Staad Pro Advanced Training

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STAAD.Pro Advanced Training

STAAD.Pro V8i

TRN017550-1/0001

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Copyright Information

STAAD.Pro Advanced Training 2 Copyright © December-2011 Bentley Systems Incorporated

Trademarks

AccuDraw, Bentley, the “B” Bentley logo, MDL, MicroStation and SmartLine are registered trademarks; PopSet and Raster Manager are trademarks; Bentley SELECT is a service mark of Bentley Systems, Incorporated or Bentley Software, Inc.

Java and all Java-based trademarks and logos are trademarks or registered trademarks of Sun Microsystems, Inc. in the U.S. and other countries.

Adobe, the Adobe logo, Acrobat, the Acrobat logo, Distiller, Exchange, and PostScript are trademarks of Adobe Systems Incorporated.

Windows, Microsoft and Visual Basic are registered trademarks of Microsoft Corporation.

AutoCAD is a registered trademark of Autodesk, Inc.

Other brands and product names are the trademarks of their respective owners.

Patents

United States Patent Nos. 5,8.15,415 and 5,784,068 and 6,199,125.

Copyrights

©2000-2008 Bentley Systems, Incorporated. MicroStation ©1998 Bentley Systems, Incorporated. IGDS file formats ©1981-1988 Intergraph Corporation. Intergraph Raster File Formats ©1993 Intergraph Corporation. Portions ©1992 – 1994 Summit Software Company. Portions ©1992 – 1997 Spotlight Graphics, Inc. Portions ©1993 – 1995 Criterion Software Ltd. and its licensors. Portions ©1992 – 1998 Sun MicroSystems, Inc. Portions ©Unigraphics Solutions, Inc. Icc ©1991 – 1995 by AT&T, Christopher W. Fraser, and David R. Hanson. All rights reserved. Portions ©1997 – 1999 HMR, Inc. All rights reserved. Portions ©1992 – 1997 STEP Tools, Inc. Sentry Spelling-Checker Engine ©1993 Wintertree Software Inc.

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1. Introduction This course is structured to look at the scope of the advanced features of STAAD.Pro. There are many supplied examples & few hands on exercises to complete, each one containing more STAAD commands and dealing with more complex problems. This document has been produced for your benefit and assistance. This document is copyright and no part of it is to be copied, reproduced electronically or otherwise without the prior written consent of Bentley Systems, inc.

2. Contents Title page ……………………………………………………………………………………………………0

1. Introduction ................................................................................................................................... 0

2. Contents ........................................................................................................................................ 0

3. Zero Stiffness............................................................................................................................... 2

4. Understanding Instabilities ......................................................................................................... 4

5. Seismic Analysis Using UBC And IBC Codes .................................................................... 13

YRANGE 20 21 FLOAD 0.3 ................................................................................................................. 15

FINISH ................................................................................................................................................... 17

6. Calculating Mode Shapes, Frequencies And Participation factors .................................. 20

7. Response Spectrum Analysis ................................................................................................. 27

8. Time History analysis of a structure for seismic accelerations .................................... 39

9. Time History Analysis for a Structure subjected to a Harmonic Loading .................. 42 JOINT LOAD ..................................................................................................................................... 43

PERFORM ANALYSIS ......................................................................................................................... 44

10. Time History Analysis for a Structure subjected to a random excitation ................... 47

11. Hands on Exercise 1 – Dynamic Analysis .............................................................................. 48 1) Structure Wizard ........................................................................................................................... 48 2) Add Properties and Supports ....................................................................................................... 49 3) Create Time History Graphs ......................................................................................................... 50 4) Create a Time History Loadcase .................................................................................................. 50

Masses ......................................................................................................................................... 50 Time History ................................................................................................................................. 50

5) Viewing Mode Shapes .................................................................................................................. 51

12. P-Delta Analysis ......................................................................................................................... 52

13. P-Delta analysis including stress stiffening effect of the KG matrix .................................... 54 Purpose ........................................................................................................................................ 54 Description .................................................................................................................................... 54

14. P-Delta analysis including Small Delta .................................................................................... 56 Purpose ........................................................................................................................................ 56 Description .................................................................................................................................... 56

15. Hands on Exercise 2 - P-Delta analysis .................................................................................. 57

16. Buckling Load analysis ............................................................................................................. 60 Purpose ........................................................................................................................................ 60 Description – Basic Solver ........................................................................................................... 60

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STAAD Pro Advanced Training V8i 1 of 77

Description – Advanced Solver .................................................................................................... 61

17. Modal Analysis including stress stiffening effect of KG Matrix ............................................ 64 Purpose ........................................................................................................................................ 64 Description .................................................................................................................................... 64

18. Non Linear Cable/Truss Analysis ............................................................................................. 66

19. Hands on Exercise 3 - Non-Linear Truss analysis .................................................................. 69

20. Hands on Exercise 4 - Non-Linear Cable analysis - I ............................................................. 70

21. Hands on Exercise 5 - Non-Linear Cable analysis –II ............................................................ 71

22. Other STAAD features ............................................................................................................... 74 OpenSTAAD ..................................................................................................................................... 74

23. Other STAAD.Pro Optional modules. ....................................................................................... 75 STAAD.beava ................................................................................................................................... 75 STAAD.foundation ............................................................................................................................ 75 Offshore Loading Program ............................................................................................................... 75 Section wizard .................................................................................................................................. 75

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3. Zero Stiffness

Question : What does a zero stiffness warning message in the STAAD output file mean? Answer : The procedure used by STAAD in calculating displacements and forces in a structure is the stiffness method. One of the steps involved in this method is the assembly of the global stiffness matrix. During this process, STAAD verifies that no active degree of freedom (d.o.f) has a zero value, because a zero value could be a potential cause of instability in the model along that d.o.f. It means that the structural conditions which exist at that node and degree of freedom result in the structure having no ability to resist a load acting along that d.o.f. A warning message is printed in the STAAD output file highlighting the node number and the d.o.f at which the zero stiffness condition exists. Question : What are examples of cases which give rise to these conditions? Answer : Consider a frame structure where some of the members are defined to be trusses. On this model, if a joint exists where the only structural components connected at that node are truss members, there is no rotational stiffness at that node along any of the global d.o.f. If the structure is defined as STAAD PLANE, it will result in a warning along the MZ d.o.f at that node. If it were declared as STAAD SPACE, there will be at least 3 warnings, one for each of MX, MY and MZ, and perhaps additional warnings for the translational d.o.f. These warnings can also appear when other structural conditions such as member releases and element releases deprive the structure of stiffness at the associated nodes along the global translational or rotational directions. A tower held down by cables, defined as a PLANE or SPACE frame, where cable members are pinned supported at their base will also generate these warnings for the rotational d.o.f. at the supported nodes of the cables. In a SPACE frame structure, connections may be modeled in such a manner that all members meeting at any given node have a moment release along all 3 axes. The joint is thus deprived of any rotational stiffness. Solid elements have no rotational stiffness at their nodes. So, at all nodes where you have only solids, these zero stiffness warning messages may appear.

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Question : Why are these warnings and not errors? Answer : The reason why these conditions are reported as warnings and not errors is due to the fact that they may not necessarily be detrimental to the proper transfer of loads from the structure to the supports. If no load acts at and along the d.o.f where the stiffness is zero, that point may not be a trouble-spot. Question : What is the usefulness of these messages : Answer : A zero stiffness message can be a tool for investigating the cause of instabilities in the model. An instability is a condition where a load applied on the structure is not able to make its way into the supports because no paths exist for the load to flow through, and may result in a lack of equilibrium between the applied load and the support reaction. A zero stiffness message can tell us whether any of those d.o.f are obstacles to the flow of the load.

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4. Understanding Instabilities Question : I have instability warning messages in my output file like that shown below. What are these? ***WARNING - INSTABILITY AT JOINT 26 DIRECTION = FX PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 5.3274384E+03 L-MATRIX DIAG= 0.0000000E+00 EQN NO 127 ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY **NOTE** STAAD DETECTS INSTABILITIES AS EXCESSIVE LOSS OF SIGNIFICANT DIGITS DURING DECOMPOSITION. WHEN A DECOMPOSED DIAGONAL IS LESS THAN THE BUILT-IN REDUCTION FACTOR TIMES THE ORIGINAL STIFFNESS MATRIX DIAGONAL, STAAD PRINTS A SINGULARITY NOTICE. THE BUILT-IN REDUCTION FACTOR IS 1.000E-09 THE ABOVE CONDITIONS COULD ALSO BE CAUSED BY VERY STIFF OR VERY WEAK ELEMENTS AS WELL AS TRUE SINGULARITIES. Answer : An instability is a condition where a load applied on the structure is not able to make its way into the supports because no paths exist for the load to flow through, and may result in a lack of equilibrium between the applied load and the support reaction. Examples and causes of Instability : Defining a member as a TRUSS when it needs shear and bending capacity. A framed structure with columns and beams where the columns are defined as "TRUSS" members is definitely a cause of instability. Such a column has no capacity to transfer shears or moments from the regions above it to the supports. When you declare all members connecting at specific nodes to be truss members, the alignment of the members must be such that the axial force from each member must be able to make its way through the common node to the other members. For example, if you have 3 members meeting at a point, one of them is purely vertical and the other 2 are purely horizontal, and they are all truss members, the axial force from the vertical member cannot be transmitted into the horizontal members. On the other hand, if they are frame members, the load will be transmitted into the horizontals in the form of shear. This is an inherent weak point of trusses, and a potential cause of instability.

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A better option to calling a member a TRUSS is to define it as a frame member and use partial moment releases at its ends. Improper support conditions. When the supports of the structure are such that they cannot offer any resistance to sliding or overturning of the structure in one or more directions. For example, a 2D structure (frame in the XY plane) that is defined as a SPACE FRAME with pinned supports and subjected to a force in the Z direction will topple over about the X-axis. Another example is that of a space frame with all the supports released for FX, FY or FZ. Connecting a very stiff member to a very flexible member. A math precision error is caused when numerical instabilities occur in the matrix decomposition (inversion) process. One of the terms of the equilibrium equation takes the form 1/(1-A), where A=k1/(k1+k2); k1 and k2 being the stiffness coefficients of two adjacent members. When a very "stiff" member is adjacent to a very "flexible" member, viz., when k1>>k2, or k1+k2 .k1, A=1 and hence, 1/(1-A) =1/0. Thus, huge variations in stiffnesses of adjacent members are not permitted. Artificially high E or I values should be reduced when this occurs. Math precision errors are also caused when the units of length and force are not defined correctly for member lengths, member properties, constants etc. Excessive number of releases. Releases completely deprive a member of any ability to transmit a particular type of force or moment to the next member. Imagine for example, a portal frame that looks like a table, with columns pinned at their base, and each column attached to 2 orthogonal beams at the top. If the beams are pinned connected to top of the column, it is customary to specify releases on the beams along the lines 2 3 START MX MY MZ The above release signifies that 100% of the resistance to MX, MY and MZ has been switched off at the beam-ends. The beam is hence behaving as a simply supported beam at that location. This condition, along with the pinned column base, deprives the column of any ability to transmit torsion to the base, leading to instability about the global MY degree of freedom at the pinned support. Improper connection between members. When members cross each in space, if a connection exists between 2 members, that point of contact should be represented by a common node between the members. Simply because lines appear to cross each other in space, it doesn’t guarantee that STAAD will assume a connection between those members. The user has to ensure that. One tool for creating such common nodes is available under the Geometry menu. It is called Intersect Selected Members. Duplicate nodes. They are 2 or more nodes, having distinct node numbers, but the same X, Y, Z coordinates. For example, if node number 5 has coordinates of (7, 10, 0), and node 83 also has coordinates of (7, 10, 0), node 5 and 83 are considered

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duplicate. If you have 2 members, one attached to node 5, and the other to node 83, then, those 2 members are not connected to each other at that point in space. Go to Tools – Check Duplicate Nodes to detect and merge such sets of nodes into a single node. Improper connection between members and plate elements. In the figure shown below, the beam goes from node 5 to node 6. The element is connected between 2, 3, 4 and 1. Thus, the beam has no common nodes with the element. No transfer of loads is possible between these entities.

In order for the above set of entities to be properly connected, the element would have to be broken into 2, and the beam too needs to be split at node 2, as shown below. While there are no simple tools for splitting

elements, using finer meshes of elements always helps. See the Generate Plate Mesh and Generate Surface Meshing options of the Geometry menu. A beam in the situation above may be broken up into pieces by using means like Insert Node, or Break Beams at Selected Nodes, both of which are in the Geometry menu. Overlapping members. When 2 members are collinear, and further, at least one of the nodes of one of those members happens to lie within the span of the other, but the 2 members are not connected at that node, those 2 members are considered as overlapping collinear members. In STAAD, the tool for detecting such members is Tools – Check Overlapping collinear members. An example of 2 members which would qualify as overlapping collinear is: STAAD SPACE

UNIT FEET KIP

JOINT COORDINATES

1 0 0 0; 2 0 10 0; 3 10 10 0; 4 10 0 0; 5 13 10 0; 6 -4 10 0;

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MEMBER INCIDENCES

1 1 2; 2 2 3; 3 3 4;

101 5 6

FINISH

Here, members 2 and 101 are overlapping collinear. Member 2 is entirely confined within the span of member 101, and collinear, but they are not attached to each other. Another example is: STAAD SPACE

UNIT FEET KIP

JOINT COORDINATES

1 0 0 0; 2 0 10 0; 3 10 10 0; 4 10 0 0; 5 13 10 0; 6 -4 10 0;

MEMBER INCIDENCES

1 1 2; 2 2 3; 3 3 4;

101 2 5

FINISH

Here, again, members 2 and 101 are overlapping collinear. But even though they are connected to each other at node 2, again member 2 is entirely confined within the span of member 101, and collinear. Overlapping plates. These are elements whose nodes intersect other elements at points other than the defined nodes. This entails plates whose boundaries with adjacent plates are not attached at the nodes or plates within other plates (in the same plane).

The figure above represents such a condition. Elements 1 and 2 share only one common node which is node 4. Though the drawing appears to indicate a common boundary along nodes 4, 5 and 3, there is no connection along that boundary. From the Tools menu, choose Check Overlapping Plates to detect such conditions in the model. The next figure shows what needs to be done

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to ensure proper connection. Our original element 1 is converted to 3 triangular elements to accomplish it.

Question : If there are instability messages, does it mean my analysis results may be unsatisfactory? Answer : There are many situations where instabilities are unimportant and the STAAD approach of adding a weak spring is an ideal solution to the problem. For example, sometimes an engineer will release the MX torsion in a single beam or at the ends of a series of members such that technically the members are unstable in torsion. If there is no torque applied, this singularity can safely be "fixed" by STAAD with a weak torsional spring. Similarly a column that is at a pinned support will sometimes be connected to members that all have releases such that they cannot transmit moments that cause torsion in the column. This column will be unstable in torsion but can be safely "fixed" by STAAD with a weak torsional spring. Sometimes however, a section of a structure has members that are overly released to the point where that section can rotate with respect to the rest of the structure. In this case, if STAAD adds a weak spring, there may be large displacements because there are loads in the section that are in the direction of the extremely weak spring. Another way of saying it is, an applied load acts along an unstable degree of freedom, and causes excessive displacements at that degree of freedom. Question : If there are instability messages, are there any simple checks to verify whether my analysis results are satisfactory? Answer : There are 2 important checks that should be carried out if instability messages are present. a. A static equilibrium check. This check will tell us whether all the applied loading flowed through the model into the supports. A satisfactory result would require that the applied loading be in equilibrium with the support reactions. b. The joint displacement check. This check will tell us whether the displacements in the model are within reasonable limits. If a load passes through a corresponding

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unstable degree of freedom, the structure will undergo excessive deflections at that degree of freedom. One may use the PRINT STATICS CHECK option in conjunction with the PERFORM ANALYSIS command to obtain a report of both the results mentioned in the above checks. The STAAD output file will contain a report similar to the following, for every primary load case that has been solved for : ***TOTAL APPLIED LOAD ( KG METE ) SUMMARY (LOADING 1 )

SUMMATION FORCE-X = 0.00

SUMMATION FORCE-Y = -817.84

SUMMATION FORCE-Z = 0.00

SUMMATION OF MOMENTS AROUND THE ORIGIN-

MX= 291.23 MY= 0.00 MZ= -3598.50

***TOTAL REACTION LOAD( KG METE ) SUMMARY (LOADING 1 )

SUMMATION FORCE-X = 0.00

SUMMATION FORCE-Y = 817.84

SUMMATION FORCE-Z = 0.00

SUMMATION OF MOMENTS AROUND THE ORIGIN-

MX= -291.23 MY= 0.00 MZ= 3598.50

MAXIMUM DISPLACEMENTS ( CM /RADIANS) (LOADING 1)

MAXIMUMS AT NODE

X = 1.00499E-04 25

Y = -3.18980E-01 12

Z = 1.18670E-02 23

RX= 1.52966E-04 5

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RY= 1.22373E-04 23

RZ= 1.07535E-03 8 Go through these numbers to ensure that i. The "TOTAL APPLIED LOAD" values and "TOTAL REACTION LOAD" values are equal and opposite. ii. The "MAXIMUM DISPLACEMENTS" are within reasonable limits. Note that from STAAD.Pro 2007 onwards the statics check results table automatically appears in the post-processing mode – node – support reactions page. Question : What is the meaning of this message, "Probable cause warning-near singular" Answer : While performing the triangular factorization of the global stiffness matrix, a diagonal matrix is computed. These computed diagonals are the same as or smaller than the global stiffness matrix diagonals. If the computed diagonals become zero then the matrix is singular and the structure is unstable. In STAAD we say that the structure is unstable/singular if any computed diagonal is less that (1.E-9) * (the corresponding stiffness matrix diagonal). Likewise in STAAD we say that the structure is nearly unstable/singular if any computed diagonal is less that (1.E-7) * (the corresponding stiffness matrix diagonal). If the overall results look OK, then ignore nearly singular messages. Question : How to avoid instabilities if TRUSSES or RELEASES are the cause? Answer : There is a rather simple way to eliminate instabilities, especially if truss members are present or when MEMBER RELEASE commands are used and certain degrees of freedom are subjected to a 100% release. In reality, connections always have some amount of force and moment capacity. Use PARTIAL RELEASES to enable the connection to retain at least a very small amount of capacity. This is a mechanism by which you can declare that, at the start node or end node of a member, rather than fully eliminating the stiffness for a certain moment degree of freedom (d.o.f), you are willing to allow the member to have a small amount of stiffness for that d.o.f. The advantage of this command is that the extent of the release is controlled by you. For example, if member 5, has a pinned connection at its start node, if you specify 5 START MY MZ it means MY and MZ are 100% released at the start node. But if you say, 5 START MP 0.99

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you are saying that the bending and torsional stiffnesses are 99% less than what they would be for a fully moment resistant connection. Thus, the 1% available stiffness might be adequate to allow the load to pass through the node from one member to the other. So, this is what may be done : a. Change the declaration of the truss members in your model from MEMBER TRUSS to MEMBER RELEASE memb-list START MP 0.99 memb-list END MP 0.99 or MEMBER RELEASE memb-list Both MP 0.99 b. Run the analysis. Check to make sure the instability warnings no longer appear. Then check your nodal displacements. c. If the displacements are large, reduce the extent of the release from 0.99 to say 0.98. Repeat steps (b) and (c) by progressively reducing the extent of the release until the displacements are satisfactory. When they look reasonable, check the magnitude of the moments and shear at the nodes of those members and make sure that the connection will be able to handle those forces and moments. STAAD.Pro 2002 onwards, you can apply these partial releases to individual moment degrees of freedom. For example, you could say MEMBER RELEASE memb-list Both MPX 0.99 MPY 0.97 MPZ 0.95 This flexibility permits you to adjust just the specific degree of freedom that is the problem area. You can refer to Section 5.22.1 of the Technical Reference Manual for details. Question : Is there any graphical facility in STAAD by which I can examine the points of instability?

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Answer : Yes, there is. Go to the Post processing mode. If instabilities are present, the Nodes page along the left side should contain a sub-page by the name Instability. If you click on this, two tables will appear along the right hand side. The upper table lists the node number, and the global degrees of freedom at that node which are unstable. A zero for a d.o.f indicates that all is well, and, 1 indicates it is unstable. Click on the row and the node and all members connected to it will be highlighted in the drawing. The lower table has all of the joints in the order that gives the stiffness matrix the minimum bandwidth which minimizes the running time. When a joint is unstable, it means that the joint and some or all of the joints before it in the list form an unstable structure. That is, even fixing every subsequent joint in the list would not make it stable. If the instability is at the last joint [or sometimes the last joint and one other joint], then the whole structure is free in that direction. Note that the instability is reported at the last joint in the list that is on the unstable component. If a column is pinned at the base and floor connections are released in global My, the column will be torsionally unstable, but only one joint on the column will be reported as unstable and it could be any joint on the column.

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5. Seismic Analysis Using UBC And IBC Codes Basic principle When a building is subjected to an earthquake, it undergoes vibrations. The weights of the structure, when accelerated along the direction of the earthquake, induce forces in the building. Normally, an elaborate dynamic analysis called time history analysis is required to solve for displacements, forces and reactions resulting from the seismic activity. However, codes like UBC and IBC provide a static method of solving for those values. The generalized procedure used in those methods consists of 3 steps Step 1 : Calculate

Base Shear = Factor f * Weight W where "f" is calculated from terms which take into consideration the Importance factor of the building, Site Class and soil characteristics, etc. W is the total vertical weight derived from dead weight of the building and other imposed weights. Step 2 : The base shear is then distributed over the height of the building as a series of point loads. Step 3 : The model is then analyzed for the horizontal loads generated in step 2. The input required in STAAD consists of 2 parts. Part 1, which appears under a heading called

DEFINE UBC LOAD or DEFINE IBC LOAD

contains the terms used to compute "f" and "W" described in step 1. Part 2, which appears within a load case, contains the actual instruction to generate the forces described in step 2 and analyze the structure for those forces. Let us examine this procedure using the example problem shown below. STAAD SPACE SET NL 5

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The structure is defined as a space frame type. The maximum number of primary load cases in the model is set to 5. UNIT KIP FEET JOINT COORD 1 0 0 0 ; 2 0 10 0 ; 3 13 10 0 ; 4 27 10 0 ; 5 40 10 0 ; 6 40 0 0 7 0 20.5 0 ; 8 20 20.5 0 ; 9 40 20.5 0 REPEAT ALL 1 0 0 11 Joint coordinates are specified using a mixture of explicit definition and generation using REPEAT command. MEMBER INCI 1 1 2 5 ; 6 1 3 ; 7 4 6 ; 8 2 7 ; 9 7 8 10 ; 11 9 5 ; 12 2 8 ; 13 5 8 21 10 11 25 ; 26 10 12 ; 27 13 15 ; 28 11 16 ; 29 16 17 30 ; 31 18 14 32 11 17 ; 33 14 17 41 2 11 44 45 7 16 47 51 1 11 52 10 2 53 2 16 54 11 7 55 6 14 56 15 5 57 5 18 58 14 9 Member incidences are specified using a mixture of explicit definition and generation. MEMBER PROPERTIES 1 5 8 11 21 25 28 31 TA ST W14X90 2 3 4 22 23 24 TA ST W18X35 9 10 29 30 TA ST W21X50 41 TO 44 TA D C12X30 45 TO 47 TA D C15X40 6 7 26 27 TA ST HSST20X12X0.5 51 TO 58 TA LD L50308 12 13 32 33 TA ST TUB2001205

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Various section types are used in this model. Among them are double channels, hollow structural sections and double angles. CONSTANTS E STEEL ALL POISSON STEEL ALL DENSITY STEEL ALL Structural steel is the material used in this model. SUPPORT 1 6 10 15 FIXED Fixed supports are defined at 4 nodes. MEMBER TENSION 51 TO 58 Members 51 to 58 are defined as capable of carrying tensile forces only. UNIT POUND DEFINE UBC ACCIDENTAL LOAD ZONE 0.3 I 1 RWX 2.9 RWZ 2.9 STYP 4 NA 1 NV 1 SELFWEIGHT FLOOR WEIGHT YRANGE 9 11 FLOAD 0.4 YRANGE 20 21 FLOAD 0.3 There are two stages in the command specification of the UBC loads. The first stage is initiated with the command DEFINE UBC LOAD. Here we specify parameters such as Zone factor, Importance factor, site coefficient for soil characteristics etc. and, the vertical loads (weights) from which the base shear will be calculated. The vertical loads may be specified in the form of selfweight, joint weights, member weights, element weights or floor weights. Floor weight is used when a pressure acting over a panel has to be applied when the structural entity which makes up the panel (like a aluminum roof for example) itself isn’t defined as part of the model. The selfweight and floor weights are shown in this example. It is important to note that these vertical loads are used purely in the determination of the horizontal base shear only. In other words, the structure is not analyzed for these vertical loads. LOAD 1 UBC LOAD X This is the second stage in which the UBC load is applied with the help of load case number, corresponding direction (X in the above case) and a factor by which the generated horizontal loads should be multiplied. Along with the UBC load, deadweight and other vertical loads may be added to the same load case (they are not in this example).

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PERFORM ANALYSIS PRINT LOAD DATA CHANGE A linear elastic type analysis is requested for load case 1. We can view the values and position of the generated loads with the help of the PRINT LOAD DATA command used above along with the PERFORM ANALYSIS command. A CHANGE command should follow the analysis command for models like this where the MEMBER TENSION command is used in conjunction with UBC load cases. LOAD 2 UBC LOAD Z We define load case 2 as consisting of the UBC loads to be generated along the Z direction. The structure will be analyzed for those generated loads. PERFORM ANALYSIS PRINT LOAD DATA CHANGE The analysis instruction is specified again. LOAD 3 SELF Y -1.0 FLOOR LOAD YRANGE 9 11 FLOAD -0.4 YRANGE 20 21 FLOAD -0.3 In load case 3 in this problem, we apply 2 types of loads. The selfweight is applied in the global Y direction acting downwards. Then, a floor load generation is performed. In a floor load generation, a pressure load (force per unit area) is converted by the program into specific points forces and distributed forces on the members located in that region. The YRANGE (and if specified, the XRANGE and ZRANGE) values are used to define the region of the structure on which the pressure is acting. The FLOAD specification is used to specify the value of that pressure. All values need to be provided in the current UNIT system. For example, in the first line in the above FLOOR LOAD specification, the region is defined as being located within the bounds YRANGE of 9-11 ft. Since XRANGE and ZRANGE are not mentioned, the entire floor within the YRANGE will become a candidate for the load. The -0.4 signifies that the pressure is 0.4 Kip/sq. ft in the negative global Y direction. The program will identify the members lying within the specified region and derive MEMBER LOADS on these members based on two-way load distribution. PERFORM ANALYSIS CHANGE The analysis instruction is specified again. LOAD 4 REPEAT LOAD 1 1.0 3 1.0

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Load case 4 illustrates the technique employed to instruct STAAD to create a load case which consists of data to be assembled from other load cases already specified earlier. We would like the program to analyze the structure for loads from cases 1 and 3 acting simultaneously. PERFORM ANALYSIS PRINT STATICS CHECK CHANGE The analysis instruction is specified again. LOAD 5 REPEAT LOAD 2 1.0 3 1.0 In load case 5, we instruct STAAD to create a load case consisting of data to be assembled from cases 2 and 3 acting simultaneously. PERFORM ANALYSIS PRINT STATICS CHECK CHANGE The analysis instruction is specified again. LOAD LIST 4 5 PRINT JOINT DISPLACEMENTS PRINT SUPPORT REACTIONS PRINT MEMBER FORCES LIST 51 TO 58 Various results are requested for just load cases 4 and 5. FINISH The STAAD run is terminated. Question : When I specify vertical weights under the DEFINE UBC LOAD command, why do I have to specify them again under the actual load case? Won't STAAD be double-counting those weights? Answer : Generally, all code related seismic methods follow a procedure called static equivalent method. That is to say, even if seismic forces are dynamic in nature, they can be solved using a static approach. That means, one has to first come up with static loads. These are calculated usually using an equation called

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H = constant x V where H is the horizontal load which is calculated. V is the applied vertical load. In STAAD, the V has to be defined under commands like

DEFINE UBC LOAD or DEFINE IBC LOAD

There, they are defined in the form of selfweight, joint weight, member weight, etc. The data specified over there is used just to compute the V. Hence, once the H is derived from the V, the V is discarded. If a user wants the structure to be analysed for the vertical loads, they have to be explicity specified with Load cases. That is what you'll find in example 14. Load cases 1 & 2 contain a horizontal load and a vertical load. The horizontal load comes from the UBC LOAD X and UBC LOAD Z commands. The vertical load comes from selfweight, joint load commands. So, there is no double counting. Question : We would like to know what Ta and Tb in the static seismic base shear output stand for. We know that both are computed time periods, but we would like to know why there are two values for it. Answer : The UBC and IBC codes involve determination of the period based on 2 methods - Method A and Method B. The value based on Method A is called Ta. The value based on Method B is called Tb. Question : What is the difference between a JOINT WEIGHT and a JOINT LOAD? Answer : The JOINT WEIGHT option is specified under the DEFINE UBC LOAD command and is used merely to assemble the weight values which make up the value of "W" in the UBC equations. In other words, it is the amount of lumped weight at the joint and a fraction of this weight eventually makes up the total base shear for the structure. A JOINT LOAD on the other hand is an actual force which is acting at the joint, and is defined through the means of an actual load case. Question : When using the "ACCIDENTAL" option in the "DEFINE UBC LOAD" command, it appears that for the mass displacement along a given axis STAAD.Pro only considers the displacement in one direction rather than a plus or minus

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displacement. Is this true? You can verify this by adding the "ACCIDENTAL" option to Example Problem 14 and comparing the reactions. Answer : Use the "ACC f2" option as explained in the command syntax in section 5.32.12 of the Technical Reference manual. You can specify a negative value for f2 if you want the minus sign for the torsional moments. You will need STAAD.Pro 2003 and above to use this. Question : How do I display the Load values of an IBC2000 load case? Answer : First run the analysis. Then go to the View menu, choose Structure Diagrams. Click on the Loads and Results tab. Select the load case corresponding to the IBC load command. Switch on the checkbox for Loads, click on OK.

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6. Calculating Mode Shapes, Frequencies And Participation factors

In STAAD, there are 2 methods for obtaining the frequencies of a structure. 1. The Rayleigh method using the CALCULATE RAYLEIGH FREQUENCY

command 2. The elaborate method which involves extracting eigenvalues from a matrix based

on the structure stiffness and lumped masses in the model. The Rayleigh method in STAAD is a one-iteration approximate method from which a single frequency is obtained. It uses the displaced shape of the model to obtain the frequency. Needless to say, it is extremely important that the displaced shape that the calculation is based on, resemble one of the vibration modes. If one is interested in the fundamental mode, the loading on the model should cause it to displace in a manner which resembles the fundamental mode. For example, the fundamental mode of vibration of a tall building would be a cantilever style mode, where the building sways from side to side with the base remaining stationary. The type of loading which creates a displaced shape which resembles this mode is a lateral force such as a wind force. Hence, if one were to use the Rayleigh method, the loads which should be applied are lateral loads, not vertical loads. For the eigensolution method, the user is required to specify all the masses in the model along with the directions they are capable of vibrating in. If this data is correctly provided, the program extracts as many modes as the user requests (default value is 6) in ascending order of strain energy. The mode shapes can be viewed graphically to verify that they make sense. Eigenvalue extraction method The input which is important and relevant to the analysis of a structure for frequencies and modes – using the eigenvalue extraction method is explained below. These are explained in association with an example problem provided at the end of this section. 1. The DENSITY command One of the critical components of a frequency analysis is the amount of "mass" undergoing vibration. For a structure, this mass comes from the selfweight, and from permanent/imposed loads on the building. To calculate selfweight, density is required, and is hence specified under the command CONSTANTS. 2. The CUT OFF MODE SHAPE command Theoretically, a structure has as many modes of vibration as the number of degrees of freedom in the model. However, the limitations of the mathematical process used

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in extracting modes may limit the number of modes that can actually be extracted. In a large structure, the extraction process can also be a very time consuming process. Further, not all modes are of equal importance. (One measure of the importance of modes is the participation factor of that mode.) In many cases, the first few modes may be sufficient to obtain a significant portion of the total dynamic response. Due to these reasons, in the absence of any explicit instruction, STAAD calculates only the first 6 modes. (Versions of STAAD prior to STAAD/Pro 2000 calculated only 3 modes by default). This is like saying that the command CUT OFF MODE SHAPE 6 has been specified.

If the inspection of the first 6 modes reveals that the overall vibration pattern of the structure has not been obtained, one may ask STAAD to compute a larger (or smaller) number of modes with the help of this command. The number that follows this command is the number of modes being requested. In our example, we are asking for 10 modes by specifying CUT OFF MODE SHAPE 10. 3. The MODAL CALCULATION REQUESTED command. This is the command which triggers the calculation of frequencies and modes. It is specified inside a load case. In other words, this command accompanies the loads which are to be used in generating the mass matrix. Frequencies and modes have to be calculated when dynamic analysis such as response spectrum or time history analysis are carried out. But in such analyses, the MODAL CALCULATION REQUESTED command is not explicitly required. When STAAD encounters the commands for response spectrum (see example 11) and time history (see examples 16 and 22), it automatically will carry out a frequency extraction without the help of the MODAL .. command. 4. The MASSES which are to be used in assembling the MASS MATRIX The mathematical method that STAAD uses is called the subspace iteration eigen extraction method. Some information on this is available in Section 1.18.3 of the STAAD.Pro Technical Reference Manual. The method involves 2 matrices - the stiffness matrix, and the mass matrix. The stiffness matrix, usually called the [K] matrix, is assembled using data such as member and element lengths, member and element properties, modulus of elasticity, poisson's ratio, member and element releases, member offsets, support information, etc. For assembling the mass matrix, called the [M] matrix, STAAD uses the load data specified in the load case in which the MODAL CAL REQ command is specified. So, some of the important aspects to bear in mind are:

i. The input you specify is weights, not masses. Internally, STAAD will convert weights to masses by dividing the input by "g", the acceleration due to gravity.

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ii. If the structure is declared as a PLANE frame, there are 2 possible directions

of vibration - global X, and global Y. If the structure is declared as a SPACE frame, there are 3 possible directions - global X, global Y and global Z. However, this does not guarantee that STAAD will automatically consider the masses for vibration in all the available directions.

You have control over and are responsible for specifying the directions in which the masses ought to vibrate. In other words, if a weight if not specified along a certain direction, the corresponding degrees of freedom (such as for example, global Z at node 34) will not receive a contribution in the mass matrix. The mass matrix is assembled using only the masses from the weights and directions specified by the user.

In our example, notice that we are specifying the selfweight along global X, Y and Z directions. Similarly, the element pressure load is also specified along all 3 directions. We have chosen not to restrict any direction for this problem. If a user wishes to restrict a certain weight to certain directions only, all he/she has to do is not provide the directions in which those weights cannot vibrate in.

iii. As much as possible, provide absolute values for the weights. STAAD is

programmed to algebraically add the weights at nodes. So, if some weights are specified as positive numbers, and others as negative, the total weight at a given node is the algebraic summation of all the weights in the global directions at that node.

STAAD SPACE * EXAMPLE PROBLEM FOR CALCULATION OF MODES AND FREQUENCIES UNIT FEET KIP JOINT COORDINATES 1 0 0 0; 2 0 0 20; 3 20 0 0; 4 20 0 20; 5 40 0 0; 6 40 0 20; 7 0 15 0; 8 0 15 5; 9 0 15 10; 10 0 15 15; 11 0 15 20; 12 5 15 0; 13 10 15 0; 14 15 15 0; 15 5 15 20; 16 10 15 20; 17 15 15 20; 18 20 15 0; 19 20 15 5; 20 20 15 10; 21 20 15 15; 22 20 15 20; 23 25 15 0; 24 30 15 0; 25 35 15 0; 26 25 15 20; 27 30 15 20; 28 35 15 20; 29 40 15 0; 30 40 15 5; 31 40 15 10; 32 40 15 15; 33 40 15 20; 34 20 3.75 0; 35 20 7.5 0; 36 20 11.25 0; 37 20 3.75 20; 38 20 7.5 20; 39 20 11.25 20; 40 5 15 5; 41 5 15 10; 42 5 15 15; 43 10 15 5; 44 10 15 10; 45 10 15 15; 46 15 15 5; 47 15 15 10; 48 15 15 15; 49 25 15 5; 50 25 15 10; 51 25 15 15; 52 30 15 5; 53 30 15 10; 54 30 15 15; 55 35 15 5; 56 35 15 10; 57 35 15 15; 58 20 11.25 5; 59 20 11.25 10; 60 20 11.25 15; 61 20 7.5 5; 62 20 7.5 10; 63 20 7.5 15; 64 20 3.75 5; 65 20 3.75 10; 66 20 3.75 15; 67 20 0 5; 68 20 0 10; 69 20 0 15; MEMBER INCIDENCES 1 1 7; 2 2 11; 3 3 34; 4 34 35; 5 35 36; 6 36 18; 7 4 37; 8 37 38; 9 38 39; 10 39 22; 11 5 29; 12 6 33; 13 7 8; 14 8 9; 15 9 10; 16 10 11;

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17 18 19; 18 19 20; 19 20 21; 20 21 22; 21 29 30; 22 30 31; 23 31 32; 24 32 33; 25 7 12; 26 12 13; 27 13 14; 28 14 18; 29 18 23; 30 23 24; 31 24 25; 32 25 29; 33 11 15; 34 15 16; 35 16 17; 36 17 22; 37 22 26; 38 26 27; 39 27 28; 40 28 33; ELEMENT INCIDENCES SHELL 41 7 8 40 12; 42 8 9 41 40; 43 9 10 42 41; 44 10 11 15 42; 45 12 40 43 13; 46 40 41 44 43; 47 41 42 45 44; 48 42 15 16 45; 49 13 43 46 14; 50 43 44 47 46; 51 44 45 48 47; 52 45 16 17 48; 53 14 46 19 18; 54 46 47 20 19; 55 47 48 21 20; 56 48 17 22 21; 57 18 19 49 23; 58 19 20 50 49; 59 20 21 51 50; 60 21 22 26 51; 61 23 49 52 24; 62 49 50 53 52; 63 50 51 54 53; 64 51 26 27 54; 65 24 52 55 25; 66 52 53 56 55; 67 53 54 57 56; 68 54 27 28 57; 69 25 55 30 29; 70 55 56 31 30; 71 56 57 32 31; 72 57 28 33 32; 73 18 19 58 36; 74 19 20 59 58; 75 20 21 60 59; 76 21 22 39 60; 77 36 58 61 35; 78 58 59 62 61; 79 59 60 63 62; 80 60 39 38 63; 81 35 61 64 34; 82 61 62 65 64; 83 62 63 66 65; 84 63 38 37 66; 85 34 64 67 3; 86 64 65 68 67; 87 65 66 69 68; 88 66 37 4 69; MEMBER PROPERTY 1 TO 40 PRIS YD 1 ZD 1 ELEMENT PROPERTY 41 TO 88 THICKNESS 0.5 CONSTANTS E CONCRETE ALL DENSITY CONCRETE ALL POISSON CONCRETE ALL CUT OFF MODE SHAPE 10 SUPPORTS 1 TO 6 FIXED UNIT POUND FEET *MASS DATA AND INSTRUCTION FOR COMPUTING FREQUENCIES AND MODES LOAD 1 SELFWEIGHT X 1.0 SELFWEIGHT Y 1.0 SELFWEIGHT Z 1.0 ELEMENT LOAD 41 TO 88 PR GX 300.0 41 TO 88 PR GY 300.0 41 TO 88 PR GZ 300.0

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MODAL CALCULATION REQUESTED PERFORM ANALYSIS FINISH Understanding the output : After the analysis is completed, look at the output file. This file can be viewed from File - View - Output File - STAAD output. i. Mode number and corresponding frequencies and periods

Since we asked for 10 modes, we obtain a report which is as follows:

ii. Participation factors in Percentage

In the explanation above for the CUT OFF MODE command, we said that one measure of the importance of a mode is the participation factor of that mode. We can see from the above report that for vibration along X direction, the first mode has a 90.89 percent participation. It is also apparent that the 4th mode is primarily a Y direction mode due to its 50.5 % participation along Y and 0 in X and Z. The SUMM-X, SUMM-Y and SUMM-Z columns show the cumulative value of the participation of all the modes up to and including a given mode. One can infer from those terms that if one is interested in 95% participation along X, the first 5 modes are sufficient.

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But for the Z direction, even with 10 modes, we barely obtained 0.6%. The reason for this can be understood by a close examination of the nature of the structure. Our model has a shear wall which spans in the YZ plane. This makes the structure extremely stiff in that plane. It would take a lot of energy to make the structure vibrate along the Z direction. Modes are extracted in the ascending order of energy. The higher modes are high energy modes, compared to the lower modes. It is likely that unless we raise the number of modes extracted from 10 to a much larger number - 30 or more - using the CUT OFF MODE SHAPE command, we may not be able to obtain substantial participation along the Z direction. Another unique aspect of the above result are the modes where all 3 directions have 0 or near 0 participation. This is caused by the fact that the vibration pattern of the model for that mode results in symmetrically located masses vibrating in opposing directions, thus canceling each other's effect. Torsional modes too exhibit this behavior. See the next item for the method for viewing the shape of vibration. Localized modes, where small pockets in the structure undergo flutter due to their relative weak stiffness compared to the rest of the model, also result in small participation factors.

iii. Viewing the mode shapes

After the analysis is completed, select Post-processing from the mode menu. This screen contains facilities for graphically examining the shape of the mode in static and animated views. The Dynamics page on the left side of the screen is available for viewing the shape of the mode statically. The Animation option of the Results menu can be used for animating the mode. The mode number can be selected from the "Loads and Results" tab of the "Diagrams" dialog box which comes up when the Animation option is chosen. The size to which the mode is drawn is controlled using the "Scales" tab of the "Diagrams" dialog box.

How are modes, frequencies and the other terms are calculated The process of calculating the MODES and FREQUENCIES is known as Modal Extraction and is performed by solving the equation:

ω2 [ m ] { q } - [ K ] { q } = o Where [ m ] = the mass matrix (assumed to be diagonal, i.e., no mass coupling) ω = the natural frequencies (eigenvalues) { q } = the normalized mode shapes (eigenvectors) Frequency (HZ or CPS) = ω/2π

The solution method used in STAAD is the Subspace iteration method.

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Please note that various nomenclature is used to refer to the normal modes of vibration. (Eigenvalue, Natural Frequency, Modal Frequency and Eigenvector, Mode Shape, Modal Vector, Normal Modes, Normalized Mode Shape. Generalized Weight and Generalized Mass Each eigenvector {q} has an associated generalized mass defined by

Generalized Mass (GM) = { q }T [ M ] { q } Generalized Weight (GW) = GM * g

Participation Factors - A participation factor (Qi) is computed for each eigenvector for each of the three global (Xi) translational directions. N is the number of modes.

Qq w

GWi

j,i j,ij

N

=∑=

( )( )1

Modal Weights - The modal weight for each mode is (GW)(Qi²). The summation of modal weights for all modes in a given direction is equal to the Base Shear

which would result from a one g base acceleration. The sum of the modal weights for the computed modes may be compared to the total weight of the structure (only the weight that has not been lumped at supports). The difference is the amount of weight missing from a dynamic, base excitation, modal response analysis. If too much is missing, then rerun the eigensolution asking for a greater number of modes.

STAAD prints the "MASS PARTICIPATION FACTOR IN PERCENT" for each mode. This is the modal weight of a mode as a percentage of the total weight of the structure. Also a running sum for all modes is given so that the last line indicates the percent of the total weight that all of the modes extracted would represent in a 1g base excitation.

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7. Response Spectrum Analysis Description Response spectra are plots of maximum response of single degree of freedom (SDOF) systems subjected to a specific excitation. For various values of frequency of the SDOF system and various damping ratios, the peak response is calculated. Structures normally have multiple degrees of freedom (MDOF). The dynamic analysis of a MDOF system having "n" DOF involves reducing it to "n" independent SDOF systems. The modal superposition method is used and the maximum modal responses are combined using SRSS, CQC and other methods available in STAAD. The command syntax for defining response spectrum data is explained in Section 5.32.10.1 of the Technical Reference manual. It is important to understand that once the combination methods like SRSS or CQC are applied, the sign of the results is lost. Consequently, results of a spectrum analysis, like displacements, forces and reactions do not have any sign. Because spectrum analysis requires modes and frequencies, the mass data and other details explained in the chapter on calculating modes and frequencies are all applicable in the case of spectrum analysis also. In other words, the mode and frequency calculation is a pre-requisite to performing response spectrum analysis. Calculation of Base Shear in a Response Spectrum Analysis The base shear, for a given mode for a given direction, reported in the response spectrum analysis is obtained as

A * B * C * D where A = Mass participation factor for that mode for that direction B = Total mass specified for that direction C = Spectral acceleration for that mode D = direction factor specified in that load case

A is calculated by the program from the mass matrix and mode shapes B is obtained from the masses specified in the response spectrum load case C is obtained by interpolating between the user provided values of period vs. acceleration and multiplying the resulting value by the SCALE FACTOR.

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D is specified by the user Bending Moment Diagram for a load case that involves the Response Spectrum Analysis In a response spectrum analysis in STAAD, the member forces are computed accurately only at the 2 ends of the member. The sign of these forces cannot be determined due to the fact that the method used to combine the contribution of modes does not allow for the determination of the sign of the forces. Further, these force values do not necessarily indicate whether these forces occur at the same instant of time. In order to draw the bending moment diagram, one needs to know the moments at the intermediate section points on the member. In order to calculate these section force values, the forces at the member ends have to be used. However, due to the special nature of these end force values as described in the paragraph above, it makes no sense to calculate the intermediate section forces based on the end force values. Due to this reasoning, the bending moment diagram simply cannot be drawn accurately for the response spectrum loading. STAAD merely plots a straight line that joins the bending moment values at the start and end joints of the member which are as mentioned earlier, absolute (positive) values. Current versions of STAAD do not let the user draw the diagram at all from certain places such as the Member Query. Comparison of results of a spectrum analysis (which uses the UBC spectrum data) with the results of an equivalent UBC static analysis For the following reasons, this comparison isn't meaningful : 1. In a spectrum analysis, the number of modes to be combined is a decision made

by the engineer. If 100% participation from the modes isn't utilized in the displacement calculation, it is obvious that the results will be only approximate.

2. In a spectrum analysis, the contribution from the various modes is combined

using an SRSS method or a CQC method, both of which are only approximate methods. One very important drawback of both these methods is that the sign of the displacements and forces cannot be determined. Also, the results can vary significantly depending on the type of method used in the combination.

3. In the UBC method, only a single period is used. Normally, the assumption is

that this period is associated with a mode that encompasses a significant portion of the overall response of the structure. This may not necessarily be true in reality. If more than one mode is required to capture the overall response of the structure, that fact is not brought to light in the UBC static equivalent approach.

4. The UBC static equivalent method involves several parameters such as

Importance factor, soil structure coefficient, etc. which are incorporated through an emperical formula. In a response spectrum analysis, there is no facility available to incorporate these factors in a direct manner.

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Due to these reasons, a direct comparison of the results of a spectrum analysis and a static equivalent approach is not recommended. Question : What is the Scale Factor (f4) that needs to be provided when specifying the Response Spectra? Answer : The spectrum data consists of pairs of values which are Period vs. Accn. or Period vs. Displacement. The acceleration or displacement values that you obtain from the geological data for that site may have been provided to you as normalized values or un-normalized values. Normalization means that the values of acceleration or displacement have been divided by a number (called normalization factor) which represents some reference value. One of the commonly used normalization factors is 'g', the acceleration due to gravity. If the spectrum data you specify in STAAD is a normalized spectrum data, you should provide the NORMALIZATION FACTOR as the SCALE FACTOR. If your spectrum data is un-normalized, there is no need to provide a scale factor(Another way of putting it is that if you provide un-normalized spectrum values, the scale factor is 1, which happens to be the default value also.) Make sure that the value you provide for the SCALE FACTOR is in accordance with the length units you have specified. (A common error is that if the scale factor is 'g', users erroneously provide 32.2 when the length unit is in INCHES.) STAAD will multiply the spectral acceleration or spectral displacement values by the scale factor. Hence, if you provide a normalized acceleration value of 0.5 and a scale factor of 386.4 inch/sq.sec., it has the same effect as providing an un-normalized acceleration value of 193.2 inch/sq.sec. and a scale factor of 1.0. Question : What is the Direction Factor that needs to be provided when specifying the Response Spectra? Answer : The Direction factor is a quantity by which the spectral displacement for the associated direction is multiplied. For example, if the command reads as SPECTRUM SRSS X 0.7 Y 0.5 Z 0.65 DISP DAMP 0.05 SCALE 32.2 the following is done:

1. For each mode, the period is determined.

2. Corresponding to the period, the spectral displacement for that mode is calculated by interpolation from the input pairs of period vs. spectral displacement. Call this "sd"

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3. Calculate the spectral displacement for each direction by multiplying "sd" by the associated Direction factor.

The X direction spectral displacement = sd * 0.7 The Y direction spectral displacement = sd * 0.5 The Z direction spectral displacement = sd * 0.65

These factored values are then multiplied by

a. the mode shape value corresponding to that degree of freedom, b. participation factor.

Call the result T(m) where "m" stands for the mode number. Once the T(m) is determined for all modes, subject them to the SRSS calculation. That will provide the node displacement corresponding to that degree of freedom. Question : The results of the response spectrum load case are always positive numbers. Why? How do I know that the positive value is always critical, especially from the design standpoint? Answer : In a spectrum analysis, the contribution of the individual modes is combined using methods such as SRSS or CQC to arrive at the overall response. The limitation of these methods is that the sign of the response cannot be determined after the method is applied. This is the reason why the output you get from STAAD for a response spectrum analysis are absolute values. One way to deal with the problem is to create 2 load combination cases for each set of load cases you wish to combine. For example, if the dead load case is 1, and the spectrum load case is 5, you could create

LOAD COMB 10 1 1.1 5 1.3 LOAD COMB 11 1 1.1 5 -1.3

and use the critical value from amongst these 2 load combination cases for design purposes. What you accomplish from this process is that you are considering a positive effect as well as the negative effect of the spectrum load case. Question : In the Technical Reference manual section 5.32.10.1, you state: " Note, if data is in g acceleration units, then set SCALE to a conversion factor to the current length unit (9.81, 386.4, etc.)" What does "g acceleration units" mean?

Related question : What is the Scale Factor (f4) that needs to be provided when specifying the Response Spectra?

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Answer : The spectrum data consists of pairs of values which are Period vs. Accn. or Period vs. Displacement. The acceleration or displacement values that you obtain from the geological data for that site may have been provided to you as normalized values or un-normalized values. Normalization means that the values of acceleration or displacement have been divided by a number (called normalization factor) which represents some reference value. One of the commonly used normalization factors is 'g', the acceleration due to gravity. If the spectrum data you specify in STAAD is a normalized spectrum data, you should provide the NORMALIZATION FACTOR as the SCALE FACTOR. If your spectrum data is un-normalized, there is no need to provide a scale factor(Another way of putting it is that if you provide un-normalized spectrum values, the scale factor is 1, which happens to be the default value also.) Make sure that the value you provide for the SCALE FACTOR is in accordance with the length units you have specified. (A common error is that if the scale factor is 'g', users erroneously provide 32.2 when the length unit is in INCHES.) STAAD will multiply the spectral acceleration or spectral displacement values by the scale factor. Hence, if you provide a normalized acceleration value of 0.5 and a scale factor of 386.4 inch/sq.sec., it has the same effect as providing an un-normalized acceleration value of 193.2 inch/sq.sec. and a scale factor of 1.0. Question : STAAD allows me to use SRSS, ABS, CQC, ASCE4-98 & TEN Percent for combining the responses from each mode into a total response. The CQC & ASCE4 methods require damping. But, ABS, SRSS, and TEN do not use damping unless Spectra-Period curves are made a function of damping. Why? Answer : The spectral acceleration versus period curve is for a particular value of damping. So the user has selected a damping when he selects the acceleration curve. The damping on the SPECTRUM command only affects the calculation of the closely spaced modal interaction matrix which SRSS, ABS, and TEN do not use. Question : I have some doubts in how to use the Spectrum command. First of all, dead loads are always applied in the Y axis direction (downwards). When I’m going to run a spectrum analysis and I use the same dead loads, do I have to modify the direction of the loads? Answer : The load data you provide in the load case in which the SPECTRUM command is specified goes into the making of the mass matrix. The mass matrix is supposed to be populated with terms for all the global directions in which the structure is capable of vibrating. To enable this, the loads must be specified in all the possible directions of vibration.

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Consequently, the load case for response spectrum might look something like this :

LOAD 20 SPECTRUM IN X DIRECTION * SELFWEIGHT X 1 SELFWEIGHT Y 1 SELFWEIGHT Z 1 MEMBER LOAD 274 TO 277 UNI GX 1.36 272 466 998 UNI GX 4.13 313 314 474 477 UNI GX 6.29 274 TO 277 UNI GY 1.36 272 466 998 UNI GY 4.13 313 314 474 477 UNI GY 6.29 274 TO 277 UNI GZ 1.36 272 466 998 UNI GZ 4.13 313 314 474 477 UNI GZ 6.29 JOINT LOAD 420 424 FX 47.32 389 TO 391 FX 560 420 424 FY 47.32 389 TO 391 FY 560 420 424 FZ 47.32 389 TO 391 FZ 560 SPECTRUM CQC X 1 ACC SCALE 9.81 DAMP 0.07 0.025 0.14; 0.0303 0.1636; 0.05 0.2455; 0.0625 0.2941; 0.0769 0.3479; 0.0833 0.3713; 0.1 0.3713; 0.125 0.3713; 0.1667 0.3713; 0.1895 0.3713; 0.25 0.2815; 0.2857 0.2463; 0.3333 0.2111; 0.4 0.1759; 0.5 0.1407; 0.6667 0.1056; 1 0.0704; 2 0.0344; 10 0.001372; LOAD 21 SPECTRUM IN Z DIRECTION SPECTRUM CQC Z 1 ACC SCALE 9.81 DAMP 0.07 0.025 0.14; 0.0303 0.1636; 0.05 0.2455; 0.0625 0.2941; 0.0769 0.3479; 0.0833 0.3713;

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0.1 0.3713; 0.125 0.3713; 0.1667 0.3713; 0.1895 0.3713; 0.25 0.2815; 0.2857 0.2463; 0.3333 0.2111; 0.4 0.1759; 0.5 0.1407; 0.6667 0.1056; 1 0.0704; 2 0.0344; 10 0.001372;

Question : Can I specify a different spectrum for each of the 3 directions (x , y or z)? Answer : Yes. Question : Can I decide how many modes I want to include in the spectrum analysis? Answer : Use the command CUT OFF MODE SHAPE. Refer to example problems 11, 28, 29, etc. Question : In the results, what are the dynamic, missing, and modal weights? Answer : The dynamic weight line contains the total potential weight for base shear calculations. Missing Weight is the amount of weight missing in the modes; Modal weight is the total weight actually used in the modes. If you algebraically add up Dynamic & Missing, you should get Modal. SRSS MODAL COMBINATION METHOD USED. DYNAMIC WEIGHT X Y Z 8.165253E+02 8.165294E+02 8.165276E+02 POUN MISSING WEIGHT X Y Z -4.118054E+01 -3.292104E+02 -4.840284E+02 POUN MODAL WEIGHT X Y Z 7.753447E+02 4.873190E+02 3.324991E+02 POUN

Question : What is meant by MASS PARTICIPATION FACTORS IN PERCENT? Answer : When the weight of the building is accelerated in a certain direction, it produces a force in that direction. That force can be broken down into small parts, with each part coming from a specific mode. The sum of the values of these parts is called the base shear. The percentage of the weight of the building, participating in the vibration in a mode in a specific direction is called the PARTICIPATION factor. It is a reflection of the "part" of the base shear, generated by that mode in that direction. Question : I am a little bit confused with the response spectrum analysis results. Refer your Example 11 results. The support reactions that we are getting are the same for both the supports for load cases 3 & 4. In combining lateral loads (response spectrum loading in this case) with vertical loads, one support should have less force than the other. At one support, the vertical reaction from the lateral load case will add to that from the vertical load case, and, at the other, it will get subtracted. Why do I not see that in the results?

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Answer : The support reaction values from a response spectrum analysis (like any other results from a response spectrum analysis) are absolute quantities. Consequently, the reactions from case 2, which is the spectrum case, are both equal and have the same sign. The primary reasons for this are

a. when the numbers are subjected to the SRSS, CQC or other methods, their sign is lost b. the values do not necessarily reflect the result at the same instant of time.

When you combine these results with those from the dead load case, it leads to the same value at both supports. If you want the results to truly reflect the sign, use a static equivalent method like that stipulated by the UBC code. Alternatively, perform a time history analysis where the sign of the values is obtained for each time step. Question : Is it possible to get the vertical distribution of the total base shear in a response spectrum analysis, like one can for a UBC analysis? Answer : Unfortunately No. Since the values from a response spectrum analysis are absolute quantities (numbers without sign), there is no reasonable way to obtain it. You may add up the shears in the columns above that level for an approximate estimate. Question : Can you please let me know if we can print nodal acceleration from response spectra runs? If so, how do I print the data in the report format or display it in the Post-Processing mode? Answer : Add the word SAVE at the end of the SPECTRUM command. A .ACC file will be created. There is unfortunately no facility available for displaying it in the post-processing mode. However, since the ACC file is simply a text file, you can open it using any text editor, and in Excel too. In Excel, you can use the graph generation facilities for plotting it. Question : In a response spectrum analysis using the STAAD.Pro, the base shear is not matching with the summation of the support reaction values in that direction. Why? Also, which values should be taken for designing the foundation? the base shear value or the support reaction value? If it is the base shear value then what is the method generally used to distribute this base shear to all the supports? Answer : The results are statistical, SRSS, CQC, etc. The numbers are all peak positive values. Since each of the reactions at the time of peak base shear could be less than that reaction's peak and could be positive or negative, it is likely that the peak base shear will be much less than the sum of the peak reactions. There is no way to distribute the base shear to the supports. Even if you could, that would not be the peak reaction at the support, the reaction printed by STAAD is the

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peak value. If there are several components of reaction at a joint, these are peak values that may have occurred at different times. Question : The base shear reported by STAAD does not match with the Summation of Support Reactions in the relevant direction. I want to know the reason for the same. Answer : When the SRSS method is used, all results from a Response Spectrum analysis are a result of a square root of a sum of the squares (SRSS) of the desired output quantity from each mode. The reactions within a single mode may have equal and opposite reactions of the various supports such that the base shear for that mode is near zero. Therefore the contribution of that mode to a SRSS of all the modal base shears will be nearly zero. However, in that same mode, a particular support may have a large reaction value. So when that value is SRSSed with that supports reaction value from all the other modes, that same mode may be a major contributor to the final result for the support reaction while that mode contributes little to the base shear. Of course if all the support reactions in all of the modes have the same sign, then the answers will be close. Question : I am getting a large Difference in the results ( Base shear ) of between Seismic Coefficient Method (UBC) Response Spectrum Method. Can you explain why? Also, the CQC method produces a higher base shear than the SRSS method. Answer : If the base shear is spread over many frequencies, the Response Spectrum method will result in a base shear that is much lower than an absolute sum of the base shears of all the modes. The theory of SRSS combination is that the peak value from each mode will occur at a different time and is statistically independent. In STAAD 200x the base shear is also printed using Absolute Sum combination which assumes that the modes are all in phase and peaks occur at the same time. You will note that in many problems the absolute sum result is much higher than the SRSS result. I believe that the UBC approach is closer to the absolute response since a static case is entirely in phase. For close spaced eigenvalues the CQC method will amplify the response of those modes as compared to the SRSS method. Question : I am trying to correlate the relationship between the base shears and the Global Support Reactions. For example, on the attached model, the total base shear in the x-direction does not add up to the total reaction in the x-direction for the dynamic load case. I'm thinking that STAAD solves a reaction for each mode and subsequently sums them in either SRSS or CQC, but I am trying to justify in my mind why the total base shear in the X direction is not also the total Global Reaction in the X direction. Could you try to explain?

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Answer : Every individual output result value in a response spectrum analysis is independent and all results are absolute (positive). Lets say you have two modes and 4 supports in the x direction. Then for the SRSS combination method the results are computed as follows: ********************************************************* Support# Mode 1 Mode 2 Sum of Squares Square root Reaction Reaction SRSS 1 10. -15. 325 18.0 2 -5. 19. 386 19.6 3 17. 43. 2138 46.2 4 -3. -12. 153 12.4 ==== ==== ==== ====

SRSS Base Shear 19 35 1586 96.2 (Sum of Reactions) 1586 = 39.8 ********************************************************* Note that SRSS base shear (39.8) does not equal the sum of the SRSS reactions (18.0+19.6+46.2+12.4=96.2). In effect the procedure says that the maximum likely reaction value at each support is as shown. However the maximum likely sum is the Base shear as shown. This is due to the fact that the individual maximums would not occur at the same time and not necessarily with the same sign. So the base shear magnitude is usually much less than the sum of the reactions. Question : For Load case 1, I have SPECTRUM SRSS X 1 ACC SCALE 0.9806 DAMP 0.05 0.03 0.8702; 0.05 1.0752; 0.1 1.5876; 0.15 2.1; 0.3 2.1; 0.5 2.1; 0.7 1.5; 0.9 1.1667; 1.1 0.9545; 1.3 0.8077; 1.5 0.7; 1.7 0.6176; 1.9 0.5526; 2.1 0.4762; 2.3 0.397; 2.5 0.336; 2.7 0.2881; 2.9 0.2497; 3.1 0.2185; 3.3 0.1928; 3.5 0.1714; 3.7 0.1534; 3.9 0.1381; 4.1 0.1249; 4.3 0.1136; 4.8 0.0911; 6 0.0583; 7 0.0429; 8 0.0328; 10 0.021; 20 0.0053; 30 0.0023; For Load case 2, I have SPECTRUM SRSS Z 1 ACC SCALE 0.9806 DAMP 0.05 0.03 0.8702; 0.05 1.0752; 0.1 1.5876; 0.15 2.1; 0.3 2.1; 0.5 2.1; 0.7 1.5; 0.9 1.1667; 1.1 0.9545; 1.3 0.8077; 1.5 0.7; 1.7 0.6176; 1.9 0.5526; 2.1 0.4762; 2.3 0.397; 2.5 0.336; 2.7 0.2881; 2.9 0.2497; 3.1 0.2185; 3.3 0.1928; 3.5 0.1714; 3.7 0.1534; 3.9 0.1381; 4.1 0.1249; 4.3 0.1136; 4.8 0.0911; 6 0.0583; 7 0.0429; 8 0.0328; 10 0.021; 20 0.0053; 30 0.0023; For Load case 3, I have

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SPECTRUM SRSS X 1 Z 1 ACC SCALE 0.9806 DAMP 0.05 0.03 0.8702; 0.05 1.0752; 0.1 1.5876; 0.2 2.1; 0.3 2.1; 0.5 2.1; 0.7 1.5; 0.9 1.1667; 1.1 0.9545; 1.3 0.8077; 1.5 0.7; 1.7 0.6176; 1.9 0.5526; 2.1 0.4762; 2.3 0.397; 2.5 0.336; 2.7 0.2881; 2.9 0.2497; 3.1 0.2185; 3.3 0.1928; 3.5 0.1714; 3.7 0.1534; 3.9 0.1381; 4.1 0.1249; 4.3 0.1136; 4.8 0.0911; 6 0.0583; 7 0.0429; 8 0.0328; 10 0.021; 20 0.0053; 30 0.0023; Load combination 5 is an SRSS of 1 & 2. LOAD COMBINATION SRSS 5 1 1.0 2 1.0 Should load case 5 produce the same answers as load case 3? Answer : Load case 1 means the earthquake is acting in the X direction at an intensity of say 100%. Load case 2 means the earthquake is acting in the Z direction at an intensity of say 100%. Then, load case 3 means the earthquake is acting at a 45 degree angle to the X and Z directions at an intensity of 141.414%. Load combination 5 will not produce the same result as load case 3. An earthquake with a 100% intensity in X and another with a 100% intensity in Z is not the same as one with a 141.4% intensity at a 45 degree angle to X and Z. The combination methods such as SRSS or CQC are not linear. Another reason for the difference has to do with the Direction factor.

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8. Time History analysis of a structure for seismic accelerations

Time history analysis is an extension to the process of calculating modes and frequencies in the sense that it occurs after those are calculated. The input which is relevant to the time history analysis of a structure for seismic accelerations is explained below. There are two stages in the command specification required for a time-history analysis. Stage 1 : The first stage is defined as shown in the following example. Here, the characteristics of the earthquake, the arrival time, and damping are defined. Example : UNIT METER DEFINE TIME HISTORY TYPE 1 ACCELERATION SCALE 9.806 READ EQDATA.TXT ARRIVAL TIME 0.0 DAMPING 0.05 Each data set is individually identified by the number that follows the TYPE command. In this file, only one data set is defined, which is apparent from the fact that only one TYPE is defined. The word ACCELERATION that follows the TYPE 1 command signifies that this data set is for a ground acceleration. (If one wishes to specify a forcing function, the keyword FORCE or MOMENT must be used instead.) Notice the expression "READ EQDATA.TXT". It means that we have chosen to specify the time vs. ground acceleration data in the file called EQDATA.TXT. That file must reside in the same folder as the one in which the data file for this structure resides. As explained in the small examples shown in Section 5.31.4 of the Technical Reference manual, the EQDATA.TXT file is a simple text file containing several pairs of time-acceleration data. A sample portion of that file is as shown below. 0.0000 0.006300 0.0200 0.003640 0.0400 0.000990 0.0600 0.004280 0.0800 0.007580 0.1000 0.010870

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While it may not be apparent from the above numbers, it may also be noted that the geological data for the site the building sits on indicate that the above acceleration values are a fraction of "g", the acceleration due to gravity. Thus, for example, at 0.02 seconds, the acceleration is 0.00364 multiplied by 9.806 m/sec^2 (or 0.00364 multiplied by 32.2 ft/sec^2). Consequently, the burden of informing the program that the values need to be multiplied by "g" is upon us. We do that by specifying the term “SCALE 9.806” alongside “TYPE 1 ACCELERATION”. The arrival time value indicates the relative value of time at which the earthquake begins to act upon the structure. We have chosen 0.0, as there is no other dynamic load on the structure from the relative time standpoint. The modal damping ratio for all the modes is set to 0.05. Stage 2 : UNIT POUND FEET LOAD 3 DYNAMIC LOAD CASE SELFWEIGHT X 1.0 SELFWEIGHT Y 1.0 SELFWEIGHT Z 1.0 ELEMENT LOAD 41 TO 88 PR GX 300.0 41 TO 88 PR GY 300.0 41 TO 88 PR GZ 300.0 Load case 3 is the dynamic load case, the one which contains the second part of the instruction set for a dynamic analysis to be performed. The data here are a. loads which will yield the mass values which will populate the mass matrix b. the directions of the loads, which will yield the degree of freedom numbers of

the mass matrix for being populated. Thus, the selfweight, as well as the imposed loads on the structural slab are to be considered as participating in the vibration along all the global directions. This information is identical to what is specified in the situation where all that we are interested is frequencies and modes. GROUND MOTION X 1 1 The above command too is part of load case 3. Here we say that the seismic force, whose characteristics are defined by the TYPE 1 time history input data, acting at arrival time 1, is to be applied along the X direction. Example: LOAD 1 Mass data in weight units

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GROUND MOTION direction Type# Arrival Time# PERF ANAL FINISH

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9. Time History Analysis for a Structure subjected to a Harmonic Loading

A sinusoidal loading is one which has the characteristic of repetitiveness, as in the case of a tower at the top of which are two radar antennas which cause a rotational type of dynamic loading with a specified rotation rate and a nominal turning circle. A sinusoidal loading usually can be described using the equation.

φ) t(ωsin 0F(t) F +=

In the above equation, F(t) = Value of the force at any instant of time "t" F = Peak value of the force ω = Frequency of the forcing function φ = Phase angle

A plot of the above equation is shown in the figure below.

Definition of input in STAAD for the above forcing function As can be seen from its definition, a forcing function is a continuous function. However, in STAAD, a set of discrete time-force pairs is generated from the forcing function and an analysis is performed using these discrete time-force pairs. What that means is that based on the number of cycles that the user specifies for the loading, STAAD will generate a table consisting of the magnitude of the force at various points of time. The time values are chosen from time '0' to n*tc in steps of "STEP" where n is the number of cycles and tc is the duration of one cycle. STEP is a value that the user may provide or may choose the default value that is built into the program. Users may refer to section 5.31.4 of the Technical Reference Manual for a list of input parameters that need to be specified for a Time History Analysis on a structure subjected to a Sinusoidal loading. A typical example of input specification for the above is shown below. Some typical input that normally appears prior to these commands is also included. UNIT KIP INCH DEFINE TIME HISTORY TYPE 1 FORCE FUNCTION SINE

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AMPLITUDE 10.8 FREQUENCY 47 PHASE 30 CYCLES 150 TYPE 2 FORCE FUNCTION COSINE AMPLITUDE 12.3 FREQUENCY 28 PHASE 40 CYCLES 200 ARRIVAL TIME 0.0 3.0 DAMPING 0.06 There are two stages in the command specification required for a time-history analysis. The first stage is defined above. Here, the parameters of the sinusoidal loading are provided. Each data set is individually identified by the number that follows the TYPE command. In this file, two data sets are defined, which is apparent from the fact that two TYPEs are defined. The word FORCE that follows the TYPE n command signifies that this data set is for a forcing function. (If one wishes to specify an earthquake motion, an ACCELERATION may be specified.) The command FUNCTION COSINE indicates that instead of providing the data set as discrete TIME-FORCE pairs, a sinusoidal function, which describes the variation of force with time, is provided. The parameters of the cosine function, such as FREQUENCY, AMPLITUDE, and number of CYCLES of application are then defined. STAAD internally generates discrete TIME-FORCE pairs of data from the sine function in steps of time defined by the default value (See section 5.31.6 of the Technical Reference Manual for more information). The arrival time value indicates the relative value of time at which the force begins to act upon the structure. The modal damping ratio for all the modes is set to 0.075. LOAD 1 DEAD LOAD SELF Y -1.0 The above is a static load case. LOAD 2 LOADING FOR TIME HISTORY ANALYSIS SELF X 1.0 SELF Y 1.0 SELF Z 1.0 JOINT LOAD 10 FX 7.5 10 FY 7.5 10 FZ 7.5 TIME LOAD 7 FX 1 1 14 FZ 2 1 17 FZ 2 2

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The above is the second stage of command specification for time history analysis. The 2 sets of data specified here are a) the weights for generation of the mass matrix and b) the application of the time varying loads on the structure.

The weights (from which the masses for the mass matrix are obtained) are specified in the form of selfweight and joint loads.

Following that, the sinusoidal force is applied using the "TIME LOAD" command. The forcing function described by the TYPE 1 load is applied on joints 7 it starts to act starting at a time defined by the 1st arrival time number. At joint 14, the TYPE 2 force is applied along FZ, also starting at arrival time number 1. Finally, at joint 17, the TYPE 2 force is applied along FZ, starting at arrival time number 2.

LOAD COMB 3 1 1.2 2 1.4 The static and dynamic load cases are combined through the above case. PERFORM ANALYSIS PRINT SUPPORT REACTIONS PRINT MEMBER FORCES PRINT JOINT DISPLACEMENTS The member forces, support reactions and joint displacements are calculated for every time step. For each degree of freedom, the maximum value of these values is extracted from these histories and reported in the output file using the above commands. How modes, frequencies and the other terms calculated The process of calculating the MODES and FREQUENCIES is known as Modal Extraction and is performed by solving the equation:

ω2 [ m ] { q } - [ K ] { q } = o Where [ m ] = the mass matrix (assumed to be diagonal, i.e., no mass coupling) ω = the natural frequencies (eigenvalues) { q } = the normalized mode shapes (eigenvectors) Frequency (HZ or CPS) = ω/2π

The solution method used in STAAD is the Subspace iteration method. Please note that various nomenclature is used to refer to the normal modes of vibration. (Eigenvalue, Natural Frequency, Modal Frequency and Eigenvector, Mode Shape, Modal Vector, Normal Modes, Normalized Mode Shape.

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Generalized weight and generalized mass Each eigenvector {q} has an associated generalized mass defined by

Generalized Mass (GM) = { q }T [ M ] { q } Generalized Weight (GW) = GM * g

Participation Factors - A participation factor (Qi) is computed for each eigenvector for each of the three global (Xi) translational directions. N is the number of modes.

Qq w

GWi

j,i j,ij

N

=∑=

( )( )1

Modal Weights - The modal weight for each mode is (GW)(Qi²). The summation of modal weights for all modes in a given direction is equal to the Base Shear

which would result from a one g base acceleration. The sum of the modal weights for the computed modes may be compared to the total weight of the structure (only the weight that has not been lumped at supports). The difference is the amount of weight missing from a dynamic, base excitation, modal response analysis. If too much is missing, then rerun the eigensolution asking for a greater number of modes.

STAAD prints the "MASS PARTICIPATION FACTOR IN PERCENT" for each mode. This is the modal weight of a mode as a percentage of the total weight of the structure. Also a running sum for all modes is given so that the last line indicates the percent of the total weight that all of the modes extracted would represent in a 1g base excitation.

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10. Time History Analysis for a Structure subjected to a random excitation

A random excitation is a force which varies with time, and not necessarily in an orderly fashion. An example of the same is a blast loading. The only difference between this type of loading and the sinusoidal loading is that the force versus time data has to be defined explicitly under the DEFINE TIME HISTORY command. An example of it is shown below. UNIT METER KNS DEFINE TIME HISTORY TYPE 1 FORCE 0.00001 -0.000001 0.005 -650 0.01 -800 0.015 -800 0.02 -800 0.025 -800 0.03 -700 0.035 -350 0.04 -250 0.045 -500 0.05 -730 0.055 -600 0.06 -350 0.065 -280 0.07 -450 0.075 -600 0.08 -550 0.085 -440 0.09 -415 0.095 -410 0.1 -420 ARRIVAL TIME 0.0 DAMPING 0.07 For a blast type of loading, there will be a sudden spike in the value of the force over a very short period of time. DEFINE TIME HISTORY TYPE 1 FORCE 0.0 0.0 0.1 80.0 0.2 0.1 0.35 0.0 0.4 0.0 1.0 0.0 ARRIVAL TIMES 0.0 DAMPING 0.05

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11. Hands on Exercise 1 – Dynamic Analysis This example looks at the dynamic analysis features within STAAD.Pro.

1) Structure Wizard Start a new structure, name it as Example1, click on the Geometry menu and select the Run Structure Wizard option. This launches the Structure Wizard. Select Frame models and double click the Bay Frame and set the parameters as shown and click Apply. To transfer the model into the STAAD.Pro structure, use the Merge model with STAAD.Pro model option from the file menu. Locate the model without a shift from the origin. We wish to replace the four top beams with trusses. Highlight them in the structure view and click on the Del key. Once again Start the Structure Wizard. This time select a and generate a Howe Bridge Frame with the dimensions as shown. Transfer it to STAAD.Pro as before, but this time locate this model 3m above the origin, i.e at the top of the columns. Note that where beams would be duplicated, they have not been created.

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2) Add Properties and Supports Go to the General page (Property sub-page), add the British section UB305x102x33 and assign it to the columns, first floor and eaves beams. Then add the British section UA100x75x8 and assign it to all the remaining roof beams. Go to the Supports sub-page and add a FIXED support. Assign the support to the base of all the columns. Right click on the Whole Structure window and select the Structure Diagrams… option from the popup menu. On 3D sections, set the option to Full Sections. The diagram should look thus:-

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3) Create Time History Graphs To create a Time History Graph, click on the menu item, Commands|Loading|Define Load|Time History|Forcing Function. Click on the Create New Type button and accept the type number as 1. Set the Type to Force. Change to the Define Forcing Function tab and set the values thus:-

Time Force (KN) 1 0.0 -20 2 0.25 100 3 0.50 200 4 0.75 500 5 1.00 800 6 1.25 500 7 1.50 70

Then click on the Save Type button to record the data and the Close button to exit the dialog box. The arrival times also need to be defined. Therefore click on the menu item Commands|Loading|Definitions|Time History|Parameters and set two arrival times thus:-

Time 1 0 2 0.25 3

4) Create a Time History Loadcase Go to the Load sub-page and create a loadcase called 'Time History'.

Masses Firstly the masses need to be defined. Click on the Selfweight button and set it to X direction with a factor of 1.0. Repeat this for Y and Z directions also with factors of 1.0.

Time History Click on the Time History… button and click on the Add button to define the command. To apply the locations at which this command is applied, use the Nodes cursor to select the two joints at the first floor level on the two central columns on one side of the structure. Select the time history command in the Loads dialog box, shown as FX 1 1, then, with the assignment option set to 'Assign to Selected Nodes' click on the Assign button. Next we are going to assign the time history load with an arrival time of 0.25 seconds to the other side of the structure. Still using the Nodes cursor, select the same joints on the central two columns, but on the opposite side of the structure. Once again click on the Time History… button. This time set the arrival time to 2:0.25 and click on the Assign button to define the command and apply it to the selected joints. Now all that remains is to add the analysis command. This time select the menu item Commands|Analysis|Perform Analysis and click on the OK button to accept the default option.

Note that this can be defined in a spreadsheet entered using copy and paste.

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5) Viewing Mode Shapes Run the analysis and go to the Post Processing Mode. Select the Time History Loadcase in the Results Setup dialog and click OK. Adjust the mode shape diagram scale by using the Ctrl key and scrolling your mouse middle button.. There should now be a distinctive displacement for the mode shape. This is best seen as an animation, therefore click on the Animation tab, select the Mode option, set the Extra Frames to 10 as before and click on the Apply button to start the animation of the first mode shape. To see the other mode shapes, click on the Loads and Results tab of the Structure Diagram dialog box, select mode shape 2 and click on the Apply button. The animation changes to that of the second mode shape. Select the third mode shape and click on Apply. Open the output file and scroll to the end to note the Calculated Frequencies of the modes and the Mass Participation Factors. Note that none of the mass is activated in the X direction when only the first three modes are considered therefore the time history load will have almost no effect. The number of modes to be considered must be increased. Close the output file. Open the STAAD Editor. Scroll down to the line:-

LOAD 1 Time History And precede it with the following line:-

CUT OFF MODE SHAPE 20 Save and close the editor. Again perform the analysis and view the output file. Note that with the 20 mode shapes, over 90% of the mass is considered in the X direction. Close the output file. Go to the Post Processing mode. Note the increase in the deflections. Click on the Time History sub-page and click on one of the joints that have had a time history load applied and note how the displacement of the joint changes against time.

10

10

10

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20

20

20

20

30

30

30

30

0.5 1 1.5 1.75

29.9

1.02-0.5010.021

X-Disp (mm)

Time - Displacement

This concludes the exercise Example 6.

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12. P-Delta Analysis Structures subjected to lateral loads often experience secondary forces due to the movement of the point of application of vertical loads. This secondary effect, commonly known as the P-Delta effect, plays an important role in the analysis of the structure. In STAAD, a unique procedure has been adopted to incorporate the P-Delta effect into the analysis. The procedure consists of the following steps:

1. First, the primary deflections are calculated based on the provided external loading.

2. Primary deflections are then combined with the originally applied loading to create the secondary loadings. The load vector is then revised to include the secondary effects.

Note that the lateral loading must be present concurrently with the vertical loading for proper consideration of the P-Delta effect. The REPEAT LOAD facility (see Section 5.32.11) has been created with this requirement in mind. This facility allows the user to combine previously defined primary load cases to create a new primary load case.

3. A new stiffness analysis is carried out based on the revised load vector to generate new deflections.

4. Element/Member forces and support reactions are calculated based on the new deflections.

It may be noted that this procedure yields very accurate results with all small displacement problems. STAAD allows the user to go through multiple iterations of the P-Delta procedure if necessary. The user is allowed to specify the number of iterations based on the requirement. To set the displacement convergence tolerance, enter a SET DISP f command before the Joint Coordinates. If the change in displacement norm from one iteration to the next is less than f then it is converged.

The P-Delta analysis is recommended by several design codes such as ACI 318, LRFD, IS456-1978, etc. in lieu of the moment magnification method for the calculation of more realistic forces and moments.

There are two options to carry out P-Delta analysis.

1) When the CONVERGE command is not specified: The member end forces are evaluated by iterating “n” times. The default value of “n” is 1 (one).

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2) When the CONVERGE command is included: The member end forces are evaluated by performing a convergence check on the joint displacements. In each step, the displacements are compared with those of the previous iteration in order to check whether convergence is attained. In case “m” is specified, the analysis will stop after that iteration even if convergence has not been achieved. If convergence is achieved in less than “m” iterations, the analysis is terminated. (DO NOT ENTER “n” when CONVERGE is provided)

3) To set convergence displacement tolerance, enter SET DISPLACEMENT f command. Default is maximum span of the structure divided by 120.

Example

Followings are some example on use of the command for P-Delta analysis.

PDELTA ANALYSIS

PDELTA 5 ANALYSIS

PDELTA ANALYSIS CONVERGE

PDELTA ANALYSIS CONVERGE 5

Without one of these analysis commands, no analysis will be performed. These ANALYSIS commands can be repeated if multiple analyses are needed at different phases.

A PDELTA ANALYSIS will correctly reflect the secondary effects of a combination of load cases only if they are defined using the REPEAT LOAD specification (Section 5.32.11). Secondary effects will not be evaluated correctly for LOAD COMBINATIONS.

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13. P-Delta analysis including stress stiffening effect of the KG matrix

Purpose

The P-Delta analysis capability has been enhanced with the option of including the stress stiffening effect of the Kg matrix into the member / plate stiffness.

Description

A regular STAAD P-Delta Analysis performs a first order linear analysis and obtains a set of joint forces from member/plates based on the large P-Delta effect. These forces are added to the original load vector. A second analysis is then performed on this updated load vector (5 to 10 iterations will usually be sufficient).

In the new P-Delta KG Analysis, that is with the Kg option selected, the effect of the axial stress after the first analysis is used to modify the stiffness of the member/plates. A second analysis is then performed using the original load vector. Large & small P-Delta effects are always included (1 or 2 iterations will usually be sufficient).

The KG option is activated by selecting the option on the P-Delta Analysis dialog thus:-

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PDELTA KG PRINT … Command solves [K + Kg] {di} = {F} In one iteration. This method can be more accurate, however it needs to form the stiffness matrix and factorize it on every iteration for every load

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14. P-Delta analysis including Small Delta

Purpose A regular STAAD P-Delta Analysis can now account for the small P-Delta effect whilst performing a P-Delta analysis.

Description

Without the Small Delta option, i.e. a regular STAAD P-Delta analysis, STAAD performs a first order linear analysis and obtains a set of joint forces, from members/plates based on the large P-Delta effect, which are then added to the original load vector. A second analysis is then performed on this updated load vector.

With the Small Delta option selected, both the large & small P-Delta effects are included in calculating the end forces, (5 to 10 iterations will usually be sufficient).

The option is activated by selecting the option on the P-Delta Analysis dialog thus:-

PDELTA 10 ANALYSIS SMALLDELTA PRINT This adds the Pdelta effect due to column bending to the Pdelta effect due to horizontal displacement of columns. Usually the additional Pdelta effect is small. However some new codes require the SMALLDELTA effect. With this command it is important to have 5 to 20 iterations specified. The following equation is solved iteratively. [K] {di+1} = {F} - [Kg] {di} This method only factorizes the matrix once for all cases.

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15. Hands on Exercise 2 - P-Delta analysis Model the simple 10 storey building as below and find out the difference in max deflection between the linear & P-Delta analysis. Assume 0.4 X 0.3m concrete sections for all the members. Three primary load cases Vz, Dead load is 3 kN/m^2 plus selfweight, Live load is 2 kN/m^2 and wind load is 1 kN/m^2 up to a height of 20m and 1.2 kN/m^2 thereafter. Use the Auto Load combination feature in STAAD.Pro to automatically combine the load cases with REPEAT LOADS.

Part of the input file is shown below, STAAD SPACE INPUT WIDTH 79

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UNIT METER KN JOINT COORDINATES ……………………… ……………………. MEMBER INCIDENCES ……………………. ………………… DEFINE MATERIAL START ISOTROPIC CONCRETE E 2.17185e+007 POISSON 0.17 DENSITY 23.5616 ALPHA 1e-005 DAMP 0.05 END DEFINE MATERIAL MEMBER PROPERTY AMERICAN 1 TO 400 PRIS YD 0.4 ZD 0.3 CONSTANTS MATERIAL CONCRETE MEMB 1 TO 400 SUPPORTS 1 TO 4 45 TO 48 89 TO 92 133 TO 136 FIXED DEFINE WIND LOAD TYPE 1 INT 1 1.2 HEIG 20 40 LOAD 1 LOADTYPE Dead TITLE LOAD CASE 1 SELFWEIGHT Y -1 FLOOR LOAD YRANGE 4 40 FLOAD -3 GY LOAD 2 LOADTYPE Live TITLE LOAD CASE 2 FLOOR LOAD YRANGE 4 40 FLOAD -2 GY LOAD 3 LOADTYPE Wind TITLE LOAD CASE 3 WIND LOAD X 1 TYPE 1 YR 0 40 LOAD 4 Generated British BS 8110 1 REPEAT LOAD 1 1.4 2 1.6 LOAD 5 Generated British BS 8110 2 REPEAT LOAD 1 1.4 3 1.4 LOAD 6 Generated British BS 8110 3 REPEAT LOAD 1 1.2 2 1.2 3 1.2 *PERFORM ANALYSIS *PDELTA ANALYSIS CONVERGE *PDELTA KG 2 ANALYSIS *PDELTA 10 ANALYSIS SMALLDELTA PDELTA KG 2 ANALYSIS SMALLDELTA FINISH

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Answer : Analysis Max Deflection

(mm) Max support Moment

(kN-M) Linear (PERFORM ANALYSIS)

95.14 116.65

P-Delta CONVERGE 99.77 122.5 P-Delta with KG 99.4 121.32 P-Delta with small delta 100.27 122.1 P-Delta with KG & small delta

99.4 121.32

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16. Buckling Load analysis

Purpose STAAD.Pro 2007 can now identify the factor by which the loads in the selected load case should be increased (or decreased if less than 1) such that Euler buckling would occur.

Description – Basic Solver

By including the command PERFORM BUCKLING ANALYSIS, the program will perform a P-Delta analysis including Kg Stiffening (geometric stiffness of members & plates) due to large & small P-Delta effects. If a non-singular stiffness matrix can be created, then buckling has not occurred. Then the load is increased from the last increment repeatedly until buckling does occur. Then the load is decreased halfway back to the prior increment. This bounds the buckling factor between the last 2 increments. Then STAAD proceeds to halve the interval until either the change between increments is 0.1% of each other, or the specified number of increments has been exceeded. The resulting factor is reported in the output file. The buckling deformed shape is simply the deformed shape from a static analysis with the near buckling load applied. This could appear more like a crushing, small displacement shape rather than a buckling mode shape. 15+ iterations are recommended. Buckling will be applied to all primary cases.

The option is activated using the new option in the Analysis/Print dialog thus:-

The results of the Buckling analysis are presented in the output file thus:-

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For a full description of the updated analysis commands see section 5.37 Analysis Specification in the Technical Reference Manual.

Description – Advanced Solver

This buckling method is automatically activated if an Advanced Analysis license is available. When using the Advanced Solver, the corresponding ‘buckling modes’ are included in the output file.

The option is activated using the new option in the Analysis/Print dialog thus:-

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The program performs a P-Delta analysis including Kg Stiffening (geometric stiffness of members & plates) due to large & small P-Delta effects.

The eigensolution,

| [K] – BF [Kg]|=0

is solved for the buckling factors and buckled mode shapes. The first 4 buckling factors and buckled shapes are calculated and included in the output file :-

The buckling modes and shapes are available to be viewed in the Post Processing Mode in a new Buckling Page.

This page includes both a Buckling Factors table:-

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And a Buckling Modes table:-

Only the primary load case just prior to the PERFORM BUCKLING command is used. The number of iterations entered is ignored. The buckling factor result is reported in the output file and in post processing.

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17. Modal Analysis including stress stiffening effect of KG Matrix

Purpose

STAAD.Pro can include the stress stiffening effect (geometric stiffness) based on the axial member forces/plate in-plane stresses from a selected load case when calculating the modes & frequencies of a structure.

Description

Position the selected load case from which the axial stresses are to be used to modify the stiffness matrix, such that it is the last static case before the dynamic case which is in turn immediately followed by a PDELTA KG command.

The dynamic load case should contain mass data followed by one of the following:-

a) A MODAL CALCULATION REQUESTED command.

b) A response spectrum definition, i.e. set of SPECTRUM command data.

c) A reference to a time history definition, i.e. include TIME LOAD commands.

d) Valid Steady State data.

Example

...

LOAD 1 LOADTYPE None TITLE LOAD CASE 1

******* This is static loading case from which the “axial stress” is

******* used to compute the stress stiffening effects (P-Delta)

******* This case will be solved as a PDelta case with large & small ******* P-Delta effects

SELFWEIGHT Y -1.0

JOINT LOAD

2 3 6 7 9 TO 12 FY -3

LOAD 2 LOADTYPE None TITLE LOAD CASE 2

******* Enter masses in weight units

SELFWEIGHT X 1

SELFWEIGHT Y 1

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SELFWEIGHT Z 1

JOINT LOAD

2 3 6 7 9 TO 12 FX 10 FY 10 FZ 10

******* Declare this to be a modes/freq analysis

******* Note that dynamic cases use the factored matrix from the last ******* load case; which is a (K+Kg) case

MODAL CALCULATION REQUESTED

PDELTA KG ANALYSIS

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18. Non Linear Cable/Truss Analysis When all of the members, elements and support springs are linear except for cable and/or preloaded truss members, then this analysis type may be used. This analysis is based on applying the load in steps with equilibrium iterations to convergence at each step. Iteration continues at each step until the change in deformations is small before proceeding to the next step. If not converged, then the solution is stopped. The user can then select more steps or modify the structure and rerun. Structures can be artificially stabilized during the first few load steps in case the structure is initially unstable (in the linear, small displacement, static theory sense). The user has control of the number of steps, the maximum number of iterations per step, the convergence tolerance, the artificial stabilizing stiffness, and the minimum amount of stiffness remaining after a cable sags. This method assumes small displacement theory for all members/trusses/elements other than cables & preloaded trusses. The cables and preloaded trusses can have large displacement and moderate/large strain. Pretension is the force necessary to stretch the cable/truss from its unstressed length to enable it to fit between the two end joints. Alternatively, you may enter the unstressed length for cables. The analysis sequence is as follows:

• Compute the unstressed length of the nonlinear members based on joint coordinates, pretension, and temperature.

• Member/Element/Cable stiffness is formed. Cable stiffness is from EA/L and the sag formula plus a geometric stiffness based on current tension.

• Assemble and solve the global matrix with the percentage of the total applied load used for this load step.

• Perform equilibrium iterations to adjust the change in directions of the forces in the nonlinear cables, so that the structure is in static equilibrium in the deformed position. If force changes are too large or convergence criteria not met within 15 iterations then stop the analysis.

• Go to step 2 and repeat with a greater percentage of the applied load. The nonlinear members will have an updated orientation with new tension and sag effects.

• After 100% of the applied load has converged then proceed to compute member forces, reactions, and static check. Note that the static check is not exactly in balance due to the displacements of the applied static equivalent joint loads.

The load cases in a non linear cable analysis must be separated by the CHANGE command and PERFORM CABLE ANALYSIS command. The SET NL command must be provided to specify the total number of primary load cases. There may not be any Multi-linear springs, compression only, PDelta, NONLINEAR or dynamic cases.

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Also for cables and preloaded trusses:

• Do not use Member Offsets. • Do not include the end joints in Master/Slave command. • Do not connect to inclined support joints. • Y direction must be up. • Do not impose displacements. • Do not use Support springs in the model. • Applied loads do not change global directions due to displacements. • Do not apply Prestress load, Fixed end load. • Do not use Load Combination command to combine cable analysis results.

Use a primary case with Repeat Load instead. Syntax

Steps = Number of load steps. The applied loads will be applied gradually in this many steps. Each step will be iterated to convergence. Default is 145. The f1 value, if entered, should be in the range 5 to 145. Eq-iterations = Maximum number of iterations permitted in each load step. Default is 15. Should be in the range of 10 to 30. Eq-tolerance = The convergence tolerance for the above iterations. Default is 0.0005. Sag minimum = Cables (not trusses) may sag when tension is low. This is accounted for by reducing the E value. Sag minimum may be between 1.0 (no sag E reduction) and 0.0 (full sag E reduction). Default is 1.0. If f4 is entered, it should be in the range 0.7 to 1.0 for a relatively simple process. As soon as SAGMIN becomes less than 0.95 the possibility exists that a converged solution will not be achieved without increasing the steps or the pretension loads. The Eq iterations may need to be 30 or more. The Eq tolerance may need to be greater or smaller. Stability stiffness = A stiffness matrix value, f5, that is added to the global matrix at each translational direction for joints connected to cables and nonlinear trusses for the first f6 load steps. The amount added linearly decreases with each of the f6 load steps (f6 is 1 if omitted). If f5 entered, use 0.0 to 2.

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Default is 0. For f6 use a max value of 145. K small stiffness = A stiffness matrix value, f7, that is added to the global matrix at each translational direction for joints connected to cables and nonlinear trusses for every load step. If entered, use 0.0 to 1.0. Default is 0.0. This parameter alters the stiffness of the structure. Frequently Asked question But would like to know how to arrive at the values for all these parameters ? Answer : There is no direct way to find the values of the parameters. If the default values fail, then try sagmin 0.5 first. If that doesn't work I try 0.7, then 0.8. If any value works then reduce it halfway to last one that failed. If 0.8 doesn't work, then try STABL 0.1 145. Then keep increasing the 0.1 value until it works. If this fails at about 95% to 100%, then try KSMALL of about 0.1 times the last STABL value that you used. If it is allowed try increasing the tension in the MEMBER CABLE command.

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19. Hands on Exercise 3 - Non-Linear Truss analysis Solve the Truss problem as below and find out the max displacement & axial force. Use the American single angle section as below and consider the self weight also.

Answer : Max deflection 243.316mm & axial force 93.606 KN (With self weight command included). Diagrams below are without considering selfweight.

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20. Hands on Exercise 4 - Non-Linear Cable analysis - I Find out the maximum deflection for the structure shown below. Assume Japanese H250X250X9 section for all the platform members and for cables use 32mm dia rods. All are steel.

Answer : Max displacement 68 mm

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21. Hands on Exercise 5 - Non-Linear Cable analysis –II Model, analyse and design the structure as below using the AISC-ASD or BS5950-2000 code. Use 16mm steel rods for the cable members and 50mm dia steel pipe with 10mm thickness for the truss members.

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Reference load case 1 is Dead Load as below.

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Reference load case 2 is Live load as below

Use reference load 1 as your 1st primary load (Dead Load) and Use both the reference loads (DL + LL) as your second load case with suitable factor of safety. i.e Create primary load cases from the reference load cases. Load case 1 (Dead Load) is reference load 1 and Load case 2 (Dead + Live) is reference load 1 + reference load 2 with suitable factor of safety.

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22. Other STAAD features

OpenSTAAD OpenSTAAD is a library of exposed functions allowing engineers access to STAAD.Pro’s internal functions and routines as well as its graphical commands. With OpenSTAAD, any user can practically use any programming language (including C, C++, VB, VBA, FORTRAN, Java and Delphi) to tap into STAAD’s database and seamlessly link input and output data to third-party applications. OpenSTAAD also empowers the STAAD user to create VBA-like macros within the STAAD.Pro environment to perform such tasks as automating repetitive modeling or post-processing tasks or embedding customized design routines. OpenSTAAD allows engineers and other users to link in-house or third-party applications with STAAD.Pro. For example, a user might create a spreadsheet in Excel to analyze and design a circular base plate using support reactions from STAAD. With OpenSTAAD, a simple macro can be written in Excel or within the STAAD environment to retrieve the appropriate STAAD data and automatically link the results. If the STAAD file changes, so will the Excel sheet! With a built-in VBA editor, macros can be written inside STAAD using VBA to create new dialog boxes or menu items which run design codes or specific structural components (like certain connections) that automatically link to STAAD’s familiar reporting tables. A cumbersome export/import link between two or three software is no longer required.

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23. Other STAAD.Pro Optional modules. STAAD.Pro has a number of optional modules. The following is an overview of those modules.

STAAD.beava STAAD.beava, the Bridge Engineering Automated Vehicle Application, is an integrated solution inside the STAAD.Pro environment for calculation of vehicle loads based on BS5400-Part II, AASHTO 2000 & IRC codes for bridge design.

STAAD.foundation STAAD.foundation is an exhaustive analysis, design and drafting solution for a variety of foundations that include isolated and combined footings, mat foundations, pile caps and slab on grade. A part of the STAAD.Pro family of products, STAAD.foundation is a cost-saving downstream application that enables engineers to analyze and design the underlying foundation for the structure they created in STAAD.Pro. STAAD.foundation can automatically absorb the geometry, loads and results from a STAAD.Pro model and accurately design isolated or combined footings, true mat foundations and even perform pile cap arrangements.

Offshore Loading Program A stand alone software which reads the STAAD.Pro input file to calculate the wave loads & transportation loads. Further design can be done using the STAAD.Pro API code. Fully compatible with STAAD.Pro.

Section wizard Section wizard is an invaluable tool for the structural engineer, allowing fast and accurate calculation of section properties of any free-form shape (including torsion & warping constants), retrieval of stress values for custom and assembled shapes, finding equivalent mill sections for general sections and exporting all properties to STAAD.Pro.

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