BIM in Analysis and Design of Steel Connections˜i/... · with Tekla Structures 18.1 as this was the current release at the beginning of 2013. Testing is performed with PowerConnect
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BIM in Analysis and Design of Steel Connections
Ellen Viddal Øi
Master of Science in Engineering and ICT
Supervisor: Tor Guttorm Syvertsen, KTCo-supervisor: Stian Roger Aarum, EDRMedeso
Department of Structural Engineering
Submission date: June 2013
Norwegian University of Science and Technology
MASTER THESIS 2013for
stud.techn. Ellen Viddal Øi
BIM in Analysis and Design of Steel Connections
Background
Design tools today enable linking of the different stages and processes of a structure’s lifetime.These tools aim for secure and fast information exchange from design to production. An issue thatrequires further research is information transfer between the tools used for analysis and design.
The master thesis should cover the flow of information between the modelling tool Tekla Structuresand the analysis tool PowerConnect. Emphasis should be put on establishing a connection forinformation transfer between the programs to increase quality and reduce errors compared to thecurrent solution.
Approach to the problem
The thesis should include:1. State of the art2. Background for the dimensioning principle of PowerConnect.3. How data is stored within Tekla and PowerConnect.4. Establish a connection between the programs.5. Alternative approaches.6. Evaluation of standard Eurocode connections.
Result
The thesis should result in a digital report which will be the main basis of assessment. The report isto be delivered at the Department of Structural Engineering before June 10, 2013.
The angle of the problem may be adjusted throughout the project due to the progress of the workand the interests of the candidate.
The paper is to be organised according to the current instructions(http://www.ntnu.no/kt/studier/masteroppgaven).
Contact EDR&Medeso AS: MSc Stian Roger Aarum (stian.roger.aarum@edrmedeso.com)Supervisor: Professor Tor G. Syvertsen (torgsyv@gmail.com)
Trondheim, 14. januar 2013
Tor G. Syvertsen (sign.)supervisor
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“ Seriously? I like that song too!I bet no two people in thehistory of the world haveever been so connected!
”http://xkcd.com/807
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Abstract
It is desired to reduce the time spent at all stages of the building process. Commu-nication between and within disciplines is a significant time consumer in structuralengineering today. As the same person is often responsible for both analysis anddesign of a structure, linking the tools for these tasks could reduce the time spentsignificantly. Today, the same item is often modelled twice or more with differentsoftware, and the goal for this thesis is to make this process more efficient.
In this work, an extension to Tekla Structures with a link to BuildSoft’s PowerCon-nect is implemented to enable connection analysis. Strength is determined in Power-Connect by the component method, according to Eurocode 3.
The thesis includes a state of the art study of links between tools for analysis anddesign of steel connections, the planning and implementation of a link between TeklaStructures and PowerConnect, along with a description of the finished solution andhow it works. Tekla’s Open API has been utilised using C# and XML in MicrosoftVisual Studio 2012.
At this stage the extension is limited to cover a bolted moment end plate connectionbetween H- and I-profiled cross-sections. Support for other types of connections andcross-sections may be included in further work.
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Sammendrag
BIM brukes i planlegging og bygging for å effektivisere prosessen fra modellering tilferdigstilling. Hovedfokuset i dag ligger på å bedre kommunikasjon mellom de ulikedisiplinene, men det er samtidig mulig å effektivisere innad i dem. Siden den sammepersonen ofte har ansvar for både beregning og dimensjonering, men er tvunget tilå bruke ulik programvare for hver av disse prosessene, går trolig mye tid bort til åmodellere den samme delen flere ganger. Målet for denne oppgaven er å kunne gjøredette arbeidet så effektivt som mulig.
I dette arbeidet er en utvidelse til Tekla Structures med en kobling til BuildSoft’sPowerConnect implementert for å gjøre analyse av stålknutepunkter mulig. Kapasi-tet beregnes i PowerConnect med komponentmetoden, i samsvar med Eurocode 3.
Oppgaven omfatter en studie i kjente løsninger for kobling av verktøy for beregningog dimensjonering av stålknutepunkter, planlegging og implementering av en koblingmellom Tekla Structures og PowerConnect, sammen med en beskrivelse av hvordanden ferdige løsningen fungerer. Tekla Open API har blitt brukt sammen med C# ogXML i Microsoft Visual Studio 2012.
I denne omgang er utvidelsen begrenset til å gjelde for boltede momentknutepunktmed endeplate mellom H- og I-tverrsnitt. Støtte for andre knutepunkter og tverrsnittkan implementeres i videre arbeid.
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Preface
This thesis is a written report on work performed during the last semester of myMaster of Science study in Engineering and ICT, Structural Engineering. The workhas been carried out at the Department of Structural Engineering at the NorwegianUniversity of Science and Technology (NTNU) during the spring term of 2013, underthe supervision of Professor Tor G. Syvertsen. The thesis is, along with the finishedextension and its source code, basis of assessment for the subject TKT4915 Compu-tational Mechanics, Master Thesis, for a total worth of 30 credits (ECTS).
It has been interesting and motivating to work on a problem where the result may beused in the industry after completion. Knowing that a working solution is desired haskept my motivation up although a link between the two programs in question had notbeen successfully developed earlier. I found it particularly interesting to get to workwith leading software in structural engineering that I did not know at the beginningof this work.
The work has in broad outline consisted of studying how data is stored within TeklaStructures and PowerConnect and working out a way for them to communicate. Thishas been done by programming an extension to Tekla Structures using C# and XMLin Microsoft Visual Studio. Several hours have been spent modelling in Tekla Struc-tures, with and without utilising Tekla’s open API, alongside writing this report inLATEX.
I would like to thank my supervisor, Professor Tor G. Syvertsen, for pushing me for-ward and for his useful feedback throughout the entire work.
None of this would have been accomplished without initiative and valuable help fromMSc Thomas B. Sousa and MSc Stian R. Aarum in EDRMedeso.
Last, but not least, I would like to express my gratitude to BuildSoft Support for theirquick and helpful response and to Tekla for their extremely useful Open API discus-sion forum.
Ellen Viddal ØiTrondheim, 6th June 2013
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CONTENTS CONTENTS
Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vSammendrag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixNotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Scope of the work . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Software and concepts 32.1 PowerConnect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Tekla Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.3 State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3 Extension development 93.1 Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 The approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.3 The steel connection . . . . . . . . . . . . . . . . . . . . . . . . . 103.4 XML interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.5 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4 Results 234.1 Short description of the plug-in . . . . . . . . . . . . . . . . . . . . 234.2 Installing the plug-in . . . . . . . . . . . . . . . . . . . . . . . . . 234.3 Using the plug-in . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.4 Example of use . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5 Discussion 295.1 Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.2 Cross-section and material properties . . . . . . . . . . . . . . . . . 305.3 Data exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6 Concluding remarks 336.1 Summary of work . . . . . . . . . . . . . . . . . . . . . . . . . . . 336.2 General conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 336.3 Suggestions for further work . . . . . . . . . . . . . . . . . . . . . 33
References 37
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CONTENTS CONTENTS
Appendices 39
A Sample .bpc-file 39
B Analysis results from PowerConnect 43B.1 Default connection . . . . . . . . . . . . . . . . . . . . . . . . . . 43B.2 Plug-in connection . . . . . . . . . . . . . . . . . . . . . . . . . . 44
C Complete source code 45
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CONTENTS CONTENTS
Notation
Acronyms
API Application Programming Interface.BIM Building Information Modelling.CAD Computer Aided Design.COM Component Object Model [1].IFC Industry Foundation Classes [2].VBA Visual Basic for Applications.XML eXtensible Markup Language [3].
Abbreviations
INP Standard (input) format for components in Tekla Structures..NET Microsoft software Framework.WinForms Windows Forms. Part of the .NET Framework.
File extensions
.bpc BuildSoft PowerConnect file. XML structure.
.dll Dynamic Link Library. For linking at load time or run time. Notdirectly executable by the user.
.dxf Drawing eXchange Format. Open source CAD format de-veloped by Autodesk.
.ifc Default IFC exchange format.
.ifcXML IFC standard XML format.
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CONTENTS CONTENTS
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1 INTRODUCTION
1 Introduction
1.1 Background
Effective flow of information in BIM systems is a popular subject today. However, itis usually focused on the communication between planning and construction. Ana-lysis and design in detailing is often done by a single person using multiple softwaretools. This work could be done more efficient by improving software integration.
It has been requested to establish a link between the BIM software Tekla Struc-tures and BuildSoft’s PowerConnect for steel connection analysis. XML-connectionsbetween different software is of current interest these days, and regarded as the mostrelevant approach for this work.
1.2 Scope of the work
The solution is limited to handle a subset of connections from the PowerConnect lib-rary. For this thesis only a bolted column-beam end plate connection is implemented.This may be extended at a later stage if desired. The created plug-in is compatiblewith Tekla Structures 18.1 as this was the current release at the beginning of 2013.Testing is performed with PowerConnect 2012 Rev. 01 and Tekla Structures 18.1SR4. Both Tekla Structures and PowerConnect require a Microsoft Windows operat-ing system.
1.3 Outline of the thesis
This introductory chapter is followed by a brief description of the main software,PowerConnect and Tekla Structures, together with a short state of the art study inChapter 2. Chapter 3 covers the work of connecting Tekla Structures and Power-Connect and is followed by a presentation of the results obtained in Chapter 4. Adiscussion on the results is covered by Chapter 5 and summarised with concludingremarks in Chapter 6 together with suggestions for further work. A sample Power-Connect file, analysis results and a text version of the complete source code is at-tached in the succeeding appendices. The finished plug-in is delivered as a separatepackage.
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1.3 Outline of the thesis 1 INTRODUCTION
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2 SOFTWARE AND CONCEPTS
2 Software and concepts
2.1 PowerConnect
PowerConnect is software used for limit state analysis of bolted and welded steelconnections in 3D, developed by BuildSoft NV [4]. The connections may be ex-posed to an arbitrary number of load combinations and are evaluated according toEurocode 3 [5]. PowerConnect has an extensive library of pre-designed connectionsto choose from, including beam-column, beam-column-beam and beam-beam con-nections in addition to column bases. PowerConnect allows for modification of thoseconnections in a 3D modelling user interface. Joints connecting H- and I-profiles aresupported alongside a selection of hollow core connections.
The PowerConnect model is saved in a .bpc file, which is basically an XML file.Geometrical data of the connection may be exported as a .dxf file that can be used asa sketch for modelling the connection in CAD software.
Design analysis principle
PowerConnect performs design analysis based on the component method accordingto Eurocode 3 [6]. This implies that a connection is decomposed into several compon-ents and the capacity is determined by the strength and stiffness of each componentin the connection [7]. All elements of the connection are calculated in detail so thatover- or undersized elements may be identified. The components may be actual ele-ments, like bolts, welds and plates, or critical stress or strain areas. Some of thosebasic components are shown in the extracts from the Eurocode 3 in Table 1.
2.2 Tekla Structures
Tekla Structures is Building Information Modelling (BIM) software for structuralmodelling [8]. The same model may be used during the entire building process fromconceptual design to construction management. Tekla Structures allow for modellingof physical and analytical geometry models, and for integration with different ana-lysis software. The analytical model may be exported to suitable analysis softwareand the results (i.e. geometry changes) may be passed back into Tekla Structures [9].
Tekla Structures offers a selection of different standard and proprietary formats forimport and export. Of those only .dxf is also supported by PowerConnect. However,Tekla Structures may be combined with various systems through its open ApplicationProgramming Interface, Tekla Open APITM.
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2.2 Tekla Structures 2 SOFTWARE AND CONCEPTS
Table 1: Basic joint components from Table 6.1 in Eurocode 3, 1-8 [5]
Components Components
1Column webpanel in shear
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Beam orcolumn flangeand web incompression
2
Column webintransversecompression
8Beam web intension
3Column webin transversetension
9Plate in tensionor compression
4Column flangein bending
10 Bolts in tension
5End plate inbending
11 Bolts in shear
6Flange cleat inbending
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Bolts in bearing(on beamflange, end-plate or cleat)
• : Most exposed area in component.
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2 SOFTWARE AND CONCEPTS 2.2 Tekla Structures
Tekla Open APITM
Tekla Open API enables interaction between Tekla Structures and other softwareby allowing the users to edit models and drawings by developing their own exten-sions [10]. These extensions may be applications or plug-ins. The main differencebetween those is that the plug-in is run inside Tekla Structures whereas the applic-ation is launched as a separate process. Thus, it cannot be guaranteed that TeklaStructures is running upon the entire execution of the application. This is solved byadding a "handle" [10] to be able to insert, select, modify, delete and query objects inTekla Structures.
Tekla suggests three ways of utilising the Tekla Open APITM to create an application:
• VBA macros utilising COM technology
• COM applications
• .NET applications
A plug-in is a component tool for automatic creation of objects in Tekla Structures[10]. It is modifiable and dependent on input objects. Some templates for creatingplug-ins exist. For instance, the base class ConnectionBase simplifies the creation ofplug-ins for connections, details and seams.
The recommended way to define the dialog box of a plug-in is by using WindowsForms, a part of the Microsoft .NET Framework, available in Visual Studio. An al-ternative to Windows Forms is using the input file format INP. This is the same defin-ition language as is used in custom and system components in Tekla Structures[10].The difference between those two approaches is mainly the way of implementing thedialog box.
The different options for creating applications and plug-ins are presented in table 2.
Table 2: Extension types in Tekla Open API
Applications Plug-insVBA COM .NET WinForms INP
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2.3 State of the art 2 SOFTWARE AND CONCEPTS
2.3 State of the art
Among others, buildingSMART International [2], National Institute of Building Sci-ences [11] and Bentley Systems [12] strive for cooperation between different softwareproviders. However, although there is an understanding that one common standardwould be better, several standards are in use at the time as the providers support dif-ferent standards.
Industry Foundation Classes (IFC)
IFC is a specification package developed by buildingSMART International. Theyoffer several different structured formats for different purposes. In addition to the de-fault .ifc exchange format they have also developed the XML based .ifcXML format.The former has become the most common standard for data exchange between thedifferent stages of a construction process. The latter is an IFC data file with the XMLdocument structure. It is typically 300-400% larger than an .ifc file. The IFC stand-ard has been accepted by most of the industry, and is widely implemented in the mostpopular BIM software.
Tekla Structures and PowerConnect
It is possible to export a .dxf file from PowerConnect and import it in Tekla Struc-tures. Together with dimension values, this may be used as a sketch for modellingthe connection from scratch [13]. This is probably the most common method forconnecting the two programs today.
BuildSoft is working on the development of an application linking Tekla Structuresand PowerConnect, using VBA and Excel. It is unknown when and whether a solu-tion will be released.
Whereas Tekla Structures supports all IFC formats, PowerConnect supports neither.If this is to be implemented, it should be performed in the PowerConnect source code,which is not public.
STAAD.Pro and RAM Connection
Bentley offers an alternative for the American market, namely the STAAD.Pro andRAM Connection link [14]. This link supports design according to the Americanstandards AISC ASD and LRFD. RAM Connection also provides support for theAISC 13th edition unified code.
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2 SOFTWARE AND CONCEPTS 2.3 State of the art
RAM Structural System and Revit Structure
The RAM Structural System - Revit Structure link offers an export and import solu-tion between Bentley’s software for modelling, analysis and design and Autodesk’sBIM software for engineering, design and documentation [15]. RAM Structural Sys-tem supports several different standards, in different parts of the system, like AISCand BS in addition to Eurocode 2 and 3 [16].
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2.3 State of the art 2 SOFTWARE AND CONCEPTS
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3 EXTENSION DEVELOPMENT
3 Extension development
3.1 Specification
The desired outcome of this work is an extension to Tekla Structures that communic-ates with PowerConnect and requires a minimum of effort from the user. This maybe an application or a plug-in and communication through XML is suggested as apossibility.
A selection of connections from the PowerConnect library should be created as com-ponents in Tekla Structures and be compatible for modification and optimisation inPowerConnect.
A simple scenario is illustrated by the Use Case Diagram [17, 18] in Figure 1. Theuser models a steel connection in Tekla Structure and exports the connection toPowerConnect where optimal values are found and confirmed by the user. The con-firmed values are imported into Tekla Structures where the original model is alteredaccordingly.
Title: Create optimal steel connection
Figure 1: Use Case Diagram
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3.2 The approach 3 EXTENSION DEVELOPMENT
3.2 The approach
As mentioned in Section 2.1, PowerConnect has a library of connections and it hasbeen decided to limit the scope of the extension to a selection of those. Because TeklaStructures has an open API, the chosen approach aim at modelling the connectionsfrom this library in Tekla Structures, with the possibility of altering dimensions andother properties of bolts, welds, plates etc.
It has been focused on one of the connections from the PowerConnect library, withthe possibility of further development to support several connections in mind. Loadsmay be added in Tekla Structures and exported to analysis software. However, it ishere assumed that loading is applied in PowerConnect manually. The procedure forapplying loads directly in PowerConnect is straight-forward and clear.
3.3 The steel connection
The connection implemented in the extension is a joint between a column and a beamwith a welded end plate and a bolt group, as this was assumed to be the best altern-ative to start with. This connection is the top-left connection in the PowerConnect2012 start-up screen shown in Figure 2 and is shown more detailed in Figure 3a.Default column profile for this connection in PowerConnect is HEA200 and beamprofile IPE270.
Figure 2: PowerConnect 2012 Start-up library
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3 EXTENSION DEVELOPMENT 3.4 XML interface
(a) Structure of the connection (b) Dimensions of the end plate
Figure 3: PowerConnect model
The end plate should be resized if beam and column profiles change. Figure 3b fromPowerConnect illustrates how the height of the plate depends on the beam height, L,with an upper and a lower offset, u1 and u2. The plate width is equal to the columnwidth, W , and the plate thickness, th is set to be the same size as the column flangethickness, as default in PowerConnect.
3.4 XML interface
PowerConnect saves projects as XML structured .bpc-files. Similar structured filesmay be generated from Tekla Structure by using the Tekla Open API. By this ap-proach data may be interchanged between the two programs.
PowerConnect does not support the IFC standard, and implementation of this is tooextensive for this thesis. Use of .ifcXML is therefore disregarded.
BuildSoft did a brief attempt to create a template for the minimum .bpc-file, butconcluded that most tags were necessary for running the analysis. A trial and er-ror approach, basically based on removing tags from a .bpc-file before opening itin PowerConnect, revealed that some tags could be removed without noticeable ef-fect, although many of them seemed to be essential for running analysis. The planthus became to generate an XML-file with the XmlTextWriter, provided by the .NETFramework, with the same tags as a working .bpc-file and replace the names and num-bers, where possible, according to the Tekla model. A sample .bpc-file is included inAppendix A.
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3.5 Implementation 3 EXTENSION DEVELOPMENT
3.5 Implementation
Two main ways of implementing the extension were considered: A custom compon-ent to be altered by a .NET application and a plug-in with INP or WinForms. Theimplementation processes are presented in the succeeding sections.
Custom component
The first approach was to model a custom component in Tekla Structures and a .NETapplication to modify its parameters, according to the specification. A custom com-ponent in Tekla Structures is a model, e.g. a connection, that is saved as one item foreasy reuse later. The component can be parametrised and the modeller choose whichvalues that may be altered.
A custom component is created in Tekla Structures, geometrically identical to theplug-in described in the next section. The parameters for this custom component isshown in Figure 4.
Figure 4: Custom component parameters
The access of the parameters through the API was more problematic than first as-sumed and the approach was early set aside to model the connection as a plug-in.
Plug-in
A selection of examples are provided with the Tekla Open API Startup Package. Withthe source code of a plug-in for a splice connection between two beams (the Splice-Connection plug-in) as a basis, the ConnectionPlugin was developed.
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3 EXTENSION DEVELOPMENT 3.5 Implementation
The dialog box of the plug-in, shown in Figure 13, is defined using the same defini-tion language as custom components and system components in Tekla Structures, theinput file format INP. Figure 5 shows the connection modelled as a plug-in using INP.
Figure 5: The connection as an INP plug-in in Tekla Structures
The ConnectionBase is a template for creating details and connections as plug-ins.Plug-ins based on this template take one main part and one or more secondary partsas input. This is done by clicking the parts in the right order inside the model.
Cross-section properties
A certain profile, e.g. HEA200, has a set of dimensions and other cross-sectionalproperties. Although PowerConnect probably have these values stored, a solution foraccessing them through XML has not been found. When only the profile name ispassed in the .bpc file, the other values are set to zero. These values are thereforeextracted from Tekla Structures, or derived from other values where necessary.
Comparison of the values found in PowerConnect and those extracted from TeklaStructures reveals that the level of precision in PowerConnect is slightly higher. Someexamples are shown in Table 3. The derived values are based on the dimension prop-erties of the connection. These are given with the same precision in Tekla Structuresand PowerConnect. For the majority of the derived parameters, the same equationshave been used in the plug-in as in PowerConnect, and the derived values tend to bemore precise than the ones extracted from Tekla Structures.
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3.5 Implementation 3 EXTENSION DEVELOPMENT
Table 3: Precision in PowerConnect vs. Tekla Structures
Parameter PowerConnect Tekla Structures Relative difference
Cross-section area 5383.58901063716 5383 + 0.01%Iy 36924429.0935206 36920000 + 0.01%Iz 13355153.1052798 13360000 - 0.03%
As the plug-in should support as many cross-sections as possible, a parametric solu-tion with equations is more convenient than looking up tabulated values, althoughthis might be the easiest for fixed cross-sections. The equations derived in this thesisare for H- and I-profiles only, but this may be extended at a later stage.
Profile dimensions appear in the PowerConnect XML scheme as a list of unspecifieddimension tags. With help from Figure 6 and human interpretation, the correspond-ing values in Tekla Structures are found through the API. They are all displayed inTable 4. The values are read as shown in the following code example and written tothe .bpc-file with a XmlTextWriter.
double beamHeight = 0.0;beam.getProperty("PROFILE.HEIGHT", ref beamHeight);
Figure 6: Profile dimensions in PowerConnect
Whereas the dimensions were rather straightforward to export from Tekla Structure,some of the more complex properties presented in Table 5 were more challenging.Most properties were found in Tekla Structures with the same technique as for thecross-section dimensions. The remaining values were derived from the found prop-erties.
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3 EXTENSION DEVELOPMENT 3.5 Implementation
Cross-section properties are derived in PowerConnect with respect to the coordinatesystem in Figure 7. Due to double symmetry, ψ and ζ equals y and z, respectively.
Figure 7: Characteristics and principal axes of inertia of HEA200 in PowerConnect
The first moment of area, Sy, is derived by [19]:
Sy =∫A xdA = ΣxiAi
Considering the I-profile in Figure 8, we get the following formula, relative to thelower left corner of the profile:
Sy = B2 tf
2 + twH2 (H − 2tf ) +Btf (H − tf
2 ) + 2Hr2(1 − π4 )
The last term in the formula represents the contribution from the the roundings. Theroundings may be approximated by the circular drawing to the right in Figure 8.
Table 4: Profile dimensions
Fig 6 XML tag in PowerConnect Tekla Structures name
<CROSS-SECTION_DIMENSION>B <DIMENSION> 200 </DIMENSION> PROFILE.WIDTHH <DIMENSION> 190 </DIMENSION> PROFILE.HEIGHTtw <DIMENSION> 6.5 </DIMENSION> PROFILE.WEB_THICKNESStf <DIMENSION> 10 </DIMENSION> PROFILE.FLANGE_THICKNESSr <DIMENSION> 18 </DIMENSION> PROFILE.ROUNDING_RADIUS_1
</CROSS-SECTION_DIMENSION>
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3.5 Implementation 3 EXTENSION DEVELOPMENT
Figure 8: Profile dimensions in PowerConnect
The corresponding formula for Sz will then be:
Sz = tfB2 + tw
B2 (H − 2tf ) + 2Br2(1 − π
4 )
The plastic section modulus, Wpl,y, may be derived from the first moment of area S′y,with respect to the neutral axis, by the following formula [20]:
Wpl,y = 2S′y
Further, this leads to the formulas:
Wpl,y = 2[tf B2 (H − tf ) + tw2 (H2 − tf ) + 2r2(1 − π
4 )(H2 − tf − r + r6(1−π4 ))]
= tfB(H − tf ) + tw(H2 − tf )2 + 4r2(1 − π4 )(H2 − tf − r + r
6(1−π4 ))
Wpl,z = 2[2B2 tfB4 + tw
2 (H − 2tf ) tw4 + 2r2(1 − π4 )( tw2 + r − r
6(1−π4 ))]
= tfB2
2 + tw2
4 (H − 2tf ) + 4r2(1 − π4 )( tw2 + r − r
6(1−π4 ))
Shear area for rolled I- and H- profiles, loaded parallell to the web is given by [21]:
Avz = A− 2Btf + (tw + 2r)tf ,
but not less than ηhwtw, where hw is the height of the web, h − 2tf . When loadedparallell to the width, the shear area is given by [21]:
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3 EXTENSION DEVELOPMENT 3.5 Implementation
Avy = A− Σ(hwtw) = A− (h− 2tf )tw
The tortional constant, IT , may be approximated by the formula [7]:
IT,approx = 13
∑bit
3i , ti << bi
This gives a value for IT that is significantly lower than tabular values and limited tothin-walled H- and I-profiles. For circular profiles a more exact value may be foundby using the correlation IT = Iz . In PowerConnect, and in the plug-in, the torsionconstant is calculated by the formula [22]:
IT = 23(B − 0.63tf )tf 3 + 1
3(H − 2tf )tw3
+2( twtf )(0.145 + 0.1 rtf
)[ (r+tw/2)2+(r+tf )2−r2
2r+tf ]4
Iw is the warping constant given by [7] as:
Iw = Cw = 124(tfb3h2
f )
The cross-section properties and how their values are found are summarised andpresented in Table 5.
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3.5 Implementation 3 EXTENSION DEVELOPMENT
Table 5: Cross-section properties for HEA 200
XML tag in PowerConnect Tekla Structures name
<PROPERTIES><SURFACE> 5383.58901063716 </SURFACE> PROFILE.CROSS_SECTION_AREA<SY> 511440.956010531 </SY> Formula<SZ> 538358.901063717 </SZ> Formula<IY> 36924429.0935206 </IY> PROFILE.MOMENT_OF_INERTIA_X<IZ> 13355153.1052798 </IZ> PROFILE.MOMENT_OF_INERTIA_Y<YS> 100 </YS> PROFILE.WIDTH / 2<ZS> 95.0000000000002 </ZS> PROFILE.HEIGHT / 2<WYU> 388678.200984428 </WYU> PROFILE.SECTION_MODULUS_X<WYB> 388678.200984427 </WYB> PROFILE.SECTION_MODULUS_X<WZL> 133551.531052798 </WZL> PROFILE.SECTION_MODULUS_Y<WZR> 133551.531052798 </WZR> PROFILE.SECTION_MODULUS_Y<RY> 82.8172767447484 </RY> PROFILE.RADIUS_OF_GYRATION_X<RZ> 49.8067824144329 </RZ> PROFILE.RADIUS_OF_GYRATION_Y<IPSI> 36924429.0935206 </IPSI> = IY<IZETHA> 13355153.1052798 </IZETHA> = IZ<WPLY> 429521.292081565 </WPLY> Formula<WPLZ> 203822.313107166 </WPLZ> Formula<YPLYZ> 100 </YPLYZ> = YS<ZPLYZ> 95 </ZPLYZ> = ZS<AVZ> 1808.58901063716 </AVZ> Formula<AVY> 4159.25 </AVY> Formula<IT> 209849.432607371 </IT> Formula<IW> 108000000000 </IW> Formula<WZETHAU> 133551.531052798 </WZETHAU> = WZL<WZETHAB> 133551.531052798 </WZETHAB> = WZR<WPSIU> 388678.200984428 </WPSIU> = WYU<WPSIB> 388678.200984427 </WPSIB> = WYB<ZPLPSIZETHA> 95 </ZPLPSIZETHA> = ZS<YPLPSIZETHA> 100 </YPLPSIZETHA> = YS<WPLZETHA> 203822.31310716</WPLZETHA> = WPLZ<WPLPSI> 429521.292081565 </WPLPSI> = WPLY<DY> 100 </DY> = YS<DZ> 95.0000000000002 </DZ> = ZS<FY_THICKNESS> 10 </FY_THICKNESS> PROFILE.FLANGE_THICKNESS
</PROPERTIES>
18
3 EXTENSION DEVELOPMENT 3.5 Implementation
Bolts
In PowerConnect bolts are positioned with horizontal and vertical distances accord-ing to Figure 9. The important values for each row are the horizontal distance and thedistance from the bolts to the row above, or to the top of the plate for the upper row.These values are passed in the .bpc file together with the bolt diameter.
Figure 9: Bolt positioning in PowerConnect
For the plug-in, a working solution using the same vertical and horizontal distances isestablished. The bolts are positioned relative to the middle of the plate, and the upperdistance of the upper bolt row is derived from the plate height and included in the.bpc file. It has been focused on bolt positioning rather than bolt types, so distancesand diameter are currently the only values that may be altered in the plug-in. Numberof bolts are fixed to six bolts distributed into three rows of two bolts at this stage.
19
3.5 Implementation 3 EXTENSION DEVELOPMENT
Welding
PowerConnect allows automatic calculation of welding lengths, see Figure 10. Theplug-in dialog includes a field for weld thickness. Apart from being able to alter thisvalue, default methods and values for welding are used in both Tekla Structures andPowerConnect.
Figure 10: Weld dialog in PowerConnect
Materials
The default material in PowerConnect is Steel S235. By including only the followinglines of material properties in the exported .bpc file, S235 will be used for that part.
<TBAR_MATERIAL><NEWMATERIALTYPE>1</NEWMATERIALTYPE><MATERIALVERSION>3</MATERIALVERSION><STANDARDID>1</STANDARDID>
</TBAR_MATERIAL>
To allow for other materials, material properties may be extracted from Tekla Struc-tures and included in the .bpc file, as for cross-section properties. The relevant prop-erties are displayed in Table 6. All values, except for one, are found by the samemethods as the cross-section properties. The transversal Young modulus, G is thenderived from the Young modulus, E, and the Poisson ratio, ν, with the formula [20]:
G = E2(1+ν)
20
3 EXTENSION DEVELOPMENT 3.5 Implementation
If the material is not already included in PowerConnect, it will be added in its mater-ial library.
The number in the tag <NEWMATERIALTYPE> may be a number from one to five,depending on type of material, see Table 7. For now, it is assumed that the materialsused in the plug-in are some sort of steel, as steel connections are the scope of thethesis. This may be extended at a later stage.
Table 6: Material properties
XML tag in PowerConnect Tekla Structures name
<NAME> column.Material.MaterialString<YOUNGMODULUS> MATERIAL.MODULUS_OF_ELASTICITY<POISSONRATIO> MATERIAL.POISSONS_RATIO<THERMDILATATIONCOEFF> MATERIAL.THERMAL_DILATATION<DENSITY> MATERIAL.PROFILE_DENSITY<TRANSVERSALYOUNGMODULUS_G> Formula
Table 7: Material types in PowerConnect
Number Material name
1 Steel2 Concrete3 Timber4 Aluminium5 Mix Concrete-Steel
21
3.5 Implementation 3 EXTENSION DEVELOPMENT
22
4 RESULTS
4 Results
Two main approaches for creating a link between Tekla Structures and PowerConnectwere tried throughout the work. A custom component with a .NET application anda plug-in. During the work the plug-in approach proved superior, and the other ap-proach was disregarded. Only the plug-in is presented in the succeeding sections.
4.1 Short description of the plug-in
A plug-in is implemented, which inserts a connection between an intersecting beamand column and immediately prompts export to PowerConnect for analysis. Theplug-in is limited to support H- and I-profiles, as only formulae for these cross-sections are implemented for the derived parameters. Some of these equations furtherrequire double symmetry and that the elastic and plastic axes intersect.
It is possible to apply the connection to both beam ends and at any height of thecolumn. However, the column must be oriented with its flange towards the beam.
The desired result was a solution for two-way communication. However, because ofthe complexity of PowerConnect’s .bpc-file, only the connection from Tekla Struc-tures to PowerConnect has been established. It is presently unknown whether a solu-tion for the other way around should or could be established with the same approach.It is assumed more convenient to establish a link through PowerConnect’s sourcecode.
4.2 Installing the plug-in
The plug-in is a .dll-file and is automatically included in Tekla Structures whencopied into Tekla’s plugins folder. Note: This will not be possible while the pro-gram is running. The file path should be something like this:
C:\Program Files\Tekla Structures\18.1\nt\bin\plugins\
In Tekla Structures, the plug-in is called ConnectionPlugin and is found in the Com-ponent Catalog (ctrl + F) as seen in Figure 11.
23
4.3 Using the plug-in 4 RESULTS
Figure 11: Component Catalog
4.3 Using the plug-in
The ConnectionPlugin may be applied wherever a column and a beam intersect as inFigure 12, at any column height. It is required that the column is oriented with itsflange towards the beam.
Figure 12: Column-beam intersection
The dialog box in figure 13 allows the user to change the values of the connectionthat is not automatically controlled by the plug-in. It is displayed by double clickingthe plug-in name in the Component Catalog. If a field is empty, or filled with invalidinput, default values will be used.
24
4 RESULTS 4.3 Using the plug-in
Figure 13: Dialog box
Step 1:Select the plug-in in the Component Catalog. The prompt line asks the user to selectthe main part, see Figure 14.
Figure 14: Prompt line: Pick main part
Step 2:The column is the main part in the connection. Select the column. The prompt lineasks for the secondary part, see Figure 15.
Figure 15: Prompt line: Pick secondary part
Step 3:In this case there is only one secondary part, the beam. Select the beam and the dialogin Figure 16 appears.
25
4.3 Using the plug-in 4 RESULTS
Figure 16: Save PowerConnect-file
Step 4:Choose a name and a location for the .bpc-file and press Save. The saved file may beopened in PowerConnect immediately for analysis, to see if any part needs modific-ation, see Figure 17.
Figure 17: Open file in PowerConnect
Step 5:Press Yes to open the saved file in PowerConnect and No to proceed without modific-ations. The file may be opened and the model altered later.
The connection is inserted together with a cone. It will be green, like in Figure 18, ifeverything is fine. If it turns yellow or red some properties should be changed.
26
4 RESULTS 4.4 Example of use
Figure 18: Connection inserted
4.4 Example of use
As a simple test example, a connection between the default beam and column inPowerConnect is modelled and analysed. First, both modelling and analysis is per-formed in PowerConnect alone, with default settings as in Figure 19 and a chosensample loading as in Figure 20. Second, the plug-in is used to connect a beam anda column in Tekla Structures, as described in Section 4.3, followed by analysis inPowerConnect with the same sample loading as before. The maximum values arepresented in Table 8, and a more detailed summary of the results from both analysesare added in Appendix B.
Figure 19: Default values in PowerConnect
27
4.4 Example of use 4 RESULTS
Figure 20: Sample loading in PowerConnect
Table 8: Maximum values from analysis
Capacity Default Plug-in
Maximum positive moment (MRd+) 38,9 kNm 38,9 kNmMax positive moment allowed by welds 77,2 kNm 77,2 kNmMaximum tension in the beam (TRd) 288,4 kN 288,4 kNMaximum compression in beam (CRd) 432,4 kN 432,3 kNMoment combined with normal force (MSd/MRd + NSd/NRd) 0,28 0,28Maximum shear force (VRd) 456,4 kN 456,4 kNMaximum shear allowed in the column web 220,8 kN 220,8 kN
The small changes in compression is assumed a result of different precision in theparameters of PowerConnect and Tekla Structures. It can be concluded that the smallchanges due to approximation and calculation have little or no impact on the capacityvalues from the analysis.
28
5 DISCUSSION
5 Discussion
5.1 Approaches
Pros and cons for four different approaches of creating steel connections are sum-marised in Table 9.
Table 9: Pros and cons
Approach Pros Cons
Manual + Support for allcross-sections andconnection types
- Time consuming
CustomComponent&Manual export
+ Support for allcross-sections+ Parametrisable+ Effective modelling(except the first time)+ May create any connectionas a Custom Component
- Time consuming export toPowerConnect
CustomComponent& .NETapplication
+ As above+ Effective export toPowerConnect (whenimplemented)
- Challenging implementation- Not implemented(no connection toPowerConnect)
Plug-in + Effective modelling+ Parametrisable+ Modifiable+ Effective export toPowerConnect+ Portability (.dll)
- Further implementationmay be demanding
The main advantage of the plug-in compared to the other more manual approaches isthe link to PowerConnect. The possibility to analyse the connection in PowerConnectas it is inserted in Tekla Structures help the modeller to achieve the optimal solutionfaster.
29
5.2 Cross-section and material properties 5 DISCUSSION
5.2 Cross-section and material properties
Some section and material properties are extracted from the Tekla Structures model.The levels of precision in PowerConnect and Tekla Structures are slightly different,PowerConnect is more precise. The relative difference of some of the values is shownin Table 3. This should have an insignificant impact on the results. Other propertiesare derived from the cross-section dimensions. As most of the equations in the plug-in are the same as in PowerConnect, the derived values are equal or very close to thosefound in PowerConnect. It seems unlikely that the small differences in the results aredue to rounding errors. They more likely come from discrepancies in formulae, butit’s even more probable that they come from the values assumed negligible.
The advantage of calculating values in the plug-in is that properties not included inTekla Structures, but required in PowerConnect, may be included in the plug-in. Onedisadvantage is that the calculations increase the length of the code and thus bothcoding time and run time of the plug-in. Further, as the equations used are limitedto specific geometrical shapes, implementation of new equations is required to sup-port cross-sections with other geometry. Only H- and I-profiles are supported in thecurrent version of the plug-in. An option could be to let the user enter the cross-sectional parameter values to support all cross-sections. However, PowerConnectonly supports H-, I- and hollow core profiles.
Extracting values from Tekla Structures may decrease the chances of errors, as it isassumed that the values in Tekla Structures are correct. The difference in precision isregarded negligible. This solution relies on that the parameters exist in Tekla Struc-tures with a valid value. As the calculated values are derived from extracted values,this will also be the case for these parameters.
It has been noticed that several of the derived parameters are included in Tekla Struc-tures, but set to zero. When a link from PowerConnect to Tekla Structures is estab-lished, values may be saved here. If it turns out that it is possible to extract any ofthese values directly from Tekla Structures, modifying the plug-in to do so wouldbe preferable. If it is the case for several parameters, unnecessary work have beenperformed here, but at least it has lead to a working solution.
It is assumed that all materials are some sort of steel, as the scope of the thesis issteel connections. Support for other materials may be implemented, see section 3.5on Materials.
30
5 DISCUSSION 5.3 Data exchange
5.3 Data exchange
Using a shared model between Tekla Structures and PowerConnect is problematic asthe implementation of reading it in PowerConnect is difficult without access to thesource code. Moreover, the set-up of a shared database is a demanding job.
Exchanging data from Tekla Structures to PowerConnect is possible as the TeklaOpen API may fetch data from a Tekla Structures model and write it to a custom-ized XML file with the structure of a PowerConnect project file. Some properties arenot transferred in the current solution, and further implementation is required. Largeamounts of code may be reused for this.
A problem with the current plug-in is the passing of data through a text file insteadof an interconnected model. Reading the PowerConnect project file requires humaninterpretation and a solution for reading this file in Tekla Structures is not implemen-ted. A link from PowerConnect to Tekla Structures is therefore not included in thecurrent plug-in. This is probably the main shortcoming of the plug-in, as modifiedproperties now must be updated manually.
There might be a better way to connect the programs with access to PowerConnect’ssource code. It should be possible to look up values for standard sections from data-bases in PowerConnect rather than deriving them in the plug-in. For non-standardcross-sections an alternative could be for the user to enter the property values ratherthan for the plug-in to derive them.
31
5.3 Data exchange 5 DISCUSSION
32
6 CONCLUDING REMARKS
6 Concluding remarks
6.1 Summary of work
A plug-in for Tekla Structures has been established. It inserts a beam-column steelconnection that may automatically be exported to PowerConnect for analysis. Theimplemented plug-in is limited to handle H- and I-profiled cross-sections of differentsteel types. Parameters are extracted from Tekla Structures to PowerConnect, and afew are calculated based on values found in Tekla Structures. Relevant parametersare written to a XML structured .bpc file to be opened and analysed in PowerConnect.No link from PowerConnect to Tekla Structures have been established.
6.2 General conclusions
Of the different approaches compared in Section 5.1, the plug-in stand out as a prom-ising alternative to the more manual approaches. The main disadvantage of the plug-in compared to the manual options is support for other connection types and cross-sections. If this and other functionality are added, the plug-in is likely to become agood choice.
The major advantage of the plug-in is the possibility to analyse the connection inPowerConnect immediately after it is inserted in Tekla Structures. Unfortunately, nolink from PowerConnect to Tekla Structures for automatic update of the connection’sparameters has been established.
6.3 Suggestions for further work
The results presented propose for further development. For some tasks parts of thecode may be reused and other parts must be implemented from scratch.
Some main functionality that should be implemented are:• Support for other cross-sections, primarily hollow core sections as these are
supported by PowerConnect. This may be done by gaining access to data fromPowerConnect, extracting the for now calculated values from Tekla Structuresor extending the calculations to include other geometry.
• Implement a wider range of connections from PowerConnect library, includingsupport for beam-column-beam and beam-beam connections. The connectionsin Figure 21 should be possible to create with the single beam-column connec-tion created in this work as a basis. This could be done as modifications to theold plug-in or as separate plug-ins.
33
6.3 Suggestions for further work 6 CONCLUDING REMARKS
• Toolbar button. A button on the toolbar would yield easier access to the plug-inthan the line in the Component Catalog.
• Export of loads from Tekla Structures to PowerConnect.
• Link from PowerConnect to Tekla Structures to update modified parametersautomatically after analysis.
(a) Bolted moment end plate on bothcolumn flanges
(b) Beam to beam with end plate
Figure 21: PowerConnect connections to be implemented
Further, the dialog box of the plug-in could be improved by for instance adding:
• Button for export to PowerConnect
• Figure of selected connection
• Combo box for connection type
• Combo box for material
The bolt section may be extended with more options for modification. It shouldamong other things be possible to:
• Edit bolt standard
• Change number of bolt rows
• Change number of bolts per row
• Allow uneven bolt distribution
34
6 CONCLUDING REMARKS 6.3 Suggestions for further work
Several controls should be added and the plug-in should undergo extensive testing.
The optimal solution for an extension for connections would involve a single functionfor automatic evaluation of all connections in the entire model at once. This requiresa considerable amount of work, and has not yet been established. Work may be pro-ceeded and a more user friendly and extensive solution might be developed based onwhat has been performed here combined with further work.
35
6.3 Suggestions for further work 6 CONCLUDING REMARKS
36
REFERENCES REFERENCES
References
[1] Microsoft Corporation, COM: Component Object Model Technologies, http://www.microsoft.com/com/ (2013-05-27).
[2] buildingSMART International Ltd., IFC Standard, http://www.buildingsmart-tech.org/specifications/ifc-overview/ifc-overview-summary (2013-04-09).
[3] World Wide Web Consortium (W3C), Extensible Markup Language (XML),http://www.w3.org/XML/ (2013-05-27).
[4] BuildSoft NV, PowerConnect, http://www.buildsoft.eu/en/product/powerconnect (2013-02-20).
[5] European Comittee for Standardization (CEN), Eurocode 3: Design of steelstructures - Part 1-8: Design of joints, EN1993-1-8, 2005.
[6] BuildSoft NV, Part 1: Getting Started with PowerConnect (Euro-code edition), http://downloads.buildsoft.eu/pdf/en/PowerConnectManual-EN-Part1AEC3-A4.pdf, 2008(2013-02-20).
[7] Larsen, P. K., Dimensjonering av stålkonstruksjoner, 2nd ed., Tapir AkademiskForlag, Trondheim, 2010.
[8] Tekla Corporation, Tekla BIM Software, http://www.tekla.com/international/products/tekla-structures/Pages/Default.aspx (2013-02-20).
[9] Tekla Corporation, Integration with analysis and design,http://www.tekla.com/international/solutions/building-construction/structural-engineers/integration-with-A-D/Pages/Default.aspx (2013-05-28).
[10] Tekla Corporation, Tekla Open API Developer’s Guide, 2011.
[11] National Institute of Building Sciences, About the National BIM Standard-United StatesTM, http://www.nationalbimstandard.org/about.php (2013-04-09).
[12] Bentley Systems Inc., Empowering Intelligent Structural Design ThroughIntegrated Structural Modeling, http://www.bentley.com/en-US/Products/Structural+Analysis+and+Design/ISM/(2013-04-09).
37
REFERENCES REFERENCES
[13] EDR MEDESO BIM, Export Power Connect to Tekla Structures, http://youtu.be/CoXMwdH-t7M, 2012 (2013-02-20).
[14] Bentley Systems Inc., STAAD.Pro and RAM Connection link,http://communities.bentley.com/administrators/the_bentley_structural_team/m/the_bentley_structural_team-files/60046/download.aspx, 2009 (2013-04-09).
[15] Bentley Systems Inc., RAM Structural System and Revit Structure link,http://www.bentley.com/en-US/Promo/Structural+Team/RSS+Revit.htm (2013-04-09).
[16] Bentley Systems Inc., RAM Structural System V8i Release 14.04 New Featuresand Enhancements, http://www.bentley.com/en-US/Products/RAM+Structural+System/New-Features-Enhancements.htm(2013-05-01).
[17] N.N., Use Case Diagram, http://en.wikipedia.org/wiki/Use_Case_Diagram (2013-05-10).
[18] Fowler, M., UML Distilled, 3rd ed., Pearson Education, Inc., Boston, MA,2004.
[19] Irgens, F., Formelsamling mekanikk, 3rd ed., Tapir Akademisk Forlag, Trond-heim, 1999.
[20] Larsen, P. K., Clausen, A. H., Aalberg, A., Stålkonstruksjoner - Profiler ogformler, 3rd ed., Tapir Akademisk Forlag, Trondheim, 2007.
[21] European Comittee for Standardization (CEN), Eurocode 3: Design of steelstructures - Part 1-1: General rules and rules for buildings, EN1993-1-1, 2005.
[22] Arcelor Mittal LCE, Sections and Merchant Bars - Sales Programme,http://www.arcelormittal.com/sections/fileadmin/redaction/4-Library/1-Sales_programme_Brochures/Sales_programme/ArcelorMittal_EN_FR_DE.pdf (2013-05-24).
38
A SAMPLE .BPC-FILE
Appendices
A Sample .bpc-file
1 <? xml v e r s i o n =" 1 . 0 " s t a n d a l o n e =" no " ?>2 < !−−E x p o r t e d f i l e from T e k l a S t r u c t u r e s−−>3 <POWERCONNECT_PROJECT>4 <DESIGNVERSION>2012< / DESIGNVERSION>5 <DESIGNREVISION>1< / DESIGNREVISION>6 <TPROJECT_NODES>7 <TPROJECT_NODE>8 <TNODE_CONNECTIONS>9 <TNODE_CONNECTION>
10 <LISTWITHCONNECTEDELEMENT / >11 <TCONNECTION_VERSION>102< / TCONNECTION_VERSION>12 <TCONNECTION_PARTOFDOUBLECONNECTION>−1< /
TCONNECTION_PARTOFDOUBLECONNECTION>13 <TCONNECTION_CONNECTIONTYPE>1< /
TCONNECTION_CONNECTIONTYPE>14 <TCONNECTION_AXISTYPE>1< / TCONNECTION_AXISTYPE>15 <TCONNECTION_NODENUM>0< /TCONNECTION_NODENUM>16 <TCONNECTION_CONNECTIONNUM>0< /
TCONNECTION_CONNECTIONNUM>17 <TCONNECTION_LISTWITHBARS>18 <TCONNECTION_BAR>19 <TBAR_SECTION>20 <SECTIONNAME>HEA200< /SECTIONNAME>21 <SECTIONTYPE>4< / SECTIONTYPE>22 <ROLLED>True < /ROLLED>23 <COOL> F a l s e < /COOL>24 <VERSION>1< / VERSION>25 <CROSS−SECTION_DIMENSION>26 <DIMENSION>200< / DIMENSION>27 <DIMENSION>190< / DIMENSION>28 <DIMENSION>6 ,5 < / DIMENSION>29 <DIMENSION>10< / DIMENSION>30 <DIMENSION>18< / DIMENSION>31 <DIMENSION>190< / DIMENSION>32 < / CROSS−SECTION_DIMENSION>33 <OTHER_CROSS−SECTION_DIMENSION>34 <OTHER_DIMENSION>190< / OTHER_DIMENSION>35 < / OTHER_CROSS−SECTION_DIMENSION>36 <PROPERTYCALCULATED>True < /PROPERTYCALCULATED>37 <LIST_OF_PROPERTIES>38 <PROPERTIES>39 < / PROPERTIES>40 < / LIST_OF_PROPERTIES>41 < / TBAR_SECTION>
39
A SAMPLE .BPC-FILE
42 <TBAR_MATERIAL>43 <NAME>S235< /NAME>44 < /TBAR_MATERIAL>45 <TBAR_AF>5< / TBAR_AF>46 <TBAR_AW>5< /TBAR_AW>47 <TBAR_SLOPE>0< / TBAR_SLOPE>48 <TBAR_CONNECTIONANGLE>1.5707963267949 < /
TBAR_CONNECTIONANGLE>49 <TBAR_BARLENGTH>2500< /TBAR_BARLENGTH>50 <TBAR_UPPERLENGTH>0< /TBAR_UPPERLENGTH>51 <TBAR_PRIORITY>0< / TBAR_PRIORITY>52 <TBAR_EXCENTRICITY>0< / TBAR_EXCENTRICITY>53 <TBAR_TYPEBAR>2< /TBAR_TYPEBAR>54 <TBAR_LISTWITHNMV>55 <TBAR_NMV>56 <VERSION>101< / VERSION>57 <COMBINATIONNR>−1< /COMBINATIONNR>58 <TOBECALCULATED>True < /TOBECALCULATED>59 <COLUMN>True < /COLUMN>60 < /TBAR_NMV>61 < /TBAR_LISTWITHNMV>62 <TBAR_ENTREDISTANCE>0< / TBAR_ENTREDISTANCE>63 <TBAR_COUPESUPERIEURE> F a l s e < / TBAR_COUPESUPERIEURE>64 <TBAR_COUPEINFERIEURE> F a l s e < / TBAR_COUPEINFERIEURE>65 <TBAR_FRICTIONCOEFFICIENT> 0 . 5 < /
TBAR_FRICTIONCOEFFICIENT>66 < /TCONNECTION_BAR>67 <TCONNECTION_BAR>68 <LISTWITHCONNECTEDELEMENT>69 <CONNECTEDELEMENT>70 <LISTWITHCONNECTEDELEMENT / >71 <TENDPLATE_VERSION>102< / TENDPLATE_VERSION>72 <TENDPLATE_H>290< / TENDPLATE_H>73 <TENDPLATE_B>CB< / TENDPLATE_B>74 <TENDPLATE_TH>CF< / TENDPLATE_TH>75 <TENDPLATE_U1>10< / TENDPLATE_U1>76 <TENDPLATE_U2>10< / TENDPLATE_U2>77 <TENDPLATE_PERPENDICULARTO>−1< /
TENDPLATE_PERPENDICULARTO>78 <TENDPLATE_PARENTBOLTS>True < /
TENDPLATE_PARENTBOLTS>79 <TENDPLATE_FRICTIONCOEFFICIENT> 0 . 5 < /
TENDPLATE_FRICTIONCOEFFICIENT>80 <TENDPLATE_MATERIAL>81 <NAME>S235< /NAME>82 < / TENDPLATE_MATERIAL>83 <TENDPLATE_BOLTS>84 < / TENDPLATE_BOLTS>85 < /CONNECTEDELEMENT>
40
A SAMPLE .BPC-FILE
86 < /LISTWITHCONNECTEDELEMENT>87 <TBAR_VERSION>103< / TBAR_VERSION>88 <TBAR_NODENUM>0< /TBAR_NODENUM>89 <TBAR_CONNECTIONNUM>0< /TBAR_CONNECTIONNUM>90 <TBAR_SECTION>91 <DEFINED>True < / DEFINED>92 <SECTIONNAME>IPE270< /SECTIONNAME>93 <SECTIONTYPE>4< / SECTIONTYPE>94 <ROLLED>True < /ROLLED>95 <COOL> F a l s e < /COOL>96 <VERSION>1< / VERSION>97 <CROSS−SECTION_DIMENSION>98 <DIMENSION>135< / DIMENSION>99 <DIMENSION>270< / DIMENSION>
100 <DIMENSION>6 ,599999905 < / DIMENSION>101 <DIMENSION>10 ,19999981 < / DIMENSION>102 <DIMENSION>15< / DIMENSION>103 <DIMENSION>270< / DIMENSION>104 < / CROSS−SECTION_DIMENSION>105 <OTHER_CROSS−SECTION_DIMENSION>106 <OTHER_DIMENSION>270< / OTHER_DIMENSION>107 < / OTHER_CROSS−SECTION_DIMENSION>108 <PROPERTYCALCULATED>True < /PROPERTYCALCULATED>109 <LIST_OF_PROPERTIES>110 <PROPERTIES>111 < / PROPERTIES>112 < / LIST_OF_PROPERTIES>113 < / TBAR_SECTION>114 <TBAR_MATERIAL>115 <NAME>S235< /NAME>116 < /TBAR_MATERIAL>117 <TBAR_AF>5< / TBAR_AF>118 <TBAR_AW>5< /TBAR_AW>119 <TBAR_SLOPE>1.5707963267949 < / TBAR_SLOPE>120 <TBAR_CONNECTIONANGLE>1.5707963267949 < /
TBAR_CONNECTIONANGLE>121 <TBAR_BARLENGTH>5000< /TBAR_BARLENGTH>122 <TBAR_UPPERLENGTH>0< /TBAR_UPPERLENGTH>123 <TBAR_PRIORITY>1< / TBAR_PRIORITY>124 <TBAR_EXCENTRICITY>0< / TBAR_EXCENTRICITY>125 <TBAR_TYPEBAR>3< /TBAR_TYPEBAR>126 <TBAR_LISTWITHNMV>127 <TBAR_NMV>128 <VERSION>101< / VERSION>129 <COMBINATIONNR>−1< /COMBINATIONNR>130 <TOBECALCULATED>True < /TOBECALCULATED>131 <COLUMN> F a l s e < /COLUMN>132 < /TBAR_NMV>133 < /TBAR_LISTWITHNMV>
41
A SAMPLE .BPC-FILE
134 <TBAR_ENTREDISTANCE>0< / TBAR_ENTREDISTANCE>135 <TBAR_COUPESUPERIEURE> F a l s e < / TBAR_COUPESUPERIEURE>136 <TBAR_COUPEINFERIEURE> F a l s e < / TBAR_COUPEINFERIEURE>137 <TBAR_FRICTIONCOEFFICIENT> 0 . 5 < /
TBAR_FRICTIONCOEFFICIENT>138 < /TCONNECTION_BAR>139 < / TCONNECTION_LISTWITHBARS>140 <TCONNECTION_LISTWITHTUBES / >141 <TCONNECTION_COMBINATIONSLIST>142 <TCONNECTION_VAL> Combina t ion1 < /TCONNECTION_VAL>143 < / TCONNECTION_COMBINATIONSLIST>144 <TCONNECTION_BRACED> F a l s e < /TCONNECTION_BRACED>145 < /TNODE_CONNECTION>146 < /TNODE_CONNECTIONS>147 < / TPROJECT_NODE>148 < / TPROJECT_NODES>149 <TPROJECT_CALCULATIONPARAMETERS>150 <VERSION>106< / VERSION>151 <BRACED>True < /BRACED>152 <AMIN>3< /AMIN>153 < / TPROJECT_CALCULATIONPARAMETERS>154 < /POWERCONNECT_PROJECT>
42
B ANALYSIS RESULTS FROM POWERCONNECT
B Analysis results from PowerConnect
B.1 Default connection
[Note : Connection analyses are based on Eurocode 3 : EN 1993-1-8:2005]
Summary
Right-hand connection
Moment Maximum positive moment (MRd+) = 38,9 kNm ≥ Applied moment (MSd) = 10 kNm Most critical combination : - Combination1 - Max positive moment allowed by welds = 77,2 kNm ≥ Applied moment (MSd) = 10 kNm Most critical combination : - Combination1 -
Normal force
Maximum tension in the beam (TRd) = 288,4 kN ≥ Applied tensile force (TSd) = 0 kN Maximum compression in beam (CRd) = 432,4 kN ≥ Applied compression force (CSd) = 10 kN Most critical combination : - Combination1 -
Moment combined with normal force
Combination name MSd MRd NSd NRd MSd/MRd + NSd/NRd < 1
Combination1 10,00 38,89 10,00 432,35 0,28 V
Shear
Maximum shear force (VRd) = 456,4 kN ≥ Applied shear force (VSd) = 10 kN Most critical combination : - Combination1 - Maximum shear allowed in the column web = 220,8 kN ≥ Applied shear in the column web = 37 kN Most critical combination : - Combination1 -
Stiffness
For a positive moment Sjini = 8297 kNm/Rad Sj = 4148 kNm/Rad The connection is Semi-Rigid. Most critical combination : - Combination1 -
43
B.2 Plug-in connection B ANALYSIS RESULTS FROM POWERCONNECT
B.2 Plug-in connection
[Note : Connection analyses are based on Eurocode 3 : EN 1993-1-8:2005]
Summary
Right-hand connection
Moment Maximum positive moment (MRd+) = 38,9 kNm ≥ Applied moment (MSd) = 10 kNm Most critical combination : - Combination1 - Max positive moment allowed by welds = 77,2 kNm ≥ Applied moment (MSd) = 10 kNm Most critical combination : - Combination1 -
Normal force
Maximum tension in the beam (TRd) = 288,4 kN ≥ Applied tensile force (TSd) = 0 kN Maximum compression in beam (CRd) = 432,3 kN ≥ Applied compression force (CSd) = 10 kN Most critical combination : - Combination1 -
Moment combined with normal force
Combination name MSd MRd NSd NRd MSd/MRd + NSd/NRd < 1
Combination1 10,00 38,89 10,00 432,30 0,28 V
Shear
Maximum shear force (VRd) = 456,4 kN ≥ Applied shear force (VSd) = 10 kN Most critical combination : - Combination1 - Maximum shear allowed in the column web = 220,8 kN ≥ Applied shear in the column web = 37 kN Most critical combination : - Combination1 -
Stiffness
For a positive moment Sjini = 8296 kNm/Rad Sj = 4148 kNm/Rad The connection is Semi-Rigid. Most critical combination : - Combination1 -
44
C COMPLETE SOURCE CODE
C Complete source code
ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss s
s
s
3
4
5
6
7
8
9
ss
ss
ss
s3
s4
s5
s6
s7
s8
s9
ss
ss
ss
s3
s4
s5
s6
s7
s8
s9
3s
3s
3s
33
34
35
36
37
38
39
4s
4s
4s
43
44
45
46
47
48
49
5s
5s
5s
53
54
55
56
57
58
59
6s
6s
6s
63
64
65
66
67
68
sssssss;sss;;
sssssss;sss;s;ssss;ss;ss;s;
sssssss;sss;s;;s;
ssssss;sssssssssssssss;
ssssss;sssssssssssssssssss;sss;3s;
ssssss;sssssssssssssssssssss;
ssssss;sssssssssssssssssssssss;
ss;ss ssssssssssssssssssss
{
ssss**s***s*s*ssssss***
ssss**sssgsssssgssss;sssgssgssssssssssssssssgsssssssss
ssss[ssssss("ssssssssssssssss"]]
ssss**s***s*s*ssssss***
ssss**sssssssssssgssssssssssssgsss
ssss[ssssssesssessssgsss(sssssssssssssssssesssessssgsssssgsssssssssssssssssssssssssee]]
ssss**s***s*s*ssssss***
ssss**sssgsssssgssss;sssssgsssssssss;s ssss
ssss[ssssssss;;; s(ssssssssssessssssssssss;;; sss]s]]s]*];]s]]]]]]]
ssss**s***s*s*ssssss***
ssss**sssgsssssgssssssss ssssssssssss; s
ssss[]ssssssssssss;; s(]ssssssssssss;; s]ss;s]e;]se*]e]ses]]
ssss**s***s*s*ssssss***
ssss**sssgsssssgss sssssssss; s
ssss[ssssssss;; s(ssssssss;; s]ss;ss]]]ese]]]s]]]]]]
ssss ssssss ssssssssssssssssssssssssssssssssssssssssssesss
ssss{
ssssssss**s***s*s*ssssss***
ssssssss**sssss;ssssssssssss ssssssgss;ssgssees;sssssssssgsssssgsss
ssssssss ssssssssssssssssssssssssssssssssssss
ssssssss{
ssssssssssss[ssssssssss;ssss("]ggssss"]]
ssssssssssss ssssssssssssssggssss;
ssssssssssss[ssssssssss;ssss("]ggssss"]]
ssssssssssss ssssssssssssssggssss;
ssssssssssss[ssssssssss;ssss("ssss;ssss"]]
ssssssssssss sssssssssssssssssssssssss;
ssssssssssss[ssssssssss;ssss("sss;sssss"]]
ssssssssssss ssssssssssssssssssss;ssss;
ssssssssssss[ssssssssss;ssss("ssss;"]]
ssssssssssss sssssssssssssssssssss;;
ssssssssssss[ssssssssss;ssss("ssss]"]]
ssssssssssss sssssssssssssssssssss];
ssssssssssss[ssssssssss;ssss(";sss]s"]]
ssssssssssss sssssssssssss;sss]s;
ssssssss}
ssssssss ssssssssssssgsssssgssssssssss(sssssssssssssssssssssssssssss]
ssssssss{
ssssssssssss**ssgsssssgssss ssssssssssssssssssgssssssssssss;gssssssssssss;
sssssssssssssgs(esssgsssssssss(ssssssggssss]s))sssssssggsssss))ss]
ssssssssssssssssssssssggsssss)sssss;
sssssssssssssgs(esssgsssssssss(ssssssggssss]s))sssssssggsssss))ss]
ssssssssssssssssssssssggsssss)sssss;
sssssssssssssgs(esssgsssssssss(sssssssssssssssss]s))sssssssssssssssssss))s""]
ssssssssssssssssssssssssssssssssss)s"799s";
sssssssssssssgs(esssgsssssssss(ssssssssssss;ssss]s))sssssssssssss;sssss))ss]
ssssssssssssssssssssssssssss;sssss)sssss;
sssssssssssssgs(esssgsssssssss(sssssssssssss;]s))ssssssssssssss;s))ss]
sssssssssssssssssssssssssssss;s)s76s6;
sssssssssssssgs(esssgsssssssss(sssssssssssss]]s))ssssssssssssss]s))ss]
sssssssssssssssssssssssssssss]s)s73ss;
sssssssssssssgs(esssgsssssssss(sssss;sss]s]s))ssssss;sss]ss))ss]
45
ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss s
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7s
7s
7s
73
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8s
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8s
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88
89
9s
9s
9s
93
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95
96
97
98
99
sss
sss
sss
ss3
ss4
ss5
ss6
ss7
ss8
ss9
sss
sss
sss
ss3
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ss8
ss9
sss
sss
sss
ss3
ss4
ss5
ss6
ss7
ss8
ss9
s3s
s3s
sssssssssssssssssssss;sss]ss)s5;
ssssssss}
ssssssss ssssssssssssesssessssgsssssgssssssss
ssssssss{
ssssssssssss sssssssssssssssssssssssssssssssssssees)s ""s+
ssssssssssssssss " sss("";ssssssssssssss"" """"]"s+s"ss"s+
ssssssssssssssss"{ss"s+
ssssssssssssssss"ssss ssss(s sssssssssssssssss]ss"s+
ssssssssssssssss"ssss{ss"s+
ssssssssssssssss "sssssssssss] sss(""ssssssssssssssss"" s""ssss;sssss"" ss]"s+s"ss"s+
ssssssssssssssss"ssssssss{ss"s+
ssssssssssssssss "ssssssssssss sss;ssss(""e ssssggssss(ss]"" s""]ggssss"" sssssssss sss;sss ss]"s +s
"ss"s+
ssssssssssssssss "ssssssssssss sss;ssss(""]s;ssssggssss(ss]"" s""]ggssss"" sssssssss sss;sss ss]"s +s
"ss"s+
ssssssssssssssss "ssssssssssss sss;ssss(""esssss; s"" sssss;ssss sssss]ssssssss sss s s3]"s +s"ss"s+
ssssssssssssssss "ssssssssssss sss;ssss(""essssss s"" ssss;sssss sssss]ss s sss;sss s4]"s +s"ss"s+
ssssssssssssssss "ssssssssssss sss;ssss(""essssssssssss sgsss sssss"" sssss; sssssssss sss;sss s5]"s
+s"ss"s+
ssssssssssssssss "ssssssssssss sss;ssss(""essssssssssss sssssssss"" sssss] sssssssss sss;sss s6]"s +s
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ssssssssssssssss "ssssssssssss sss;ssss("";ssssss ss(s]"" s"";sss]s"" sssssssss sss;sss s7]"s +s"ss"s
+
ssssssssssssssss"ssssssss}ss"s+
ssssssssssssssss"ssss}ss"s+
ssssssssssssssss"}ss";
ssssssss}
ssssssss ssssssssssssss;sssssss];ssss;
ssssssss ssssssssssssss;ssssssssssssssssssssssssss]ssss;
ssssssss sssssss;;s;s s;ssssss;sssss;
ssssssss sssssssesss]sss;sssssssss;;
ssssssss sssssssess;sssssssss;
ssssssss sssssssess;ssss;ss;ssss;s;
ssssssss sssssssess;sssssssss;ess;;
ssssssss**s***s*s*ssssss***
ssssssss**sssssssssssssgssssgsssssssssssssssssssss
ssssssss ssssssssssssssssssssss(sssssssssssssssssssssssssssss]
ssssssss{
ssssssssssss];sssss)sss;ssssss(];
ssssssssssss]sssss)sssss;
ssssssss}
ssssssss**s***s*s*ssssss***
ssssssss**s;gsssssss;gssgsssss ssssssssgsssssgssss sssgss;ssgssssssssssss; ssss
ssssssss ssssssssssssssssssss*ss(]
ssssssss{
sssssssssssssssss*ssssss)sgssss;
ssssssssssssss;
ssssssssssss{
ssssssssssssssss**ssgssssssssssssssgssssssssssssgss;ssgssee
sssssssssssssssssgsssssgssssssssss(]ssss];
ssssssssssssssss**sssss ss;ss;sssssssssssss;s ssss
sssssssssssssssssss;ss;ssss;ss)s];ssssssssssssssss]s sss(sss;ss;]ssssess;;
ssssssssssssssssssssssss;ess;s)s];ssssssssssssssss]s sss(sssssssssss[s]]ssssess;;
ssssssssssssssss**ssgsssssgsssss ssssssssssssssssssss sssss
sssssssssssssssssgs(eses sssssss(sss;ss;ssss;s sssssssss;ess;]]
ssssssssssssssss{
ssssssssssssssssssss**sssssssssgssssssssssss
ssssssssssssssssssss*ssssss)sssssssssssssssss(sss;ss;ssss;s sssssssss;ess;];
ssssssssssssssss
ssssssssssssssssssss**ssssssssssesss(essssssgssss;sssssssss]sgsss
ssssssssssssssssssssssss;ssssssssssssss;sssssss)sss;sssss;sssssssss(];
ssssssssssssssssssssssss;sssssss;ssssss)s"esss;sss)*ss s";
46
ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss 3
s3s
s33
s34
s35
s36
s37
s38
s39
s4s
s4s
s4s
s43
s44
s45
s46
s47
s48
s49
s5s
s5s
s5s
s53
s54
s55
s56
s57
s58
s59
s6s
s6s
s6s
s63
s64
s65
s66
s67
s68
s69
s7s
s7s
s7s
s73
s74
s75
s76
s77
s78
s79
s8s
s8s
s8s
s83
s84
s85
s86
s87
s88
s89
s9s
s9s
s9s
ssssssssssssssssssssssss;sssssss;sssss)s"sssssssss;ssssssssss;sss";
ssssssssssssssssssssssss;ssssssssgs;ssssss(];
ssssssssssssssssssss**segssgssgssssss;sssssssssssss; s;sssssss
sssssssssssssssssssssgs(ssss;sssssss;sss]s;ss )s""]
ssssssssssssssssssss{
ssssssssssssssssssssssss**sssssssssss;s](ess]sgssss;ssgssssssssss ssgsssssgssssss;s
ssssssssssssssssssssssss;ssssss)sss;s;;s;s s;sssss(ssss;sssssss;sss]s;s sssss];
ssssssssssssssssssssssss;ssssss;ss;sssssss)s;ss;sssssssesssssss;
ssssssssssssssssssssssss;ssss;;s(sss;ss;ssss;s sssssssss;ess; sssssssss sssssssss;];
ssssssssssssssssssssssss**ssss; ssssss sssesssgsssssssss;sssssssss
ssssssssssssssssssssssssssssss*sssssssss)sssssssses ssgs;("sss;sss;ssssssss sss"s+s
ssss;sssssss;sss]s;ss+s"ssssss;ssssssssssss;"" s"] sssgsssssss
ss;sssssssss" sssssssses esssssss]ss]s sssssssses essss sssssss s
ssssssses ssgssssessssssessssss];
sssssssssssssssssssssssssgs(sss))sssssss*ssssss]ss]
sssssssssssssssssssssssssssss;sss;ssssssssssssssssssssssssss(ssss;sssssss;sss]s;s];sss
ssssssssssssssssssss}
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ssssssssssssssssgs(] ss ssssss s]
ssssssssssss{
ssssssssssssssssssssssses ssgs;(s ss;sssssss(]];
ssssssssssss}
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ssssssssssss**s*sssssssssgsssssgss;s*ss(]s;ssss sssssssssssssssssssssssssssssssssgss;ssssss
sssssssssssssssssss*sssss;
ssssssss}
ssssssss**sssssssssssss ss
ssssssss sssssssssssseses sssssss(ess;ssss;ss; sess;sssssssss;]
ssssssss{
sssssssssssssssssssssss)sssss;
sssssssssssssgs(sss;ss;s))ssssss))sssssssss;s))sssss]
ssssssssssss{
ssssssssssssssssssssss)sgssss;
ssssssssssss}
ssssssssssssssss
ssssssssssss{
ssssssssssssssssssssssssss;ss;sssgsss;; ss)s"";
sssssssssssssssssssssssssssssss;sssgsss;; ss)s"";
sssssssssssssssssss;ss;ssss*s ssssss sss;("s*];e]]];]s]" sssgssss;ss;sssgsss;; s];
ssssssssssssssssssssssss;ssss*s ssssss sss;("s*];e]]];]s]" sssgsssssssss;sssgsss;; s];
ssssssssssssssss**ssgssssssgssss;sssssssss;sssssssssss
ssssssssssssssssssssss)sssssss sssssssssssssss;s]sss(ssssssss;sssssssssss sss;s]sss
(sss;ss;sssssssssss ssss;ss;s]sssssss]]s)sss5s))sssssssssssssss;s]sss
(ssssssss;s]sssssss sss;s]sss(sss;ss;sssssssssss ssss;ss;s]sssssss]]s)sss5;
ssssssssssss
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ssssssssssssssssssssss)sssssss ssssssssssssssss;sssssss(sss;ss;sssssssssssssss;sss;(]s] ss] s
ssssssss;sssssssssssssss;sss;(]s] ss;];
ssssssssssss}
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ssssssss**sssssssssgssssssssssss
ssssssss ssssssssssssssssssssssssssss(ess;sssss;s sess;ssss;]
ssssssss{
sssssssssssssssss*ssssss)sgssss;
ssssssssssss;ssssgss;sssssssssssssssssss;ssssgss;sssssssssss)s];ssssssss;ssssssssrssssss
(]sssssssssss;ssssgss;ssssssssss(];
sssssssssssssssssssssss;srsssgss)ssss;
sssssssssssssssssssssss;s;sssgs)ssss;
sssssssssssssssssssssss;s;ssssss)ssss;
ssssssssssssssssssssss;rsssgss)ssss;
47
ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss 4
s93
s94
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s96
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s98
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sss
sss
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ss3
ss4
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ss6
ss7
ss8
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ss3
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ss7
ss8
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sss
sss
sss
ss3
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ss6
ss7
ss8
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s3s
s3s
s3s
s33
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s36
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s38
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s4s
s4s
s4s
s43
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s45
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s5s
s5s
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s53
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ssssssssssss**s;ssssssssssss;sssssssssssss;sss;ssgssss;sssss sssssssssssss;sssssssssss
sssssssssssssgs(ssssssssssssss;s]sss(sss;s]sssssss sss;s]sss(ssss;ssssssssssss sssss;ss]sssssss]]
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ssssssssssssssssssssss;ss]ssssss;ssssssss(ssssss;ss] ss;s; sssssss;ss] ss;s] sssssss;ss] ss;s;];
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ssssssssssss
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sssssssssssssssssssssssssssssssss)sss;ssssss((ssss;srsssgss+sssss;s;sssss]s*ss (sss;rsssgs*ss+s
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sssssssssss;];s**ss;sss ssss
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ssssssssssssssssssssssssssssssssssss sgs)ssssssssssss sg]ss;ssess]];
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ssssssssssssssssnsssssssss
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ssssssssssssssss;ssss;ssss)sss;s;sss(];
ssssssssssssssss;ssssss s]sssss)s]sssss;sss]s;
ssssssssssssssss;ssssss sesss;s)s]sssss;sss]s;
ssssssssssssssss;ssssssss]s ssss)ssss;;
ssssssssssssssss;ssssssssssss;]s ssss)sssssssss;
ssssssssssssssss;sssssgs ;ssss)sssss;
ssssssssssssssss;ssssesssss(];
ssssssssssssssssnsssssssss
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48
ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss 5
s55
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s57
s58
s59
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3ss
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3s3
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ssssssssssss}
sssssssssssssssssss*sssss;
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ssssssss**sssssssssgsssssssssss;
ssssssss ssssssssssssssssssesss]sss;(ess;ssss; sess;s ssss]
ssssssss{
ssssssssssssssssssssssss)sgssss;
sssssssssssssssssss ssss;sssgs)ssss;
sssssssssssssssssss ssssrsssgss)ssss;
sssssssssssssssssss ssss;gssssssss)ssss;
ssssssssssssssssssssss;;sss)ssss;
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ssssssssssss ssssssss*s ssssss sss;("s*];e]]sr]esr;" sssgs ssss;sssg];
ssssssssssss ssssssss*s ssssss sss;("]]]s;r" sssgs ssssrsssgs];
ssssssssssss ssssssss*s ssssss sss;("s*];e]]s;es;r" sssgs ssss;gsssssss];
sssssssssssssss;ssss*s ssssss sss;("s*];e]]s;]e];res"]]ss" sssgssss;;ss];
ssssssssssssesss]sss;ses)sss;sesss]sss;(];
ssssssssssssesssss;sesss;ss)ssss;;
ssssssssssssesssss;sesessssss)s ssss;
ssssssssssssesesssss ss)s]ssssssssssss;ssss;
sssssssssssses;sssssssss)sssss;
ssssssssssssesessssssssssss)s]sssssssssssssssss;
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ssssssssssssessssssssssssssss)sss;ssssss( ssssrsssgss*ss s- ssss;sssg*ss-sssss;*s s ssss;gsssssss*s];
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ssssssssssssesessss)sssss;
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sssssssssssses]ssss)sssss;
sssssssssssses]ssss)sgssss;
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sssssssssssses]ssesssssss](ssss]];
sssssssssssses]ssesssssss](ssss]];
sssssssssssses]ssesssssss;(ssss;];
ssssssssssss
sssssssssssssgs(esesssss(]]
ssssssssssss{
ssssssssssssssssssssssss;s)se;
sssssssssssssssssssssss)sssss;
ssssssssssss}
sssssssssssssssssssssssss;
ssssssss}
49
ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss 6
3ss
3ss
3s3
3s4
3s5
3s6
3s7
3s8
3s9
33s
33s
33s
333
334
335
336
337
338
339
34s
34s
34s
343
344
345
346
347
348
349
35s
35s
35s
353
354
355
356
357
358
359
36s
36s
36s
363
364
365
366
367
368
369
37s
37s
37s
373
374
375
376
377
378
379
38s
38s
38s
383
384
385
386
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ssssssssssssssssssssssssss;s]sss;
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sssssssssssssssssssssssssss;srsssgss)ssss;
sssssssssssssssssssssssssss;s;ssssss)ssss;
sssssssssssssssssssssssss s)ssss;
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ssssssssssssssssssss;ssssssss]ss;sss s(ss];
ssssssssssssssssssssssssss;sssssss)sss;sssssss(sss;s]ssssssss;s-ssss;ssssssssssss;
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ssss;ss]sssssss]]s)sss5]
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ssssssssssssssssssss**ssssssssgssssssssgssss;ssss
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ssssssssssssssssssssgs(] ss ssssss]
ssssssssssssssss{
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sssssssssssssssss*ssssss)sgssss;
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sssssssssssssssssssssss;sss;ssss;ss;sssssssssss;sss;s)sssss;ssssssssssssssss;sss;(];
ssssssssssss
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50
ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss 7
387
388
389
39s
39s
39s
393
394
395
396
397
398
399
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4ss
4ss
4s3
4s4
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4ss
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4s3
4s4
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4s7
4s8
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43s
43s
43s
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434
435
436
437
438
439
44s
44s
44s
443
444
445
446
447
448
449
45s
45s
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ssssssssssssgsssss;ss;sssssss)sss;ssssss(];
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ssssssssssssgsssss;ss;sssssss] ss;s)sss;sssssss(ssssssssssss(sss;ss;sssssssssss;sss;s] ss;
ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss(sss;ss;sssssssssss;sss;s] ss; s
sss;ss;sssssssssss;sss;s] ss]]]];
ssssssssssssgsssss;ss;sssssss] ss;s]ss;sss s(5ss];
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ssssssssssssgsssss;ss;sssssss] ss]s]ss;sss s(5ss];
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ssssssssssssssss**ssssssss ss sssssss
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sssssssssssssssssssssssssss;s;sss)ssss;s**s;
sssssssssssssssssssssssssss;s*s)ssss;s**s
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sssssssssssssssssssssssssss;se s)ssss;
sssssssssssssssssssssssssss;s*;s)ssss;
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ssssssssssssssssssss;sssss*s ssssss sss;("s*];e]]sr]esr;" sssgsssss;srsssgs];
ssssssssssssssssssss;sssss*s ssssss sss;("s*];e]]s;es;r" sssgsssss;s;sssg];
ssssssssssssssssssss;sssss*s ssssss sss;("s*];e]]s;]e];res"]]ss" sssgsssss;s;ss];
ssssssssssssssssssss;sssss*s ssssss sss;("s*];e]]s*]e]se]s]*]sees]s" sssgsssss;s*];
ssssssssssssssssssss;sssss*s ssssss sss;("s*];e]]ss*]ss]s]s;e]]]]*]]" sssgsssss;ssssgsss];
51
ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss 8
453
454
455
456
457
458
459
46s
46s
46s
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464
465
466
467
468
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47s
47s
47s
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483
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485
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488
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49s
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494
495
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498
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ssssssssssssssssssss;sssss*s ssssss sss;("s*];e]]ss]s]];]];]e]]*;e]]]" sssgsssss;se ];
ssssssssssssssssssss;sssss*s ssssss sss;("s*];e]]s*]sees]];]s]*];e]]];" sssgsssss;s*;];
ssssssssssssssssssss;sssss*s ssssss sss;("s*];e]]s*]sees]];]s]*];e]]]]" sssgsssss;s* ];
ssssssssssssssssssss;sssss*s ssssss sss;("s*];e]]ss]s;e]]]s]se]es];" sssgsssss;s;;];
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ssssssssssssssssssss;sssss*s ssssss sss;("s];]*e]]ss]se]es]];]]]]s;ese;]" sssgsssss;s]];
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ssssssssssssssssssss;sssss*s ssssss sss;("s];]*e]]ss*];e]]]s]]se;]" sssgsssss;sssssss;];
ssssssssssssssssssss;sssss*s ssssss sss;("s];]*e]]s;r]*s]]]se]];];e]]" sssgsssss;s;gss;ss];
ssssssssssssssssssss;s]s)sssss;s]s*ss]+6;s**s]s ssssgssssssssssssss;sssssssss
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52
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sssssssssssssssssss;ssss*s ssssss sss;("s*];e]]s;es;r" sssgssss;;sssg];
sssssssssssssssssss;ssss*s ssssss sss;("s*];e]]s;]e];res"]]ss" sssgssss;;ss];
sssssssssssssssssss;ssss*s ssssss sss;("s*];e]]s*]e]se]s]*]sees]s" sssgssss;*];
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sssssssssssssssssss;ssss*s ssssss sss;("s*];e]]s*]sees]];]s]*];e]]];" sssgssss;*;];
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sssssssssssssssssss;ssss*s ssssss sss;("s*];e]]ss]s;e]]]s]se]es];" sssgssss;;;];
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sssssssssssssssssss;ssss*s ssssss sss;("s];]*e]]ss]se]es]];]]]]s;ese;]" sssgssss;]];
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ssssssssssssssss**;ssssssss ss sssssss
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sssssssssssssssssssssss ssssssssssss)ssss;
sssssssssssssssssssssss ssssssssss;s)ssss;
sssssssssssssssssssssss ssss;gss;sss)ssss;
sssssssssssssssssssssss ssssss)ssss;
ssssssssssssssss**ssssssssssssgss;s;sssss;ssss
ssssssssssssssss ssssssss*s ssssss sss;("]]]s;r" sssgs ssssrsssgs];
ssssssssssssssss ssssssss*s ssssss sss;("s];]*e]]ss]se]es]];]]]]s;ese;]" sssgs ssss]];
ssssssssssssssss ssssssss*s ssssss sss;("s];]*e]]ss]ess]]s]*];e]" sssgs sssssssssss];
ssssssssssssssss ssssssss*s ssssss sss;("s];]*e]]ss*];e]]]s]]se;]" sssgs ssssssssss;];
ssssssssssssssss ssssssss*s ssssss sss;("s];]*e]]s;r]*s]]]se]];];e]]" sssgs ssss;gss;ss];
ssssssssssssssss ssss]s)s ssss]s*ss]+6;s**s]s ssssgssssssssssssss;sssssssss
ssssssssssssssss ssssss)s ssss]s*s(ss*s(ss+s sssssssssss]];
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ssssssssssssssss**ssssssssssss;s;s]sssss;ssss
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ssssssssssssssss**;sssssss;;sssss
53
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sssssssssssssssss;ssssss;sssssssss]ss;sss(";e]]s]*se]]"];
sssssssssssssssss;ssssss;ssssssssss("63"];
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sssssssssssssssss;ssssss;sssssssss]ss;sss("]]*s"];
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54
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55
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56
ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss s3
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57
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69
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ssssssss}
ssss}
}
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