STAAD.pro Advanced Training Manual

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Advanced Topics in

STAAD.Pro

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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

2000-2006 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.

Sentry Spelling-Checker Engine 1993 Wintertree Software Inc.

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STAAD.Pro

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RAINING

M

ANUAL

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DVANCED TOPICS

A Bentley Solutions Center www.reiworld.com www.bentley.com/staad

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STAAD.Pro is a suite of proprietary computer programs of

Research Engineers, a Bentley Solutions Center. Although every effort has been made to ensure the correctness of these programs, REI will not accept responsibility for any mistake, error or misrepresentation in or as a result of the usage of these programs.

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About STAAD.

Pro

STAAD.Pro is a general purpose structural analysis and design program with applications primarily in the building industry - commercial buildings, bridges and highway structures, industrial structures, chemical plant structures, dams, retaining walls, turbine foundations, culverts and other embedded structures, etc. The program hence consists of the following facilities to enab le this task.

1. Graphical model generation utilities as well as text editor based commands for creating the mathematical model. Beam and column members are represented using lines. Walls, slabs and panel type entities are represented using triangular and quadrilateral finite elements. Solid blocks are represented using brick elements. These utilities allow the user to create the geometry, assign properties, orient cross sections as desired, assign materials like steel, concrete, timber, aluminum, specify supports, apply loads explicitly as well as have the program generate loads, design parameters etc.

2. Analysis engines for performing linear elastic and pdelta analysis, finite element analysis, frequency extraction, and dynamic response (spectrum, time history , steady state, etc.).

3. Design engines for code checking and optimization of steel, aluminum and timber members. Reinforcement calculations for concrete beams, columns, slabs and shear walls. Design of shear and moment connections for steel members.

4. Result viewing, result verification and report generation tools for examining displacement diagrams, bending moment and shear force diagrams, beam, plate and solid stress contours, etc.

5. Peripheral tools for activities like import and export of data from and to ot her widely accepted formats, links with other popular softwares for niche areas like reinforced and prestressed concrete slab design, footing design, steel connection design, etc.

6. A library of exposed functions called OpenSTAAD which allows users to access STAAD.Pro’s internal functions and routines as well as its graphical commands to tap into STAAD’s database and link input and output data to third -party software written using languages like C, C++, VB, VBA, FORTRAN, Java, Delphi, etc. Thus, OpenSTAAD allows users to link in-house or third-party applications with STAAD.Pro.

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About the STAAD.

Pro

Documentation

The documentation for STAAD.Pro consists of a set of manuals as described below. These manuals are normally provided only in the electronic form at, with perhaps some exceptions such as the Getting Started Manual which may be supplied as a printed book to first time and new-version buyers.

All the manuals can be accessed from the Help facilities of STAAD.Pro. Users who wish to obtain a printed co py of the books may contact Research Engineers. REI also supplies the manuals in the PDF format at no cost for those who wish to print them on their own. See the back cover of this book for addresses and phone numbers.

Getting Started and Tutorials : This manual contains information on the contents of

the STAAD.Pro package, computer system requirements, installation process, copy protection issues and a description on how to run the programs in the package. Tutorials that provide detailed and step -by-step explanation on using the programs are also provided.

Examples Manual

This book offers examples of various problems that can be solved using the STAAD engine. The examples represent various structural analyses and design problems commonly encountered by structural engineers.

Graphical Environment

This document contains a detailed description of the Graphical User Interface (GUI) of STAAD.Pro. The topics covered include model generation, structural analysis and design, result verification, and report gene ration.

Technical Reference Manual

This manual deals with the theory behind the engineering calculations made by the STAAD engine. It also includes an explanation of the commands available in the STAAD command file.

International Design Codes

This document contains information on the various Concrete, Steel, and Aluminum design codes, of several countries, that are implemented in STAAD.

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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.

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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.

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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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

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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.

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.

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STAAD.Pro Training Manual – Advanced Topics

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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 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.

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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.

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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; 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

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

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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.

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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 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 :

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***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 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.

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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.

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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

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

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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?

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.

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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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Seismic Analysis Using

UBC And IBC Codes

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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

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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

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.

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STAAD.Pro Training Manual – Advanced Topics 3 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

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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).

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

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6 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

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

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program to analyze the structure for loads from cases 1 and 3 acting simultaneously.

PERFORM ANALYSIS PRINT STATICS CHECK CHANGE

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

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

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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

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 IBC 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.

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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 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 to use this.

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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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Calculating Mode Shapes, Frequencies

And

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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.

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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 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

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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.

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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.

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

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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; 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;

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6 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:

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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.

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 -

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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.

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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.

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

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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.

Q q w GW i j,i j,i j 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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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.

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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.

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.

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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

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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. 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.)

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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"

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.

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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.

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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?

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.

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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.

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

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STAAD.Pro Training Manual – Advanced Topics 9 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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Seismic Analysis Using

UBC And IBC Codes

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Calculating Mode Shapes, Frequencies

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