup no : Support number, between 1 to 2’. Support 1 is the left-most support.

C,F : The left-most and right-most supports can be freed, i.e. cantilevered, or made fixed by entering ’C’ or ’F’ respectively. By fixing a support, full rotational fixity is assumed, e.g. the beam/slab frames into a very stiff shaft or column.

D : Depth/diameter of a rectangular/circular column (mm). The depth is measured in the span direction of the beam/slab.

B : Width of the column (mm). If zero or left blank, a circular column is assumed.

H : Height of the column (m).

Tip: For the sake of accurate reinforcement detailing, you can specify a width for simple supports at the ends of the beam/slab. Simply enter a value for D and leave B and H blank. In the analysis, the support will still be considered as a normal simple support. However, when generating reinforcement bars, the program will extend the bars a distance equal to half the support depth past the support centre line.


Code : A column can be pinned at its remote end by specifying ’P’. If you enter ’F’ or leave this field blank, the column is assumed to be fixed at the remote end.

Tip: You may leave the Support input table blank if all supports are simple supports.

Loads input Dead and live loads are entered separately. The entered loads are automatically patterned during analysis. For more detail on the pattern loading technique, refer to page 6-7.

Distributed loads, point loads and moments can be entered on the same line. Use as many lines as necessary to define each load case. Defined loads as follows:

Case D,L : Enter ’D’ or ’L’ for dead load or live load respectively. If left blank, the previous load type is assumed. Use as many lines as necessary to define a load case.

Span : Span number on which the load is applied. If left blank, the previous span number is assumed, i.e. a continuation of the load on the current span.

Wleft : Distributed load intensity (kN/m) applied at the left-hand starting position of the load. If you do not enter a value, the program will use a value of zero.


Wright : Distributed load intensity (kN/m) applied on the right-hand ending position of the load. If you leave this field blank, the value is made equal to Wleft, i.e. a uniformly distributed load is assumed.


M : Moment (kNm).


b : The end position of the distributed load, measured from the start position of the load (m). Leave this field blank if you want the load to extend up to the right-hand edge of the beam.

Note: A portion of the live load can be considered as permanent for deflection calculation. For more detail, refer to the explanation of the Parameters input on page 6-9.

Note: If you enter a concrete density on the Parameters input page, the own weight of the beam/slab is automatically calculated and included with the dead load.


Design

The analysis is performed automatically when you access the Design pages.

Analysis procedure Two separate analyses are performed for SLS and ULS calculations.

Serviceability limit state analysis

Elastic deflections are calculated by analysing the beam/slab under pattern loading using the gross un-cracked sections.

When determining long-term deflections, however, the all spans of the beam/slab are subjected to the maximum design SLS load. Sections are then evaluated for cracking at 250 mm intervals, assuming the reinforcement required at ultimate limit state. The long-term deflections are then calculated by integrating the curvature diagrams.

Tip: After having generated reinforcement for a beam, the long-term deflections will be recalculated using the actual reinforcement.

Refer to page 6-9 for more detail on calculation of long-term deflections.

Ultimate limit state analysis

At ultimate limit state, the beam/slab is subjected to pattern loading as described on page 6-7. The resultant bending moment and shear force envelopes are then redistributed. Finally, the required reinforcement is calculated.

Fixing errors that occurred during the analysis The Input pages incorporate extensive error checking. However, serious errors sometime still slip through and cause problems during the analysis. Common input errors include:

• Using incorrect units of measurement. For example, span lengths should be entered in metre and not millimetre.

• Entering too large reinforcement cover values on the Parameters input screen, gives incorrect reinforcement. Cover values should not be wrongly set to a value larger than half the overall section depth.

• Not entering section numbers when defining spans on the Spans input screens causes numeric instability. Consequently, the program uses zero section properties.


Long-term deflection problems

The cause of unexpected large long-term deflections can normally be determined by careful examination of the analysis output. View the long-term deflection diagrams and determine which component has the greatest effect:

• The likely cause of large shrinkage deflection is vastly unsymmetrical top and bottom reinforcement. Adding bottom reinforcement over supports and top reinforcement at in the middle of spans generally induces negative shrinkage deflection, i.e. uplift.

• Large creep deflections (long-term deflection under permanent load) are often caused by excessive cracking, especially over the supports. Compare the span to depth ratios with the recommended values in the relevant design code.

• Reduced stiffness due to cracking also has a direct impact on the instantaneous deflection component.

To verify the extent of cracking along the length of the beam/slab, you can study the contents of the Crack file. Check the cracked status and stiffness of the relevant sections. The extent of cracking along the length of the beam/slab is usually a good indication of its serviceability.


Viewing output graphics The analysis results can be viewed graphically or in tabular format. Output data, including graphics and tabled values, can be selectively appended to the Calcsheets using the Add to Calcsheets function on each output page.

Diagrams can be displayed for deflection, member forces and stress and shell reinforcement of any load case.

Deflections

The elastic deflection envelope represents the deflections due to SLS pattern loading.

The long-term deflection diagram represents the behaviour of the beam/slab under full SLS loading, taking into account the effects of shrinkage and creep:

• The green line represents the total long-term deflection.

• The shrinkage deflection is shown in red.

• The creep deflection (long-term deflection due to permanent loads) is given by the distance between the red and blue lines.

• The distance between the blue and green lines represents instantaneous deflection due to transient loads.

Note: Long-term deflections in beams are influenced by reinforcement layout. Initial long-term deflection values are based on the reinforcement required at ultimate limit state. Once reinforcement has been generated for a beam, the long-term deflections will be based on the actual reinforcement instead.


Moments and shear forces

The bending moment and shear force diagrams show the envelopes due to ULS pattern loading.

Steel diagrams

Bending and shear reinforcement envelopes are given for ULS pattern loading. The bending reinforcement diagram sows required top steel above the zero line and bottom steel below.

Viewing output tables Open the Output file page for a tabular display of the beam/slab design results. Results include moments and reinforcement, shear forces and reinforcement, column reactions and moments and deflections.

The Crack file gives details of the cracked status, effective stiffness and concrete stresses in the beam/slab at regular intervals. You should find the information useful when trying to identify zones of excessive cracking.


Reinforcing

Reinforcement can be generated for the most types of continuous beam and slabs using the automatic bar generation feature. Reinforcement is generated in accordance to the entered detailing parameters after which you can edit the bars to suit your requirements.

To create a bending schedule, use each detailing function in turn:

• Detailing parameters: Select the detailing mode, enter you preferences and generate the reinforcement.

• Main reinforcement: Review the main bars and adjust as necessary.

• Stirrups: Enter one or more stirrup configurations.

• Shear reinforcement: Distribute stirrups over the length of the beam.

• Sections: Specify positions where of cross-sections details should be generated.

• Bending schedule: Create the Padds file.

Detailing parameters The detailing parameters set the rules to be used by the program when generating reinforcement:

• Beam/slab type: Different detailing rules apply to different types of beams and slabs:

Type Description Main reinforcement Shear reinforcement

1 Normal beam Nominal reinforcement as for beams

Beam shear reinforcement

2 One way spanning flat slab

Nominal reinforcement as for slabs.

No shear reinforcement.

3 Column strip portion of flat slab on columns

4 Middle strip portion of flat slab on columns

Main reinforcement in accordance with moment distribution between column and middle strips. Nominal reinforcement as for slabs.

No shear reinforcement. Separate punching shear checks should be performed.

5 Rib Nominal reinforcement as for slabs.

Shear reinforcement as for beams.


• Maximum bar length: Absolute maximum main bar length to be used, e.g. 13 m.

• Minimum diameter for top bars, bottom bars and stirrups: The minimum bar diameter to be used in each if the indicated positions.

• Maximum diameter for top bars, bottom bars and stirrups: The maximum main bar diameter to be used in each if the indicated positions.

Tip: To force the program to use a specific bar diameter, you can enter the same value for both the minimum and maximum diameters.

Note: The default bar types used for main bars and stirrups, e.g. mild steel or high tensile, are determined by the yield strength values entered on the Parameters input page – refer to page 6-9 for detail. High tensile steel markings, e.g. 'T' or 'Y', will be used for specified values of fy and fyv exceeding 350MPa.

• Stirrup shape code: Preferred shape code to use for stirrups. Valid shape codes include:

• BS 4466: 55, 61, 77, 78 and 79.

• SABS 082: 55, 60, 72, 73 and 74.


• First bar mark - top: The mark of the first bar in the top of the beam/slab. Any alphanumerical string of up to five characters may be specified. The rightmost numerical or alpha portion of the bar mark is incremented for subsequent bars. Examples of valid marks include:

• ’001’ will increment to 002, 003 etc.

• ’A’ will increments to B, C, etc.

• ’B002’ will increment to B003, B004 etc.

• First bar mark - middle: The mark of the first bar in the middle of the beam/slab. If you do not enter a mark, the bar marks continue from those used for the top reinforcement. Middle bars are generated for all beams with effective depth of 650 mm or greater.

• First bar mark - bottom: The mark of the first bar in the bottom the beam/slab. If you leave this field blank, the bar marks will continue from those used for the top or middle reinforcement.

• Cover to stirrups: Concrete cover to use at the top, bottom and sides of all stirrups.

• Minimum stirrup percentage: Nominal shear reinforcement is calculated according to the code provisions for beams and slabs. In some cases, it may be acceptable to provide less than the nominal amount stirrups, e.g. for fixing top bars in a flat slab. The minimum amount of stirrups to be generated can be entered as a percentage of the nominal shear reinforcement.

Note: For beams and ribs, the minimum stirrup percentage should not be taken less than 100% of nominal shear reinforcement.

• Loose method of detailing: The envisaged construction technique can be taken into account when detailing reinforcement:

• With the ’loose method’ of detailing, also referred to as the ’splice-bar method’, span reinforcement and link hangers are stopped short about 100 mm inside each column face. This is done at all internal columns were congestion of column and beam reinforcement is likely to occur. The span bars and stirrups are often made into a cage, lifted and lowered between supports. For continuity, separate splice bars are provided through the vertical bars of each internal column to extend a lap length plus 100 mm into each span. Top bars will extend over supports for the required distance and lapped with nominal top bars or link hangers. Allowance is made for a lap length of 40·φ and a 100 mm tolerance for the bottom splice bars that are acting in compression.

• Alternatively, where accessibility during construction allows, the 'normal' method of detailing usually yields a more economical reinforcement layout. This method allows bottom bars to be lapped at support centre lines. Top bars will extend over supports for the required distance and lapped with link hangers. Where more practical, top bars over adjacent supports may be joined. Adjacent spans are sometimes detailed together.


Note: The ’normal’ method of detail may give rise to congested reinforcement layouts at beam-column junctions, especially on the bottom beam/slab layer. Reinforcement layout details at such points should be checked.

Generating reinforcement

Use the Generate reinforcing to have the program generate bars according the detailing parameters.

Note: The aim of the automatic reinforcement generation function is to achieve a reasonable optimised reinforcement layout for any typical beam or slab layout. More complicated layouts will likely require editing of the generated reinforcement as described in the text that follows. Very complicated layouts may require more detailed editing using Padds.

Editing reinforcement

You can modify the generated reinforcement to suite your requirements by editing the information on the Main reinforcing, Stirrups, Shear reinforcing and Sections pages.

Main reinforcing The main reinforcement bars are defined as follows:

• Bars: The quantity, type and diameter of the bar, example ’2T20’ or ’2Y16’. The bar defined at the cursor position is highlighted in the elevation.

• Mark: An alphanumerical string of up to five characters in length, example ’A’, ’01’ or ’A001’.

• Shape code: Standard bar shape code. Valid shape codes for main bars include 20, 32, 33, 34, 35, 36, 37, 38, 39 and 51.

• Span: The beam/slab span number.

• Offset: Distance from the left end of the span to the start point of the bar (m). A negative value makes the bar start to the left of the beginning of the span, i.e. in the previous span.

• Length: Length of the bar as seen in elevation (m).

• Hook: If a bar has a hook or bend, enter ’L’ or ’R’ to it on the left or right side. If this field is left blank, an ’L’ is assumed.

• Layer: Position the bar in the top, middle or bottom layer. Use the letters ’T’, ’M’ or ’B’ with an optional number, e.g. ’T’ or ’T1’ and ’T2’.


The bending reinforcement diagram is shown on the lower half of the screen. The diagrams for required (red) and entered (blue) reinforcement are superimposed for easy comparison. Bond stress development is taken into consideration in the diagram for entered reinforcement.

Stirrups Define stirrup layouts as follows:

• Stirrup number: Enter a stirrup configuration number. Configuration numbers are used on the Shear reinforcing input page (see page 6-9) to reference specific configuration. If left blank, the number applicable to the previous row is assumed, i.e. an extended definition of the current configuration.

• Section number: Concrete cross section number as defined on the Sections input page (see page 6-9). If left blank, the number applicable to previous row in the table is used.

• Bars: Type and diameter of bar, example ’R10’.


Note: Mild steel bars are normally used for shear reinforcement. However, in zones where much shear reinforcement is required, you may prefer using high yield stirrups. You can do this by entering ’T’ or ’Y’ bars instead of ’R’ bars. In such a case, the yield strength ratio of the main and shear reinforcement, i.e. fy/fYV as entered, will be used to transpose the entered stirrup areas to equivalent mild steel areas.

• Mark: Any alphanumerical string of up to five characters in length, e.g. ’SA1’, ’01’ or ’S001’.

• Shape code: Standard double-leg bar shape code. The following shape codes can be used:

• BS4466: 55, 61, 77, 78 and 74.

• SABS082: 55, 60, 72, 73 and 74.

Bars are automatically sized to fit the section web. The first stirrup entered is put against the web sides. Subsequent stirrups are positioned in such a way that vertical legs are spaced equally.

Tip: Open stirrups, e.g. shape code 55, can be closed by entering a shape code 35.


Shear reinforcing Stirrup layouts defined on the Stirrups input page (see page 6-9) are distributed over the length of the beam/slab:

• Stirrup number: The stirrup configuration number to distribute.

• Spacing: Link spacing (mm).

• Span: The beam/slab span number.

• Offset: Distance from the left of the span to the start point of the distribution zone (m). A negative value makes the zone start to the left of the beginning of the span, i.e. in the previous span.

• Length: Length of the stirrup distribution zone (m).

The diagrams for required and entered shear reinforcement are superimposed. The required steel diagram takes into account shear enhancements at the supports.

It may sometimes be acceptable to enter less shear steel than the calculated amount of nominal sheer steel, e.g. when the stirrups are only used as hangers to aid the fixing main steel in slabs.


This option can be set as default on the Detailing parameters input screen – see page 6-9 for detail.

Sections Cross-sections can be generated anywhere along the length of the beam/slab to show the main and shear steel layout:

• Label: The cross-section designation, e.g. 'A'.

• Span no: The beam/slab span number.

• Offset: The position of the section, given as a distance from the left end of the span (m).

Sections are displayed on the screen and can be used to check the validity of steel entered at the different positions. Stirrup layouts defined on the Stirrups input (see page 6-9) rely on appropriate section positions specified. All specified sections will be included in the final bending schedule.


Bending schedule The Bending schedule input page is used generate a complete Padds compatible bending schedule. The parameters allow flexibility in the bending schedule creation, e.g. you can have the details of a beam/slab on a single bending schedule or split it onto more than one schedule to improve clarity. Each bending schedule can then be given a unique name and the associated spans entered.

The following information should be entered:

• File name: The name of the Padds drawing and bending schedule file

• First span: For clarity, a beam/slab with many spans can be scheduled put on more than one bending schedule. Enter the first span number to be included in the bending schedule.

• Last span: Enter the last span number to be included in the bending schedule.

• Grid lines: Optionally display grid lines and numbers appear on the bending schedule drawing.

• Columns: Optionally display column faces on the bending schedule drawing.

• First grid: The name or number of the first grid. Use one or two letters and/or numbers.

• Number up or down: Specify whether grids must be numbered in ascending or descending order, i.e. ’A’, ’B’ and ’C’ or ’C’, ’B’ and ’A’

• Drawing size: Select A4 or A5 drawing size. If A4 is selected, the drawing is scaled to fit on a full page and the accompanying schedule on a separate page. The A5 selection will scale the drawing to fit on the same page with the schedule. Typically, a maximum of three to four spans can be shown with enough clarity in A5 format and four to six spans in A4 format.

Note: When combining a drawing and schedule on the same page, the number of schedule lines is limited to a maximum of twenty-four in Padds. Using more lines will result in the drawing and schedule being printed on separate pages.

Use the Generate schedule function to create and display the Padds bending schedule.

Editing and printing of bending schedules

Detailed editing and printing of bending schedules are done with Padds. For this, following the steps below:

• Exit the program and launch Padds.

• Choose Open on the File menu and double-click the relevant file name. The file will be opened and displayed in two cascaded widows. The active windows will contain the drawing of the beam and the second window the bar schedule.


• Make any necessary changes to the drawing, e.g. editing or adding bars and adding construction notes.

• Click on any visible part of the window containing the cutting list to bring it to the front. Enter the following information at the relevant positions:

• Member description: Use as many lines of the member column to enter a member description, e.g. ’450x300 BEAM’.

• General schedule information: Press PgDn to move to the bottom of the bending schedule page and enter the detailers name, reference drawing number etc.

• Bending schedule title: Enter the project name and bending schedule title in the centre block at the bottom of the bending schedule.

• Bending schedule number: The schedule number in the bottom right corner defaults to the file name, e.g. ’BEAM.PAD’. The schedule number can be edited as required to suite your company’s schedule numbering system, e.g. ’P12346-BS001’.

Note: The bottom left block is reserved for your company logo and should be set up as described in the Padds User’s Guide.

Finally, combine the beam drawing and schedule onto one or more A4 pages using the Make BS Print Files command on the File menu. Use Alt+P to print the schedule immediately or Alt+F to save it as a print file for later batch printing.


Calcsheets

The beam/slab design output can be grouped on a calcsheet for printing or sending to Calcpad. Various settings are available to include input and design diagram and tabular result.


Recalling a data file If you enable the Data File option before sending a calcsheet to Calcpad, you can later recall the design by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the design module as well.


Appendix: Suggested design procedures for slabs

Some suggestions are made below with regards the design and detailing of solid slabs and coffer slabs.

Suggested design procedure for solid slabs The suggestions are explained by way of an example. A flat slab with a regular rectangular column layout of 6.0 m by 5.5 m is considered.

Typical strip over a row of internal columns (Strip A)

The strip is modelled as a 6000 mm wide panel, i.e. 3000 mm either side of the columns. The program calculates moments and shear forces for the whole panel width. It then details a column strip, 1500 mm wide, and middle strip, 4500 mm wide. For an explanation of the division into column and middle strips, see page 6-9.

External strip (Strip B)

The external strip, strip B, is defined as the portion over the external columns that extending halfway to the first row of internal columns. Strip C is the first internal strip and it extends to midspan on both sides.

Consider the end panel, i.e. the portion between edge columns and the first row of internal columns or, in other word, strip B together with half of strip C. The portion over the internal columns (portion of strip C) will tend to attract more moment than the portion over the external columns (strip B). Using a rule of thumb, a reasonable moment distri-bution ratio would be about 62.5% to 37.5%.

The external strip (strip B) can thus be conservatively modelled


as a panel with width equal to half the transverse column spacing, i.e. 3000 mm, carrying the full load for that area. The program will analyse the strip and the generate reinforcement for a column strip, 750 mm wide, and a middle strip, 2250 mm wide.

First internal strip (Strip C)

The first internal strip can subsequently be modelled using the same width as a typical internal panel, i.e. 6000 mm. Because of the moment distribution explained above, the loading is increased to 50% + 62.5% = 112.5% of the typical panel loading. The small overlap in loading between the edge and first internal panels should take care of any adverse effects due to pattern loading.

Note: If the own weight is modelled using a density, you should account for the increased loading by either increase the density value by 12.5% or increasing the applied dead load.

The program will analyse the panel and generate a column strip, 1500 mm wide, and a middle strip 4500 mm wide.

Reinforcement layout

Careful combination of the column and middle strips generated above, should yield a reasonably economical reinforcement layout:

• For typical internal strips (strip A), use the generated column strip (CA) and middle strip (MA).

• For the column strip over the external row of columns, use no less than the column strip reinforcement (CB) generated for the external strip (strip B).

• For the column strip over the first row of internal columns, use no less than the column strip reinforcement (CC) generated for the first internal strip (strip C).

• The first middle strip from the edge (MC/MB) can be conservatively taken as the worst of middle strip generated for the first internal strip (MC) and twice that generated for the external strip (MB).

Suggested design procedure for coffer slabs Coffer slabs can normally be designed and detailed using the design procedure for solid slabs. The procedure suggested for solid slabs should be also a reasonable design approach for coffer slabs if the following conditions are met:

• The solid bands should be as wide or slightly wider than the generated column strips, i.e. L/4 or wider.

• Assuming that the concrete compression zone of each coffer rib falls in the coffer flange, the slab can be modelled as a solid slab.


• Setting the density to zero and appropriately increasing the applied dead load can model the own weight of the slab.

• The linear shear requirements should be verified for the column strips, i.e. solid bands. The areas around columns slab should also be checked for punching shear.

• The coffer webs should be checked for linear shear and compression reinforcement.

Note: You should validate the design procedure by checking that, in zones of sagging moment, the concrete compression zones of coffer ribs fall within the coffer flanges. Zones of hogging moment should be located inside solid bands.

Pre-stressed Beam and Slab Design 6-39

Pre-stressed Beam and Slab Design

Captain (Computer Aided Post Tensioning Analysis Instrument) can be used to design and detail most types of continuous pre-stressed beam and slab systems encountered in typical building projects. The design incorporates automated pattern loading and moment redistribution.

Both unbounded systems, e.g. flat slabs, and bonded systems, e.g. bridge decks, can be designed. Estimates for quantities are calculated and tendon profile schedules can be generated for use with Padds.




Design scope The program designs and details continuous pre-stressed concrete beams and slabs. You can design structures ranging from simply supported single span to twenty-span continuous beams or slabs.

Cross-sections can include a mixture rectangular, I, T and L-sections. More complex sections, e.g. box bridge decks, can be modelled with the aid of the section properties calculation module, Prosec. Spans can have constant or tapered sections.

Entered dead and live loads are automatically applied as pattern loads during the analysis. You can also enter individual load cases and group them in load combinations. At ultimate limit state, moments and shears are redistributed to a specified percentage.

Pre-stressed tendons can be generated to balance a specified percentage of dead load. Conventional reinforcement can be added to help control cracking, deflection and increase the ULS capacity.

Tendon profiles can be scheduled and saved as Padds compatible drawings.

Design codes The following codes are supported:

• BS 8110 - 1985.

• BS 8110 - 1997.

• SABS 0100 - 1992.

Reinforcement bending schedules are generated in accordance to the guidelines given by the following publications:

• Report No 2 of the Joint Structural Division of SAICE and ISA (JSD), ’Design of Pre-stressed Concrete Flat Slabs’.

• Technical Report 25 of the Concrete Society, published in 1984.

• Attached torsional members are treated in accordance with ACI 318 - 1989.


Sub-frame analysis A two-dimensional frame model is constructed from the input data. Section properties are based on the gross un-cracked concrete sections. Columns can optionally be specified below and above the beam/slab and can be made pinned or fixed at their remote ends.

Note: No checks are made for the slenderness limits of columns or beam flanges.

Column stiffness

BS 8110 and SABS 0100 - 1992 assume that columns are rigidly fixed to slabs over the whole width of the panel. If the ultimate negative moment at an outer column exceeds the moment of resistance in the adjacent slab width, the moment in the column should be reduced and the sagging moment in the outer span should be increased to maintain equilibrium.

In ACI 318 - 1989, on the other hand, allowance is made for the reduction of column stiffness due to torsion. Report 2 of the JSD adapts a similar column stiffness reduction approach. The program incorporates this approach by allowing you to optionally enable attached torsional members.

Note: When the approach to include the attached torsional members is followed, column heads will also be taken into account in the column stiffness.

Pattern loading At ultimate limit state, the dead and live loads are multiplied by the specified ULS load factors (see page 6-9). Unity load factors are used at serviceability limit state. The following load cases are considered (the sketch uses the load factors applicable to BS8110):

• All spans are loaded with the maximum design load.

• Equal spans are loaded with the maximum design ultimate load and unequal spans with the minimum design dead load.

• Unequal spans are loaded with the maximum design load and equal spans loaded with the minimum design dead load.


Note: The case where any two adjacent spans are loaded with maximum load and all other spans with minimum load, as was the case with CP 110 - 1972 and SABS 0100 - 1980, is not considered.

The following are special considerations with pertaining to design using SABS 0100 - 1992:

• SABS 0100 - 1992 suggests a constant ULS dead load factor of 1.2 for all pattern load cases. In contrast, the BS 8110 codes suggest a minimum ULS dead load factor of 1.0 for calculating the minimum ultimate dead load. The program uses the more approach given by the BS 8110 codes at all times, i.e. a ULS load factor of 1.0 for minimum dead load and the maximum load factor specified for maximum dead load.

• The South African loading code, SABS 0162 - 1989, prescribes an additional load case of 1.5×DL. This load case is not considered during the analysis – if required, you should adjust the applied loads manually. In cases where the dead load is large in comparison with the live load, e.g. lightly loaded roof slabs, increasing the entered dead load or increasing the ULS dead load factor can incorporate this load case. This adjustment applies to cases where 1.5×DL > 1.2×DL + 1.6×LL or, in other words, LL < 19%. Using an increased dead load factor of 1.4 instead of the normal 1.2 will satisfy all cases except where 1.5×DL > 1.4×DL + 1.6×LL or, in other words, LL < 6%×DL.

Moment redistribution Ultimate limit state bending moments are redistributed for each span by adjusting the support moments downward with the specified percentage. If the method of moment redistribution is set to 'optimised', the design moments are further minimised by redistributing span moments upward as well.

Note: No moment redistribution is done for serviceability limit state calculations.

The moment envelopes are calculated for pattern loading and then redistributed using the procedures explained in the following text.

Code requirements

The JSD Report 2 recommends that the maximum moment redistribution should not exceed 20%.

Downwards redistribution

The downward distribution method aims to reduce the hogging moments at the columns without increasing the sagging moments at midspan. The redistribution of moments and shear forces procedure is performed as follows:

4. The maximum hogging moment at each column or internal support is adjusted downward by the specified maximum percentage.


5. The corresponding span moments are adjusted downward to maintain static equilibrium. The downward adjustment of hogging moments above is limited to prevent any increase in the maximum span moments of end spans.

6. The shear forces for the same load cases are adjusted to maintain static equilibrium.

Optimised redistribution:

The optimised distribution procedure takes the above procedure a step further by upward distribution of the span moments. The envelopes for the three pattern load cases are redistributed as follows:

11. The maximum hogging moment at each internal support is adjusted downward by the specified percentage. This adjustment affects the moment diagram for the load case where the maximum design load is applied to all spans.

12. The relevant span moments are adjusted accordingly to maintain static equilibrium.

13. The minimum hogging moment at each internal support is subsequently adjusted upward to as close as possible to the reduced maximum support moment, whilst remaining in the permissible redistribution range. A second load case is thus affected for each span.

14. The relevant span moments are adjusted in line with this redis-tribution of the column moments to maintain static equilibrium.


15. For each span, the moment diagram for the remaining third load case is adjusted to as near as possible to the span moments obtained in the previous step. The adjustment is made in such a way that it remains within the permissible redistribution range.

16. Finally, the shear force envelope is adjusted to maintain static equilibrium.

17. The following general principles are applied when redistributing moments:

18. Equilibrium is maintained between internal and external forces for all relevant combinations of design ultimate load.

19. The neutral axis depth is checked at all cross sections where moments are redistributed. If, for the specified percentage of moment redistribution, the neutral axis depth is greater than the limiting value of (ßb−0.4)⋅d, compression reinforcement is added to the section to sufficiently reduce the neutral axis depth.

20. The amount of moment redistribution is limited to the specified percentage. The maximum amount of redistribution allowed by the codes is 30%.

Note: As would be the case in typical pre-stressed sections, the program assumes that all sections have adequate ductility to allow moment redistribution. The actual ductility of sections is not verified.

Tendon generation procedures Captain is capable of generating tendons for typical beam and slabs. The procedure aims to balance a specified percentage of the dead load in the span.

For purposes of the generation, all the dead loads on the span, including self weight, UDL's, partial UDL's, trapezoidal and point loads, are summed and divided by the span length to obtain an equivalent UDL for the span.

Parabolic or harped tendons are then selected to balance the required percentage of this equivalent dead load. In the case of harped tendons, the tendons are chosen to provide two upward point loads per span that balance the selected percentage of the sum of all the dead load components.

Note: The program uses load balancing only for the purpose of generating tendons.

Since long-term losses are not known beforehand, a 15% loss of pre-stress is assumed. Further, the generation procedure that tendons are stressed to 70% of their ultimate tensile strength (UTS).

The details of the tendon generation procedure are explained in the following text.


Parabolic tendons in cantilever spans

Consider a typical cantilever span with a tendon following a parabolic profile. The profile is chosen with a zero eccentricity at the cantilever end. At the internal support the tendon is taken as high as possible.

The program chooses the following values:

• The left offset, L, is chosen as zero.

• The right offset, R, is chosen equal to the span length divided by twenty, with a minimum of 250 mm.

• The eccentricity at the cantilever end is taken as zero, i.e. b1 (b3 for a cantilever on the right end) is chosen on the neutral axis.

• The tendon position over the internal support is taken as high as possible. The value of b3 (b1 for a cantilever on the right end) is thus taken as the top cover plus half the sheathed tendon diameter.

The tendon force, T, required to produce the balanced load Wbal is given by

))((2)(15.1

13

2

RLengthbbLengthRLengthW

T balreq −−

−=

and the number of tendons required by

tendon

reqtendons UTS

TN

7.0=

Parabolic tendons in internal spans and end spans

For a typical internal span, a parabolic tendon profile is chosen to give maximum eccentricities over supports and at midspan.

The same also applies to an end span, except that the tendon as moved to the neutral axis at the anchor.

The program chooses the following default values:

• The left and right offsets, L and R, are chosen by the program to be equal to the span length divided by twenty, with a minimum of 250 mm.


• Over the supports, the tendons are taken as high as possible. The values of b1 and b2 are made equal to the top cover plus half the sheathed tendon diameter. At the end of the beam/slab, i.e. at an anchor, the tendons are taken on the neutral axes.

• At midspan, tendons are taken as low as possible. The value of b2 is therefore chosen as being equal to the bottom cover plus half the sheathed tendon diameter.

The drape of the tendon is then calculated as

( )( )( )Length

RLLengthbbbdrape

−−−+= 22/31

The tendon force required to produce the balanced load Wbal is then given by

drapeLengthRLLengthW

T balreq ×

−−=

8)(15.1 2


tendon

reqtendons UTS

TN

7.0=

Harped tendons in cantilever spans

For a cantilever span with a harped tendon profile, the profile is taken as a straight line from the neutral axis at the cantilever end to the highest position over the internal support.

In the calculations, the minimum radius Rmin specified is used in determining the final slopes of the tendons. The program chooses the following values:

• The left offset, L, is chosen as zero.

• The right offset, R, is set equal to the span length.

• The eccentricity at the cantilever end is taken as zero, i.e. b1 (b3 for a cantilever on the right end) is chosen on the neutral axis.

• The tendon position over the internal support is taken as high as possible. The value of b3 (b1 for a cantilever on the right end) is thus taken as the top cover plus half the sheathed tendon diameter.


The position of the start of the radius of the internal support, xw, is calculated as

)(2 13min2 bbRLengthLengthxw −−−=

Further, the corresponding vertical offset for the start of the radius, yw, is given by

min

2

2Rx

y ww =

and the slope of the tendon as

−−−

=Θw

w

xLengthybb 13arctan


Θ=

sin15.1 bal

reqW

T


tendon

reqtendons UTS

TN

7.0=

Harped tendons in end spans

For an external span, a harped tendon profile is chosen to give maximum eccentricities over the internal support and at midspan. The eccentricity at the end support is chosen to be zero to eliminate moments.

The following values are chosen:

• The left and right offsets, L and R, are set to span length divided by four.

• The eccentricity at the end of the beam/slab end is taken as zero, i.e. b1 (b3 for a right end span) is chosen on the neutral axis.

• The eccentricities at both ends are taken as high as possible. The value of b3 (b1 for a right end span) is thus taken as the top cover plus half the sheathed tendon diameter.

• At midspan, tendons are taken as low as possible. The value of b2 is therefore chosen as being equal to the bottom cover plus half the sheathed tendon diameter.



)(244 23min

2

bbRLengthLength

xw −−

−=

Further, the corresponding vertical offset for the start of the radius, yw, is taken as

min

2

2Rx

y ww =


( )w

balreq

xLengthd

Lengthd

WT

−⋅+

⋅

=

316

316

15.1

21

where

3)(2 21

1bb

d−

=

3)(2 23

2byb

d w −−=

The number of tendons required is then given by

tendon

reqtendons UTS

TN

7.0=

Harped tendons in internal span

Maximum eccentricities are chosen over the supports and at midspan for an internal span with a harped tendon profile.

The following values are chosen:

• The left and right offsets, L and R, are set to span length divided by four.

• The eccentricities at both ends are taken as high as possible. The values of b1 and b3 are thus taken as the top cover plus half the sheathed tendon diameter.

• At midspan, tendons are taken as low as possible. The value of b2 is therefore chosen as being equal to the bottom cover plus the half the sheathed tendon diameter.



)(244 23min

2

bbRLengthLength

xw −−

−=

Further, the corresponding vertical offset for the start of the radius, yw, is taken as

min

2

2Rx

y ww =


( )( )

−⋅

+=

w

balreq

xLengthdd

WT

31616

15.1

22

where

3)(2 21

1byb

d w −−=

3)(2 23

2byb

d w −−=

The number of tendons required is then given by

tendon

reqtendons UTS

TN

7.0=

Pre-stress losses In the following text, an explanation as given for the various components of pre-stress losses:

• Friction losses.

• Wedge-set.

• Long-term losses.

Friction losses in parabolic tendons

Friction losses are calculated for each span in turn. The calculation is started at the active end of each tendon. The effective tendon force is calculated at the end of the span taking into account the friction losses. This force is then carried over to the start of the next span for the process to be repeated.


The following is applicable to parabolic tendon profiles, including those cases where L and R are zero:

LengthLengthRan

LaRLengthm

)(

)2(

1

2

−=−−=

where

12 aaadif −=

These values are used to determine the position of the lowest point on the parabola, X, and are derived from the basic parabolic equations describing the tendon profiles. The position of the lowest point is at midspan if adif is equal to zero, otherwise it is calculated as

difap

x2

=

where

namp dif−= 2

If x ≠ 0, then the vertical position of the left inflection point, c1, is given by

XLa

c 11 = else c1 is zero.

If L ≠ X then the vertical position of the right inflection point, cs, is given by

XLengthRa

c−

= 22 else c2 is zero.

The following can then be calculated:

2321

22

22112

11

)(168

32

)()(8

3

Length

ddd

cd

cacad

cd

++=

=

−+−=

=

α


The effective pre-stressing force at the end of the span, Pe, can now be calculated:

Lengthkoe ePP )( += µα

where

Po = Applied tendon force

µ = Friction coefficient of the tendon against the sheath

α = Cumulative angle of curvature over length

k = Friction coefficient for unintentional variation form specified profile (’wobble’ in sheath)

Friction losses in harped tendons

The following is applicable to harped tendon profiles, including those cases where L and R are zero:

RLLengthl −−=2

The position of the end of the left minimum radius, xwL, is given by

1min2 2 aRLLxwL −−= for 1min

2 2 aRL >

0=wLx otherwise.

Corresponding to this

min

2

2Rx

y wLwL =

Similarly, the position of the start of the right minimum radius, xwR, is given by

2min3 2 aRRRxwR −−= for 2min

2 2 aRR >

0=wRx in all other cases.

Corresponding to this

min

2

2Rx

y wRwR =


The slopes of the three sections of tendon are now known. The change in slope α at each kink is then determined. At the first kink, friction losses occur over a length xwL and at the second kink over a length of 2 xwL. At the Last kink, friction losses occur over a length xwR and at the third kink over a length of 2 xwR.

Starting from the one side the force at the end of each kink is calculated as:

fricLkbeginend ePP )( += µα

where

Lfric = Portion over which the losses occur.

Wedge-set

As soon as the stressing jacks are released, a phenomenon known as ’wedge-set’ or ’wedge pull-in’ occurs.

In typical building slabs, the tendons normally pull in by about 5mm to 10 mm before the tendons grip onto the wedges in the anchor head. The influence on the tendon force is significant.

Because of frictional losses, the effect of wedge-set is to reduce the effective pre-stress over a limited length of tendon only. This length, labelled lw, is calculated by considering the average force loss over the entire length of the tendon:

lengthtendonTotal

PPm endbegin −

=

The length effected by wedge-set is then given by

m

EAdl spswsw =

where

Aps = Area of tendons

Es = Modulus of elasticity of tendons

ds = Wedge-set


The force loss over the length affected by the wedge-set can then be calculated:

w

psswslossws l

AEdP =

The tendon force profile can then be adjusted by reducing the tendon force at the live anchor by 2Plossws and taking the negative pre-stress loss gradient up to the position of wedge-set influence, lw.

Long-term tosses

The average steel strain in all the tendons is given by

pss

endpanbeginspanst AE

PsP

Σ+Σ

=2

)(ε

This summation is carried out over all spans for all tendons.

The creep strain is estimated as

φεcc

avgcreep EA

P=

where

Pavg = Average pre-stressing force

Ac = Concrete area

Ec = Concrete modulus of elasticity

φ = Creep factor

The percentage total losses can be calculated as

pss

creepshrinkage

AErelaxationLoss

Σ+

+=)(100

%%εε

where

εshrinkage = Shrinkage strain

εcreep = Strain due to creep


Load balancing Captain uses a load balancing approach when generating tendons. The average tendon force, Pav, is calculated for each span and each tendon. Pav is used to calculate the equivalent load from the central portion of the tendon. The tendon force values at the beginning and end of each span are used to calculate the equivalent loads for the reversed parabolic portions of parabolic tendons and for the point loads from harped tendons at supports.

Equivalent load for parabolic tendons

Consider a typical span with parabolic tendons. The procedure described next for calculating the equivalent loads is applicable to cantilever and end spans as well.

The following values are used to determine the position of the lowest point on the parabola and are derived from the basic parabolic equations describing the tendon profiles.

LengthLengthRan

LaRLengthm

)(

)2(

1

3

−=−−=

where

13 aafadi −=

These values are used to determine the position of the lowest point on the parabola, X, and are derived from the basic parabolic equations describing the tendon profiles. The position of the lowest point is at midspan if adif is equal to zero, otherwise it is calculated as

difap

X2

=

where

namp dif−= 2

If x ��WKHQ�YHUWLFDO�SRVLWLRQ�RI�OHIW�LQIOHFWLRQ�SRLQW��c1, is given by

XLa

c 11 = else c1 is zero.


If L ��X then the vertical position of right inflection point, cs, is given by

XLengthRa

c−

= 32 else c2 is zero.

If L > 0, the equivalent load starting at the left support is given by

21

2

L

PW begin=

If L = 0 then W1 = 0.

The central portion of the equivalent tendon load is calculated by using a length lcalc. The distance lcalc is measured from the lowest point of the parabola to the nearest inflection point.

If the left inflection point is nearest to the lowest point, then

LXlcalc −=

and the equivalent load in the centre portion

211

2)(

calc

av

l

caPW

−=

Else, if the right inflection point is nearest to the lowest point, then

RXLengthlcalc −−=

and the equivalent load in the centre portion

223

2)(

calc

av

l

caPW

−=

If R > 0, the equivalent load ending at the right support is given by

232

R

PW end=

If R = 0 then W3 = 0.

If the value of X is equal to zero, it implies that the tendon is horizontal at the beginning or end of the span. If the value of L or R is equal to zero, it means that there is no reverse portion of the parabola. In such a case a point load is calculated which acts downwards at the support.


If L is zero, the slope of the tendon is calculated as

=Θ

Xa12

arctan

The downward point load is then given by

Θ= sinPP begint

Similarly, if R is zero, the slope of the tendon is calculated as

=Θ

Xa32

arctan

The downward point load is then given by

Θ= sinendt PP

If a tendon is stopped off away from the neutral axis, a point moment is generated in the slab. The magnitude of this moment is given by:

tendontendont ePM ⋅=

where

etendon = Tendon eccentricity measured from the section neutral axis.

Equivalent load for harped tendons

Consider a typical span with harped tendons. The procedure described next for calculating the equivalent loads is applicable to both cantilever and end spans.

The four point loads caused by the typical harped tendon are labelled P1 to P4. The central portion of the tendon is assumed to be horizontal, causing no vertical components of force.

The sloped ends with offset lengths L and R cause upward or downward point loads where they change direction at the support or at the offset points to the horizontal portion. In practice, the change in direction of the tendon occurs over a short distance dictated by the allowable minimum radius of the tendon. For calculation purposes the vertical components are calculated as point loads at the theoretical intersection points of the straight portions.


The tendon forces used in the calculation are Pbegin end Pend, which are the tendon forces at the beginning and end of each span. For calculating the values of P2 and P3, the tendon force is interpolated linearly between the end values.

The equivalent loads are given by

223

34

43

12

221

11

)(1

)(1

Rb

bPP

LengthP

RPPPP

LengthP

LPPPP

Lb

bPP

end

end

endbegin

begin

endbegin

begin

+=

−+=

−+=

+=

Calculation of concrete stresses Tensile stresses calculated on un-cracked sections do not always correlate well with cracking. For this reason, Report 2 of the JSD does attach great value to concrete stresses as a serviceability limit state. However, tensile stresses are a good indicator of where cracking may be a problem and could therefore be useful during preliminary design. The stress checks will be useful if you have been using the Report 25 provisions in the past.

Stress envelopes are calculated for the following two cases:

• At transfer of tendon forces: Only initial dead loads are considered at transfer. Additional dead loads are only considered later at SLS. On the Loads input screen, a dead load is considered as an initial dead load except if the letter ’A’ is entered before or after the load value. In that case, the load is taken as an additional dead load to be considered at SLS only and will not be considered at transfer.

• At SLS: The full SLS loads, i.e. initial dead load, additional dead load and live load, are applied and long-term losses in tendon forces are included.

Note: Tensile concrete stresses are not considered when generating tendon profiles. The pre-stressing is considered as an external load with a load balancing effect. Typical bridge design code checks for class 1, 2 and 3 structures should be done in an iterative way by manually checking the stress diagrams.


Reports 2 and 25 gives the following allowable concrete stresses for flat slab construction:

Permissible Tension Loading

Condition Permissible

Compression Bonded Un-bonded

Transfer

Sagging 0.33fci 0.45√fci 0.15√fci

Hogging 0.24fci 0.45√fci 0

Serviceability limit state

Sagging 0.33fcu 0.45√fcu 0.15√fcu

Hogging 0.24fcu 0.45√fcu 0

The allowable stresses tabled above apply to post-tensioned flat slab design. Different values may apply to the design of other types of members. Refer to the relevant design code for allowable stresses for class 1, 2 and 3 pre-tensioned and post-tensioned members.


Deflection calculation Both short-term and long-term deflections are calculated. No moment redistribution is done at serviceability limit state.

Code guidelines

Deflection can generally be controlled in the preliminary design by limiting span to depth ratios. Report 2 of the JSD gives the following guidelines for flat slabs where at least half of the dead plus live load is balanced by pre-stress:

Type of Slab Loading Intensity

Maximum span to depth ratio

Light 40 to 48

Normal 34 to 42 Flat Slabs

Heavy 28 to 36

Waffle Slabs Heavy 28 to 32

Elastic deflections

Short-term elastic deflections are calculated using un-factored SLS pattern loading. Gross un-cracked concrete sections are used.

Long-term deflections

Long-term deflections are determined by first calculating the cracked transformed sections:

3. The full SLS design load is applied to all spans to obtain the elastic moment diagram.

4. The cracked transformed sections are then calculated at 250 mm intervals along the length of the beam. The results of these calculations are tabled in the Crack files on the View output pages.

Note: The calculation of the cracked transformed section properties is initially based on the amount of reinforcement required at ULS. However, once reinforcement is generated for beams, the actual entered reinforcement is used instead. You can thus control deflections by manipulating reinforcement quantities.


Next, the long-term deflection components are calculated by numerically integrating the curvature diagrams:

5. Shrinkage deflection is calculated by applying the specified shrinkage strain. Unsymmetrical beams and unsymmetrical reinforcement layouts will cause a curvature in the beam.

6. The creep deflection is calculated by applying the total dead load and the permanent portion of the live load on the beam. The modulus of elasticity of the concrete is reduced in accordance with the relevant design code.

7. The instantaneous deflection is calculated by applying the transient portion of the live load on the transformed crack section.

8. The long-term deflection components are summed to yield the total long-term deflection.

Note: When calculating the curvatures for integration, elastic moments are used together with cracked transformed sections, which implies plastic behaviour. Although this procedure is performed in accordance with the design codes, the use of elastic moments together with cracked sections in the same calculation is a contradiction of principles. As a result of this, long-term deflection diagrams may show slight slope discontinuities at supports, especially in cases of severe cracking.

Crack width calculation In the calculation of crack widths, the program takes into account all bonded tendons and also any additional reinforcement that has been entered. The effect of the axial compressive concrete stress due to pre-stressing is also taken into account. Un-bonded tendons are ignored.

The crack spacing is calculated on the assumption that all unstressed bars and bonded tendons are spaced equally across the widest portion of the section. In flat slab design, it is common practice to have tendons banded in one direction. In such cases, tensile concrete stresses will tend to be concentrated at the position of the tendons. Therefore, the assumption that all unstressed bars and bonded tendons are spaced equally across the section, will likely yield conservative crack width values.

Calculation of additional flexural reinforcement The required reinforcement is based on supplying reinforcement for the tensile force in the concrete at a stress of 0.58fy. This is the method employed by the British Concrete Society Technical Report 25, published in 1984.

Note: Because the additional reinforcement is calculated using stress considerations, the suggested values are normally conservative. In the final analysis, you should check that the beam/slab has adequate strength at ultimate limit state.


Calculation of ULS capacity Ultimate limit state calculations are performed for the following:

• Bending moment.

• Linear shear.

• Punching shear.

Moment capacity

The moment capacity is calculated using general flexural theory. The tendon strain at ultimate limit state is given by

papepb εεε +=

where

εpe = Strain due to tendon pre-stress after losses

εpa = Additional strain due to applied loading

The strain due to pre-stress is determined from the stress-strain curve. If the pre-stress is within the elastic limit, the strain is given by

s

pepe E

f=ε

The additional strain, εpa, is determined by considering the change in concrete strain at the level of the tendon. The concrete strain distribution resulting from the effective pre-stress force is shown as a dashed line in the figure.


Thus, for bonded tendons, the additional tendon strain is given by

uepa εεε +=

where

ce E

prestressConcrete=ε at the level of the tendons

For un-bonded tendons

uepa εεε +<

In general, one can say

uepa εβεβε 21 +=

where

β1 and β2 = Bond coefficients

The program uses the following typical bond coefficients values:

Tendon bond coefficients

Pre-tensioned and bonded post-tensioned tendons

Un-bonded post-tensioned tendons

β1 1.0 0.5

β2 1.0 0.1

It now follows that

cuepa xxd εβεβε −+= 21

and

cuape

papepb

xxd εβεβε

εεε−++=

+=

21

This can be rewritten as

cpepbcu

cu

dx

εβεεεβεβ

12

2

−−+=


From equilibrium it follows that

bxfkAf cupspb 1=

Therefore

cpepbcu

cu

ps

cupb A

bdfkf

εβεεεβεβ

12

21

−−+⋅=

The values of fpb and εpb are solved by iteration using the stress-strain curve to subsequently yield the neutral axis depth, x.

The ultimate moment of resistance is then calculated as

)( 2xkdAfM pspbu −=

The calculated ULS capacity envelopes for bending moment and shear force incorporate all tendons and additional reinforcement entered. Strain is calculated on the assumption that plane sections remain plane and concrete and steel stresses are then calculated correspondingly.

Note: The secondary moments, or a portion thereof, caused by pre-stressing may optionally be included in the ULS calculations. Refer to page 6-9 for information on specifying the percentage of secondary moment to be included in the analysis.

Linear shear

The linear shear checks performed by the program are done according to the provisions of codes using the procedure described below.

An analysis is done on the sub-frame with only the equivalent tendon loads applied. The minimum fibre stress as a result of the tendon forces is then calculated as

ZM

AP

fconcrete

tendonspt +=

The section modulus, Z, is taken at the top for negative bending and at the bottom for positive bending.

The cracking moment is then calculated as

Z

f.M pt

o

80=

The section is considered as cracked in areas where the ultimate moment exceeds the cracking moment.


In areas that are un-cracked, the shear capacity is calculated as

tcptwco ff.fhb. V 80670 2 +=

where

ft = Concrete tensile strength

= cuf.240

fcp = Average concrete compressive pre-stress

= concrete

tendons

AP

for rectangular sections

= I

zP

AP ftendons

concrete

tendons + for flanged sections

zf = Distance from the neutral axis to the junction of the flange and the web of the section which falls inside the compression zone

In areas that are cracked, the shear capacity s given by

MVM

db)vf

f.- ( V o

wcpu

pecr += 5501

where

tendon

tendons

pu

pe

UTSP

f

f

×=

tendonsofNo

The value of vc is calculated by taking into account the total area of pre-stressing tendons and unstressed steel.

In areas that are cracked, the shear capacity Vcap is the minimum of Vco and Vcr calculated above.

The shear forces are reduced by the vertical components of the tendon forces if this was specified. Where the shear force V is less than 0.5 × the shear capacity Vcap, no shear reinforcement is required. Shear reinforcement must be supplied in zones where (Vcap + 0.4bwd) ≥ V ≥ 0.5Vcap:

f.

b.

SA

yv

w

v

sv

87040=


If V > Vcap + 0.4bwd then

tyv

cap

v

sv

df.

V - V

SA

870=

where

dt = Depth to the bottom reinforcement or tendons about which the stirrups are taken.

Linear shear is normally not a problem in flat slabs, but comes into play if ribbed slabs and beams are analysed. For flat slabs, punching shear is normally the main shear design criterion.

Evaluation of punching shear The first item to be determined is the enhanced shear. Columns have to be considered as either internal, edge or corner columns. For purposes of calculations done by the program, the following is assumed:

• If no edges are closer than 5d from the column centre, the column is considered to be an internal column.

• If one edge is closer than 5d from the column centre, the column is considered to be an edge column.

• If two edges are closer than 5d from the column centre, the column is taken as a corner column.

The enhanced shear force, Veff, for an internal column is then calculated as the largest of

V. V

)Vx

M. V( V

)VyM

. V( V

eff

b

yeff

b

xeff

151

0511

0511

=

+=

+=


where

Mx = Moments transferred between slab and column in the X direction, i.e. about the Y-Y axis

My = Moments transferred between slab and column in the Y direction

xb = Projected width of the critical perimeter in the X directions

yb = The projected width of the critical perimeter in the Y direction

Note: The factor 1.05 is derived from 1.5M as given by the codes, with a 30% reduction allowed if the equivalent frame method with pattern loading has been used in calculating the moments.

For an edge column, the enhanced shear force is the largest of

V. V

)VxM

.. V( V

eff

eff

251

051251

=

+=

If the edge lies parallel with the X-axis, then M = Mx and x = yb. Similarly M = My and x = xb for the edge parallel to the Y-axis.

For a corner column, the enhanced shear force is given by

V. Veff 251=

The effective shear force is then adjusted by the vertical components of the tendon forces as specified. The shear capacity is subsequently checked for each perimeter and reinforcement calculated.

The shear capacity on a specific perimeter is given by

duvV critccap =

where

ucrit = Critical perimeter

d = Effective slab depth

The value of vc is calculated for both the x and y-directions and the average of the two values used. If Veff exceeds Vcap, shear reinforcement is calculated as

yv

crit

yv

critceffsv f

duf

duvVA

87.04.0

87.0≥

−=Σ

The shear reinforcement represents vertical links to be placed in slabs deeper than 200 mm.


Circular columns

Given modern design trends, e.g. the approaches by ACI 318 - 1995 and Eurocode 2 - 1992, the use of circular perimeters seems a more rational approach to evaluating punching shear for circular columns. The program recognises this and uses the following design approach for checking punching by circular columns:

• As in the case of a rectangular column, the shear capacity vc is taken as the average of vcx and vcy. Put differently, one could consider an imaginary square shear perimeter when determining vc.

• The shear force capacity, Vc, is calculated using the actual circular perimeter. The shorter circular perimeter (compared to a rectangular perimeter) yields a lower (conservative) shear force capacity.


Input

The beam/slab definition has several input components:

• Parameters: Material properties, load factors and general design parameters.

• Tendon data: Tendon properties and profile generation options.

• Sections: Enter rectangular, I, T and L-sections.

• User-defined sections: Complex section geometries.

• Spans: Define spans and span segments.

• Supports: Define columns, simple supports and cantilevers.

• Column heads: Square and tapered drop panels.

• Loads: Uniform distributed loads, point loads and moments.

• Load combinations: User-defined combination of load cases.

Parameters input The following general parameters are required for analysis and design:

• fcu: Characteristic 28day strength of concrete (MPa).

• fy: Characteristic strength of additional un-tensioned reinforcement (MPa).

• fyv: Characteristic strength of shear reinforcement (MPa).

• fci: Characteristic strength of concrete at transfer of pre-stress (MPa).

• Ec: Concrete modulus of elasticity (kPa).

• Est: Modulus of elasticity of unstressed steel (kPa).

• Density: Concrete density used for calculation of own weight.

Note: Own weight is automatically added to the dead load with the ’auto load combination’ mode selected and to the first load case with the ’user load combination’ mode selected – refer to page 6-9 for more detail on the load combination modes.

• Top cover: Concrete cover to top of tendon sheaths (mm).

• Bottom cover: Concrete cover to bottom of tendon sheaths (mm).

• Reduce moments to column face: If selected, this option will take the moments at the column faces as the design moments rather than the moments at support centres.


• Reduce shear by tendon force component: Select this option to include the effect of tendons in punching shear checks.

• SLS DL factor: Serviceability limit state dead load factor used for calculation of deflection, stresses and crack widths.

• SLS LL factor: Serviceability limit state live factor.

• ULS DL factor: Ultimate limit state dead load factor used for calculation of moments, shear and reactions.

• ULS LL factor: Ultimate limit state live load factor.

Note: In the automatic load combination mode, the ULS load factors are used with the patterned dead and live loads. The load factors are ignored when using the user load combination mode. Refer to page 6-9 for more detail on specifying your own load combinations. The procedure of automated pattern loading is explained on page 6-9.

• Redistribution: Percentage of moment redistribution to be applied. Redistribution should be limited 10% in structures over four storeys high where the frame provides lateral stability.

• Optimised/downward: Method of moment redistribution.


• Secondary moment: Moments resulting from reactions to the pre-stress in statically indeterminate beams. Some design methods, e.g. the method given in Report 25, ignore secondary moments. Report 2 of the JSD recommend the tendons be considered as external forces with a load-balancing effect and hence secondary moments are to be taken into account.

• Live load permanent: Percentage of live load to consider as permanent when calculating long-term deflections.

• Attached torsional members: This option enables the reduction in column stiffnesses as allowed for by ACI 318 - 1989. To prevent overestimation of column moments, it is recommended that this option should be enabled. For more detail on the sub-frame analysis technique used by the program, refer to page 6-9.

• Edge beam: This option only applies if attached torsional members are used and allows for the case where the columns are framing into the slab on one side only.

• I: The thirty-year creep factor used for calculating the final concrete creep strain.

• Hcs: Thirty-year drying shrinkage of plain concrete.

The graphs displayed on-screen give typical values for the creep factor and drying shrinkage strain. In both graphs, the effective section thickness is defined for uniform sections as twice the cross-sectional area divided by the exposed perimeter. If drying is prevented by immersion in water or by sealing, the effective section thickness may be taken as 600 mm.

Note: Creep and shrinkage of plain concrete are primarily dependent on the relative humidity of the air surrounding the concrete. Where detailed calculations are being made, stresses and relative humidity may vary considerably during the lifetime of the structure and appropriate judgements should be made.

Tendon data input Characteristics can be entered for up to three types of tendons or cables:

• Bonded: Classify tendons as bonded (grouted after stressed) or un-bonded.

• Ultimate strength: Ultimate tensile strength (UTS) of one tendon or cable (kN).

• Maximum stress: Maximum tensile stress as a percentage of the UTS.

• Outside diameter of sheath: The diameter of a tendon or cable, including sheath or duct (mm). The program measures concrete cover to the outside diameter.

• Tendon area: The cross sectional area of the tendon or cable itself (mm2).

• k: Friction coefficient due to unintentional variation from the specified profile (’wobble’ in the sheath). Both BS 8110 and SABS 0100 - 1992 recommend a value of not less than 33E-4 in general. Where wobbling is limited, e.g. rigid ducts with close supports, a


reduced value of 17E-4 may be used. For greased tendons in plastic sheaths, a value of 25E-4 may be taken. However, for greased tendons, both FIP and Report 2 of the JSD recommend a value of 10E-4.

• � Friction coefficient due to curvature of the tendon. BS 8110 - 1997 and SABS 0100 - 1992 recommend values ranging from 0.55 to 0.05, depending on the condition of the strand and the duct. For greased tendons, FIP and Report 2 of the JSD recommend values of 0.05 and 0.06 respectively.

• Wedge pull-in: Movement of the tendon will occur when the pre-stressing force is transferred from the tensioning equipment to the anchorage, causing a loss in pre-stress. The magnitude of the draw-in depends on the type of tendons used and the tensioning equipment. Values of 4 to 8 mm are common for flat slab construction.

• Tendon / Cable relaxation: Percentage long-term loss of force due to cable steel relaxation.

• Es: Modulus of elasticity of tendon (kPa). This value is typically set to 195E6 kPa.

• Minimum radius: The minimum radius to use for harped tendons at change of slope (m). This value is ignored when using parabolic tendons.


Sections input You can define rectangular, I, T, L and inverted T and L-sections. Every section comprises a basic rectangular web area with optional top and bottom flanges.

The top levels of all sections are aligned vertically by default and they are placed with their webs symmetrically around the vertical beam/slab centre line. The web and/or flanges can be move horizontally to obtain eccentric sections, for example L-sections. Whole sections can also be moved up or down to obtain vertical eccentricity.

Note: In the sub-frame analysis, the centroids all beam segments are assumed to be on a straight line. Vertical offsets of sections are used when calculation of tendon eccentricities and has no other effect on the design results.

Section definitions are displayed graphically as they are entered. Section cross-sections are displayed as seen from the left end of the beam/slab.

The following dimensions should be defined for each section:

• Sec no: The section number is used on the Spans input page to identify specific sections (see page 6-9).

• Bw: Width of the web (mm).


• D: Overall section depth, including any flanges (mm).

• Bf-top: Width of optional top flange (mm).

• Hf-top: Depth of optional top flange (mm).

• Bf-bot: Width of optional bottom flange (mm).

• Hf-bot: Depth of optional bottom flange (mm).

• Y-offset: Vertical offset the section (mm). If zero or left blank, the top surface is aligned with the datum line. A positive value means the section is moved up.

• Web offset: Horizontal offset of the web portion (mm). If zero or left blank, the web is taken symmetrical about the beam/slab centre line. A positive value means the web is moved to the right.

• Flange offset: Horizontal offset of both the top and bottom flanges (mm). If zero or left blank, the flanges are taken symmetrical about the beam/slab centre line. A positive value means the flanges are moved to the right.

Note: There is more than one way of entering a T-section. The recommended method is to enter a thin web with a wide top flange. You can also enter wide web (actual top flange) with a thin bottom flange (actual web). The linear shear steel design procedure works with the entered web area, i.e. Bw × D, as the effective shear area. Although the two methods produce similar pictures, their linear shear modelling is vastly different.


User-defined sections input Complicated sections can be defined with the aid of the section properties calculation module, Prosec.

If Prosec is included in your set of programs, it can be used for entering sections as follows:

• Enter the section dimensions in millimetres.

• Save the input data to a file, e.g. ’Deck.G01’.

• Calculate the bending sect-ion properties.

Section properties calculated by Prosec are subsequently used to derive an equivalent I-section. It is important that the area and inertia values of the effective I-section tie up. The program limits the non-dimensional parameter I/(Ad2) to the range 0.02 to 0.225.

The properties of the user-defined sections are:

• Sec no: Number of the section to be referenced when you enter spans on the Spans input page (see page 6-9).

• Designation: Prosec file name. If the cursor is on a defined section when you press the Prosec button, the relevant section will automatically be loaded and displayed in Prosec.

• Area: Gross sectional area as calculated by Prosec (mm2).

• Shear Area: Enter the area likely to transmit the vertical shear (mm2). Use your own judgement on what portions of the section are suitable for transmitting shear.

• Ix: Second moment of inertia about the X-axis calculated by Prosec (mm4)

• Neut Axis: Position of the neutral axis as measured from the bottom of the section (mm).

• Y-plas: Plastic neutral axis position. (mm).

• Y-top: Offset of top surface from the datum line (mm). This value will initially be set to zero but can be adjusted to move the section up (positive) or down.

• Y-bottom: Offset of bottom surface from the datum line (mm). The section depth is given by Y-top minus Y-bottom.


Note: The derived equivalent I-section is not unique – more than one solution is possible. The derived section merely serves the purpose of simplifying the section for use by the program. If a particular equivalent section does not seem like a realistic approximation of the original section, you should consider entering the section as a normal I-section on the preceding input page, using more appropriate section dimensions.

Spans input Sections specified on the Sections input and User sections input pages are used here with segment lengths to define spans of constant or varying sections.

Spans are defined by specifying one or more span segments, each with a unique set of section properties. The following data should be input for each span:

• Span no: Span number between 1 and 20. If left blank, the span number as was applicable to the previous row is used, i.e. another segment for the current span.

• Section length: Length of span or span segment (m).

• Sec No Left: Section number to use at the left end of the span segment.


• Sec No Right: Section number to use at the right end of the span segment. If left blank, the section number at the left end is used, i.e. a prismatic section is assumed. If the entered section number differs from the one at the left end, the section dimensions are varied linearly along the length of the segment.

Tip: When using varying cross sections on a span segment, the section definitions are interpreted literally. If a rectangular section should taper to an L-section, for example, the flange will taper from zero thickness at the rectangular section to the actual thickness at the L-section. If the flange thickness should remain constant, a dummy flange should be defined for the rectangular section. The flange should be defined marginally wider, say 0.1mm, than the web and its depth made equal to the desired flange depth.

Supports input You can specify simple supports, columns below and above, fixed ends and cantilever ends. To allow a complete sub-frame analysis, columns can be specified below and above the beam/slab. If no column data is entered, simple supports are assumed.

The following input is required:

• Sup no: Support number, between 1 to 2’. Support 1 is the left-most support.


• C,F: The left-most and right-most supports can be freed, i.e. cantilevered, or made fixed by entering ’C’ or ’F’ respectively. By fixing a support, full rotational fixity is assumed, e.g. the beam/slab frames into a very stiff shaft or column.

• D: Depth/diameter of a rectangular/circular column (mm). The depth is measured in the span direction of the beam/slab.

• B: Width of the column (mm). If zero or left blank, a circular column is assumed.

• H: Height of the column (m).

Tip: For the sake of accurate reinforcement detailing, you can specify a width for simple supports at the ends of the beam/slab. Simply enter a value for D and leave B and H blank. In the analysis, the support will be considered as a normal simple support. However, when generating reinforcement bars, the program will extend the bars a distance equal to half the support depth past the support centre line.

• Code: A column can be pinned at its remote end by specifying ’P’. If you enter ’F’ or leave this field blank, the column is assumed to be fixed at the remote end.

Tip: You may leave the Support input table blank if all supports are simple supports.


Column heads input The punching shear capacity of a flat slab can be enhanced by defining column heads or drop panels. If the ACI approach of column stiffness reduction is used, the stiffness of column heads is also included in the sub-frame analysis.

The following data can be entered at each column head:

• S/T: Specify a square or tapered column head. If left blank, a tapered head is used.

• Diameter/Depth: The depth (in span direction) or diameter, in the case of circular column heads (mm).

• Width: The width of a rectangular column head (mm). Leave this field blank if the column head is circular.

• Height: The height of the column head (mm).

Note: The program will not check the validity of a column head in relation to column. It is possible, for example, to define an unpractical circular column head for a rectangular column.


Loads input Dead and live loads are entered separately. The entered loads are automatically patterned during analysis. For more detail on the pattern loading technique, refer to page 6-9.

Distributed loads, point loads and moments can be entered on the same line. Use as many lines as necessary to define each load case. Defined loads as follows:

• Case D,L: Enter ’D’ or ’L’ for dead load or live load respectively. If left blank, the previous load type is assumed. Use as many lines as necessary to define a load case.

• Span: Span number on which the load is applied. If left blank, the previous span number is assumed, i.e. a continuation of the load on the current span.

• Wleft: Distributed load intensity (kN/m) applied at the left-hand starting position of the load. If you do not enter a value, the program will use a value of zero.

• Wright: Distributed load intensity (kN/m) applied on the right-hand ending position of the load. If you leave this field blank, the value is made equal to Wleft, i.e. a uniformly distributed load is assumed.

• P: Point load (kN).

• M: Moment (kNm).


• a: The start position of the distributed load, position of the point load or position of the moment (m). The distance is measured from the left-hand edge of the beam. If you leave this field blank, a value of zero is used, i.e. the load is taken to start at the left-hand edge of the beam.

• b: The end position of the distributed load, measured from the start position of the load (m). Leave this field blank if you want the load to extend up to the right-hand edge of the beam.

Note: A portion of the live load can be considered as permanent for deflection calculation. For more detail, refer to the explanation of the Parameters input on page 6-9.

Note: If you enter a concrete density on the Parameters input page, the own weight of the beam/slab is automatically calculated and included with the dead load.

Load combinations input Load cases can be optionally be combined into load combinations.


Two loading modes are available:

• ’Automatic load combinations’ allows for automatic pattern loading of dead and live loads, e.g. as for typical building slabs.

• ’User load combinations’ allows for combinations of the entered load cases, e.g. as for bridge decks.

Note: No load combinations need be entered if the automatic load combination mode is selected.

As many lines as necessary may be used to input combinations of the various load cases:

• Load Combination: Name of the load combination. If this field is left blank, the load combination is taken to be the same as for the previous row in the table.

• Load Case: Number or name of the load case.

• ULS Factor: Load factor with which the load case should be multiplied for the ultimate limit state.

• SLS Factor: Load factor with which the load case should be multiplied for the serviceability limit state.


Tendon Profiles

You can let the program generate tendon profiles or you can enter profiles as required. The program is capable of generating reasonable tendon profiles for typical beams and slabs that you can adjust and change to obtain the required result.

Generated tendons can have parabolic or harped profiles. The program attempts to generate tendons to balance the specified percentage of dead load. Profiles generated will not be perfect for all cases and may require some manual adjustment.

Tendon profiles are displayed one set at a time, where a set is defined as one or more tendons with the same profile and force distribution. The following parameters define the profile for each span:

• L: Left offset of tendon inflection point (parabolic) or slope change (harped) from left end of span (m).

• R: Right offset of tendon inflection point or slope change from right end of span (m).

• b1: Distance from top surface to tendon centre line at left end of the span (mm).

• b2: Distance from bottom surface at midspan to tendon centre line (mm).


• b3: Distance from top surface to tendon centre line at right end of the span (mm).

Tip: The values of L and R are normally taken is the greater of span divided by and 250mm for parabolic cables and span divided by four for harped cables.

The following properties cab be set for each group of tendons:

• Number of tendons: Number of tendons in the set.

• Tendon property no: Tendon property number 1, 2, or 3 as defined in the original input.

• Life end position: Position of live end from left hand side of entire beam or slab.

• Dead end position: Position of dead end from left hand side of entire beam or slab.

• Parabolic / Harped: Parabolic or harped tendons.

The plotted tendon force diagrams represent the total force of all tendons:

• The initial tendon forces are shown in blue and include losses due to friction, wedge slip and elastic shortening of the concrete.

• The final tendon forces are shown in red and include the long-term effects, tendon relaxation, shrinkage and creep of the concrete.

The equivalent balancing loads are also displayed. The balancing loads are shown as percentage of the equivalent dead load. The latter is defined as the total dead load for each span, including own weight and any applied dead load, divided by span length.

Tip: Even if you want to specify your own tendon profile, it is nearly always easier to allow the program to generate the tendon profiles and then edit them, delete some or add more tendon groups.


Reinforcement

Additional bending reinforcement and punching shear reinforcement can be designed interactively.

Additional bending reinforcement Diagrams are displayed for additional reinforcement required (blue lines) and reinforcement entered (red lines). Anchorage and bond lengths are taken into account.

The required additional unstressed reinforcement is calculated in accordance with the Concrete Society Technical Reports 17 (paragraph 3.3 and 4.3) and 25 (paragraph 4.11):

• A minimum of 0.15% unstressed reinforcement is taken over columns over a width equal to the column width plus four times the slab width.

• Where tensile stress prevails over supports, reinforcement is supplied to resist tensile force.

• At midspan and where the tensile concrete stress exceeds 0.15fcu, a working stress of 0.58fy is used in the reinforcement.


Tip: The method used to calculate reinforcement aims to limit tensile concrete stress by adding sufficient reinforcement and tends to be conservative. Less reinforcement can normally be used, say three quarters of the peak values. In the final analysis you should check that the various requirements for crack width, ULS capacity and nominal reinforcement are met.

Reinforcement bars are entered as follows:

• Span: Span number

• T/B: Reinforcement at Top or Bottom

• Bar: Specify the steel as individual bars, e.g. 3T16, 2Y20 or 4R16, or groups of bars, e.g. Y25@300. One can also combine bars, e.g. 2T16 + T10@250.

• L/R: If a hook or bend is required on the left end of the bar, enter an ’H’ or ’B’ in the L column. For a hook or bend on the right end of the bar, use the R column.

• X: Position of left end of the bar measured from the left end of the span (m).

• Length: Length of the bar (m).

Punching shear reinforcing The data required for punching shear design is categorised as follows:

• Geometrical input.

• Forces and parameters required calculating the effective shear force Veff.

• Tendons and additional reinforcement to consider when calculating the allowable shear stress, vc.

The following parameters are required to define the column and slab geometry:

• A: Column dimension in longitudinal direction (mm). If a column below was originally input, its D value will be used as default.

• B: Column dimension in transverse direction (mm). If a column below was originally input, its B value will be used as default.

• C: Column head dimension in longitudinal direction (mm). Leave this field blank if there is no column head.

• D: Column head dimension in the transverse direction (mm). Leave this field blank if there is no column head.

• Deffx: Effective depth for reinforcement orientated in the X-direction (mm).

• Deffyx: Effective depth for reinforcement orientated in the Y-direction (mm).


• X: Longitudinal distance from the support centre to the edge of the slab (mm).

• Y: Transverse distance from the support centre to the edge of the slab (mm).

• Corner: Enter ’Y’ for an outside corner or ’N’ for an inside corner.

For the calculation of the effective shear force Veff, the program detects internal, edge and corner columns as follows:

• Internal column: Both edges further than 5deff from the column centre.

• Edge column: One edge closer than 5deff from the column centre.

• Corner column: Two edges closer than 5deff from the column centre.

Information required calculating the effective shear force Veff:

• Vt: Total Shear force transferred from slab to column.

• Mtx: Moment transferred between slab and column in X-direction.

• Mty: Moment transferred between slab and column in Y-direction.

Note: Irrespective of the selected loading combination mode, the program will assume that pattern loading would have been applied. The program therefore automatically reduces the entered values for Mtx and Mty by 30%. Refer to BS 8110 - 1997 clauses 3.7.6.2 and 3.7.6.3 and SABS 0100 - 1992 clauses 4.6.2.2 and 4.6.2.3 for detail.

• UDL: Uniform ultimate load in the region of the column (kN/m). The shear force is reduced by the portion of load within each perimeter considered.

• Pcx: The pre-stressing force in the longitudinal direction deemed to have a shear relieving effect (kN). The value will default to the total pre-stressing force of all tendons. This may be accurate for banded tendons. However, for tendons spaced further apart, only those passing through the shear perimeters should be considered. The vertical component of the entered total pre-stressing force is deducted from the effective shear force.

• Pcy: The pre-stressing force in the transverse direction deemed to have a shear relieving effect (kN). This value must be entered manually.

• Slope-X: Average slope of tendons in X-direction crossing the punching shear perimeters. The slope is used to calculate the vertical component of the pre-stress relieving the effective shear force. The program will base the initial value on the generated tendon profiles.

• Slope-Y: Average slope of tendons in Y-direction crossing the punching shear perimeters. The value must be entered manually.

Note: Although the program performs a uni-directional analysis for bending moment, deflections, etc, bi-directional effects are included in the punching shear design procedure.


Tip: For orthogonally stressed slabs, it is recommended that you design one direction, e.g. the banded direction, and record the relevant punching shear values. On analysing the other direction, you can enter these parameters for the Y-direction entered for complete bi-directional punching shear checks.

The shear capacity is based on the following parameters:

• Type: The number of the tendon types entered on the Parameters input page – refer to page 6-9 for detail. The specified type's properties are used to calculate the pre-stressed reinforcement passing through each perimeter.

• N cables: Number of cables passing longitudinally through each perimeter (average per side) in the X (longitudinal) and Y-directions (transverse). The area of the pre-stressed cables is then incorporated in the calculation of the shear resistance Vc.

Note: When calculating the shear resistance Vc, both bonded and un-bonded tendons are considered.


• Ast: Amount of conventional reinforcement passing longitudinally through each shear perimeter in the X and Y-directions. The reinforcement values Asx and Asy represent the minimum amount of main reinforcement crossing each perimeter in the X and Y-directions. For a perimeter edge on both side if the column, e.g. y1 in the sketch, you should use the minimum of the amount of reinforcement crossing the left edge and the amount crossing the right edge. For a perimeter edge on one side only, e.g. y2 in the sketch, use the amount of reinforcement crossing that single edge.

Note: The amount of conventional reinforcement can be taken as the average (minimum for unsymmetrical reinforcement) amount passing through the perimeter on the left and the right (as seen on the screen) of the column. For an edge or corner column, the amount should be taken equal to the amount passing through the perimeter on the span side.


Design

The analysis is performed automatically when you access the View output pages.

Analysis procedure Two separate analyses are performed for SLS and ULS calculations.

Serviceability limit state analysis

Elastic deflections, concrete stresses and cracking are calculated by analysing the beam/slab under pattern loading using the gross un-cracked sections.

When determining long-term deflections, however, the all spans of the beam/slab are subjected to the maximum design SLS load. Sections are then evaluated for cracking at 250 mm intervals, assuming the reinforcement required at ultimate limit state. The long-term deflections are then calculated by integrating the curvature diagrams.

Tip: After having generated reinforcement for a beam, the long-term deflections will be recalculated using the actual reinforcement.

Refer to page 6-9 for more detail on calculation of long-term deflections.

Ultimate limit state analysis

At ultimate limit state, the beam/slab is subjected to pattern loading as described on page 6-9. The resultant bending moment and shear force envelopes are then redistributed. Finally, the required reinforcement is calculated.

Fixing errors that occurred during the analysis The Input pages incorporate extensive error checking. However, serious errors sometime still slip through and cause problems during the analysis. Common input errors include:

• Entering too large reinforcement cover values on the Parameters input screen, gives incorrect reinforcement. Cover values should not be wrongly set to a value larger than half the overall section depth.

• Not entering section numbers when defining spans on the Spans input screens causes numeric instability. Consequently, the program uses zero section properties.


Long-term deflection problems

The cause of unexpected large long-term deflections can normally be determined by careful examination of the analysis output. View the long-term deflection diagrams and determine which component has the greatest effect:

• The likely cause of large shrinkage deflection is vastly unsymmetrical top and bottom reinforcement. Adding bottom reinforcement over supports and top reinforcement at in the middle of spans generally induces negative shrinkage deflection, i.e. uplift.

• Large creep deflections (long-term deflection under permanent load) are often caused by excessive cracking, especially over the supports. Compare the span to depth ratios with the recommended values in the relevant design code.

• Reduced stiffness due to cracking also has a direct impact on the instantaneous deflection component.

Viewing output graphics The analysis results can be viewed graphically or in tabular format. Output data, including graphics and tabled values, can be selectively appended to the Calcsheets using the Add to Calcsheets function on each output page.

Diagrams can be displayed for deflection, member forces and stress and shell reinforcement of any load case.

Deflections

The elastic deflection envelope represents the deflections due to SLS pattern loading. The long-term deflection diagram represents the behaviour of the beam/slab under full SLS loading, taking into account the effects of shrinkage and creep:

• The green line represents the total long-term deflection.

• The shrinkage deflection is shown in red.


• The creep deflection (long-term deflection due to permanent loads) is given by the distance between the red and blue lines.

• The distance between the blue and green lines represents instantaneous deflection due to transient loads.

Note: Long-term deflections in beams are influenced by reinforcement layout. Initial long-term deflection values are based on the reinforcement required at ultimate limit state. Once reinforcement has been generated for a beam, the long-term deflections will be based on the actual reinforcement instead.


Moments and shear forces

The bending moment and shear force diagrams show the envelopes due to ULS pattern loading. The capacities are calculated from the entered tendons and conventional rein-forcement. Capacities are shown in blue and actual moments and shear forces in red.

Concrete stress

Serviceability limit state stress envelopes are displayed for the following cases:

• At transfer of tendon forces: Only initial dead loads and no additional dead loads are considered.

• At SLS: The full SLS loads are applied and long-term losses in tendon forces included.

The actual stress envelopes are shown in red and the allowable stresses in blue. Guidelines for allowable concrete stresses are given on page 6-9.


Crack widths

In the calculation of crack widths, the program takes into account all bonded tendons and also any additional reinforcement that has been entered. The crack spacing is calculated on the assumption that all the bars and bonded tendons are spaced equally across the widest portion of the section.

Un-bonded tendons are ignored when calculating crack widths. If too few bars or bonded tendons are present, rotations in the sections will be high and unrealistic values of deflection will result. The program will give a warning when this occurs.


Calcsheets

The beam/slab design output can be grouped on a calcsheet for printing or sending to Calcpad. Various settings are available to include input and design diagram and tabular result.




Profile Scheduling

Designed tendons can be scheduled as Padds compatible drawings. Profile properties are taken from the Tendon profiles input page. Enter Padds file name special notes that should appear on the schedules and then click Generate schedules.

The resulting schedule can be opened in Padds for further editing and printing.

Tendon detailing in Padds

Apart from other reinforcement detailing commands, Padds cab also draw tendons in plan.


Finite Element Slab Analysis 6-97

Finite Element Slab Analysis

Fesd (Finite Element Slab Design) can perform linear elastic plate bending analyses of two-dimensional concrete slab structures. Reinforcement can be calculated from moments transformed using the Wood and Armer equations.

To design concrete membranes, use the Space Frame Analysis module instead.




Sign conventions Slab input is done using the global axes. The analysis output is given in a mixture of global axis and local axes values.

Global axes

The global axis system is nearly exclusively used when entering slab geometry and loading. Global axes are also used in the analysis output for deflections and reactions.


• For the sake of this definition, the X-axis is chosen to the right.

• The Y-axis always points vertically upward.


Note: Unlike some other 3D programs that put the Z-axis vertical, this program takes the Y-axis vertical.

Local axes

Local axes are used in the output for bending stresses:

• The local x-axis is chosen parallel to the global X-axis.

• The y-axis is taken parallel to the negative Z-axis.

• The z-axis is then taken vertical parallel to the Y-axis.

Shell element stresses

Shell element stresses are given using the local axes:


• Bending stresses: The entities Mx and My are moment per unit width about the local x and y-axes.

• Mxy represents a torsional moment in the local x-y plane.

• The principal bending moments per unit width are represented as Mmax and Mmin.

Note: To assist you in evaluating shell element stresses, stress contour diagrams show orientation lines at the centre of each shell element. An orientation line indicates the direction the direction (not axis) of bending or plane stress. In a concrete shell, the orientation line would indicate the direction of reinforcement resisting the particular stress.

Wood and Armer moments and shell reinforcement axes

Reinforcement is calculated in the user-defined x’ and y’-directions. Unlike the shell bending stresses that are taken about the x and y-axes, the Wood and Armer moments are given in the x’ and y’-directions. Refer to page 6-9 for detail.



Distance mm,m ft, inch

Force N, kN lb, kip

Finite element analysis Fesd uses four-node quadrilateral and three-node triangular isoparametric shell elements with plate bending behaviour. The bending formulation of the quadrilateral shell element was derived from the Discrete Kirchoff-Midlin Quadrilateral.

Accuracy of triangular elements

Both the quadrilateral and triangular elements yield accurate stiffness modelling. However, stress recovery from the triangular elements is not as accurate as is the case for quadrilateral elements. This means that deflections calculated using triangular elements are generally quite accurate, but moments may be less accurate.

Stress smoothing

A reduced integration technique is used to calculate the element stiffness matrices. The stresses are calculated at the Gaussian integration points and subsequently extrapolated bi-linearly to


the corner point and centre point of each element. Stresses at common nodes are smoothed by taking the average of all contributing stress components.

Element layout

Consider a typical continuous flat concrete slab supported on columns or walls. To ensure accurate modelling of curvature, a minimum of about four elements should be used between bending moment inflection points. This translates to a minimum of about eight elements per span in both directions.

Using more elements per span often does not yield a significant improvement in analysis accuracy. In addition, the particular finite element formulation yields its most accurate results when the element thickness does not greatly exceed its plan dimensions.

For a typical concrete slab with a thickness of about one-tenth or one-fifteenth of the span length, a reasonable rule of thumb is to make the plan dimensions of the shell elements no smaller than the thickness of the slab. In other words, use a maximum of about ten to fifteen elements per span.

Concrete design Fesd can perform reinforced concrete design for shell elements. The Wood and Armer equations are used to transform the bending and torsional stresses to effective bending moments in the user-defined x’ and y’-directions.

Note: The Space Frame Analysis modules can design shells for in-plane stresses as well. Refer to Chapter 3 for detail.

Codes of practice

The following concrete design codes are supported:

• ACI 318 - 1995.

• BS 8110 - 1997.

• CSA A23.3 - 1993.


• SABS 0100 - 1992.


Input

Work through the relevant Input pages to enter the slab geometry and loading:

• General input: Enter special design parameters.

• Nodes input: Slab coordinates.

• Shell elements input: Define shell elements.


• Point loads input: Point loads and moments.

• Shell loads input: Apply uniform distributed loads to shells.

• Load combinations input: Group dead and live loads in load combinations.

Alternative methods of generating slab analysis input are discussed on page 6-9.

Viewing the structure during input You may want to enlarge portions of the picture of the structure or rotate it on the screen. Several functions, all of which are described in detail in Chapter 2, are available to help you using pictures of the structure:


• Use the View Point Control to set a new viewpoint or camera position.

• Use the View Planes Control to view a slice through the slab.

The Options menu makes the following additional functions available:

• Graphics:


• Display the structure with full 3D rendering, e.g. to verify the thickness of slab sections.



• All surfaces are drawn as polygons. You can choose to make the surfaces transparent or have them filled and outlined.

• Contour values, like those on the reinforcement contour diagrams, can optionally be shown.


• Views: You can save the current viewpoint and graphic display options. The current view’s name is displayed on the picture. To re-use a saved view, click the view name on the picture to drop down a list of saved views. A detailed explanation is given in Chapter 2.


General input The General input page handles several important analysis parameters.

Concrete design parameters

Specify the concrete and reinforcement material properties, concrete cover to reinforcement and orientate the reinforcement axes. Refer to page 6-9 for more detail.

Envelope of load cases

Fesd calculates a set of results, including reinforcement values, for each load case or combination analysed. To enable you to easily identify the worst-case scenario, you can specify an envelope of load cases for which the minimum and maximum values are extracted.

The envelope can comprise load cases and/or load combinations. Results for the envelope is presented and can be accessed as if a separate load case.

Wizards

The wizards are suitable for the rapid generation of complete input files for some typical slabs.

Input generated this way can optionally be appended to existing data – you can therefore repeatedly use the wizards to generate complicated structures.


Note: The program is not limited to modelling only those slabs generated by the parametric modules. Any general two-dimensional slab can be treated. The parametric modules merely serve to simplify input of typical slabs.

Own weight



• By default, the own weight of the frame is set to not be included in the analysis. Be sure to select the appropriate load case for own weight or, alternatively, to include the frame’s own weight in the values of the loads entered.

• The list of load cases from which you can select is based on the load cases defined on the Point loads and Shell loads input pages. You may thus prefer to specify the own weight load case only after completing all other input for the frame. However, you can also enter the own weight load case at the start of the frame input process in which case you may ignore the warning message (that the load case does not exist).





Title

Enter a descriptive name for the frame. It should not be confused with the file name you use when you save the input data.


Nodes input Use as many lines as necessary to enter the nodes defining the slab. A unique number must be assigned to each node. The node number is entered in the No column, followed by the X and Z-coordinates in the X and Z columns. If you leave X or Z blank, a value of zero is used.

You are allowed to skip node numbers to simplify the definition of the slab. You may also leave blank lines in the input to improve readability. If a node number is defined more than once, the last definition will be used.


Error checking

The program checks for nodes lying at the same coordinate. If a potential error is detected, an Error list button will appear.



• The X-coordinate of node 4 is left blank. Therefore, node 4 is put at the coordinate (0,14.614).

• The No of is set to ’2’, meaning that two additional nodes must be generated.


• The values in the X-inc and Z-inc columns set the distance between copied nodes. The coordinates 4 to 18 are spaced at 1.140 m and 0.472 m along the X and negative Z-axis respectively. The coordinates of the additional nodes are thus (1.140,14.142) and (2.280,13.670).



• Set the values of X-inc and Z-inc to the total co-ordinate difference to the last node and enable the Inc to End option. The last node’s coordinates are then first calculated and the specified number of intermediate nodes then generated.


Once you have defined one or more nodes in the table, you can copy that relevant row’s nodes by entering a '–' character in the No column of the next row. Then enter the number of additional sets of nodes to be generated in the No of column and the coordinate increments in the X-inc and Z-inc columns.




No X Z 15 0.00 5.12 16 2.00 5.22 17 4.00 5.32 18 0.50 6.12 19 2.50 6.22 20 4.50 6.32

Block generation

A group of nodes can be repeated by entering a ’B’ in the No column followed by the first and last table row numbers in which the nodes were defined. Separate the row numbers with a ’–'.


The nodes defined in rows 11 to 26 are copied twice. Node numbers are incremented by thirty for each copy. The X and Z-coordinate increments are 10 m and zero respectively.

To copy one row only, simply omit the end row number, e.g. 'B10' to copy row 10 only.

The block generation function may be used recursively. That means that the rows specified may themselves contain further block generation statements.

Tip: To move a group of nodes to a new location without generating any new nodes, set the No-of to '1' and Inc to '0'.

Arc generation

A group of nodes can be repeated on an arc by entering an 'A' in the No column, followed by the start and end row numbers. Enter the centre of the arc in the X and Z columns and use the X-inc column to specify the angle increment.

Example:


All nodes defined in rows 5 to 9 of the table will be repeated eleven times on an imaginary horizontal arc. The centre point of the arc is located at the coordinate (10,1.5). The node number increment is set to 5, i.e. node number 3 becomes node 8, etc. The rotation angle between the generated groups of nodes is 30 degrees about the Y-axis, i.e. anti-clockwise using a right-hand rule.

To copy one row only, simply omit the end row numbers, e.g. ’A5’ to copy row 5 only.


Rotating nodes


Deleting nodes

Nodes can be deleted by entering a special X-coordinate of ’1E-9’ or by entering ’Delete’ in the Inc to end column. This can be especially handy if you have generated a large group of nodes and then need to remove some of them again.

Example:


Rigid links input Point loads and supports invariably result in stress concentrations. In the case of slabs supported on columns, it may be reasonable to ignore stress concentrations within the column areas and rather work with the stress values at the column faces. An alternative approach could be to smooth the stresses that prevail with the close surrounds of each of the columns, e.g. within a perimeter at a distance equal to the depth of the slab away from the column face.

Another more rational approach to modelling a slab at column supports is to introduce rigid links. This approach entails stopping shell elements at the column face and then linking the perimeter with the supported node at the position of the column centre. The high bending stiffness of the rigid links gives a reasonable approximation of the increased stiffness of the slab inside the perimeter of the column. The approach has the advantage of ridding the analysis of high shell bending stress peaks at the points of support.


Shell elements input Elements are defined by referring to corner nodes, four in the case of quadrilaterals and three for triangles. You should enter the node numbers in sequence around the perimeter, either clockwise or anti-clockwise, in the Node 1 to Node 4 columns. Leave Node 4 blank to define a triangular element.

Note: Quadrilateral elements generally yield more accurate analysis results than triangular elements. Refer to page 6-9 for more detail.


Selecting materials

Each slab element should have an associated material.

To add one or more materials to a slab analysis data file, click Materials. Open the relevant material type screen and select the materials that are required for the current slab input.





Error checking



You can generate additional elements with the same section and fixity code values using the No of extra and Node No Inc columns.

Example:

The element enclosed by nodes 15, 16, 26 and 25 are copied ten times with a node number increment of three, i.e elements (18,19,29,28), (21,22,32,310 etc.

Block generation

A group of elements can be repeated by entering a ’B’ in the No column. Then enter the first and last table row numbers in which the elements were defined, separated with a ’–'.


All elements defined in rows 5 to 7 will be copied ten times with a node number increment of twelve. The copied elements will use the same thickness and material properties as the original elements.

To copy one row only, simply omit the end row number, e.g. 'B5' to copy row 5 only.


Tip: When entering a complicated slab it may help to leave a few blank lines between groups of elements. Not only will it improve readability, but it will also allow you to insert additional elements at a later stage without upsetting block and arc generations.


Deleting elements

Shell elements can be deleted by entering ’Delete’ in the Material column. This can be useful if you have generated a large group of elements and need to remove some of them again. Example:

Elements 15-16-26-25 and 18-19-29-28 are deleted.

Supports input Slabs require external supports to ensure global stability. Supports can be entered at nodes to prevent any of the three degrees of freedom associated with plate bending, i.e. translation in the Y-direction and rotation about the X and Z-axes. You can also define elastic supports and prescribed displacements, e.g. foundation settlement.

Enter the node number to be supported in the Node No column. In the next column a combination of the letters ’Y’, ’x’ and ’z’ can be entered to indicate the direction of fixity. Use capitals and lowercase to define restraint of translation and rotation respectively, e.g. ’Yxz’ means fixed against movement in the Y-direction and rotation about the X and Z-axes.



Tip: To enter a simple support with no moment restraint, one would typically enter a ’Y’.

If you want to repeat the supports defined on the previous row of the table, you need only enter the node number, i.e. you may leave the Fixity column blank. If the Yxz column is left blank, the supports applicable to the previous row will be used automatically.

Skew supports

The rotational supports ’x’ and ’z’ can be made skew by entering a value in the Angle column. This feature may be useful when modelling slabs with rotational support perpendicular to skew edges.

Prescribed displacements

Use the X, x, and z columns to enter prescribed displacements and rotations. Being a global support condition, the effect of the prescribed displacement is added once only to the analysis results of each load case and load combination. Optionally enter a ’P’ in the P/S column to designate the values as prescribed displacements.

Elastic supports

Elastic supports, or springs, are defined by entering spring constants in the X, x, and z columns. The spring constant is defined as the force or moment that will cause a unit displace-ment or rotation in the relevant direction. Enter an ’S’ in the P/S column to indicate that an entered value is a spring constant rather than a prescribed displacement. If you leave the P/S column blank, the entered values are taken as prescribed displacements.

Tip: The effect of a column above or below the slab can be modelled by entering their bending stiffnesses as rotational spring supports about the x and z-axes. From simple elastic theory, the rotational stiffness of a column that is fixed at the remote end is given as 4EI/L. The stiffness of a column that is simply supported at the remote end is equal to 3EI/L.

Error Checking

The program does a basic check on the structural stability of the slab. If a potential error is detected, an Error list button will appear.




Additional supports and prescribed displacements can be generated using the Number of extra and Node number inc columns. The procedure is similar to that described on page 6-9 for generating additional nodes.

Note: The display of supports can be enabled by editing the Display Options.

Point loads input Loads on shell elements are categorised as point loads, i.e. concentrated loads at specific coordinate, and element loads, i.e. uniform distributed loads.

All loads are organised in load cases, e.g. ’DL’ for own weight, ’ADL’ for additional dead loads, ’LL’ for live load, etc. Load cases apply equally to the various load input screens, meaning that you can build up a load case using different types of loads.

To define a load case, type a descriptive name for each load case in the Load Case column. Use up to six characters to describe each load case. If the load case name is not entered, the load case applicable to the previous row in the table is used.


Enter the coordinates and load values in the appropriate columns, using the global axis sign conventions given on page 6-9. The load case at the cursor position is displayed graphically. Press Enter or Display to update the picture.

Error checking


Generating additional point loads

Additional point loads can be generated using the Number of extra and X-increment and Z-increment columns.

Shell loads Distributed loads can be applied on shell elements. Enter a load case description in the Load case column followed by the relevant element numbers in the Shell numbers column. The program automatically assigns numbers to all shell elements in the sequence they are defined on the Shells input page.


A series of elements can be entered by separating the first and last element numbers by a ’–' character, e.g. '1–6' to define elements 1 up to 6.Enter the distributed load intensity in the UDL column.


Error checking

The program checks that the entered element numbers are valid. If an error is detected, an Error list button will appear.


The No of extra and Shell number Inc columns can also be used to generate additional shell loads. The procedures are similar to that used to generating additional shell elements – see page 6-9 for detail.

Load combinations input You can model practical scenarios by grouping load cases together in load combinations. Enter the load combination number in the Load Combination column; followed by the load case name and relevant load factors.

If the Load Combination column is left blank, the load combination is taken to be the same as for the previous row of the table. The load cases to consider in a load combination are entered one per row in the Load case column. Enter the relevant ultimate and serviceability limit state load factors in the ULS factor and SLS factor columns.



• Deflections are calculated using the entered SLS loads. A set of reactions is also calculated at SLS for the purpose of evaluating stability and bearing pressures.

• A second set of reactions and all element forces are determined using the entered ULS forces.


Error checking


Alternative slab input methods Alternative means of slab input are available:

• Parametric input: Modules are available for the rapid generation of input for typical slab structures.

• Graphical input: Structures can be drawn in Padds or another CAD system and converted to slab analysis input.

Wizards A number of typical frames can be input by entering a number of parameters. The Wizards do most of the data input. See page 6-103 for detail on the wizards.

Graphical input In some situations, it may be easier to define a slab’s geometry graphically. With Padds you can draw a slab and then generate a slab analysis input file.

Using Padds for slab input

To use Padds to define a slab’s geometry:

1. Use Padds to draw the slab. Alternatively, import a DXF drawing from another CAD system.

2. The slab should be drawn to scale using millimetres as unit.

3. The element grid is drawn using lines.

Tip: You may sometimes find it quicker to hatch an area with a line pattern and then vectorise the hatch to turn it into normal lines.

4. Use the Generate input command on the Macro to display the drawing conversion options. Choose the Fesd and press OK to start the conversion procedure.

The resultant Fesd input file will be compatible with both the Dos and Windows versions of the slab analysis modules. The file is saved in the working folder as a last file, e.g. ’Lastfesd.a01’.

5. Close Padds.


Tip: To see a graphical input example, open ’\prokon\data\demo\inputgen.pad’ in Padds.


Analysis parameters input

The General input page allows you to set the parameters relevant to the analysis.

Concrete design parameters input It is generally impractical to design reinforcement to resist torsional moments in slabs. Reinforcement is usually fixed in two directions approximately, but not necessarily, perpendicular to each other. This justifies the use of transformed moments to calculate reinforcement.

Fesd uses the Wood and Armer theory; to convert calculated bending and torsional moments to transformed bending moments. More detail is given on page 6-9.

The required concrete design parameters are:

• Enter the concrete and reinforcement material characteristics, fcu and fy.

• Define the orientation for the ’main’ and ’secondary’ reinforcement, i.e. the x’ and y’-axis. Looking from the top, the x’-axis is measured anti-clockwise from the local x-axis to the reinforcement x’-axis. The y’-axis is in turn measured anti-clockwise from the x’-axis.

• Define the reinforcement levels in the slab by entering the concrete cover values for the top and bottom reinforcement in both directions.

Reinforcement contours can be displayed on the Bending stresses output page.


Analysis

On completing the slab input, you should set the analysis options before commencing the actual analysis.

Analysis options

Analysis options available on the General input page include:

• Concrete design: If the model includes finite shell elements, you can optionally design the shells as reinforced concrete members.

• Add own weight: Select a load case to which the self-weight of the beam and shell members should be added.

On the Analysis page, select the following:

• Output file: Enter an output file name or accept the default file name, e.g. ’Fesd.out’.

• Analyse load combinations only: Enable this option if the results of only the load combinations are required. Generally, one would require results for the load combinations only. However, you may have a special need to view the results of specific load cases as well. Disable this option to include the results for the individual load cases as well.

Analysing the slab To analyse the slab, open the Analysis page and press Start Analysis. The analysis progress of displayed to help you judge the time remaining to complete the analysis.

After a successful analysis, the deflected shape is displayed for the first load case or load combination or, in the case of modal or buckling analysis, the first mode shape.



During the input phase, the slab geometry and loading data is checked for errors. Not all reported errors are necessarily serious. To define duplicate elements between two nodes, for example, could be an accidental error on your side. However, the program can deal with a situation like this and will allow the analysis procedure to continue.


The first step of any analysis is the final verification of the input data. In the case of critical errors still present, a warning message will be displayed. If you then choose to not proceed with the analysis, you will be taken to the input table with the error. However, choosing to proceed and ignore the warning will have an unpredictable result.

Fixing errors that occurred during the analysis Even if all input data seems valid, numeric errors may still occur during an analysis. For example, if you entered incorrect section properties, such as a very small E-value, the mistake may go by unnoticed. However, the analysis will then yield an invalid value in the stiffness matrix or extremely large deflections. The same applies to the stability of the slab.





Viewing output

The analysis results can be viewed graphically or in tabular format.

Viewing output graphics Diagram can be displayed for the following:

• Deflections: Deflections are generally small in relation to dimensions of the structure. To improve the visibility of the elastic deflection diagram, you can enter a screen magnification factor.

• Bending stresses in shells:

• The x, y and xy bending stresses: The bending stresses about the local x and y-axes and the torsional stresses. The direction (not axis) of bending is shown as a small line on each shell element.

• Maximum and minimum bending stresses: The principal bending stresses.

• Reinforcement and Wood and Armer moments: Contours of the effective bending moments and corresponding required reinforcement at the top and bottom in the x’ and y’-directions. The reinforcement direction is shown as a small line on each shell. Refer to page 6-9 for an explanation of the use of the Wood and Armer equations and to page 6-9 for the definition of the reinforcement directions.

Note: Shell bending stresses are taken about the x and y-axes. In contrast, the Wood and Armer bending moments are given in the x’ and y’-directions.


Viewing output tables Open the Output file page for a tabular display of the slab analysis output file. You can filter the information sent to the calcsheets by enabling or disabling the relevant sections.

You can also quickly locate a section of the output file using the Find output function.


Calcsheets

Slab analysis output can be grouped on a calcsheet for printing or sending to Calcpad. To include a particular component of the output in the calcsheets, view the relevant output information and then click Add to Calcsheets.

Recalling a data file The Data File is automatically included in the calcsheet sent to Calcpad. You can later recall the slab by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the slab analysis module as well.

Rectangular Slab Panel Design 6-124

Rectangular Slab Panel Design

The Rectangular Slab Panel Design module designs rectangular flat slab panels with a variety of edge supports. The program should best be used for designing slabs with approximately rectangular panel layouts. You can use the Space Frame Analysis or Finite Element Slab Design module to analyse slabs with irregular panel layouts and openings.




Design scope The program designs rectangular reinforced concrete flat slab panels. Design loads include own weight, distributed and concentrated dead and live loads. Slab edges can be made free, simply supported or continuous.

Bending moment is transformed to include torsional moment using the Wood and Armer equations. Reinforcement is calculated using the normal code formulae.

Irrespective the selected design codes, long-term deflections are estimated in accordance with clause 9.5.2.3 of ACI318 - 1992


• ACI 318 - 1995.

• BS 8110 - 1997.

• CSA A23.3 - 1993.


• SABS 0100 - 1992.


List of symbols The design code symbols are used as far as possible:

Slab geometry

dx : Effective depth for reinforcement in the longer span direction, i.e. parallel to the X-axis (mm or in).

dy : Effective depth for reinforcement in the shorter span direction, i.e. parallel to the Y-axis (mm or in).

h : Overall slab depth (mm or in).


Lshort : Length of the short side of the slab, taken parallel to the Y-axis (m or ft).

Llong : Longer side length of the slab, taken parallel to the X-axis (m or ft).

Material properties

fcu : Concrete cube strength (MPa or psi).

fy : Reinforcement yield strength (MPa or psi).

: Time factor for long-term deflection

ν : Poisson’s ratio, typically equal to 0.2.

γ : Unit weight of concrete (kN/m³ or lb/ft³)

Applied loads

WADL : Additional distributed dead load (kN/m² or kip/ft²).

WLL : Additional distributed dead load (kN/m² or kip/ft²).).

PDL : Additional dead point load (kN or kip).

PLL : Additional live point load (kN or kip).

Design output

Abotx : Bottom steel parallel to the X-axis (mm²/m or in²/ft).

Atopx : Top steel parallel to the X-axis (mm²/m or in²/ft).

Aboty : Bottom steel parallel to the Y-axis (mm²/m or in²/ft).

Atopy : Top steel parallel to the Y-axis (mm²/m or in²/ft).

Analysis of the slab The program calculates bending stresses and elastic deflection by means of a finite element analysis. Thirty-six plate elements are placed on a 6 x 6 grid. The program uses eight-noded isoparametric finite elements that are well suited for thin plate analysis.

The analysis procedure employs a 2 x 2 Gaussian integration technique to calculate the element stiffness matrix. The stresses are calculated at the Gaussian integration points and subsequently extrapolated to the eight nodes and centre point of each element. The stresses at common nodes are smoothed by taking the average of all contributing stress components.


Long-term deflections The program estimates long-term deflections by adjusting the stiffness of the slab based on the leveO� RI� FUDFNLQJ��7KH�XVH�RI�D� WLPH� IDFWRU� � IRU�HVWLPDWLQJ�FUHHS�EHKDYLRXU�� LV�EDVHG�RQ� WKH�approach by ACI 318 – 1992 clause 9.5.2.3.

7\SLFDO�YDOXHV�IRU� �DUH�

Duration of load 7LPH�IDFWRU�

5 years or more 2.0

12 months 1.4

6 months 1.2

3 months 1.0

Instantaneous 0.0

Note: The calculated long-term deflections are not exact and should be considered a reasonable estimate only.

Reinforcement calculation The finite element analysis yields values for bending stresses about the X and Y-axes and torsional stresses. Due to the practical difficulties involved in reinforcing a slab to resist torsion, the Wood and Armer equations are used to transform the bending and torsional stresses to effective bending moments in the X and Y-directions.

Correlation with the design code values The moments and reinforcement calculated by the program are generally lower than the values given by the design codes. The discrepancy can be ascribed to the differences in the analysis techniques used. In particular, the code values include allowances for pattern loading and moment redistribution.

Considering continuous slabs, negative moments will generally correlate well while positive span moments would be about ten to fifteen percent too low.

Note: In cases where pattern loading is important, e.g. continuous slabs, it is suggested that the calculated bottom reinforcement be increased by about fifteen percent.


Input

Use the single input table to define the slab and its loading.

Geometry and loads input The following general points should be noted:

• If the aspect ratio of the slab exceeds 3:1, it may be more appropriate to design it as spanning in one direction only.

• Long-term deflections are calculated if you specify a time factor, ��ODUJHU�WKDQ�RQH�

• Own weight is modelled by entering a value for the unit weight. The own weight is automatically added to each load case entered.

• For the ultimate limit state calculations, the own weight, additional dead load and dead point loads are multiplied by the entered dead load factors. All live loads are similarly multiplied by the live load factor.


• To create load combinations, simply repeat the relevant loads in the table. Copying lines in the table is easily accomplished using the table editor commands.

Tip: You can use the mouse to click on the slab picture and stretch its dimensions.

Supports input The corners of the slab are supported vertically at all times. The edges can be supported using the following codes:

• Displacement: To support an edge in the vertical direction, i.e. simply supported. A typical example would be a slab simply supported on a masonry wall that provides no rotational support.

• Rotation: To restrain rotation about an axis parallel to the slab edge, i.e. continuous. This could be a reasonable model for a slab panel supported on columns if it is continuous with one or more adjacent panels.

• Displacement and rotation: The support conditions can be used together to support an edge vertically and prevent rotation, e.g. a continuous slab resting on a wall.

Note: Edges that are made continuous are given zero rotation during the analysis. This could be a reasonable assumption provided that the adjacent panel has a similar flexural stiffness. Where adjacent spans differ significantly in terms of span length and thickness, spans should be modelled individually with continuous supports. Differences in the negative moments on the continuous edges should then be redistributed manually according to the relative stiffness of each panel.


Design

Due to the simple finite element arrangement used, the analysis procedure will complete almost instantaneously. You can view the design results graphically:

• Moments: Transformed moment diagrams, using the Wood and Armer equations, for the top and bottom in the X and Y-directions are shown. Values are given per unit width. The transformed moments in the top and bottom fibres represent the moments to be resisted by the calculated reinforcement.

• Deflections: Short-term elastic deflections, based on the un-cracked gross concrete section are shown. The deflections do not include long-term effects like shrinkage and creep.

• Reinforcement: Required reinforcement for the top and bottom in the X and Y-directions is shown. The calculated reinforcement is based on the transformed moments and therefore includes the effects of torsion.


Calcsheets

The slab panel design output can be grouped on a calcsheet for printing or sending to Calcpad. Various settings can be made with regards to the inclusion of design results and pictures.


Recalling a data file If you enable the Data File option before sending a calcsheet to Calcpad, you can later recall the design by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the column design module as well.


Detailing

Reinforcement bending schedules can be generated for designed slab panels. Bending schedules can be edited and printed using Padds.

Generating a bending schedule Based on your initial input and the design results, initial values are chosen for the reinforcement. Change the values to suit your detailing requirements.


• Schedule file name: Name of the Padds drawing and schedule file.

• Detailing parameters:

• First bar mark: Mark to use for the main bar. You may use any alphanumeric string of up to five characters, e.g. ’A’, ’01’ or ’A01’. The mark is incre-mented automatically for subsequent bars.

• Concrete cover to reinforcement

• Reinforcement bond length.

• Drawing scale: The drawing paper is sized to fit the complete detail.

• Reinforcement for top and bottom layers in each of the X and Y-directions.

Press Generate to create a Padds bending schedule with the entered settings. To discard all changes you have made and revert to the default values for the designed column, press Reset.

Note: To detail slabs of more complex shape, use Padds.


Editing and printing of bending schedules Detailed editing and printing of bending schedules are done with Padds. For this, follow the steps below:

• In Padds, choose Open on the File menu and double-click the relevant file name. The file will be opened and displayed in two cascaded widows. The active windows will contain the drawing of the slab panel and the other window the bar schedule.



• Member description: Use as many lines of the Member column to enter a description, e.g. ’SLAB PANEL E’.



• Bending schedule number: The schedule number in the bottom right corner defaults to the file name, e.g. ’SLABE.PAD’. The schedule number can be edited as required to suit your numbering system, e.g. ’P123456-BS405’.


Finally, combine the column drawing and schedule onto one or more A4 pages using the Make BS Print Files command on the File menu. Use Alt-P to print the schedule immediately or Alt-F to save it as a print file for later batch printing.

Column Design 6-134

Column Design

The concrete column design modules are suitable for the design of the following column types:

• Rectangular Column Design, RecCol: Solid rectangular columns of which the larger column dimension does not exceed four times the smaller dimension.

• Circular Column Design, CirCol: Solid circular columns where the simplified design approach applicable to rectangular columns may be applied.

• General Column Design, GenCol: Columns of any general shape and columns with openings.

All column design modules can design reinforced concrete columns subjected to bi-axial bending. Bending schedules can be generated for editing and printing using the PROKON Drawing and Detailing System, Padds.

Column Design 6-135



Design scope The column design modules design reinforced concrete columns subjected to axial force and bi-axial bending moment.

The following conditions apply to the design of rectangular and circular columns:

• The design codes give simplified procedures for designing columns of which the ratio of the larger to the smaller dimension does not exceed 1:4.

• The procedure used for the design of rectangular columns is applied to the design of circular columns.

• The reinforcement layout is assumed to be symmetrical.

Reinforcement bending schedules can be generated for designed columns. Schedules can be opened in Padds for further editing and printing.


• ACI 318 - 1993.

• BS 8110 - 1987.

• BS 8110 - 1997.

• CSA-A23.3 - 1994.

• Eurocode 2 -1992.

• SABS 0100 - 1992.



Column Design 6-136

Rectangular column geometry

b : Width of cross section, perpendicular to h (mm or in). This smaller column dimension is taken parallel the X-axis.

d’x : Distance from the column face to the centre of the reinforcement resisting moments about the X-axis (mm or in).

d’y : Distance from the column face to the centre of the reinforcement resisting moments about the Y-axis (mm or in).

h : Depth of the cross section (mm or in). This larger column dimension is taken parallel the Y-axis.

Circular column geometry

d’ : Distance from the column face to the centre of the reinforcement (mm or in).

Ø : Diameter of column (mm or in).

Effective lengths

ßx : Effective length factor for bending about the X-axis

ßy : Effective length factor for bending about the Y-axis

Material properties



Es : Modulus of elasticity of reinforcement (GPa or ksi).

Applied loads

Mx top : Moment about the X-axis applied at the top end of the column (kNm or kipft). If left blank, a value of zero is used. A positive moment is taken anti-clockwise.

Mx bot : Moment about the X-axis applied at the bottom (kNm or kipft).

My top : Moment about the Y-axis applied at the top (kNm or kipft). A positive moment is taken anti-clockwise.

My bot : Moment about the Y-axis applied at the bottom (kNm or kipft).

P : Axial force in the column (kN of kip). A positive value denotes a downward compression force and a negative value an uplift force.

Design output

Ac : Gross concrete area (mm² or in²).

Column Design 6-137

Ascx : Area of vertical reinforcement to resist the effective design moment about the X-axis (mm² or in²).

Ascy : Area of vertical reinforcement to resist the effective design moment about the Y-axis (mm² or in²).

b' : Effective depth to reinforcement in shorter direction of rectangular column (mm or in).

h' : Effective depth to reinforcement in longer direction of rectangular column (mm or in).

Lex : Effective length for bending about the X-axis (m or ft).

Ley : Effective length for bending about the X-axis (m or ft).

Madd : Additional moment about the design axis of a circular column (kNm or kipft).

Madd x : Additional slenderness moment about the X-axis due to the column deflection (kNm or kipft).

Madd y : Additional moment about the Y-axis (kNm or kipft).

Mmin x : Minimum design moment for bending about the X-axis (kNm or kipft).

Mmin y : Minimum design moment about the Y-axis (kNm or kipft).

Mx : Design moment about the X-axis for rectangular column (kNm or kipft).

My : Design moment about the X-axis for rectangular column (kNm or kipft).

M' : Design moment (kNm or kipft).

M'x : Effective uniaxial design moment about the X-axis for rectangular column (kNm or kipft).

M'y : Effective uniaxial design moment about the Y-axis for rectangular column (kNm or kipft).

Code requirements The supported design codes have similar clauses with respect to bracing and end fixity conditions.

Braced and un-braced columns

A column is braced in a particular plane if lateral stability to the structure as a whole is provided in that plane. A column should otherwise be considered as un-braced.

Global lateral stability is normally provided by means of shear walls or other bracing systems. Such bracing systems should be sufficiently stiff to attract and transmit horizontal loads acting on the structure to the foundations.

Column Design 6-138

RecCol and Circol allow you to set independent bracing conditions for bending about the X and Y-axis of rectangular columns.

Effective length of columns

The effective length or height of a column depends on its end conditions, i.e. the degree of fixity at each end. Four end condition categories are defined in the design codes:

• End condition 1: The end of the column is connected monolithically to beams or slabs that are deeper than the column dimension in the relevant plane.

• End condition 2: The end of the column is connected monolithically to beams or slabs which are shallower than the overall column dimension in the relevant plane.

• End condition 3: The end of the column is connected to members that provide some nominal restraint. In the context of this program, this condition is regarded as pinned.

• End condition 4: The end of the column has no lateral or rotational restraint, i.e. a free end of a cantilever column. In the context of this program, this condition is regarded as free.

The codes suggest the follow values for the effective length factor, ß:

End condition at the top

End condition at the bottom

ß (Effective length factor)

Column in braced frame (ß ≤ 1.0)

Fixed Fixed

Pinned

0.75 to 0.85

0.90 to 0.95

Pinned Fixed

Pinned

0.90 to 0.95

1.00

Column in unbraced frame (ß > 1.0)

Fixed Fixed

Pinned

1.2 to 1.5

1.6 to 1.8

Pinned Fixed

Pinned

1.6 to 1.8

N.A.

Free Fixed 2.2

Note: The column design modules automatically calculate the effective length factors in relation to the specified end conditions. You may however manually adjust the effective length factors if necessary.

Column Design 6-139

Short and slender columns

A column is considered to be short if the effects of its lateral deflection can be ignored.

Slenderness in a given plane is expressed as the ratio between the effective length and the column dimension in that plane. The slenderness limits for short and slender columns set by some of the supported codes of practice are:

Slenderness limit BS 8110 - 1997 SABS 0100 – 1992

Short Braced

hlex and

b

ley < 15 h

lex and b

ley < 2

1

MM

717 −

Column Unbraced

hlex and

b

ley < 10 h

lex and b

ley < 10

Maximum All lo ≤ 60b Lo ≤ 60b and b ≥ 4h

Slenderness Cantilevers b60

hb100

lo2

≤≤ lo ≤ 25b and b ≥ 4h

Note: In the above expressions for maximum slenderness, h and b are taken as the larger and smaller column dimensions respectively.

Column Design 6-140

Input

The column definition has several input components:


• Bracing conditions and fixity at the column ends.

• Load cases.

Geometry input The RecCol and CirCol modules have been simplified for the design of rectangular and circular columns. Entering a column’s geometry input in either of these modules is therefore straightforward.

Tip: You can use the mouse to click on the column pictures and stretch certain dimensions, e.g. the column length.

Column Design 6-141

General column geometry input

GenCol is used to design columns of any general shape and hence has a reasonably intricate input procedure. A column section is entered as one or more shapes or polygons:

• The Code column is used for categorise the data that follows in the next columns:

+ : The start of a new polygon. An absolute reference coordinate must be entered in the X/Radius and Y/Angle columns. If you leave either blank, a value of zero is used.

– : Start of an opening. An absolute reference coordinate must be entered in the X/Radius and Y/Angle columns.

R : If you enter an 'R' or leave the Code column blank, a line is drawn using relative coordinates, i.e. measured from the previous coordinate.

L : Enter an 'L' in the Code column blank to make the following coordinate absolute.

A : To enter an arc that continues from the last line or arc. The arc radius and angle are entered in the X/Radius and Y/Angle columns respectively. The angle is measured clockwise from the previous line or arc end point.

Column Design 6-142

C : A circle with the radius entered in the X/Radius column.

B : A reinforcement bar with its diameter entered in the X/Radius column.

Note: Bar positions and diameters do not need to be entered when using RecCol and CirCol.

• The X/Radius/Bar dia and Y/Angle columns are used for entering coordinates:

X : Absolute or relative X coordinate (mm or in). Values are taken positive to the right and negative to the left.

Y : Absolute or relative Y coordinate (mm or in). Values are taken positive upward and negative downward.

You do need to close the polygon – the starting coordinate is automatically used as the ending coordinate. If two polygons intersect, the geometry of the last polygon takes preference and the previous polygon is clipped. A hole in a structure can, for example, be entered on top of previously entered shapes.

Tip: You can leave blank lines between polygons/bars to improve readability.

If convenient, e.g. to simplify loading input, the column can be rotated by entering an angle.

Material properties input The following material property values are required:

• Concrete cube strength, fcu (MPa or psi).

• Reinforcement yield strength, fy (MPa or psi).

• GenCol also requires a value for the modulus of elasticity of the reinforcement, Es (GPa or ksi).

Specifying bracing and fixity conditions Define the bracing and fixity conditions by making the appropriate selections. For an explanation of the terms used, refer to page 6-9. The effective length factors are automatically adjusted in relation to the specified bracing and end fixity conditions. If necessary, you may manually edit the effective length factors.

Note: RecCol allows the bracing and end fixities to be set independently for bending about the X and Y-axis.

Column Design 6-143

Loads input More than one ultimate load case can be entered:

• Enter a case number and description for each load case.

• Axial load (kN or kip). A positive value denotes a compression force. The program does not automatically include the self-weight of the column. The self-weight should be calculated and manually included in the applied loads.

• Moment values (kNm or kipft). Use the same sign for the top and bottom moments about an axis to define double-curvature about that axis.

Note: All entered loads should be factored ultimate loads.

You can use as many lines as necessary to define a load case – all values applicable to a specific load case are added together.

Column Design 6-144

Design

The column design modules follow different design approaches:

• RecCol and CirCol calculate the required reinforcement for the column.

• GenCol evaluates the column for the entered reinforcement or calculates a single bar diameter to be used at each defined bar position.

Irrespective the approach followed, additional moments are calculated for slender columns and automatically added to the applied moments. The design moment is taken to be equal to or larger than the minimum moment set by the code.

Rectangular column design The design procedure given in the codes is applied. The column is evaluated at the top, middle and bottom and the critical section identified as the section requiring the greatest amount of reinforcement.

The design procedure can be summarised as follows:

• Column design charts are constructed for bending about the X and Y-axis.

• If the column is slender, additional slenderness moments are calculated as required about a single or both axes.

• For slender columns, the applied moments and additional moments are summed for each axis.

• In the case of bi-axial bending, the moments are converted to an effective design moment about a single design axis.

• The reinforcement required to resist the design moment is read from the applicable column design chart.

• Using the same procedure, a design moment is derived about the axis perpendicular to the design axis. Reinforcement resisting the secondary design moment is read from the relevant chart.

Column Design 6-145

Circular column design The same simplified design procedure as for rectangular columns is used. The major and minor column dimensions, h and b, are both set equal to the column diameter.

The column is evaluated at the top, middle and bottom and the critical section identified as the section requiring the greatest amount of reinforcement.

Note: The design procedure for bi-axially bent slender columns tend to be conservative due to he codes’ allowance for additional moment about both the X and Y axes.

General column design GenCol designs columns that do not necessarily fall inside the scope of the code requirements. The program therefore reverts to basic principles, e.g. strain compatibility and equilibrium, to analyse columns. This is achieved using an automated finite difference analysis.

The following calculations are followed:

• The section properties are calculated and the column slenderness evaluated.

• For a slender column, the additional slenderness moment is calculated and applied about the weak axis, i.e. axis of lowest second moment of inertia. The output gives the X and Y-axis components.

• The design moment and axis are determined by taking the

Column Design 6-146

vector sum of the applied and additional moments.

• An iterative solution is obtained using strain compatibility and equilibrium as criteria. The simplified rectangular stress block given by the codes is used.

Note: Given the differences in the design procedures described above, GenCol will not yield identical results to RecCol and Circular Column Design modules when designing simple rectangular or circular columns.

Column Design 6-147

Design charts

The column design charts can be displayed for the specified column geometry and material properties:

• Rectangular columns: Separate charts are given for bending about the X and Y-axis for various percentages of reinforcement.

• Circular columns: Due to axial symmetry, a single design chart is shown.

• General columns: Separate charts are given for bending about the X and Y-axis.

Displaying design charts about other axes You can use Gencol to define a column and then rotate it about any angle. Design charts can then be displayed for the resultant horizontal and vertical axes.

Column Design 6-148

Calcsheets

The column design output can be grouped on a calcsheet for printing or sending to Calcpad. The different column design modules allow various settings, including design charts, tabular design summaries and detailed design calculations.


Recalling a data file If you enable the Data File option before sending a calcsheet to Calcpad, you can later recall the design by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the column design module as well.

Column Design 6-149

Detailing

Reinforcement bending schedules can be generated for designed columns. Bending schedules can be edited and printed using Padds.




• Main bars (high yield steel is assumed):

• Rectangular columns: Bar diameter for the corner bars and the number and diameter of the intermediate bars in the horizontal and vertical faces of a rectangular column, as displayed on the screen.

• Circular columns: The diameter and number of main bars. It is generally assumed good practice to use at least six bars.

• General columns: Main bar diameters are defined in the initial input. The shape code can be selected for each individual bar.

• Lap length factor for main bars.

Column Design 6-150

Note: To ensure that the amount of reinforcement supplied is not less than the amount required, the relevant values are shown in a table.

• Level at the bottom of the column (m or ft).

• Level at the top of the column or, in the case of starter bars, at the top of the base (m or ft).

• Links:

• Rectangular columns: Enter a link diameter and spacing, e.g. ’R10@200, and choose a link layouts. Link type ’2’ should only be used with square columns.

• Circular columns: Enter a link diameter and spacing and choose between using circular or spiral links.

• General columns: Select a shape code and follow the prompts to indicate the link coordinates. Available shape codes include ’35’ (normally used for holding intermediate bars in position), ’60’ or ’61’ (used to enclose four bars by a rectangular link) and ’86’ or ’87’ (spiral bar for use with circular columns).

• Link type: Choose one of the displayed link layouts.

• Concrete cover on links (mm or in).

• Detailing style to use:

• First bar mark: Mark to use for the first main bar. You may use any alphanumeric string of up to five characters, e.g. ’A’, ’01’ or ’A01’. The mark is incremented automatically for subsequent bars.

• Select a size for the sketch: If A4 is selected, the drawing is scaled to fit on a full page and the accompanying schedule on a separate page. The A5 selection will scale the drawing to fit on the same page with the schedule.

The following additional settings should be made:

• Column continuous: Enable this option to make the column bars continuous and have it detailed with a splice at the top. If this option is disabled the column is detailed with bends at the top to anchor it in a beam or slab.

• Starter bars only: If enabled, starter bars are generated instead of complete column bars.

• Double links at kinks: If enabled, a set of double links is provided at the position of the main bar kinks. Circular columns are detailed with straight bars, removing the need for this option.


Column Design 6-151


• In Padds, choose Open on the File menu and double-click the relevant file name. The file will be opened and displayed in two cascaded widows. The active windows will contain the drawing of the column and the other window the bar schedule.



• Member description: Use as many lines of the Member column to enter a member description, e.g. ’COLUMN TYPE 5’.



• Bending schedule number: The schedule number in the bottom right corner defaults to the file name, e.g. ’COLUMN5.PAD’. The schedule number can be edited as required to suit your numbering system, e.g. ’P123456-BS201’.



Retaining Wall Design 6-152

Retaining Wall Design

The Retaining Wall Design module is used to analyse retaining walls for normal soil and surcharge loads or seismic load conditions. Various types of walls can be considered, including cantilever, simply supported and propped cantilever walls.

Padds compatible bending schedules can also be generated for designed walls.



The following text gives an overview of the application of retaining wall analysis theory. For more detailed information, reference should be made to specialist literature.

Design scope The program can design most conventional retaining walls, including cantilever, simply supported and propped cantilever walls. Both static and seismic load conditions are supported. Analyses are performed using either the Coulomb or the Rankine theory.

Walls can be made to slope forward or backwards and the wall thickness can vary with height. Toes may optionally be included. Line loads, point loads and distributed loads can be placed on the backfill. A water table can be defined behind the wall. If required, the soil pressure coefficients can be adjusted manually.

Padds compatible bending schedules can be generated for designed walls.


• ACI 318 - 1995.

• BS 8110 - 1997.

• CSA A23.3 - 1993.


• SABS 0100 - 1992.

List of symbols Where possible, the same symbols are used as in the design codes.

Wall geometry

At : Wall thickness at the top (m).

Ab : Wall thickness at the bottom (m).

B : Horizontal base dimension in front of the wall (m).

C : Depth of the base (m).

D : Horizontal base dimension at back of the wall (m).

F : Depth of the shear key (m).


H1 : Total wall height (m).

H2 : Height of soil in front of the wall (m).

H3 : Height from top of wall to soil level at back of wall (m).

Hr : Height of the support point from the top of the wall for a simply supported or propped cantilevered wall (m).

Hw : Height of water table, measured from the top of wall (m).

x : Inclination of the wall (m).

xf : Position of the shear key, measured from the front of the base (m).

xL : Position of the line load, measured from the front edge of the wall (m).

xP : Position of the point load, measured from the front edge of the wall (m).

ß : Angle of soil behind wall (°).

Material properties

fcu : Concrete cube compressive strength (MPa).

fy : Reinforcement yield strength (MPa).

δ : Angle of friction between wall and soil (°). Must be zero if Rankine theory is specified.

φ : Angle of internal friction (°).

ν : Poisson’s ration for the soil. The plane strain value should be used rather than the triaxial value – see geometry and loads input.

Applied loads

kh : Horizontal acceleration for seismic analysis (g).

kv : Vertical acceleration for seismic analysis (g).

L : Line load on or behind the wall (kN/m).

Lh : Horizontal line load at top of wall (kN/m).

P : Point load on or behind the wall (kN).

W : Uniform distributed load behind the wall (kN/m2).

Design parameters

DLfact : Ultimate limit state dead load factor.

LLfact : Ultimate limit state live load factor.


Pmax : Design bearing pressure at serviceability limit state (kPa)

SFOvt : Allowable safety factor for overturning at serviceability limit state.

SFSlip : Allowable safety factor for slip at serviceability limit state.

Design output

As1 : Flexural reinforcement in the wall (mm2).

As2 : Flexural reinforcement in the back part of the base (mm2).

As3 : Flexural reinforcement in the front part of the base (mm2).

Ac1 : Compression reinforcement in the wall (mm2).

Ac2 : Compression reinforcement in the back part of the base (mm2).

Ac3 : Compression reinforcement in the front part of the base (mm2).

Ds : Density of soil (kN/m3).

K : Active pressure coefficient, including seismic effects.

Ka : Active pressure coefficient.

Kp : Passive pressure coefficient.

Kps : Passive pressure coefficient including seismic effects.

M1 : Maximum ultimate moment in the wall (kNm).

M2 : Maximum ultimate moment in back part of the base (kNm).

M3 : Maximum ultimate moment in front part of the base (kNm).

Pfac : Pressure factor used for Terzaghi-Peck pressure distribution diagram.

V : Shear force in wall at base-wall junction (kN).

v : Shear stress in wall at base-wall junction (MPa).

vc : Allowable shear stress in wall at base-wall junction (MPa).

µ : Friction coefficient between base and soil.

General assumptions The following assumptions are applicable to the analysis:

• A unit width of the wall is considered.

• Predominantly active soil pressures are assumed to act on the right-hand side of the wall

• Predominantly passive pressures are present on the left-hand side of the wall.


• Soil pressure, soil weight and wall self-weight are taken as dead loads.

• Applied distributed loads, line loads and point loads are considered to be live loads.

• If a water table is specified behind the wall, a linear pressure distribution is used along its depth. The pressure applied on the bottom of the base is varied linearly from maximum at the back, to zero at the front.

• Point loads are distributed along the depth of the soil. In contrast, line loads are taken constant in the transverse direction of the wall.

Application of Coulomb and Rankine theories The program can analyse retaining walls using either the Coulomb wedge theory or the Rankine theory.

Note: This manual does not attempt to explain the applicable theories in detail, but merely highlights some aspects of their application. For more detail, reference should be made to specialist literature.

Friction between the wall and soil

The higher the value of the angle of friction between the wall and soil, δ, the greater the degree of rotation of the system is implied. If the Coulomb theory is used, the friction angle should preferable be set equal to the internal angle of friction, φ. This will yield pressures that correlate better with the Rankine theory, than would be the case if δ is set equal to zero.

Active pressure on the shear key

Depending on its position, the shear key (if any) may be subjected to active pressure. The program allows for active pressure to be included or excluded from the analysis.

Saturated and submerged soil

To keep input as simple as possible, the program does no provide an option to enter values for specific gravity, void ratio, moisture content and degree of saturation. However, reasonable modelling of saturated soil and submerged conditions is still possible:

• If no water table is present, ρsoil should be taken as a value that includes moisture content that can reasonably expected.

• If a water table is present, the portion of the soil above the water table will likely have a degree of saturation close to unity. Using the wet density rather than the dry density should yield reasonable results.

Point loads and line loads

Point loads and line loads behind the wall are incorporated using the Boussinesq theory. The


theory can be found in ‘Foundation Analysis and Design’ by Joseph E Bowles, chapter 11-13, published by McGraw – Hill. It is recommended that the plane strain ν be used instead of the tri-axial ν. Values of plain strain ν versus tri-axial ν can be found in the table below.

Tri-axial ν 0.30 0.33 0.35 0.40 0.45 0.50 0.60

Plane strain ν 0.42 0.50 0.54 0.67 0.82 1.00 1.50

Seismic analysis

The program uses the Okabe-Monobe equations, based on the Coulomb wedge theory, to calculate revised active and passive pressure coefficients. The seismic portion of the active pressure is assumed to act at 60% of the soil height behind the wall, effectively increasing the lever arm of the soil pressure.

The densities of the materials are also adjusted by multiplying with (1-kv). An upward acceleration therefore effectively decreases the stabilising effect of the wall and soil weight.

Live loads can be optionally included in a seismic analysis. If included, live loads are applied with the same pressure coefficients as for dead loads.

Modelling of soil pressure behind rigid walls The program suggests values for the active and passive pressure coefficients, Ka and Kp. These values generally yield reasonable results for cantilever walls. However, simply supported and propped cantilever walls tend to be very rigid. This means that the actual active soil pressures could potentially rise well above the level normally assumed. The program therefore allows uniform pressure distribution to be specified, i.e. Factive = Pfac ⋅ Hwall ⋅ γsoil ⋅ Ka. Typical values for the uniform pressure coefficient, Pfact, was determined by Terzaghi and Peck. An average value of 0.65 should yield reasonable results in most cases.

Seepage modelling When a water table is modelled, seepage can optionally be allowed below the wall. If seepage is allowed, hydrostatic pressure is modelled as follows:

• The pressure behind the wall is taken as zero on the level of the water table and then linearly increased with depth.

• At the front of the wall, the pressure is taken as zero at ground level and linearly varied with depth.

• The hydrostatic pressure below the base is varied linearly between the values calculated behind and in front of the wall. If seepage is not allowed, the hydrostatic pressure in front of the wall or below the base is taken as zero.


Input

Use the input tables to enter the wall geometry, loading and general design parameters.

Geometry and loads input When entering the dimensions and loads working on the wall, you should keep the following in mind:

• Leave the value for F blank if a shear key is not required.

• The value for Hr is only required for simply supported and propped cantilever walls.

• Leave the Hw field blank if you do not want to define a water table. If you wish to design a liquid retaining wall, you may set the water table above the soil level.

• All applied loads work downward. Point loads are distributed at 45° through the depth of the soil. Line loads are applied uniformly along the width of the wall.


• Disable the option to allow seepage below the base if applicable, e.g. for liquid retaining walls.

• Allow active pressure to be applied to the back of the shear key (if any) if applicable, e.g. if it is positioned towards the back of the base with compacted backfill.

Note: For suggestions on modelling saturated soil and submerged conditions, refer to page 6-9.

Enabling seismic analysis When enabling Seismic analysis, you should also enter the following analysis parameters:

• Enter the equivalent seismic accelerations in the horizontal and vertical directions.

• Optionally include live loads in the analysis.

Soils pressure coefficients The program will calculate the soil pressure coefficients by default. To use your own coefficients, select User defined design values:

• Active and passive pressure coefficients, Ka and Kp.

• Soil friction constant below the base, µ.

• For simply supported and propped cantilever walls, you can choose between triangular or uniform pressure distributions. In the case of rigid walls, a uniform pressure coefficient can also be entered. See page 6-9 for more detail.


Selecting a wall type Choose one of the following wall types:

• Cantilever: The base is fixed against rotation with the wall cantilevering from it.

• Simply supported: The base has no fixity, i.e. free to rotate. The wall is supported horizontally at the bottom and at the level defined by Hr.

• Propped cantilever: Fixed at the bottom and simply supported at the level defined by Hr.

Selecting an analysis theory Choose between the Column and Rankine analysis theories. The Rankine theory cannot be used if the slope of the backfill is less than zero. Due to this and other limitations of the Rankine theory, use of the Coulomb wedge theory is often preferred.


Design

You can design the entered wall configuration or use the optimisation functions to obtain a more economic design.

Analysing the entered wall configuration The analysis includes several ultimate and serviceability limit state checks.

Calculating the ultimate design loads

Loads due to soil pressure and all weights, including concrete and soil, are multiplied by the dead load factor. Applied loads are considered to be live loads and are therefore multiplied with the live load factor.

Additional checks for propped cantilever walls

In the case of a propped cantilever wall, the program checks whether fixity can be obtained at the base. Fixity is attained by balancing loads such as own weight and soil weight plus the pressure distribution under the base against the fixity moment. If the fixity moment attainable is less than one and a half times the theoretical fixed moment, the fixity moment is reduced and the bending moment diagram and soil pressures adjusted accordingly.

Checking stability

Stability against overturning of the wall is checked by assuming rotation about the lower front corner of the base. If a shear key is used and it is located within one quarter of base width from the front, the program also checks for rotation about the bottom of the shear key.

Design results

The design output gives the following values at ultimate limit state:

• Bending moment diagrams (kNm).

• Required reinforcement in the base and wall (mm2).

• Maximum shear stress in the wall, v, and concrete shear capacity, vc (MPa).


Note: The wall design does not include any axial effects due to friction or applied loads.

Results for serviceability limit state checks include:

• Safety factor for overturning.

• Safety factor for slip.

• Bearing pressure diagram below the base.

Optimising the wall dimensions Optimise the wall using the following functions:

• Select B: Optimise the horizontal base dimension in front of the wall. The smallest value of B is calculated to not exceed the allowable bearing pressure and safety factor for overturning. A warning message is displayed if an appropriate value could not be calculated.

• Select D: Optimise the horizontal base dimension behind wall. The smallest value of D is calculated to satisfy the requirements set for the allowable bearing pressure and safety factor for overturning.


• Select F: The value of F is optimised using the safety factor for slip as only criterion.

Note: None of the optimisation functions considers all design criteria. It is therefore possible that after optimising the value of B, for example, the safety factor for slip is exceeded. You may thus need to alternate optimisation functions to arrive at a workable solution.


Calcsheets

The retaining wall design output can be grouped on a calcsheet for printing or sending to Calcpad. Various settings can be made with regards to the inclusion of design results and pictures.


Recalling a data file If you enable the Data File option before sending a calcsheet to Calcpad, you can later recall the design by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the wall design module as well.


Detailing

Reinforcement bending schedules can be generated for designed retaining wall. Bending schedules can be edited and printed using Padds.




• Wall and base reinforcement:

• Reinforcement is generated at various positions in the wall and base using the calculated ultimate bending moments. Change the diameters and spacing as required.

• Bond stress: Allowable stress for evaluating bar anchorage of the wall starter bars. If 90° bends proof insufficient, the program automatically uses full 180° hooks. Bar spacing is also reduced to lower bond stress.


• First bar mark: Mark to use for the first main bar. You may use any alphanumeric string of up to five characters, e.g. 'A', '01' or 'A01'. The mark is incremented automatically for subsequent bars.

• Select a size for the sketch: If A4 is selected; the drawing is scaled to fit on a full page and the accompanying schedule on a separate page. The A5 selection will scale the drawing to fit on the same page with the schedule.

Press Generate to create a Padds bending schedule with the entered settings. To discard all changes you have made and revert to the default values for the designed retaining wall, press Reset. Also press Reset if you have changed the reinforcement bond stress and want to recalculate the reinforcement.



• In Padds, choose Open on the File menu and double-click the relevant file name. The file will be opened and displayed in two cascaded widows. The active windows will contain the drawing of the retaining wall and the other window the bar schedule.



• Member description: Use as many lines of the Member column to enter a description, e.g. ’WALL TYPE C’.



• Bending schedule number: The schedule number in the bottom right corner defaults to the file name, e.g. ’WALLC’. The schedule number can be edited as required to suit your numbering system, e.g. ’P123456-BS303’.




Column Base Design 6-168

Column Base Design

The Column Base Design module is used to design and optimise rectangular column bases. Padds compatible bending schedules can be generated for designed bases.




Design scope The program designs rectangular concrete column bases subjected to vertical force and bi-axial bending moment. The program designs the base at ultimate limit state for bending moment and shear.

The program also verifies the stability requirements for overturning and bearing pressure. Stability checks can be performed at ultimate limit state or using the working force method. Refer to page 6-9 for details.

Reinforcement bending schedules can be generated for designed bases. Schedules can be opened in Padds, for further editing and printing.


• ACI 318 - 1993.

• BS 8110 - 1987.

• BS 8110 - 1997.

• CSA-A23.3 - 1994.

• Eurocode 2 -1992.

• SABS 0100 - 1992.


List of symbols The design code symbols are used as far as possible.

Geometry:

A, B : Horizontal and vertical base dimensions as shown on the screen (m or ft).

C, D : Horizontal and vertical column dimensions as shown on the screen (m or ft).

E, F : Horizontal and vertical column eccentricity as shown on the screen (m or ft).


X : Stub column height (m or ft).

X : Base thickness (m or ft).

Z : Soil cover on base (m or ft).

Rebar depth : Concrete cover plus half of the reinforcement diameter (mm or in).

Materials:

Density : Concrete and soil densities (kN/m³ or lb/ft³).

Friction angle : Internal friction angle for calculating passive soil stress.

Friction constant : Coefficient for calculating horizontal friction between the base and soil.

fci : Concrete cylinder strength of base and column (MPa or psi).

fcu : Concrete cube strength of base and column (MPa or psi).


Safety factors:

SFover : Safety factor for overturning.

SFslip : Safety factor for slip.

Loads:

Hx, Hy : Horizontal forces in X and Y direction (kN or kip).

LFovt : Load factor to use for evaluating overturning stability.

LFuls : Load factor for ultimate limit state calculations.

Mx, My : Moment in X and Y direction (kNm or kipft).

P : Vertical load (kN or kip).


Sign conventions The X and Y-axes lie in the horizontal plane. Using a right-hand rule, the Z-axis points vertically upward.

The sign conventions applicable to forces and moments are as follows:

• The vertical force, P, works downward.

• The horizontal forces Hx and Hy are applied parallel to the X and Y-axes.

• The moments Mx and My are applied in the X and Y-directions, i.e. about the positive Y and negative X-axes respectively

Post-processing frame analysis results

Forces are usually obtained using the reaction values calculated by frame analysis. When extracting frame analysis output, the differences in the sign conventions and axis systems used should be kept in mind:

• Applied load in Column Base Design module

• P • Hx

• Hy

• Mx

• My

• Frame Analysis Mode

• Frame analysis reaction value to use

• Plane Frame Analysis

• Ry

• – Rx

• None • M • N

one

• Grillage Analysis • Ry

• None

• None

• Mz

• Mx

• Space Frame Analysis

• Ry

• – Rx

• Rz

• Mz

• Mx


Input

The column base definition has several input components:


• Load cases and stability criteria.

Geometry input Enter the base and column dimensions, omitting the values for the either column if only one column is used. A column is positioned at the centre of the base unless non-zero values are entered for E and/or F.

Tip: You can use the mouse to click on the base pictures and stretch certain dimensions, e.g. the base thickness and column sizes.


Material properties input You are required to enter the properties of the concrete and soil fill and also specify the concrete cover to the reinforcement.

Setting the stability criteria Relevant limits should be entered for checking overturning, slip and bearing pressure at serviceability and ultimate limit state.

Modern design codes tend to consider stability checks like overturning at ultimate limit state. Depending on your own preference, you can use the program to check stability at ultimate limit state or using the older method of working loads (permissible working stress):

Checking overturning at ultimate limit state

The ratio of the cumulative effects of factored destabilising loads to the effect of the factored stabilising forces should not exceed unity. In this ratio, all forces are multiplied by the appropriate ULS factors that exceed unity and only the self-weight components of stabilising forces by the minimum ULS load factor that does not exceed unity.

When using this approach in the program, you will likely want to set the load factors for overturning for all stabilising components of self-weight to the minimum prescribed ULS dead load factor, typically between 0.9 and 1.0. For all other loads, a ULS load factor of between 1.2 and 1.6 (depending on the relevant code) will be appropriate.

Checking overturning using working loads

The older method requires the ratio of the cumulative effects of destabilising loads to stabilising loads to be greater than an appropriate safety factor, typically 1/0.7 or 1.5.

When using this approach, you should enter unity values for all load factors for overturning and specify relevant safety factors for overturning.

Checking slip at ultimate limit state

The program uses the entered load factors for ultimate limit state, LFuls, to evaluate slip. The safety factor for slip should thus normally be set to unity.


Loads input Enter one or more load cases. The following should be kept in mind:

• All loads are applied at the centre of the columns. A column is positioned at the centre of the base unless values for E and/or F are entered.

• For the case of a concrete column extending to the slab above, no stub column should be entered, i.e. the value for X should be left blank.

• For a steel base plate bearing directly on the base, enter the plate dimensions for the column dimensions, C and D, and use zero for the stub column height, X.

• Seen in elevation, the horizontal forces Hx and Hy are applied at the top of the stub column.

• All loads are entered un-factored. The ultimate design loads are obtained by multiplying the entered forces by the specified load factor.

• A positive value of P denotes a downward force. Use a negative value for uplift.

• Moments are applied in the X and Y directions, rather than about the X and Y-axes.

For detail on the sign conventions used for loads, refer to page 6-9.

Load factors

Each load has two load factors:

• LFovt: Load factor to use for overturning stability check.

• LFULS: Load factor to use for calculating bending moment, shear and reinforcement at ultimate limit state analysis.

Own weight of the base is considered as a separate load case. Load factors for own weight is entered in the geometry input table.


Note: Although overturning is also considered an ultimate limit state, the ULS abbreviation is used to designate the strength ultimate limit state.

For more detail on calculating the safety factor for overturning at ultimate limit state, refer to page 6-9.


Design

A column base is designed for compliance with ultimate limit state and serviceability limit state conditions:

• The required reinforcement to resist ultimate moments is calculated.

• Linear and punching shear checks are performed.

• The stability of the base is evaluated at both ultimate and serviceability limit state.

Stability checks Stability values for overturning, slip and bearing pressure are calculated at both ultimate limit state and serviceability limit state. The following general principles apply:

• Overturning: When considering overturning at ultimate limit state, the applied loads are multiplied by the entered load factors for overturning to calculate the ratio of destabilising to stabilising effects. At serviceability limit state calculations are performed using the entered un-factored working loads.

• Slip: At ultimate limit state, all forces are multiplied by their ULS load factors. The safety factor for slip is calculated by dividing the resisting passive soil pressure and friction by the horizontal forces causing slip. The same calculation is performed at serviceability limit state using un-factored forces.

• Bearing pressure: Entered loads are multiplied by their respective ULS load factors before calculating the bearing pressure. The un-factored loads are used at serviceability limit state.

Note: With careful manipulation of the load factors for overturning, you can manipulate the program to evaluate overturning stability at ultimate limit state or using the working loads method. Refer to page 6-9 for more information.

Reinforcement calculation The loads are multiplied by the specified load factor to obtain the ultimate design loads. The design forces, including the base self weight and weight of the soil cover, are used to calculate the ultimate bearing pressure below the base. The program calculates the bending moments in the base and uses the normal code formulae to obtain the required reinforcement. Nominal reinforcement is also calculated where applicable.

Shear checks


The required reinforcement for bending is used to calculate the shear resistance, vc, in the X and Y-directions. For punching shear, the value is based on the average required reinforcement in the two directions.

Linear shear

When considering linear shear, lines are considered at a distance equal to the base depth in front of each face of the column. The contribution of the soil pressure block outside the lines is then used to calculate the shear stress.

Punching shear

For punching shear, shear perimeters are considered at one and a half time the base thickness from the column faces.

Various combinations as for internal, edge and corner columns are considered.

Design results Results of stability checks:

• Bearing pressure beneath the base. The 3D pressure diagram is shown in elevation.

• Safety factor for overturning.

• Safety factor for slip.

Note: Stability checks are performed at ultimate limit state (modern limit state approach) and serviceability limit state (older working load approach). Depending of your way of working and the design code used, you may prefer to use only one or both sets of results.

Results of strength checks at ultimate Limit State:

• Design moments in the X and Y-directions in the bottom and top of the base (kNm or kipft).

• The corresponding required reinforcement (mm² or in²)

• Linear and punching shear stresses and allowable shear stresses (MPa or psi).


Optimising base dimensions The base dimensions can be optimised using the following functions:

• Optimise A, B and Y: Calculate the optimum values for all the base dimensions. The optimisation procedures take into account the specified material costs.

• Select B: Calculate the optimum value for the base dimension in the Y-direction. All other dimensions are left unchanged.

• Select A: Calculate the optimum value for the base dimension in the X-direction. All other dimensions are left unchanged.

Note: When optimising the base dimensions A and B, the base thickness is kept constant and no shear checks are performed. Where necessary, the base thickness should be adjusted manually.


Calcsheets

The column base design output can be grouped on a calcsheet for printing or sending to Calcpad. Various settings can be made with regards to the inclusion of design results and pictures.




Detailing

Reinforcement bending schedules can be generated for designed columns. Bending schedules can be edited and printed using Padds.




• Main reinforcement:

• Change the displayed bottom and top steel in the X and Y-directions as necessary.

• Top steel will only be given for bases thicker than 600 mm, or where tension reinforcement is required.

• Column reinforcement:

• At each column portion used, specify whether a normal column, stub column or no column should be detailed.

• Main bars: Diameter of column corner bars.

• Middle bars: The number and diameter of intermediate bars in the horizontal and vertical column faces, as displayed on the screen.

• Lap length factor: Splice length to allow for column starter bars.

• Links: Diameter, dimensions and number of stirrups to hold column starter bars in position.


• First bar mark: Mark to use for the first main bar. You may use any alphanumeric string of up to five characters, e.g. ’A’, ’01’ or ’A01’. The mark is incremented automatically for subsequent bars.


• Select a size for the sketch: If A4 is selected; the drawing is scaled to fit on a full page and the accompanying schedule on a separate page. The A5 selection will scale the drawing to fit on the same page with the schedule.

• Choose a configuration of bar shape codes to use for the bottom and, where applicable, the top reinforcement.



• In Padds, choose Open on the File menu and double-click the relevant file name. The file will be opened and displayed in two cascaded widows. The active windows will contain the drawing of the column base and the other window the bar schedule.



• Member description: Use as many lines of the Member column to enter a description, e.g. ’BASE 6’.



• Bending schedule number: The schedule number in the bottom right corner defaults to the file name, e.g. ’BASE6.PAD’. The schedule number can be edited as required to suit your numbering system, e.g. ’P123456-BS206’.





Section Design for Crack width 6-184

Section Design for Crack width

The Section Design for Crack width can be used to design reinforced concrete sections to meet specific crack requirements. Both beam and slab sections can be designed for the combined effects of axial tension, bending moment and temperature.



The following text gives an overview of the application of the theory.

Design scope The program can determine reinforcement layouts to contain cracks. Both rectangular beam and slab sections can be designed to resist the effects of axial tension, bending moment and temperature and the combination thereof. Temperature effects are also included to evaluate early cracking and long-term thermal cracking.

Shrinkage

Concrete shrinkage due to hydration is accounted for by a combination of the thermal expansion coefficient and the restraint factor. The design method employed by the codes is ideally suited for non-temperate regions like Europe.

Reinforcement type

Concrete cracking has traditionally been correlated with the prevailing tensile steel stress. Eurocode 2 - 1984 also takes account of the type of reinforcement, i.e. bond between concrete and reinforcement.

Codes of practice Design calculations are done according to BS 8007 - 1987 and Eurocode 2 - 1984.



Section dimensions

bt : Width of the section (mm or in).

h : Overall height of the section (mm or in).

he : Effective surface zone depth (mm or in).

Material properties



fy : Main reinforcement yield strength (MPa or psi).

Applied loads

R : Restraint factor.

T1 : Hydration temperature difference (°C).

T2 : Seasonal temperature variation (°C).

α : Thermal expansion coefficient of concrete (m/m per °C or in/in per °C).

TSLS : The tensile force on the full section at serviceability limit state (kN or kip).

TULS : The tensile force on the full section at ultimate limit state. (kN or kip).

MSLS : Serviceability limit state moment (kNm or kipft).

MULS : Ultimate limit state moment (kNm or kipft).

Ro critical : The minimum percentage of reinforcement to be supplied.

Design output

Ast : Area of suggested reinforcement layout. (mm² or in²).

fst : Tensile stress in reinforcement (MPa or psi).

Mu : Ultimate moment capacity of section (kNm or kipft).

TU : Ultimate tensile capacity of surface zone (kN or kip).


Input

The section geometry and loading is entered using the single input table. The following points require special attention.

• The program evaluates an effective surface zone where crack control would be effective, rather than the complete section. The surface zone is normally entered as half the section depth but not more than 250 mm.

• Because only a surface zone is considered, only half of the entered tensile forces (applicable to the overall section) is used.

• Reinforcement is calculated for the surface zone. The same reinforcement should be supplied in full in both faces of the section.

• Eurocode 2 requires additional information regarding the type of reinforcement bond applicable i.e. high-bond or plain bars.

• Select Beam mode if you wish cracking to be evaluated at the section corners as well.

Tip: It is recommended that wide sections be designed using Slab mode.


• The hydration temperature, T1, is defined as the difference between the environmental temperature and the peak temperature due to hydration. The value is used to evaluate early thermal cracking. Typical values, taken from Table A.2 of the code, are given below.

OPC content (kg/m3) Section 325 350 400 325 350 400

Thickness (mm) Steel formwork 18 mm plywood formwork 300 11* 13* 15* 23 25 31

500 20 22 27 32 35 43

700 28 32 39 38 42 49

1000 38 42 49 42 47 56

* Generally a minimum value of 20°C should be used. • The seasonal temperature variation, T2, is used to calculate long term thermal cracking:

• If movement joints are provided as per Table 5.1 of the code, the seasonal variation can normally be set equal to zero when considering early cracking only.

• The seasonal temperature variation should always be considered for long-term thermal cracking in combination with the applied moments and tensile forces.

Section OPC content (kg/m3) Thickness (mm) 325 350 400

300 15 17 21

500 25 28 34

• The restraint factor describes the amount of restraint in the system. The factor varies between 0.0 to 0.5. For more detail, refer to Figure A3 of the code.

Tip: A higher restraint factor generally gives rise to more severe cracking. Therefore, when in doubt, use a restraint factor of 0.5.

• Enter a value for Ro critical, i.e. the minimum percentage of reinforcement to be supplied. The value applies to the gross concrete section of the surface zone. The program gives a default value of 100 · fct / fy, where fct is the three-day tensile strength of the immature concrete. For more detail, refer to paragraph A.2 of the code.


Design

The following checks are considered for each load case at serviceability limit state:

• The combined effect of bending moment, tensile force and the seasonal temperature variation, i.e. MSLS + TSLS + T2.

• Early thermal movement, T1 only.

• Early thermal movement and seasonal variation combined, i.e. T1 + T2.

• The section is also evaluated at ultimate limit state by considering the combined effect of bending moment and tensile force, i.e. MULS + TULS.

Up to four sets of bars are calculated for slab sections. Each set has a different diameter and spacing to comply with the crack width requirements. A fifth column is provided where you could enter a bar configuration of choice.

For beams, up to four sets of bars are calculated. Each set of bars consists of a number of bars of not more than two different diameters. The bar diameters are chosen to not differ by more than one size.


Calcsheets

The crack width design output can be grouped on a calcsheet for printing or sending to Calcpad. Various settings can be made with regards to the inclusion of design results and pictures.


Recalling a data file If you enable the Data File option before sending a calcsheet to Calcpad, you can later recall it by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the design module as well.


Concrete Section Design 6-192

Concrete Section Design

The Concrete Section Design module is a simple utility for designing concrete sections for combined bending, shear and torsion. Rectangular and T-sections are accommodated.



The following text gives an overview of the application of the theory.

Design scope The program performs reinforced concrete design of rectangular and T-sections to resist bending moment, shear and torsion.


• ACI 318 - 1995.

• BS 8110 - 1985.

• BS 8110 - 1997.

• CSA A23.3 - 1993.


• SABS 0100 - 1992.


Section dimensions

B : Width of the web (mm).

Bf : Width of the flange (mm).

Dct, Dcb : Distance from the top or bottom face to the centre of the steel (mm).

H : Overall height of the section (mm).

Hf : Depth of the flange (mm).

Material properties

fcu : Concrete cube strength (MPa).

fy : Main reinforcement yield strength (MPa).

fy : Shear reinforcement yield strength (MPa).

Design output


As : Bottom steel required for bending (mm2).

A’s : Top steel required for bending (mm2).

Anom : Nominal flexural reinforcement (mm2).

Asv : Required shear reinforcement (mm2/mm).

Asvn : Nominal shear reinforcement (mm2/mm).

Mu : Ultimate moment capacity for bottom reinforcement only (kNm).

v : Shear stress (MPa)

vc : Allowable shear stress (MPa).

vt : Torsional shear stress (MPa).

Calculation of flexural reinforcement The normal code formulae apply when calculating flexural reinforcement for rectangular sections and for flanged sections where the neutral axis falls inside the flange. If the neutral axis falls outside the flange, the section is designed as two separate sub-sections:

• The first sub-section consists of the flange without the central web part of the section and the remaining central portion defines the second sub-section.

• By considering the total section, the moment required to put the flange portion in compression can be calculated using the normal code formulae. This moment is then applied to the flange sub-section and the required reinforcement calculated using the effective depth of the total section.

• The same moment is then subtracted from the total applied moment, the resulting moment applied to the central sub-section and the reinforcement calculated.

The tension reinforcement for the actual section is then taken as the sum of the calculated reinforcement for the two sub-sections. If compression reinforcement is required for the central sub-section, it is used as the required compression reinforcement for the entire section.

Calculation of shear reinforcement The program assumes that shear is resisted by the web portion of the section only. Shear stress, v, is therefore calculated using the web area and checked to not exceed the ultimate allowable shear stress given in the code. The shear capacity, vc, is calculated using the required bending reinforcement, As, and the shear reinforcement calculated using the normal code formulae.


Calculation of torsion reinforcement Depending on the option chosen, torsion can be resisted by the section as a whole or by the web portion only. For flanged beams, the torsion is calculated separately for the flange and web along the guidelines given in the code. The torsional shear stresses are checked so as not to exceed the ultimate allowable shear stress. Reinforcement requirements are also evaluated separately for the flange and web using the normal code formulae.


Input

The section geometry and ultimate loading are entered using the single input table. The following should be kept in mind:

• If the values for Bf and Hf are left blank, a rectangular section is assumed.

• A positive moment is assumed to cause compression in the top flange.

• The program puts the flange at the top. To model the case where the flange is at the bottom or where the flange is in tension, enter a rectangular section without a flange. The effects of bending and shear will still be evaluated correctly. In the absence of a flange, the torsion checks will however be conservative.

Tip: You can use the mouse to click on the picture and stretch certain section dimensions, e.g. flange width or overall depth.


Design

Press Analyse to design the section for the entered moment, shear and torsion. The following results are given:

• The moment capacity of the section using tensile reinforcement only. The tabled flexural reinforcement values are the required values at the top (compression) and bottom (tension) and the nominal reinforcement.

• Shear stress in the web and the shear capacity of the section together with the required and nominal shear reinforcement.

• For torsion in the web and flanges, values are tabled for the torsional shear stress and required shear and longitudinal reinforcement.

Some reinforcement configurations are also suggested:

• Number and diameters of reinforcement bars to resist bending only.

• Links to resist shear only in the web.

• Links to resist torsion only in the web and flange.

• Longitudinal reinforcement bars to resist combined bending and torsion in the web. The bottom and top bar configurations are chosen to exceed the required flexural reinforcement at that position plus half the total longitudinal torsional reinforcement.

Note: The suggested reinforcement configurations are given as guidelines only. You can use the tabled values for required reinforcement to determine rebar layouts more suitable to your requirements.


Calcsheets

The section design output can be grouped on a calcsheet for printing or sending to Calcpad. Various settings can be made with regards to the inclusion of design results and pictures.


Recalling a data file If you enable the Data File option before sending a calcsheet to Calcpad, you can later recall it by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the design module as well.

6-199

Punching Shear Design 6-200

Punching Shear Design

The Punching Shear Design module designs flat slabs for punching shear at edge, corner or internal columns. Only reinforced concrete slabs are designed – to design pre-stressed concrete slabs for punching shear, use the Pre-stressed Beam/Slab Design module, Captain, instead.




Design scope The program designs reinforced concrete flat slabs for punching shear at edge, corner and internal columns.


• ACI 318 - 1995.

• BS 8110 - 1985.

• BS 8110 - 1997.

• CSA A23.3 - 1993


• SABS 0100 - 1992.



Slab geometry

A : Horizontal column dimension, as shown on the screen, or diameter of circular column (mm or in).

B : Vertical column dimension, as shown on the screen (mm or in).

Deff : Average effective depth of the slab (mm or in).

X : Horizontal distance, as shown on the screen, from the column centre to the slab edge (mm or in).

Y : Vertical distance from the column centre to the slab edge (mm or in).


Material properties

fcu : Concrete cube compressive strength (MPa of psi).

fy : Yield strength of flexural reinforcement (MPa or psi)

fyv : Yield strength of shear reinforcement (MPa or psi).

Slab reinforcement

Asx1-4 : Average area of main steel parallel to the X-axis crossing each of the four perimeters (mm² or in²). The first perimeter denotes the innermost perimeter.

Asy1-4 : Average area of main steel parallel to the Y-axis crossing each of the four perimeters (mm² or in²).

Design output

Asv : The total area of stirrups to be provided within 1.5Deff inside a perimeter (mm² or in²).

Ucrit : Length of critical perimeter (mm or in).

vc : Allowable punching shear stress (MPa or kip).

Vc : Shear force capacity at a stress of vc (MPa of psi).

Veff : The effective shear force as a function of Vt, Mtx and Mty (kN or kip).

Applied loads

Mtx : Ultimate bending moment about the X-axis (kNm or kipft).

Mty : Ultimate bending moment about the Y-axis (kNm or kipft).

Vt : Ultimate vertical load on column (kN or kip).

Effective shear force The effective shear force, Veff, is calculated using the code formulae. The following minimum values are assumed:

• Internal columns: 1.15Vt.

• Edge columns: 1.25Vt, irrespective of the direction the column is bent.

• Corner columns: 1.25Vt.


Edge, corner and internal columns The following rules are used to determine whether a column should be considered an internal, edge or corner column:

• If one edge is closer than five times the effective slab depth, i.e. 5 · Deff, from the column centre, the column is considered to be an edge column.

• If two edges are closer than five times the effective slab depth from the column centre, the column is taken to be a corner column.

• If all edges are further than five times the effective slab depth from the column centre, the column is analysed as an internal column.

Reduction of design moments The program assumes that the design forces are obtained from an equivalent frame analysis that incorporates pattern loading. As allowed for by the codes, the values of the ultimate moments, Mtx and Mty, are subsequently reduced by 30% prior to calculating the effective shear force, Veff.

Shear capacity The program calculates the shear capacity in the X and Y-directions, vcx and vcy, based on the main reinforcement in those directions and the average effective depth. The design shear capacity, vcx, is then taken as the average of the values in the X and Y-direction.

Circular columns Given modern design trends, e.g. the approaches by ACI 318 - 1995 and Eurocode 2 - 1992, the use of circular perimeters seems a more rational approach to evaluating punching shear for circular columns. The program recognises this and uses the following design approach for checking punching by circular columns:

• As in the case of a rectangular column, the shear capacity vc is taken as the average of vcx and vcy. Put differently, one could consider an imaginary square shear perimeter when determining vc.

• The shear force capacity, Vc, is calculated using the actual circular perimeter. The shorter circular perimeter (compared to a rectangular perimeter) yields a lower (conservative) shear force capacity.


Input

The slab geometry and loading is entered using the single input table. The following parameters may require special attention:

• The reinforcement values Asx and Asy represent the minimum amount of main reinforcement crossing each perimeter in the X and Y-directions. For a perimeter edge on both side if the column, e.g. y1 in the sketch, you should use the minimum of the amount of reinforcement crossing the left edge and the amount crossing the right edge. For a perimeter edge on one side only, e.g. y2 in the sketch, use the amount of reinforcement crossing that single edge.

• By careful choice of the values for X and Y, you can force a column to be considered as an edge, corner of internal column. See page 6-9 for detail.

• The program assumes pattern loading and subsequently reduces Mtx and Mty by 30%.

Note: If the ultimate moments, Mtx and Mty, do not incorporate pattern loading, their values should be increased by 30% to ensure a correct analysis.


Design

The design procedure includes the following steps:

• The effective shear force, Veff, is calculated. See page 6-9 for an explanation of the assumptions that apply.

• The program chooses four shear perimeters. The first perimeter is taken a distance 1.5 · Deff away from the column face. Subsequent perimeters are spaced at 0.75 · Deff. The perimeters are chosen to be as short as possible, extending to the slab edge when necessary.

• For each perimeter, the allowable stress, vc, is taken as the weighted average of the values calculated for the X and Y-directions, using the flexural reinforcement ratio for the respective directions. Refer to page 6-9 for more detail.

• The required shear reinforcement for each perimeter is then calculated using the normal code formulae. The calculated reinforcement should be supplied within a distance 1.5 · Deff inside the relevant perimeter.


Calcsheets

The slab design output can be grouped on a calcsheet for printing or sending to Calcpad. Various settings can be made with regards to the inclusion of design results and pictures.



Timber Design 7-1

Chapter

Timber Design

The timber design module can be used to design timber members in frames and trusses.

Timber Design 7-2

Quick Reference

Timber Design using PROKON 3 Timber Member Design 5

Timber Design using PROKON 7-3

Timber Design using PROKON

The PROKON suite includes a module that is suitable for design of timber members in frames and trusses. A suite of timber connection design modules is planned.

Timber Design using PROKON 7-4

Timber Member Design 7-5

Timber Member Design

The timber member design module, Timsec, is used to check and optimise timber members subjected to a combination of axial and biaxial bending stresses, e.g. beams, frames and trusses.

The program primarily acts as a post-processor for the frame analysis modules. It also has an interactive mode for the quick design or checking of individual members without needing to perform a frame analysis.




Design scope The timber member design module can design timber and glued laminated timber load bearing members. Timsec currently has the following limitations:

• Only rectangular sections bent about their major or minor axes can be designed.

• Design of tapered and haunched sections is not supported.

Design codes The program designs timber members according to the following allowable stress design codes:

• BS 5268 - 1991.

• SABS 0163 - 1989.

Units of measurement Timsec supports Metric units of measurement only.


Dimensions

B : Section breadth (mm).

D : Section depth (mm).

L/r : Slenderness ratio.

Leff : Effective length (m).

Design parameters

Ke : Factor with which the member length is multiplied to obtain the effective length for lateral torsional buckling. Refer to page 8 for detail.

Kx : Factor with which the member length is multiplied to obtain the effective length for buckling about the x-x axis of the member. Refer to page 9 for more detail.


Ky : Factor with which the member length must be multiplied to obtain the effective length for buckling about the local y-y axis of the member.

Modification factors

k1 to k5 : Stress modification factors for SAB 1063 - 1989.

K1 to K14 : Stress and dimensional modification factors for BS 5268 - 1991. Refer to page 11 for detail.

Stresses

fb : Allowable bending stress (MPa).

fc : Allowable compression stress (MPa).

ft : Allowable tension stress (MPa).

sb : Actual bending stress (MPa)

sc : Actual compression stress (MPa)

st : Actual tension stress (MPa)

Sign conventions Member design is done in the local element axes. Bending about the x-x axis corresponds to strong axis bending and bending about the y-y axis to weak axis bending.

Axial force and moment

The local axes system and force directions are defined as follows:

• Axial force: The local z-axis and axial force is chosen in the direction from the smaller node number to the larger node number. A positive axial force indicates compression and a negative force tension.

• Bending: Moments about the x and y-axes represent bending about the section’s strong and weak axes respectively. Positive moments are taken anticlockwise in all diagrams.


P-delta effects Trusses are normally not sensitive to sway. However, in any structure, if you judge P-delta effects to be an important part of the analysis, you should perform a second order frame analysis.

Design parameters Different design parameters can be set for each group of elements designed:

Effective length factors beams

The lateral torsional stability of a beam depends on the degree of restraint to be expected at each end of the beam and of the compression edge along the length of the beam.

The codes treat lateral buckling by limiting section dimensions and specifying effective length factor, Ke:

• BS 5268 - 1991: To ensure there is no risk of lateral buckling of beams, limiting depth to breadth rations are given in clause 14.8, Table 19.

Degree of lateral support Maximum D:B ratio

• No lateral support • 2

• Ends held in position • 3

• Ends held in position and members held in line at centres not more than 30 times the breadth of the member, e.g. by purlins or tie rods

• 4

• Ends held in position and compression edge held in line, e.g. direct connection of sheathing, deck or joists

• 5

• Ends held in position and compression edge held in line, e.g. direct connection of sheathing, deck or joists, together with adequate bridging or blocking spaced at intervals not exceeding 6 times the depth

• 6


• Ends held in position and both edges held firmly in line • 7

• SABS 0163 - 1989: Lateral stability of beams is treated in clause 6.2.3.2. The laterally unsupported should be multiplied with the effective length factor given in Table 11:

Type of beam span Position of applied load Effective length factor, Ke

• Concentrated at centre • 1.61

• Uniformly distributed • 1.92 • Single span beam

• Equal end moments • 1.84

• Concentrated at unsupported end

• 1.69 • Cantilever beam

• Uniformly distributed • 1.06

The effective length factor may conservatively be taken as 1.92 for all situations.

Effective length factors for struts and ties

The effective length factors depend on the degree of restraint to be expected at each end of compression members. Guidelines are given in the codes:

• BS 5268 - 1991: Refer to clause 15.3, Table 21.

• SABS 0163 - 1989: Compression members are discussed in clause 6.4.3, Table 12


Effective length factors of compression members are summarised below:

End condition Effective length factor

• Fully restrained at both ends in position and direction

• 0.7

• Restrained at both ends in position and one end in direction

• 0.85

• Restrained at both ends in position only • 1.0

• Restrained at one end and in position and direction and at the other end in direction only

• 1.5

• Restrained at one end in position and direction and free at the other end

• 2.0

Considering a typical plane timber truss, the effective length Lx relates to in-plane buckling. For struts where rotational fixity is provided by the connection, e.g. two or more fasteners, a value between 0.70 and 0.85 is usually appropriate. Where rotation at the joints are possible, e.g. single bolted connection, a value of 1.0 would normally be applicable.

For a typical plane truss, the effective length Ly relates to buckling out of the vertical plane. This phenomenon can often govern the design of the top and bottom chords of a truss that can buckle in a snakelike ’S’ pattern, giving an effective length equal to unrestrained length. Lateral restraints are normally provided to reduce this effective length. For example, with braced purlins connected to the top chord of the truss, the effective length could be taken equal to the purlin spacing.

The effective length Le relates to lateral torsional buckling of a member about its weak axis. The length depends on the spacing and type of restraint of the member’s compression edge. Using an effective length factor Ke of 1.92 would be conservative for all cases.


Stress modification factors

The codes list several stress and other modification factors, not all of which are applicable to Timsec. Some factors are not covered by scope of the program and other are supported indirectly only by modification of other factors or design parameters. BS 5268 – 1991:

K1 : Modification factor by which the geometrical properties of timber in the dry condition should be multiplied to obtain values for the wet exposure condition. If applicable, you should manually adjust section sizes for the wet exposure condition.

K2 : Modification factor to be applied to dry stresses and moduli (Tables 9 through 13 and 15 of the code) to obtain values for the wet exposure condition. The same K2 factor is applicable to bending and tension while a different factor is applicable to compression.

K3 : Modification factor for duration of loading. Values from Table 17 of the code are summarised below:

Duration of load K3

• Long term, e.g. dead and permanent imposed loads

• 1.00

• Medium term, e.g. snow and temporary imposed loads

• 1.25

• Short term, e.g. temporary imposed loads

• 1.50

• Very short term, e.g. wind loads • 1.75

Note: Since load duration factor may differ for different loads on the structure, you should divide the relevant loads with this factor at the analysis stage.

K4 : Modification factor for bearing stress. Not applicable.

K5 : Shear strength factor to allow for notches. Not applicable.

K6 : Form factor for solid non-rectangular sections. Not applicable.


K7 : Multiplication factor for grade bending stresses for members graded to BS 4978, BS 5756 or "NGLA and NGRDL Joist and Plank rules". Likewise grade tension stresses can be multiplied with K14. The factors K7 and K14 are depended on the section dimensions and are automatically calculated during the design process if required.

K8 : Factor for load sharing by members connected in parallel. All grade stresses are multiplied by this factor.

Tip: You may use the factor for load sharing to include any other modification factors that are not applicable to standard timber sections, e.g. factors applicable to glued laminated timber.

K9 : Load sharing factor for calculating deflections. Not applicable.

K10, K11 : Size factor for modification of grade compression stresses and moduli of elasticity for members graded in accordance with North American NLGA and NGRDL rules. If applicable, the K10 and K11 modification factors can be included by adjusting the grade stresses.

K12 : Factor for allowable compression stress due to slenderness. This factor is automatically calculated during the design process.

K13 : Modification factor for the effective length of spaced columns. Instead of using this factor, you should adjust the effective length factors Kx, Ky and Ke if required.

K14 : See K7.

SABS 0163 – 1980:

k1 : Load duration factor. Since load duration factor may differ for different loads on the structure, you should divide the relevant loads with the Cr factor at the analysis stage. Load division coefficients are given in Table 9 of the code and summarised below:

Duration of load Cf

• Longer than three months, e.g. dead and permanent imposed loads

1.0

• Medium term (one day to three months), e.g. snow and temporary imposed loads

0.8

• Short term (less than one day), e.g. 0.66


wind loads and infrequently imposed loads

k2 : Factor for load sharing by members connected in parallel. All grade stresses are multiplied by this factor.

Tip: You may use the factor for load sharing to include any other modification factors that are not applicable to standard timber sections, e.g. factors applicable to glued laminated timber.

k3 : Stress modification factor for the type of structure. The value may be taken as 1.10 where the consequences of failure are small. For other structures a value of unity should be used.

k4 : Modification factor for quality of fabrication. If the fabricated member complies with an SABS specification, the value may be taken as 1.05.

k5 : Stress modification factor for moisture content. If the moisture content in a compression member may occasionally exceed 20%, use a value of 0.75.

Slenderness limits

BS 5269 - 1991 (clause 15.4) and SABS 0163 - 1989 (clause 6.4.4) specify similar slenderness ratios for members in compression. The slenderness limit for compression is taken as 180 in most cases. For tension members, a maximum slenderness ratio of 250, as specified by BS 5268 - 1991, is generally used.

When launching Timsec, the slenderness limits given by the selected design code will be used by default. You are free to alter the maximum slenderness ratio for each individual load case or combination if required. For example, in the case where a member is carrying self-weight and wind load only, the codes allow the maximum slenderness ratio for compression members to be increased to 250.


Member design techniques

The programs have two basic modes of operation:

• Read and post-process the frame analysis results.

• Alternatively, you can do an independent interactive design of one or more members.

The following text gives details of the design techniques and also explains how the database of timber grades and sections sizes can be customised.

Limitations of the timber member design module Timsec can be used to design timber members subjected to any combination of axial force, uni-axial and biaxial bending moment. The program cannot design non-rectangular sections or members of varying section.

Reading and post-processing frame analysis results Working through the input and design pages, the frame design procedure can be broken up into the following steps:

• The Input page: Defining design tasks by choosing a design approach, selecting members to be designed, setting the design parameters and selecting load cases and slenderness limits. The concept of tasks is described in detail on page 18.

• The Members page: Define internal nodes and enter effective lengths. Refer to page 24 for detail.

• The Design page: Evaluating the design results. See page 26 for detail.

• The Calcsheet page: Accumulate design results. See page 28 for detail.

Re-analysis of the frame

Having evaluated the various member sizes, you may find it necessary to return to the original frame analysis and make some changes to section sizes. Before exiting the member design module, first save the task list using the Save command on the File menu. After re-analysing the frame, you can return to the member design module and recall the task list to have the modified structure re-checked without delay.

Note: For a task list to be re-used with a modified frame, a reasonable degree of compatibility is required. Tasks that reference specific laterally supported nodes, for example, will require modification if relevant node numbers have changed.


Interactive design of members As an alternative to the above procedure, individual members can be designed without needing to perform a frame analysis. To enable the interactive design mode, select ’Interactive input of data’ on the Input page.

Design steps

Working through the input and design pages, the interactive design procedure can be broken up into the following steps:

• The Input page: Choose a design approach, set the design parameters and enter the element loads.

• The Design page: Evaluate the design results. More detail is given on page 26.

• The Calcsheet page: Accumulate design results to print or send to Calcpad. See page 28 or detail.

Modifying timber grades and sections Depending on the selected design codes, the program uses the relevant timber grades and nominal rough-sawn dimensions, i.e. as typically available in the United Kingdom or South Africa. You can customise the default grades and sections to include grades and sections readily available in your country.


To add, delete or modify grade properties or section sizes:

• Use the Edit Timber Grades (F5) function on the Input page to display the database of grades and sections. Refer to page 15 for details.

• Edit the properties on the Timber Grades page as required. Note that each grade requires a size number.

• On the Section Sizes page, enter available section dimensions for each size number used on the Timber Grades page.

• Press OK to permanently save your changes.

• Use Save as Default and Load Defaults to record your preferred grades and sections independent from the selected design code.


Tasks input

On entering Timsec, it defaults to reading the last compatible frame analysis for post-processing. You can then choose to:

• Read and post-process the frame analysis results: Define one or more design tasks by grouping members with relevant design parameters.

• Interactive design: Ignore the frame analysis and interactively input and design members.

The text that follows describe the use of the programs for reading and post-processing frame analysis results. Information regarding interactive design is given on page 21.

Choosing the data input and design mode

The appearance of the Input page determined by your selection of the mode of operation:

• If you choose to read and post-process the results of the frame analysis modules, you will use the Input page to define design tasks.


• However, if you opt for interactive design of members, the Input page displays a table for entering member geometry and loading.

Reading frame analysis output files You can select another frame output file or view the current file:

• Read data from: Use this option to load the output of a different frame module than the one displayed. Click the box and select the relevant file from the list or enter a file name.

• View output: To display the current frame analysis output file.

Defining design tasks Central to the process of post-processing frame analysis results, are design tasks. By grouping selective members with their relevant design parameters into one or more design tasks, you should find it easy to manage the vast amount of frame analysis data generated for larger frames.

The design of a frame should be simplified by breaking it into one or more manageable tasks. Each task then defines a group of members to be designed together with the relevant design parameters to be used, e.g. timber grade, section sizes and load cases considered.

Once you have defined one or more design tasks, the Design page is enabled – viewing that page automatically performs all design tasks.

After having carefully defined a number of tasks, you can save the task list to disk for later re-use. This means that you can return to the relevant frame analysis module, make some changes to the structure, re-analyse it and then repeat the previous design tasks by simply reloading the task list.

Defining tasks

To define design tasks, you have to select or enter the following information:

1. Select the timber grade to use

2. Select the members to be designed.

3. Enter the design parameters and select the section dimensions to use.

4. Select the load cases to be considered and enter the maximum slenderness ratios.

To save a task, enter a Task title and click Add task. Once added to the task list, a task will be automatically performed when you go to the Calcsheet page. Define as many tasks as necessary to design the frame in the required detail.


Modifying design tasks

To modify an exiting task:

1. Click Task title to display a list of defined tasks.

2. Select the task you want to modify.

3. Make the necessary changes to the selected members, design parameters etc.

4. Click Update task to save the changes.

Deleting tasks

To remove a task from the list, first select the task and then click Delete task. To save the complete task list to disk, use the Save commands on the File menu.

Note: Saving the task list with File | Save also saves the intermediate nodes and effective lengths entered in the Members page.



• Select lightest sections: Elements can be optimised for economy using mass as the criterion. You can optimise the section breadth and height separately or simultaneously by setting the respective values to ’Auto’.

• Evaluate specific sections: To check specific section sizes, select the required sized for breadth and depth.

Selecting the timber grade Select the required timber grade from the list. To modify the grade properties, add a new grade or delete existing grades, use Edit Timber Grades (F5). Refer to page 15 for details.

Selecting members for design Use the Element groups (F6) function to select one or more element groups from the list or by clicking members in the picture. A lateral supports is assumed at each node. If certain internal


nodes are not laterally supported, you can indicate them on the Members page. Refer to page 24 for detail.

Note: To modify the available section sizes for the selected timber grade, click Edit Timber Grades (F5). Refer to page 15 for details.

Setting the design parameters Use the Design parameters (F8) function to enter appropriate design parameters and material properties. You can select a different set of design parameters with each task.

Refer to page 7 for a discussion of the K-factors for modifying stress and other parameters.

Note: Effective length factors are entered on the Members page.

Selecting load cases and limiting slenderness ratios When loading the last frame analysis results, the program automatically displays a list of all load cases and combinations that can be designed and also the default slenderness limits for struts and ties. In the Maximum L/r ratios (F9) table, you can exclude any load case or combination from the design by clicking its right-most column.

Tip: In the frame analysis modules you can also select to analyse load combinations only. The analysis output will then be more compact due to the omission of individual load case results.

You are free to modify the slenderness limit for each individual load case or combination as required. In the case where uplift due to wind is dominant, for example, you may be able to set a higher slenderness limit. Refer to page 11 for more detail.

Controlling design output The amount of information that will be added to the Calcsheet page can be controlled using the Settings function on the Input page. You can choose between showing detailed calculation with or without diagrams or a tabular summary of results.

The option to add the Timsec Data File to the output on the Calcsheet page, allows you to later recall the design tasks by double-clicking the data file object in Calcpad.


Interactive input

The interactive design mode offers an alternative method of designing members. Instead of performing a frame analysis and then and post-processing the results, you can enter member length and forces and design them interactively.

To enable the interactive design mode, select ’Interactive input of data’ on the Input page.

The pages that follow describe the use of the programs for interactive member design. The procedure to reading and post-processing frame analysis results is explained on page 14.



• Select lightest sections: Elements can be optimised for economy using mass as the criterion. You can optimise the section breadth and height separately or simultaneously by setting the respective values to ’Auto’.


• Evaluate specific sections: To check specific section sizes, select the required sized for breadth and depth.

Setting the design parameters Use the Effective lengths (F6) function to enter effective length factors. Use Design parameters (F8) to enter appropriate design parameters. All members designed in a particular interactive session use the same set of design parameters.

Refer to page 6 for a discussion of the K-factors for modifying stress and other parameters.

Effective length factors Specify the effective length factors to be used for bending about the major and minor axes and for lateral torsional buckling. For more detail on the code requirements regarding effective length factors, refer to page 8.

Specifying slenderness limits Use the Maximum L/r ratios (F9) function to enter appropriate maximum allowable slenderness ratios for compression and tension.

Entering member lengths and forces One or more lines of information can be entered for each member. The program automatically accumulates multiple lines of loads for the same member. The following input data is required:

• Name: A descriptive name for each member.

• L: Length of the member (m).

• F: Axial force with compression being positive (kN).

• X/Y: Axis of bending relating to the values that follow next. Use as many lines as necessary to define the loading on the member about the x-x and y-y axes.

• M1: Moment applied at the left end (anti-clockwise positive) about the X or Y-axis (kNm).

• M2: Moment at the right end (anti-clockwise positive) (kNm).

• W1: Distributed load at the left end. The load works over the whole length of the member load and varies linearly between the left and right ends (downward positive) (kN/m).

• W2: Value of distributed load on right side (kN/m).

• P: Point load applied on the member (downward positive) (kN).

• A: Position of the point load, measured from the left end (m).


Note: For allowable stress design with BS 5268 - 1991 or SABS 0163 - 1989, you should enter working loads.

The profile of the members to evaluate is chosen using the Profile (F5) function. On opening the Design page, the lightest section will be chosen for each member. Lighter or heavier sections of the same profile can then be browsed as required.

Viewing design results The design results are presented on the Design page. Refer to page 26 for detail.


Member definition

Internal nodes and effective lengths are defined on the Members page. The data entered on the Members page are applicable to all design tasks defined on the Input page.

Defining internal nodes An internal node is defined as a node in-between the end nodes of a member. When you add internal nodes, the program joins relevant members to allow for easy input of effective lengths

Adding an internal node

You can add internal as follows:

• Enter internal node numbers in the table or click them with the mouse.

• Use the Auto Select function to let the program detect all internal nodes.

Removing an internal node


You can remove an internal node by deleting it form the list or by clicking it again in the picture.

Consolidation of members

With the addition of each internal node, the relevant node is ’removed’ by joining the two adjacent members into a single member. The table of members is continuously updated to show the new member layout.

The program uses the following guidelines to when joining members at an internal node:

• For the automatic selection of internal nodes, adjoining members must have the same section.

• Only members with an included angle greater than 100° (where 180° corresponds to a perfectly straight member) are joined.

• Where members of different sections intersect, the larger section defines the main member that should be joined.

• Where two or more members intersect, the internal node is taken to belong to one of the intersecting members only. The chosen member will be the straightest member or, if the same, the first in the table of members.

Entering effective lengths Enter effective length factors as follows:

• Apply the same value of Kx, Ky or Ke to all members by clicking the Kx, Ky and Ke buttons in the table heading.

• Enter the effective length factors for individual elements.

Note: The list of internal nodes and effective length factors are automatically saved when you save the task list. See page 18 for detail.

Tip: You can quickly find a member in the table by pressing Ctrl+F. Enter the member name by referring to one or both of its end node numbers.


Design results

Select the Design page to perform all design tasks and display the design results. All specified load cases and combinations are considered for each member designed. Unless a very large number of elements and load cases are involved, the design procedure will normally be completed almost instantaneously.

By default, the results for the design task active on the Input page are displayed. The results of any other design task can be displayed by selecting the task from the list (see description below). If an interactive member design was performed, the displayed results will be for the interactive design task instead.

The design criteria The following criteria are used in the design:

• The interaction formulae given by the relevant design code are used to evaluate the combined effect of axial stress and bending stress. In calculating the allowable stresses, the program takes account of the member slenderness.


• The slenderness ratio checked against the specified maximum allowable slenderness ratio for compression and tension.

Viewing results The complete interaction formulae are displayed for the critical load case of the first member of the first design task. Individual calculations have ’OK’ and ’FAIL’ remarks to indicate success or failure.

To view the results of another task, member, section or load case:

• Use the Up and Down buttons to move up or down the list of available options. Tasks and load cases are listed in the order of definition. Sections are ordered by mass. Alternatively click the item, i.e. sections, and use the Up and Down arrow keys.

• Alternatively click the relevant input box and select an item from the list that drops down.

Adding results to the Calcsheet page The following options are available when adding design results to the Calcsheet page:

• Member to Calcsheet: Add the current displayed member only. This option is not available when the design results are set to include only a tabular summary.

• Task to Calcsheet: Add the design results of all members in the current task, including those members not currently displayed.

• All tasks to Calcsheet: Add all members of all tasks. This option is not available in the interactive design mode because only a single design task, i.e. the interactive design task, is involved.

Note: The level of detail of the information added to the Calcsheet can be set using the Settings function on the Input page. Refer to page 20 for detail.


Calcsheet

The design results of all tasks are grouped on the Calcsheet page for sending to Calcpad or immediate printing.

Use the Output settings function on the Calcsheet page and Settings function on the Input page for the following:

• Embed the Data File in the calcsheet for easy recalling from Calcpad.

• Clear the Calcsheet page.

Recalling a data file If you enable the Data File option (Settings function on the Input page) before sending a calcsheet to Calcpad, you can later recall the design tasks by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the member design module as well.

General Applications 8-1

Chapter

General Applications

The general analysis modules can be used to calculate section properties, wind pressures on buildings and evaluate drainage systems of building roofs.


Quick Reference

General PROKON Analysis Tools 3 Section Properties Calculation 5 Wind Pressure Analysis 17 Gutter and Down pipe Design 23


General PROKON Analysis Tools

The PROKON suite includes a number of simple analysis tools to simplify everyday calculations. These include:

• Section Properties Calculation: For the calculation of bending and torsional properties of any generalised section.

• Wind Pressure Analysis: For determining the free stream velocity pressure on a building.

• Gutter Design: Use this module to design a drainage system for a roof by sizing a gutter, outlet and down pipe.


Section Properties Calculation 8-5

Section Properties Calculation

The Section Properties Calculation module, Prosec, is used to calculate the bending and torsional properties of any arbitrary section. The section can be solid or have openings.



An overview is given below regarding the theories used to calculate section properties.

Scope Prosec can be used to calculate the properties of any arbitrary section. The section can be solid or have openings. For bending property calculation, the program uses a simple technique of division into sub-sections. The Prandtl membrane analogy is used to determine the torsional section properties, including the shear centre, St. Venant torsional constant and torsional warping constant.

Sign convention A simple Cartesian sign convention applies:

• X-coordinates are taken positive to the right and negative to the left.

• Y-coordinates are taken positive upward and negative downward.

Units of measurement All input and output values are used without a unit of measurement. Whether you define a section using sizes for millimetres, metres, inches or feet, the output will effectively be given in the same unit of measurement.

List of symbols Below is a list of symbols used for the bending and torsional section properties:

Bending properties

A : Area of the cross section.

Ixx, Iyy : Second moment of inertia about X and Y-axis.

Ixy : Deviation moment of inertia.

Iuu, Ivv : Second moment of inertia about major axis and minor axis.

Ang : Anti-clockwise angle from the X-axis to the U-axis.

Zxx : Elastic section modulus in relation to the top or bottom edge.

Zyy : Elastic section modulus in relation to the left or right edge.

Zuu : Minimum section modulus in relation to the U-axis.

Zvv : Minimum section modulus in relation to the V-axis.


Zplx, Zply : Plastic modulus about X and Y-axis.

Xc : Horizontal centroid position measured from the leftmost extremity of the section.

Yc : Vertical centroid position measured from the bottom most extremity of the section.

rx, ry : Radius of gyration about the X or Y-axis.

ru, rv : Radius of gyration about the U or V-axis.

Xpl : Horizontal distance from leftmost extremity to centre of mass.

Ypl : Horizontal distance from topmost extremity to centre of mass.

Torsional properties

τ : Shear stress.

X : Horizontal position of shear centre from the leftmost extremity of the section.

Y : Vertical position of shear centre from the bottom of the section.

J : St. Venant torsional constant.

Zt : Torsional modules.

Cw : Warping torsional constant.


Input

A section is defined by entering one or more shapes in the input table. A shape may comprise straight lines and arcs or may be a circle. When more than one shape is entered, the shapes will accumulate and form one section. You can create openings by entering negative shapes that are subtracted from the section.

Note: If preferred, section input can be done graphically. Use Padds to draw a polygon to scale or import a DXF drawing from another CAD system. Then generate an input file for Prosec.

Entering a section The Code column is used for categorise the data that follows in the next columns:

’+’ : The start of a new polygon or circle. An absolute reference coordinate must be entered in the X/Radius and Y/Angle columns.

’–' : Start of an opening. An absolute reference coordinate must be entered in the X/Radius and Y/Angle columns.

'R' : Indicates a line drawn with relative coordinates.

'L' : Indicates a line drawn with absolute coordinates.

'A' : An arc that continues from the last line or arc. The arc radius and angle are entered in the X/Radius and Y/Angle columns respectively. The angle is measured clockwise from the previous line or arc end point.

'C' : A circle with the radius entered in the X/Radius column.

Tip: If the Code column is left blank, relative coordinates are used.

The X/Radius and Y/Angle columns are used for entering coordinates, radii and angles:

X : Absolute or relative X-coordinate. Values are taken positive to the right and negative to the left.

Radius : Radius of a circle or an arc.

Y : Absolute or relative Y-coordinate. Values are taken positive upward and negative downward.

Angle : Angle that an arc is extending through.

Note: If the X/Radius or Y/Angle column is left blank, a zero value is used.


Entering a shape A shape has two basic components:

• A reference coordinate, which gives the starting point of a polygon or the centre of a circle.

• One or more entries defining the polygon’s coordinates of lines and arcs or a circle’s radius.

After entering each coordinate, the image of the polygon updated.

Note: The starting point of a polygon is also used as the ending point and the polygon is closed automatically. It is therefore not necessary to re-enter the starting coordinate to close a polygon.


The reference coordinate

Every polygon has a start point and every circle has a centre point. These points are called reference points and are entered as absolute coordinates:

• In the Code column, enter either a ’+’ or ’–' to indicate the start of a new shape. Entering a '+' means that the shape will be added to the section. Likewise, a '–' means that the shape will be subtracted, e.g. an opening.

• Enter the absolute values of the reference coordinate in the X/Radius and Y/Angle columns.

Coordinates defining the polygon

Given a reference coordinate, two or more additional coordinates are required to define the shape of a polygon. In the case of a circle, only a reference coordinate and radius is required. A coordinate may be entered using absolute or relative values:

• If the Code column is left blank, the coordinate is taken relative from the last point entered.

• Set the Code to 'L' if you want to enter an absolute coordinate.

• The coordinate values are entered in the X/Radius and Y/Angle columns. A negative X or Y-coordinate must be preceded by a minus sign. The plus sign before a positive X or Y-coordinate is optional.

• A circular arc is defined by setting the Code to 'A' and entering the radius in the X/Radius column. The arc is then taken to extend from the end point of the last line or arc, starting at the angle that the previous line or arc ended and extending through the angle specified in the Y/Angle column.

• Define a circle by setting the Code to 'C' and entering the coordinate for the centre point. On the next line, enter the radius in the X/Radius column.

Note: You can rotate by choosing Settings.

Procedures for entering shapes Step-by-step procedures for entering typical section Codes are given below:

Entering a polygon comprising straight lines

A polygon is defined by entering a start point followed by a few lines of additional coordinates. The polygon can be defined using relative or absolute coordinates or both.

Using relative coordinates:


• Define the start position of the polygon by setting the Code to ’+’ and entering the absolute coordinate in the X/Radius and Y/Angle columns.

• Next, leaving the Code column blank, enter the consecutive corner points of the polygon in the X/Radius and Y/Angle columns. By leaving the Code column blank, the entered coordinates are set to relative coordinates.

Using absolute coordinates:


• For each following coordinate, enter an L in the Code column and enter the absolute coordinate values in the X/Radius and Y/Angle columns.

Entering a polygon comprising lines and arcs

A polygon with one or more arcs is defined in a similar way as a normal polygon:


• Define straight lines by entering the consecutive corner points using relative or absolute coordinates.

• For an arc, set the Code to A and enter its radius and angle in the X/Radius and Y/Angle columns. The arc will be taken to extend from the previous line/arc through the specified angle. A positive angle is taken as a clockwise rotation and a negative angle as an anti-clockwise rotation.

Tip: If an arc is to start at a certain angle, simply precede it with a short line at that angle.

Entering a circle

A circle is defined by entering the centre point followed by its radius in the next line:

• Define the centre point of the circle by setting the Code to ’+’ and entering the absolute X and Y-coordinates. If you leave either of the coordinates blank, a value of zero is used.

• On the next line, set the Code to C and enter the radius of the circle in the X/Radius column.

Note: A circle should be considered as a complete shape. If a circle has to be incorporated in another shape, a polygon with arcs should be used.


Entering an opening

An opening is defined exactly like any other shape, with the exception that it is entered as a negative shape:

• Define the start position of the polygon by setting the Code to ’–' and entering the absolute coordinate in the X/Radius and Y/Angle columns.

• Define lines, arcs or a circle by entering the relevant points as described in the examples above.


Analysis

Two separate analysis procedures are used to calculate the bending and torsional section properties. The bending analysis is completed almost instantaneously. However, the torsional analysis procedure uses a sophisticated finite difference analysis technique and therefore takes longer to complete.

Analysis settings Click Settings to adjust the analysis settings applicable to the bending and torsional analyses:

• Rotation angle: Enter an angle if you wish to calculate the bending properties for a rotated section.

• Poisson ratio: The ratio influences the torsional shear stress distributions in a section. It therefore also has an effect on the position of the shear centre and warping torsion constant.

Material Poisson Ratio

Aluminium 0.16

Concrete 0.20

Steel 0.30

• Number of equations: For determination of the torsional section properties, the finite difference mesh is sized to yield approximately the specified number of equations. More equations will take longer to solve, but may yield better accuracy, especially when analysing thin-walled sections.


Calculating bending section properties The bending section properties are calculated using a simple method of division into sub-sections:

• Circles and arcs are first converted to polygons with approximately the same shapes. The program uses lines at 30° angle increments for this purpose.

• The section is then sub-divided into a series of trapeziums and the properties are calculated for each trapezium.

• The global section properties are finally calculated through summation of the values obtained for each trapezium.


Calculating torsional section properties A sophisticated finite difference analysis method is used for calculating the torsional section properties. The Prandtl membrane analogy is used for determining the Y and X-shear stresses and J, the St. Venant torsional constant. The membrane is modelled using a finite difference mesh.

The shear stress distributions in the Y and X-directions are determined for a unit load applied in the Y-direction. The shear centre is then calculated by considering the moment of shear stresses about the centre of mass.

The torsional constant, J, is taken as twice the volume below the membrane. The maximum slope of the membrane then gives the torsional modulus. The maximum torsional shear stress can be obtained by dividing the torsional moment with the torsional modulus Zt.

Warping torsion is evaluated by using the relationship between shear and axial deformation from classical elastic theory. The shear deformation is obtained from the pure torsion analysis. The warping constant, Cw, is then determined from the longitudinal displacements.


Calcsheet

The section property calculations can be grouped on a calcsheet for printing or sending to Calcpad. Various settings can be made with regards to the inclusion of design results and pictures.


Recalling a data file If you enable the Data File option before sending a calcsheet to Calcpad, you can later recall it by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the analysis module as well.

Wind Pressure Analysis 8-17

Wind Pressure Analysis

The Wind Pressure Analysis module is a simple utility for the calculation of free stream velocity pressure on building structures.


Theory and Application

A brief summary is given below with respect to the supported design codes and symbols used.

Design codes The following codes of practice are supported:

• CP3 - 1972.

• SABS 0160 - 1989.

List of symbols The code symbols are used as far as possible:

k : Pressure coefficient that depends on altitude.

Qz : Free stream velocity pressure (kPa).

V : Regional wind speed (m/s).

vz : Characteristic wind speed at a height z (m/s)

zg : Gradient height that depends on the terrain category and class of structure (m).

α : Height exponent that depends on the terrain category and class of structure.


Input

The following structural and environmental parameters are required:

• Height of building: The total height exposed to wind loading.

• Height above sea level: Altitude to use for calculating the design wind speed.

• Wind speed: Regional design wind speed for a fifty-year return period. Refer to the relevant design code for regional values.

• Terrain category: This value indicates the likely exposure of the structure to wind loading. A higher value denotes increased shielding and lower wind pressures:

Terrain Category Description

1 Open terrain

2 Outskirts of towns

3 Built-up and residential areas

4 City centres

• Class: The class of structure quantifies the importance of the analysis:

Class Description

A Structural component

B Structure as a whole

C For checking structural stability


• Return period: Enter a return period to indicate the importance of the structure:

Return Period Description

100 High risk buildings, e.g. hospitals and communication centres

25 Low risk structures, e.g. farm outbuildings

5 Temporary structures

50 Most other structures


Calcsheet

Press Analyse to calculate and display the wind pressure distribution. Use the Calcsheets page to print the results or send the displayed information to Calcpad.

Recalling a data file The Data File is automatically included when sending a calcsheet to Calcpad. You can later recall the data file by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the Wind Pressure Analysis module as well.


Gutter and Down pipe Design 8-23

Gutter and Down pipe Design

The Gutter Design Module is used to design gutters and down pipes to drain roofs of typical building structures.



Below is a brief summary of the application of the theory.

Scope The program can evaluate roof drainage systems subjected to intense short duration rains. It takes into account the shape of the gutter, the outlet into which the gutter discharges and the pipe-work that conveys the flow to below.

Design code The program is based on the requirements of BS 6367 - 1983.

Units of measurement The program supports both Metric and Imperial units of measurement.

Assumptions The same assumptions used in the code are applicable. These include:

• The gutter slope does not exceed 1:350.

• The gutter has a uniform cross-sectional shape.

Note: Reference should be made to the code for guidance on the positioning and sizing of gutter outlets and other requirements.


Input

Define the drainage system and storm to be drained:

• Storm characteristics

• Gutter geometry

• Outlet and down pipe definition.

Storm characteristics The following parameters should be entered to define the storm:

• Return period (years): This parameter is used as a measure of the security of an acceptable degree of damage. A return period of between five and fifty years is normally used for typical situations. For higher risk scenarios, a value of one and a half times the expected life of the building and higher should be used. Refer to the code for detail.

• Two minute M5 rainfall (mm): This quantity is defined as the expected rainfall in a two minute period during a one in five year storm. Press 2 Minute M5 Rainfall Constants to display regional data for the United Kingdom and South Africa. Refer to the code or other relevant hydrological data for regions not listed.

• Design duration (1 to 10 minutes): Adjust the default two-minute design duration if necessary. The M5 rainfall is then adjusted in accordance with Table 10 of the code.

• Effective drainage area: Roof area to be drained, taking into account any adverse effect of wind on sloping roofs and vertical surfaces and other factors.

Note: Gutters and down pipes may normally be omitted for roofs with area of 6 m2 or less.


Gutter geometry Rectangular and trapezium shaped gutters can be defined:

• Top width (mm): Width at the top of the gutter.

• Base width (mm): The bottom width of the gutter. Set the base width equal to the top width for rectangular gutters.

• Sloping depth (mm): For a trapezium shaped gutter, enter the depth in which the gutter slopes outward from the base.

Note: You are not required to enter the total depth of the gutter. The program calculates the depth required for proper draining.


Outlet and down pipe parameters The type of outlet influences the flow collected from the gutter. The following types of outlets can be specified:

• Type 1: Outlet with sharp corners.

• Type 2: Outlet with rounded corners.

• Type 3: Outlet with tapered edges not exceeding 45° with the vertical.

The down pipe dimensions are defined using the following values:

• Aspect ratio: The ratio of the larger to smaller down pipe dimensions. Use a unity value for square and circular down pipes.

• Larger dimension: Enter the larger dimension of the down pipe. Use the diameter in the case of a circular down pipe.


Calcsheets

The Calcsheets page displays the design calculations. The program evaluates the following three components of the drainage system:

• The gutter or channel that collects the flow from the roof.

• The outlet into which the flow from the gutter discharges.

• The pipe-work that conveys the flow from the outlet to a lower drainage system.

The three parts of the system can be designed separately if the outlet and down pipe is made large enough for flow to freely discharge from the gutter. The actual down pipe and outlet may however be smaller than that required for this method, prompting the program to perform a more detailed analysis.


Free-flow design In the phase of the analysis, the gutter and down pipe sizes for free flow are determined:

• Flow in the gutter is evaluated to establish whether free flow is possible.

• The upstream and downstream free flow depths are determined and the required gutter depth calculated.

• The flow through the outlet is check to see if orifice or weir-type flow is present.

• The required free-flow sizes are determined for circular and rectangular down pipes.

Evaluation of the entered system The second phase of the analysis involves the evaluation of the entered down pipe and gutter sizes:

• The specified down pipe and outlet are evaluated to determine their flow capacity.

• If the down pipe is smaller than that required for free flow in the gutter, the restricted flow characteristics of the gutter are determined and a gutter depth suggested.

• The checking procedure is performed for both rectangular and circular down pipes.

• Finally, the design flow volume is calculated.

Recalling a data file The Data File is automatically included when sending a calcsheet to Calcpad. You can later recall the data file by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the Gutter and Downpipe Design module as well.


Masonry Design 7-1

Chapter

Masonry Design

The masonry design section contains modules for the analysis of reinforced masonry beams subjected to pure bending and unreinforced masonry walls subjected to axial compression and out of plane bending about two axes.

Masonry Design 7-2

Quick Reference

Masonry Design using PROKON 3 Masonry Section Design 4 Masonry Wall Design 14

Masonry Design using PROKON 7-3

Masonry Design using PROKON

The masonry section design module, MasSec, is mainly used for the design of members such as lintels and masonry that span large openings in walls. MasWall, on the other hand is ideally suited for the design of wall panels and bearing walls.

Code of practice support is currently limited to SABS 0164-1992. Characteristic compression strengths for masonry units are calculated based on unit geometry, nominal strengths and tables in the abovementioned code of practice.

All the masonry modules provide a detailed Calcsheet on design methodology and results, i.e. a complete record of the design is generated automatically. Current development includes support for reinforced masonry walls, columns and arches.

Masonry Section Design 7-4

Masonry Section Design

The masonry section design module, MasSec, determines the resistance of a reinforced masonry section loaded in pure bending.

The module is standalone, i.e. it does not post process results from any of the analysis modules.




Design scope The masonry section design module verifies the resistance of a reinforced masonry beam at a critical section. It is assumed that the loads imposed on the beam causes uniaxial bending and a shear force only.

The following limitations apply:

• No direct support for composite action, e.g. masonry beam and prestressed a lintel.

• No support for doubly reinforced sections.

Design codes The program designs masonry sections according to the following codes of practice:

• SABS 0164 - 1992.

Units of measurement MasSec supports both Metric and Imperial units.

Symbols Where possible, the same symbols are used as in the codes of practice:

Dimensions

b : Section breadth (mm).

d : Effective depth, i.e. distance from the compression face to the tension steel centroid (mm).

z : Moment lever arm (mm).


Design results

Mr : Moment resistance (kNm).

Mu : Applied ULS moment (kNm).

Vr : Shear resistance (kN).

Vu : Applied ULS shear (kN).

a : Shear span (m), or unit correction factor (unitless).

Design parameters

As : Tension steel area (mm²).

γmm : Partial material safety factor for the masonry unit.

γms : Partial material safety factor for the reinforcement.

Lmax1,2 : Limiting lengths due to stability considerations (m).

Stresses

fy : Ultimate tensile strength of the tension steel (Mpa).

fyy : Ultimate tensile strength of the shear steel (Mpa).

fnom : Nominal compression strength of the masonry unit (MPa).

fk : Characteristic compression strength of the masonry unit (MPa), i.e. the strength of the unit in a beam or wall, dependence on unit aspect ratio removed.

fv : Shear stress due to Vu (MPa).

fv’ : Adjusted shear stress (MPa), modified based on the shear span.

fbr : Bond resistance (MPa).

fbu : ULS bond stress due to Vu (MPa).

Design parameters

Tension steel area

As MasSec only verifies the resistance of a section, the diameter and number of bars are required parameters during the input stage.


Physically, the tension reinforcement is usually either conventional bars, as used for concrete, or hard drawn wires. The conventional bars are used with special concrete block masonry units which have voids specifically intended for reinforcement. These voids are then filled with concrete after steel placement to form a solid, reinforced unit.

Wires are placed in bedding joints, and as such, are suitable for use with standard format brickwork.

Partial material safety factors

The safety factors for masonry units have a fairly wide range, due to the wide range of materials and the measure of control during manufacturing and construction. See the applicable code of practice for details.

Stresses

Manufacturers usually quote a nominal compression strength for the masonry units that they provide. This nominal strength is derived from a simple crushing test.

Due to the variability in masonry unit dimensions, this nominal strength cannot be used as the actual crushing strength of the unit. Values from crushing tests are very sensitive to aspect ratio and this dependence must be removed from the strength parameter.

This can be by testing a small, standard, wall panel to failure and using equations provided in the applicable code of practice to determine characteristic compression strength for the unit.

Alternatively, most codes of practice also provide tables of characteristic strengths versus aspect ratio and nominal strengths.

In MasSec, any one of the two approaches can be used.


Design of masonry beams

The module consists of three pages or tabs:

• Input, which is further subdivided:

o General, for parameters concerning materials and masonry unit.

o Geometry and loads, for parameters concerning the beam and loading.

• Design, which displays a summary of the design results.

• Calcsheet, which provides fully annotated design documentation

General input


The masonry unit to be used in the beam is completely defined by the first table on this tab. The three available unit types and associated input parameters are tabulated below.

Solid unit Width, Length, Height, Joint size

Hollow unit Width, Length, Height, Joint size

Shell thickness*, % solid material

Hollow grouted unit Width, Length, Height, Joint size


*This parameter is only used for the graphical output.

Percentage solid material refers to the area perpendicular to the loading in the crushing test, usually this would be width x length. The percentage solid material would then be (total area – void area) as a percentage of the total area.

Masonry unit sizes are based on the modular concept, i.e. any dimension of the unit added to a joint thickness of 10mm yields a multiple of 100.

The table below indicates the recommended nominal unit dimensions applicable to South Africa.

Burnt clay

190 x 90 x 90 mm

290 x 90 x 90 mm

390 x 90 x 190 mm

390 x 190 x 190 mm

Calcium silicate

190 x 90 x 90 mm

290 x 90 x 90 mm

390 x 90 x 190 mm

390 x 100 x 190 mm

Concrete

190 x 90 x 90 mm

290 x 90 x 90 mm

390 x 90 x 190 mm

390 x 190 x 190 mm


The second table on this tab contains the parameters pertaining to material strengths and reinforcement position. If the masonry units have been tested to failure as specified by the applicable code then fk can be entered directly in this table. If only nominal strengths are available, enter the nominal strength and MasSec will calculate fk.

The table below lists the available nominal strengths available in South Africa.

Burnt clay

3.5 MPa

7 MPa

10.5 MPa

14 MPa

17 MPa

Calcium silicate

7 MPa

14 MPa

21 MPa

35 MPa

Concrete

3.5 MPa

7 MPa

10.5 MPa

14 MPa

21 MPa

Steel strength, positioning and type, as well as mortar class must be chosen in this table as well.


Geometry and loads input

The first table on this tab defines the type and geometry of the masonry beam.

The following beam types are supported:

• Single leaf - Single leaf of masonry

• Collar jointed - Double leaf of masonry, where the small void between the two leaves of masonry is filled with mortar or concrete

• Grouted cavity - Double leaf of masonry, where the larger void between the two leaves is filled with concrete with strength of at least fk.

The dimensions of the beam section, the clear span and the type of support are also chosen on this table.

The second table provides parameters for the steel as well as a load distance parameter and a bearing length. The load distance is the distance of the critical section from the left hand support – the resulting shear enhancement is allowed in certain cases. The last table requires the input of ULS loads on the critical section.


Design summary

This tab provides a tabular and diagrammatic summary of the design. Two cases of bending failure are presented on the diagram and the minimum chosen as the section strength in bending:

• Compression failure – Over-reinforced beam, masonry ruptures in compression before the steel yields.

• Tension failure – Under-reinforced beam, steel yields before the masonry ruptures in compression.

Other design checks are tabulated with action effect (loading) versus the resistance effect (strength). Steel required and provided is tabulated in the left bottom corner of the tab.


Calcsheets

The Calcsheet provides a fully annotated design document which can be printed or sent to the CalcPad for permanent storage.

Display settings for the Calcsheet are controlled by the output settings button, on the left bottom corner of the tab.

Note: The Calcsheet is not saved with the rest of the input when the file is saved. All changes to the Calcsheet will then be lost. To edit the Calcsheet output, send it to the CalcPad where it can be edited and saved.

Masonry Wall Design 7-14

Masonry Wall Design

The masonry wall design module, MasWall, determines the resistance of an unreinforced masonry wall axially loaded in its plane or loaded out of plane.

The module is standalone, i.e. it does not post process results from any of the analysis modules.




Design scope The masonry wall design module verifies the resistance of an unreinforced masonry wall, subjected to one of the following loads:

• In plane axial loading (Bearing walls)

• Out of plane loading, causing biaxial plate bending (Wall panels)

The following limitations apply:

• Currently no support for combined loading, i.e. bending and compression.

• No support for reinforced walls.

Design codes The program designs unreinforced masonry walls according to the following codes of practice:

• SABS 0164 - 1992.

Units of measurement MasSec supports both Metric and Imperial units.

Symbols Where possible, the same symbols are used as in the codes of practice:

Dimensions

t : Wall thickness (mm).

h : Wall height (mm)

ex : Calculated or actual eccentricity (mm).


Design results

Mr : Moment resistance (kNm).

Mcr : Cracked moment resistance (kNm).

Mu : Applied ULS moment (kNm).

Cr : Axial resistance (kN/m).

Cu : Applied ULS axial force (kN/m).

qlat : Lateral pressure resistance, assuming a three pin arch collapse mechanism. (kN/m²)

Design parameters

γmm : Partial material safety factor for the masonry unit.

R : Slenderness ratio

Z : Section modulus (mm³)

ea : Additional eccentricity due to slenderness (mm).

et : Total eccentricity (mm).

em : Design eccentricity (mm), maximum of et and ex.

β : Capacity reduction factor

teff : Effective wall thickness (mm)

heff : Effective wall thickness (mm)

Stresses

fnom : Nominal compression strength of the masonry unit (MPa).

fk : Characteristic compression strength of the masonry unit (MPa), i.e. the strength of the unit in a beam or wall, dependence on unit aspect ratio removed.

fkx perp : Flexural tensile strength perpendicular to the bedding joints (MPa).

fkx par : Flexural tensile strength parallel to the bedding joints (MPa).


Design parameters

Eccentricities

Actual load eccentricity is assumed to vary from ex at the top of the wall to zero at the bottom, subject to additional eccentricity due to slenderness effects.

Partial material safety factors

The safety factors for masonry units have a fairly wide range, due to the wide range of materials and the measure of control during manufacturing and construction. See the applicable code of practice for details.

Stresses

Manufacturers usually quote a nominal compression strength for the masonry units that they provide. This nominal strength is derived from a simple crushing test.

Due to the variability in masonry unit dimensions, this nominal strength cannot be used as the actual crushing strength of the unit. Values from crushing tests are very sensitive to aspect ratio and this dependence must be removed from the strength parameter.

This can be by testing a small, standard, wall panel to failure and using equations provided in the applicable code of practice to determine characteristic compression strength for the unit.

Alternatively, most codes of practice also provide tables of characteristic strengths versus aspect ratio and nominal strengths.

In MasWall, any one of the two approaches can be used. Similarly flexural tensile resistances parallel and perpendicular to the bed joints can be specified or left to MasWall for calculation.


Design of masonry walls

The module consists of three pages or tabs:

• Input, which is further subdivided:

o General, for parameters concerning materials and masonry unit, as well as wall design type.

o Wall geometry for parameters concerning the wall type and dimensions.

o Loading, which allows the entry of multiple load cases.

• Design, which displays a summary of the design results.

• Calcsheet, which provides fully annotated design documentation

General input


The masonry unit to be used in the beam is completely defined by the first table on this tab. The three available unit types and associated input parameters are tabulated below.

Solid unit Width, Length, Height, Joint size

Hollow unit Width, Length, Height, Joint size


Hollow grouted unit Width, Length, Height, Joint size


*This parameter is only used for the graphical output.

Percentage solid material refers to the area perpendicular to the loading in the crushing test, usually this would be width x length. The percentage solid material would then be (total area – void area) as a percentage of the total area.

Masonry unit sizes are based on the modular concept, i.e. any dimension of the unit added to a joint thickness of 10mm yields a multiple of 100.

The table below indicates the recommended nominal unit dimensions applicable to South Africa.

Burnt clay

190 x 90 x 90 mm

290 x 90 x 90 mm

390 x 90 x 190 mm

390 x 190 x 190 mm

Calcium silicate

190 x 90 x 90 mm

290 x 90 x 90 mm

390 x 90 x 190 mm

390 x 100 x 190 mm

Concrete

190 x 90 x 90 mm

290 x 90 x 90 mm

390 x 90 x 190 mm

390 x 190 x 190 mm


The second table on this tab contains the parameters pertaining to material strengths. If the masonry units have been tested to failure as specified by the applicable code then fk can be entered directly in this table. If only nominal strengths are available, enter the nominal strength and MasWall will calculate fk.

The table below lists the available nominal strengths available in South Africa.

Burnt clay

3.5 MPa

7 MPa

10.5 MPa

14 MPa

17 MPa

Calcium silicate

7 MPa

14 MPa

21 MPa

35 MPa

Concrete

3.5 MPa

7 MPa

10.5 MPa

14 MPa

21 MPa

Similarly values for flexural tensile resistances should be available in the applicable code of practice.

The design type should be chosen on this tab:

• Vertical loads – axially loaded bearing walls

• Lateral loads on panels – design for biaxial plate bending

The layout of subsequent tabs in the input process will vary according to the design type chosen.


Wall geometry input – Vertical loads

The table on this tab defines the type, geometry and stiffeners (if any) of the masonry wall.

The following wall types are supported:



• Cavity - Double leaf of masonry, with a void between the two leaves.

Wall height, length and cavity size (if required) can be entered on this tab.

Possible values for the horizontal restraint are: (Refer to SABS 0164 for details)

• Simple – No rotational fixity at the top of the wall.

• Enhanced – Partial rotational fixity at the top of the wall.

Similar rotational fixities can be specified for the vertical edge(s) of the wall.


MasWall also supports vertical stiffeners between the wall edges. These stiffeners can be either piers (small columns) or intersecting walls. Once vertical stiffeners have been selected, they need to be dimensioned as well.

Wall geometry input – Lateral loads on panels

The table on this tab defines the type, geometry and edge restraint of the masonry wall panel.

The following wall types are supported:



• Cavity - Double leaf of masonry, with a void between the two leaves.

Wall height, length and cavity size (if required) can be entered on this tab.

Edge restraints can be specified for each edge individually as free, simple or fixed.


Loads input – Vertical loading

For this loading type, axial forces and eccentricity with respect to the wall centreline can be entered on this tab. Multiple load cases are supported. Note that all loads should be ULS loads.


Loads input – Lateral loads on panels

For this loading type, moments parallel and perpendicular to the bedding joints can be entered directly. A dead load pressure on the level of moment parallel to the bedding joints is required to calculate the cracked moment resistance.

Alternatively the moment calculator button can be used to calculate moments based on a lateral pressure.

This calculation makes use of the moment tables in the code of practice which are in turn derived from yield line equations.


Design summary

This tab provides a tabular and diagrammatic summary of the design. The two resistance moments are shown on the diagram.

Other design checks are tabulated with action effect (loading) versus the resistance effect (strength).


Calcsheets

The Calcsheet provides a fully annotated design document which can be printed or sent to the CalcPad for permanent storage.

Display settings for the Calcsheet are controlled by the output settings button, on the left bottom corner of the tab.

Note: The Calcsheet is not saved with the rest of the input when the file is saved. All changes to the Calcsheet will then be lost. To edit the Calcsheet output, send it to the CalcPad where it can be edited and saved.