technical reference 2002

STAAD.Pro 2002

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STAAD.Pro 2002

7(&+1,&$/5()(5(1&(0$18$/

a division of netGuru, Inc.

www.reiworld.comwww.reel.co.uk

STAAD.Pro 2002 is a proprietary computer program ofResearch Engineers, Intl. (REI), a division of netGuru, Inc.Although every effort has been made to ensure the correctnessof this program, REI will not accept responsibility for anymistake, error or misrepresentation in or as a result of the usageof this program.

RELEASE 2002

CopyrightResearch Engineers, Intl.Division of netGuru, Inc.

Published April, 2002

STAAD.Pro 2002 is a proprietary computer program ofResearch Engineers, Intl. (REI), a division of netGuru, Inc.Although every effort has been made to ensure the correctnessof this program, REI will not accept responsibility for anymistake, error or misrepresentation in or as a result of the usageof this program.

RELEASE 2002

CopyrightResearch Engineers, Intl.Division of netGuru, Inc.

Published April, 2002

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STAAD.Pro is a widely used software for structural analysis and designfrom Research Engineers International.

The STAAD.Pro software consists of the following:

The STAAD.Pro Graphical User Interface (GUI): It is used to generate themodel, which can then be analyzed using the STAAD engine. Afteranalysis and design is completed, the GUI can also be used to view theresults graphically.

The STAAD analysis and design engine: It is a general-purposecalculation engine for structural analysis and integrated Steel, Concrete,Timber and Aluminum design.

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STAAD.Pro is a widely used software for structural analysis and designfrom Research Engineers International.

The STAAD.Pro software consists of the following:

The STAAD.Pro Graphical User Interface (GUI): It is used to generate themodel, which can then be analyzed using the STAAD engine. Afteranalysis and design is completed, the GUI can also be used to view theresults graphically.

The STAAD analysis and design engine: It is a general-purposecalculation engine for structural analysis and integrated Steel, Concrete,Timber and Aluminum design.

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The documentation for STAAD.Pro consists of a set of manuals as describedbelow.

Getting Started and Tutorials : This manual contains information on thecontents of the STAAD.Pro package, computer system requirements, installationprocess, copy protection issues and a description on how to run the programs inthe package. Tutorials that provide detailed and step-by-step explanation onusing the programs are also provided.

Examples : This book offers examples of various problems that can be solvedusing the STAAD engine. The examples represent various structural analysesand design problems commonly encountered by structural engineers.

Graphical Environment : This manual contains a detailed description of theGraphical User Interface (GUI) of STAAD.Pro. The topics covered includemodel generation, structural analysis and design, result verification, and reportgeneration. This manual is generally provided only in the electronic form andcan be accessed from the Help facilities of STAAD.Pro. Users who wish toobtain a printed copy of this book may contact Research Engineers. See the backcover of this book for addresses and phone numbers.

Technical Reference : This manual deals with the theory behind theengineering calculations made by the STAAD engine. It also includes anexplanation of the commands available in the STAAD command file.

International Design Codes : This document contains information on thevarious Concrete, Steel, and Aluminum design codes, of several countries, thatare implemented in STAAD. Generally, this book is supplied only to those userswho purchase the international codes utilities with STAAD.Pro.

OpenSTAAD : This document contains information on the library of functionswhich enable users to access STAAD.Pros input and results data for importinginto other applications.

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RFXPHQWDWLRQ

The documentation for STAAD.Pro consists of a set of manuals as describedbelow.

Getting Started and Tutorials : This manual contains information on thecontents of the STAAD.Pro package, computer system requirements, installationprocess, copy protection issues and a description on how to run the programs inthe package. Tutorials that provide detailed and step-by-step explanation onusing the programs are also provided.

Examples : This book offers examples of various problems that can be solvedusing the STAAD engine. The examples represent various structural analysesand design problems commonly encountered by structural engineers.

Graphical Environment : This manual contains a detailed description of theGraphical User Interface (GUI) of STAAD.Pro. The topics covered includemodel generation, structural analysis and design, result verification, and reportgeneration. This manual is generally provided only in the electronic form andcan be accessed from the Help facilities of STAAD.Pro. Users who wish toobtain a printed copy of this book may contact Research Engineers. See the backcover of this book for addresses and phone numbers.

Technical Reference : This manual deals with the theory behind theengineering calculations made by the STAAD engine. It also includes anexplanation of the commands available in the STAAD command file.

International Design Codes : This document contains information on thevarious Concrete, Steel, and Aluminum design codes, of several countries, thatare implemented in STAAD. Generally, this book is supplied only to those userswho purchase the international codes utilities with STAAD.Pro.

OpenSTAAD : This document contains information on the library of functionswhich enable users to access STAAD.Pros input and results data for importinginto other applications.

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1.1 Introduction 1 - 11.2 Input Generation 11.3 Types of Structures 21.4 Unit Systems 31.5 Structure Geometry and Coordinate Systems 4

1.5.1 Global Coordinate System 41.5.2 Local Coordinate System 61.5.3 Relationship Between Global & Local Coordinates 10

1.6 Finite Element Information 171.6.1 Plate/Shell Element 171.6.2 Solid Element 30

1.7 Member Properties 331.7.1 Prismatic Properties 331.7.2 Built-In Steel Section Library 351.7.3 User Provided Steel Table 351.7.4 Tapered Sections 361.7.5 Assign Command 361.7.6 Curved Members 36

1.8 Member/Element Release 361.9 Truss/Tension/Compression - Only Members 371.10 Tension/Compression - Only Springs 371.11 Cable Members 381.12 Member Offsets 411.13 Material Constants 411.14 Supports 421.15 Master/Slave Joints 431.16 Loads 43

1.16.1 Joint Load 441.16.2 Member Load 441.16.3 Area Load / Floor Load 451.16.4 Fixed End Member Load 471.16.5 Prestress and Poststress Member Load 471.16.6 Temperature/Strain Load 491.16.7 Support Displacement Load 501.16.8 Loading on Elements 50

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1.1 Introduction 1 - 11.2 Input Generation 11.3 Types of Structures 21.4 Unit Systems 31.5 Structure Geometry and Coordinate Systems 4

1.5.1 Global Coordinate System 41.5.2 Local Coordinate System 61.5.3 Relationship Between Global & Local Coordinates 10

1.6 Finite Element Information 171.6.1 Plate/Shell Element 171.6.2 Solid Element 30

1.7 Member Properties 331.7.1 Prismatic Properties 331.7.2 Built-In Steel Section Library 351.7.3 User Provided Steel Table 351.7.4 Tapered Sections 361.7.5 Assign Command 361.7.6 Curved Members 36

1.8 Member/Element Release 361.9 Truss/Tension/Compression - Only Members 371.10 Tension/Compression - Only Springs 371.11 Cable Members 381.12 Member Offsets 411.13 Material Constants 411.14 Supports 421.15 Master/Slave Joints 431.16 Loads 43

1.16.1 Joint Load 441.16.2 Member Load 441.16.3 Area Load / Floor Load 451.16.4 Fixed End Member Load 471.16.5 Prestress and Poststress Member Load 471.16.6 Temperature/Strain Load 491.16.7 Support Displacement Load 501.16.8 Loading on Elements 50

1.17 Load Generator 511.17.1 Moving Load Generator 1 - 521.17.2 UBC and IBC Seismic Load Generator 1 - 521.17.3 Wind Load Generator 53

1.18 Analysis Facilities 531.18.1 Stiffness Analysis 541.18.2 Second Order Analysis 58

1.18.2.1 P-Delta Analysis 581.18.2.2 Non Linear Analysis 601.18.2.3 Multi-Linear Springs 611.18.2.4 Tension / Compression Only 621.18.2.5 Nonlinear Cable/Truss 63

1.18.3 Dynamic Analysis 641.19 Member End Forces 69

1.19.1 Secondary Analysis 741.19.2 Member Forces at Intermediate Sections 741.19.3 Member Displacements at Intermediate Sections 741.19.4 Member Stresses at Specified Sections 751.19.5 Force Envelopes 75

1.20 Multiple Analyses 761.21 Steel/Concrete/Timber Design 771.22 Footing Design 771.23 Printing Facilities 771.24 Plotting Facilities 781.25 Miscellaneous Facilities 781.26 Post Processing Facilities 78

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2.1 Design Operations 2 - 12.2 Member Properties 2

2.2.1 Built - in Steel Section Library 22.3 Allowables per AISC Code 6

2.3.1 Tension Stress 62.3.2 Shear Stress 62.3.3 Stress Due To Compression 72.3.4 Bending Stress 72.3.5 Combined Compression and Bending 82.3.6 Singly Symmetric Sections 92.3.7 Torsion per Publication T114 92.3.8 Design of Web Tapered Sections 11

2.4 Design Parameters 112.5 Code Checking 122.6 Member Selection 12

2.6.1 Member Selection by Optimization 132.6.2 Deflection Check With Steel Design 13

2.7 Truss Members 14

1.17 Load Generator 511.17.1 Moving Load Generator 1 - 521.17.2 UBC and IBC Seismic Load Generator 1 - 521.17.3 Wind Load Generator 53

1.18 Analysis Facilities 531.18.1 Stiffness Analysis 541.18.2 Second Order Analysis 58

1.18.2.1 P-Delta Analysis 581.18.2.2 Non Linear Analysis 601.18.2.3 Multi-Linear Springs 611.18.2.4 Tension / Compression Only 621.18.2.5 Nonlinear Cable/Truss 63

1.18.3 Dynamic Analysis 641.19 Member End Forces 69

1.19.1 Secondary Analysis 741.19.2 Member Forces at Intermediate Sections 741.19.3 Member Displacements at Intermediate Sections 741.19.4 Member Stresses at Specified Sections 751.19.5 Force Envelopes 75

1.20 Multiple Analyses 761.21 Steel/Concrete/Timber Design 771.22 Footing Design 771.23 Printing Facilities 771.24 Plotting Facilities 781.25 Miscellaneous Facilities 781.26 Post Processing Facilities 78

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2.1 Design Operations 2 - 12.2 Member Properties 2

2.2.1 Built - in Steel Section Library 22.3 Allowables per AISC Code 6

2.3.1 Tension Stress 62.3.2 Shear Stress 62.3.3 Stress Due To Compression 72.3.4 Bending Stress 72.3.5 Combined Compression and Bending 82.3.6 Singly Symmetric Sections 92.3.7 Torsion per Publication T114 92.3.8 Design of Web Tapered Sections 11

2.4 Design Parameters 112.5 Code Checking 122.6 Member Selection 12

2.6.1 Member Selection by Optimization 132.6.2 Deflection Check With Steel Design 13

2.7 Truss Members 14

2.8 Unsymmetric Sections 142.9 Composite Beam Design as per AISC-ASD 192.10 Plate Girders 2 - 212.11 Tabulated Results of Steel Design 2 - 212.12 Weld Design 232.13 Steel Design per AASHTO Specifications 26

2.13.1 General Comments 262.13.2 Allowable Stresses per AASHTO Code 272.13.3 Stability Requirements per AASHTO Code 302.13.4 Minimum Metal Thickness Requirement 30

2.14 Steel Design per AISC/LRFD Specification 302.14.1 General Comments 302.14.2 LRFD Fundamentals 312.14.3 Analysis Requirements 332.14.4 Section Classification 332.14.5 Axial Tension 332.14.6 Axial Compression 342.14.7 Flexural Design Strength 352.14.8 Combined Axial Force And Bending 352.14.9 Design for Shear 362.14.10 Design Parameters 362.14.11 Code Checking and Member Selection 362.14.12 Tabulated Results of Steel Design 37

2.15 Steel Design per AISI Cold Formed Specification 392.15.1 General 392.15.2 Design Procedure 42

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3.1 Design Operations 3 - 13.2 Section Types for Concrete Design 13.3 Member Dimensions 23.4 Design Parameters 33.5 Slenderness Effects and Analysis Consideration 33.6 Beam Design 73.7 Column Design 113.8 Slab/Wall Design 14

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4.1 Timber Design 4 - 14.2 Design Operations 24.3 Input Specification 44.4 Code Checking 64.5 Orientation of Lamination 64.6 Member Selection 7

2.8 Unsymmetric Sections 142.9 Composite Beam Design as per AISC-ASD 192.10 Plate Girders 2 - 212.11 Tabulated Results of Steel Design 2 - 212.12 Weld Design 232.13 Steel Design per AASHTO Specifications 26

2.13.1 General Comments 262.13.2 Allowable Stresses per AASHTO Code 272.13.3 Stability Requirements per AASHTO Code 302.13.4 Minimum Metal Thickness Requirement 30

2.14 Steel Design per AISC/LRFD Specification 302.14.1 General Comments 302.14.2 LRFD Fundamentals 312.14.3 Analysis Requirements 332.14.4 Section Classification 332.14.5 Axial Tension 332.14.6 Axial Compression 342.14.7 Flexural Design Strength 352.14.8 Combined Axial Force And Bending 352.14.9 Design for Shear 362.14.10 Design Parameters 362.14.11 Code Checking and Member Selection 362.14.12 Tabulated Results of Steel Design 37

2.15 Steel Design per AISI Cold Formed Specification 392.15.1 General 392.15.2 Design Procedure 42

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3.1 Design Operations 3 - 13.2 Section Types for Concrete Design 13.3 Member Dimensions 23.4 Design Parameters 33.5 Slenderness Effects and Analysis Consideration 33.6 Beam Design 73.7 Column Design 113.8 Slab/Wall Design 14

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4.1 Timber Design 4 - 14.2 Design Operations 24.3 Input Specification 44.4 Code Checking 64.5 Orientation of Lamination 64.6 Member Selection 7

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5.1 Command Language Conventions 5 - 25.1.1 Elements of The Commands 35.1.2 Command Formats 55.1.3 Listing of Members by Specification of Global Ranges 8

5.2 Problem Initiation And Title 5 - 105.3 Unit Specification 125.4 Input/Output Width Specification 145.5 Set Command Specification 155.6 Separator Command 195.7 Page New Command 205.8 Page Length/Eject Command 215.9 Ignore Specifications 225.10 No Design Specification 235.11 Joint Coordinates Specification 245.12 Member Incidences Specification 295.13 Element Incidence Specification 335.14 Element Mesh Generation 375.15 Redefinition of Joint and Member Numbers 435.16 Listing of Members/Joints by Specification of GROUPS 455.17 Rotation of Structure Geometry 485.18 Inactive/Delete Specification 495.19 User Steel Table Specification 515.20 Member Property Specification 60

5.20.1 Specifying Properties from Steel Table 625.20.2 Prismatic Property Specification 655.20.2.1 Prismatic Tapered Tube Property Specification 665.20.3 Tapered Member Specification 685.20.4 Property Specification from User Provided Table 695.20.5 Assign Profile Specification 705.20.6 Examples of Member Property Specification 715.20.7 Curved Member Specification 73

5.21 Element Property Specification 775.22 Member/Element Releases 78

5.22.1 Member Release Specification 795.22.2 Element Release Specification 82

5.23 Member Truss/Cable/Tension/Compression Specification 845.23.1 Member Truss Specification 855.23.2 Member Cable Specification 865.23.3 Member Tension/Compression Specification 895.23.4 Spring Tension/Compression Specification 95

5.24 Element Plane Stress and Inplane Rotation Specification 1005.25 Member Offset Specification 1025.26 Constant Specification

5.26.1 Definition of Material Constants 104

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5.1 Command Language Conventions 5 - 25.1.1 Elements of The Commands 35.1.2 Command Formats 55.1.3 Listing of Members by Specification of Global Ranges 8

5.2 Problem Initiation And Title 5 - 105.3 Unit Specification 125.4 Input/Output Width Specification 145.5 Set Command Specification 155.6 Separator Command 195.7 Page New Command 205.8 Page Length/Eject Command 215.9 Ignore Specifications 225.10 No Design Specification 235.11 Joint Coordinates Specification 245.12 Member Incidences Specification 295.13 Element Incidence Specification 335.14 Element Mesh Generation 375.15 Redefinition of Joint and Member Numbers 435.16 Listing of Members/Joints by Specification of GROUPS 455.17 Rotation of Structure Geometry 485.18 Inactive/Delete Specification 495.19 User Steel Table Specification 515.20 Member Property Specification 60

5.20.1 Specifying Properties from Steel Table 625.20.2 Prismatic Property Specification 655.20.2.1 Prismatic Tapered Tube Property Specification 665.20.3 Tapered Member Specification 685.20.4 Property Specification from User Provided Table 695.20.5 Assign Profile Specification 705.20.6 Examples of Member Property Specification 715.20.7 Curved Member Specification 73

5.21 Element Property Specification 775.22 Member/Element Releases 78

5.22.1 Member Release Specification 795.22.2 Element Release Specification 82

5.23 Member Truss/Cable/Tension/Compression Specification 845.23.1 Member Truss Specification 855.23.2 Member Cable Specification 865.23.3 Member Tension/Compression Specification 895.23.4 Spring Tension/Compression Specification 95

5.24 Element Plane Stress and Inplane Rotation Specification 1005.25 Member Offset Specification 1025.26 Constant Specification

5.26.1 Definition of Material Constants 104

5.26.2 Constant Specification 1065.26.3 Modal Damping Information 5 - 112

5.27 Support Specifications 5 - 1145.27.1 Global Support Specification 1155.27.2 Inclined Support Specification 1185.27.3 Automatic Spring Support Generator for Foundations 1205.27.4 Multi-linear Spring Support Specification 124

5.28 Master/Slave Specification 1285.29 Draw Specifications 1295.30 Cut-Off Frequency, Mode Shapes or Time 1305.31 Definition of Load Systems 131

5.31.1 Definition of Moving Load System 1325.31.2 UBC Definitions 136

5.31.2.1 UBC 1997 Load Definition 1375.31.2.2 UBC 1994 or 1985 Load Definition 1415.31.2.3 Colombian Seismic Load 1455.31.2.4 Japanese Seismic Load 1485.31.2.5 Definition of Lateral Seismic Load per IS:1893 1515.31.2.6 IBC 2000 Load Definition 154

5.31.3 Definition of Wind Load 1595.31.4 Definition of Time History Load 162

5.32 Loading Specifications 1685.32.1 Joint Load Specification 1695.32.2 Member Load Specification 1705.32.3 Element Load Specification 1735.32.4 Area Load/Floor Load Specification 1765.32.5 Prestress Load Specification 1825.32.6 Temperature Load Specification 1895.32.7 Fixed-End Load Specification 1915.32.8 Support Joint Displacement Specification 1925.32.9 Selfweight Load Specification 1955.32.10 Dynamic Loading Specification 196

5.32.10.1 Response Spectrum Specification 1975.32.10.2 Application of Time Varying Load for Response

History Analysis 2025.32.11 Repeat Load Specification 2045.32.12 Generation of Loads 206

Generation of Moving Loads 206 Generation of UBC / IBC Loads 208 Generation of Wind Loads 214

5.33 Rayleigh Frequency Calculation 2175.34 Modal Calculation Command 2195.35 Load Combination Specification 2205.36 Calculation of Problem Statistics 2245.37 Analysis Specification 2255.38 Change Specification 2295.39 Load List Specification 231

5.26.2 Constant Specification 1065.26.3 Modal Damping Information 5 - 112

5.27 Support Specifications 5 - 1145.27.1 Global Support Specification 1155.27.2 Inclined Support Specification 1185.27.3 Automatic Spring Support Generator for Foundations 1205.27.4 Multi-linear Spring Support Specification 124

5.28 Master/Slave Specification 1285.29 Draw Specifications 1295.30 Cut-Off Frequency, Mode Shapes or Time 1305.31 Definition of Load Systems 131

5.31.1 Definition of Moving Load System 1325.31.2 UBC Definitions 136

5.31.2.1 UBC 1997 Load Definition 1375.31.2.2 UBC 1994 or 1985 Load Definition 1415.31.2.3 Colombian Seismic Load 1455.31.2.4 Japanese Seismic Load 1485.31.2.5 Definition of Lateral Seismic Load per IS:1893 1515.31.2.6 IBC 2000 Load Definition 154

5.31.3 Definition of Wind Load 1595.31.4 Definition of Time History Load 162

5.32 Loading Specifications 1685.32.1 Joint Load Specification 1695.32.2 Member Load Specification 1705.32.3 Element Load Specification 1735.32.4 Area Load/Floor Load Specification 1765.32.5 Prestress Load Specification 1825.32.6 Temperature Load Specification 1895.32.7 Fixed-End Load Specification 1915.32.8 Support Joint Displacement Specification 1925.32.9 Selfweight Load Specification 1955.32.10 Dynamic Loading Specification 196

5.32.10.1 Response Spectrum Specification 1975.32.10.2 Application of Time Varying Load for Response

History Analysis 2025.32.11 Repeat Load Specification 2045.32.12 Generation of Loads 206

Generation of Moving Loads 206 Generation of UBC / IBC Loads 208 Generation of Wind Loads 214

5.33 Rayleigh Frequency Calculation 2175.34 Modal Calculation Command 2195.35 Load Combination Specification 2205.36 Calculation of Problem Statistics 2245.37 Analysis Specification 2255.38 Change Specification 2295.39 Load List Specification 231

5.40 Section Specification 2335.41 Print Specifications (includes CG and Story Drift) 2355.42 Print Section Displacement 5 - 2425.43 Print Force Envelope Specification 5 - 2445.44 Post Analysis Printer Plot Specifications 2465.45 Post Analysis Graphics Display 2475.46 Size Specification 2485.47 Steel Design Specifications 250

5.47.1 Parameter Specifications 2515.47.2 Code Checking Specification 2535.47.3 Member Selection Specification 2545.47.4 Member Selection by Optimization 2555.47.5 Weld Selection Specification 256

5.48 Group Specification 2575.49 Steel Take Off Specification 2595.50 Timber Design Specifications 260

5.50.1 Timber Design Parameter Specifications 2615.50.2 Code Checking Specification 2625.50.3 Member Selection Specification 263

5.51 Concrete Design Specifications 2645.51.1 Design Initiation 2655.51.2 Concrete Design-Parameter Specification 2665.51.3 Concrete Design Command 2675.51.4 Concrete Take Off Command 2685.51.5 Concrete Design Terminator 269

5.52 Footing Design Specifications 2705.52.1 Design Initiation 2735.52.2 Footing Design Parameter Specification 2745.52.3 Footing Design Command 2755.52.4 Footing Design Terminator 277

5.53 End Run Specification 278

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6.6.4.2 Tapered Beam Elements 126.6.4.3 Pipe and Elbow Beam Elements 126.6.4.4 Beam Element End Releases 126.6.4.5 Tension - Only Elements 6 - 136.6.4.6 Cable Elements 6 - 136.6.4.7 Beam Element Offsets 13

6.7 Rigid System of Nodes STARDYNE 136.8 Material Constants STARDYNE 146.9 Supports STARDYNE 156.10 Loads (STARDYNE) 15

6.10.1 Node Load 156.10.2 Element Loads 166.10.3 Node Temperature Load 176.10.4 Support Displacement Specification 18

6.11 STARDYNE Analysis Capabilities 186.11.1 STARDYNE Static Analysis 196.11.2 STARDYNE Second Order Static Analysis 236.11.3 STARDYNE Dynamic Response Analysis 26

6.11.3.1 STARDYNE Response Spectrum Analysis(Dynre4) 30

6.11.3.2 STARDYNE Linear Time History ResponseAnalysis (Dynre1) 31

6.12 References (STARDYNE) 34

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7.1 STAPLE Command Language Conventions 7 - 37.1.1 Elements of the Commands 47.1.2 Command Formats 5

7.2 STAPLE Commands 97.2.1 STAPLE Initiation 97.2.2 UNIT Specification 107.2.3 The OPEN Command 127.2.4 The FOR Command 137.2.5 The WRITE and FORMAT Commands 15

7.2.5.1 Write Commands 167.2.5.2 Format Specification 24

7.2.6 The SORT Command 287.2.7 The EXECUTE Command 337.2.8 The CALL Command 367.2.9 The End Script Language Command 38

7.3 Graphics Commands in STAPLE 39

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6.6.4.2 Tapered Beam Elements 126.6.4.3 Pipe and Elbow Beam Elements 126.6.4.4 Beam Element End Releases 126.6.4.5 Tension - Only Elements 6 - 136.6.4.6 Cable Elements 6 - 136.6.4.7 Beam Element Offsets 13

6.7 Rigid System of Nodes STARDYNE 136.8 Material Constants STARDYNE 146.9 Supports STARDYNE 156.10 Loads (STARDYNE) 15

6.10.1 Node Load 156.10.2 Element Loads 166.10.3 Node Temperature Load 176.10.4 Support Displacement Specification 18

6.11 STARDYNE Analysis Capabilities 186.11.1 STARDYNE Static Analysis 196.11.2 STARDYNE Second Order Static Analysis 236.11.3 STARDYNE Dynamic Response Analysis 26

6.11.3.1 STARDYNE Response Spectrum Analysis(Dynre4) 30

6.11.3.2 STARDYNE Linear Time History ResponseAnalysis (Dynre1) 31

6.12 References (STARDYNE) 34

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7.1 STAPLE Command Language Conventions 7 - 37.1.1 Elements of the Commands 47.1.2 Command Formats 5

7.2 STAPLE Commands 97.2.1 STAPLE Initiation 97.2.2 UNIT Specification 107.2.3 The OPEN Command 127.2.4 The FOR Command 137.2.5 The WRITE and FORMAT Commands 15

7.2.5.1 Write Commands 167.2.5.2 Format Specification 24

7.2.6 The SORT Command 287.2.7 The EXECUTE Command 337.2.8 The CALL Command 367.2.9 The End Script Language Command 38

7.3 Graphics Commands in STAPLE 39

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1-1

General Description

1.1 Introduction

The STAAD.Pro 2002 Graphical User Interface (GUI) is normally usedto create all input specifications and all output reports and displays (Seethe Graphical Environment manual). These structural modeling andanalysis input specifications are stored in a text file with extension.STD. When the GUI does a File Open to start a session with an existingmodel it gets all of its information from the STD file. A user mayedit/create this STD file and have the GUI and the analysis engine bothreflect the changes.

The STD file is processed by the STAAD analysis engine to produceresults that are stored in several files with extensions such as ANL, BMD,TMH, etc. The ANL text file contains the printable output as created bythe specifications in this manual. The other files contain the results(displacements, member/element forces, mode shapes, sectionforces/moments/displacements, etc.) that are used by the GUI in postprocessing mode.

This section of the manual contains a general description of the analysisand design facilities available in the STAAD engine. Specific informationon Steel, Concrete, and Timber design are available in Sections 2, 3, and 4of this manual, respectively. Detailed STAAD engine STD file commandformats and other specific user information is presented in Section 5.

The objective of this section is to familiarize the user with the basicprinciples involved in the implementation of the various analysis/designfacilities offered by the STAAD engine. As a general rule, the sequence in

Section 1

1-1

General Description

1.1 Introduction

The STAAD.Pro 2002 Graphical User Interface (GUI) is normally usedto create all input specifications and all output reports and displays (Seethe Graphical Environment manual). These structural modeling andanalysis input specifications are stored in a text file with extension.STD. When the GUI does a File Open to start a session with an existingmodel it gets all of its information from the STD file. A user mayedit/create this STD file and have the GUI and the analysis engine bothreflect the changes.

The STD file is processed by the STAAD analysis engine to produceresults that are stored in several files with extensions such as ANL, BMD,TMH, etc. The ANL text file contains the printable output as created bythe specifications in this manual. The other files contain the results(displacements, member/element forces, mode shapes, sectionforces/moments/displacements, etc.) that are used by the GUI in postprocessing mode.

This section of the manual contains a general description of the analysisand design facilities available in the STAAD engine. Specific informationon Steel, Concrete, and Timber design are available in Sections 2, 3, and 4of this manual, respectively. Detailed STAAD engine STD file commandformats and other specific user information is presented in Section 5.

The objective of this section is to familiarize the user with the basicprinciples involved in the implementation of the various analysis/designfacilities offered by the STAAD engine. As a general rule, the sequence in

Section 1

General Description Section 11-2

which the facilities are discussed follows the recommended sequence oftheir usage in the STD input file.

STAAD.Pro 2002 also offers a second analysis engine, the STARDYNEAdvanced Analysis engine, which is discussed in Section 6.

1.2 Input Generation

The GUI (or user) communicates with the STAAD analysis engine throughthe STD input file. That input file is a text file consisting of a series ofcommands which are executed sequentially. The commands contain eitherinstructions or data pertaining to analysis and/or design. The elements andconventions of the STAAD command language are described in Section 5of this manual.

The STAAD input file can be created through a text editor or the GUIModeling facility. In general, any text editor may be utilized to edit/createthe STD input file. The GUI Modeling facility creates the input filethrough an interactive menu-driven graphics oriented procedure.

1.3 Types of Structures

A STRUCTURE can be defined as an assemblage of elements.STAAD is capable of analyzing and designing structures consisting of bothframe, plate/shell and solid elements. Almost any type of structure can beanalyzed by STAAD.

A SPACE structure, which is a three dimensional framedstructure with loads applied in any plane, is the most general.

A PLANE structure is bound by a global X-Y coordinatesystem with loads in the same plane.

A TRUSS structure consists of truss members which canhave only axial member forces and no bending in the members.A FLOOR structure is a two or three dimensional structure having

no horizontal (global X or Z) movement of the structure [FX, FZ & MYare restrained at every joint]. The floor framing (in global X-Z plane) of abuilding is an ideal example of a FLOOR structure. Columns can also bemodeled with the floor in a FLOOR structure as long as the structure has

For input,see section5.2


which the facilities are discussed follows the recommended sequence oftheir usage in the STD input file.

STAAD.Pro 2002 also offers a second analysis engine, the STARDYNEAdvanced Analysis engine, which is discussed in Section 6.

1.2 Input Generation

The GUI (or user) communicates with the STAAD analysis engine throughthe STD input file. That input file is a text file consisting of a series ofcommands which are executed sequentially. The commands contain eitherinstructions or data pertaining to analysis and/or design. The elements andconventions of the STAAD command language are described in Section 5of this manual.

The STAAD input file can be created through a text editor or the GUIModeling facility. In general, any text editor may be utilized to edit/createthe STD input file. The GUI Modeling facility creates the input filethrough an interactive menu-driven graphics oriented procedure.

1.3 Types of Structures

A STRUCTURE can be defined as an assemblage of elements.STAAD is capable of analyzing and designing structures consisting of bothframe, plate/shell and solid elements. Almost any type of structure can beanalyzed by STAAD.

A SPACE structure, which is a three dimensional framedstructure with loads applied in any plane, is the most general.

A PLANE structure is bound by a global X-Y coordinatesystem with loads in the same plane.

A TRUSS structure consists of truss members which canhave only axial member forces and no bending in the members.A FLOOR structure is a two or three dimensional structure having

no horizontal (global X or Z) movement of the structure [FX, FZ & MYare restrained at every joint]. The floor framing (in global X-Z plane) of abuilding is an ideal example of a FLOOR structure. Columns can also bemodeled with the floor in a FLOOR structure as long as the structure has


Section 1 1-3no horizontal loading. If there is any horizontal load, it must beanalyzed as a SPACE structure.

Specification of the correct structure type reduces the number ofequations to be solved during the analysis. This results in a faster andmore economic solution for the user. The degrees of freedom associatedwith frame elements of different types of structures is illustrated in Figure1.1.

Structure Types

Figure 1.1

1.4 Unit Systems

The user is allowed to input data and request output in almost allcommonly used engineering unit systems including MKS, SI andFPS. In the input file, the user may change units as many times asrequired. Mix and match between length and force units fromdifferent unit systems is also allowed. The input-unit for angles (orrotations) is degrees. However, in JOINT DISPLACEMENToutput, the rotations are provided in radians. For all output, theunits are clearly specified by the program.


Section 1 1-3no horizontal loading. If there is any horizontal load, it must beanalyzed as a SPACE structure.

Specification of the correct structure type reduces the number ofequations to be solved during the analysis. This results in a faster andmore economic solution for the user. The degrees of freedom associatedwith frame elements of different types of structures is illustrated in Figure1.1.

Structure Types

Figure 1.1

1.4 Unit Systems

The user is allowed to input data and request output in almost allcommonly used engineering unit systems including MKS, SI andFPS. In the input file, the user may change units as many times asrequired. Mix and match between length and force units fromdifferent unit systems is also allowed. The input-unit for angles (orrotations) is degrees. However, in JOINT DISPLACEMENToutput, the rotations are provided in radians. For all output, theunits are clearly specified by the program.



1.5 Structure Geometry and Coordinate Systems

A structure is an assembly of individual components such as beams,columns, slabs, plates etc.. In STAAD, frame elements and plate elementsmay be used to model the structural components. Typically, modeling ofthe structure geometry consists of two steps:

A. Identification and description of joints or nodes.

B. Modeling of members or elements through specification ofconnectivity (incidences) between joints.

In general, the term MEMBER will be used to refer to frameelements and the term ELEMENT will be used to refer toplate/shell and solid elements. Connectivity for MEMBERs may beprovided through the MEMBER INCIDENCE command whileconnectivity for ELEMENTs may be provided through theELEMENT INCIDENCE command.

STAAD uses two types of coordinate systems to define the structuregeometry and loading patterns. The GLOBAL coordinate system is anarbitrary coordinate system in space which is utilized to specify the overallgeometry & loading pattern of the structure. A LOCAL coordinate systemis associated with each member (or element) and is utilized in MEMBEREND FORCE output or local load specification.

1.5.1 Global Coordinate SystemThe following coordinate systems are available for specification of thestructure geometry.

A. Conventional Cartesian Coordinate System: This coordinate system(Fig. 1.2) is a rectangular coordinate system (X, Y, Z) which followsthe orthogonal right hand rule. This coordinate system may be used todefine the joint locations and loading directions. The translationaldegrees of freedom are denoted by u1, u2, u3 and the rotationaldegrees of freedom are denoted by u4, u5 & u6.

For input,see sections5.11 to 5.17


1.5 Structure Geometry and Coordinate Systems

A structure is an assembly of individual components such as beams,columns, slabs, plates etc.. In STAAD, frame elements and plate elementsmay be used to model the structural components. Typically, modeling ofthe structure geometry consists of two steps:

A. Identification and description of joints or nodes.

B. Modeling of members or elements through specification ofconnectivity (incidences) between joints.

In general, the term MEMBER will be used to refer to frameelements and the term ELEMENT will be used to refer toplate/shell and solid elements. Connectivity for MEMBERs may beprovided through the MEMBER INCIDENCE command whileconnectivity for ELEMENTs may be provided through theELEMENT INCIDENCE command.

STAAD uses two types of coordinate systems to define the structuregeometry and loading patterns. The GLOBAL coordinate system is anarbitrary coordinate system in space which is utilized to specify the overallgeometry & loading pattern of the structure. A LOCAL coordinate systemis associated with each member (or element) and is utilized in MEMBEREND FORCE output or local load specification.

1.5.1 Global Coordinate SystemThe following coordinate systems are available for specification of thestructure geometry.

A. Conventional Cartesian Coordinate System: This coordinate system(Fig. 1.2) is a rectangular coordinate system (X, Y, Z) which followsthe orthogonal right hand rule. This coordinate system may be used todefine the joint locations and loading directions. The translationaldegrees of freedom are denoted by u1, u2, u3 and the rotationaldegrees of freedom are denoted by u4, u5 & u6.

For input,see sections5.11 to 5.17

Section 1 1-5B. Cylindrical Coordinate System: In this coordinate system, (Fig. 1.3) the X

and Y coordinates of the conventional cartesian system are replaced by R(radius) and (angle in degrees). The Z coordinate is identical to the Zcoordinate of the cartesian system and its positive direction is determined bythe right hand rule.

C. Reverse Cylindrical Coordinate System: This is a cylindrical typecoordinate system (Fig. 1.4) where the R- plane corresponds to theX-Z plane of the cartesian system. The right hand rule is followed todetermine the positive direction of the Y axis.

Figure 1.2 : Cartesian (Rectangular) Coordinate System

Figure 1.3 : Cylindrical Coordinate System

Section 1 1-5B. Cylindrical Coordinate System: In this coordinate system, (Fig. 1.3) the X

and Y coordinates of the conventional cartesian system are replaced by R(radius) and (angle in degrees). The Z coordinate is identical to the Zcoordinate of the cartesian system and its positive direction is determined bythe right hand rule.

C. Reverse Cylindrical Coordinate System: This is a cylindrical typecoordinate system (Fig. 1.4) where the R- plane corresponds to theX-Z plane of the cartesian system. The right hand rule is followed todetermine the positive direction of the Y axis.

Figure 1.2 : Cartesian (Rectangular) Coordinate System

Figure 1.3 : Cylindrical Coordinate System


Figure 1.4 : Reverse Cylindrical Coordinate System

1.5.2 Local Coordinate SystemA local coordinate system is associated with each member. Each axis ofthe local orthogonal coordinate system is also based on the right hand rule.Fig. 1.5 shows a beam member with start joint 'i' and end joint 'j'. Thepositive direction of the local x-axis is determined by joining 'i' to 'j' andprojecting it in the same direction. The right hand rule may be applied toobtain the positive directions of the local y and z axes. The local y and z-axes coincide with the axes of the two principal moments of inertia. Notethat the local coordinate system is always rectangular.

A wide range of cross-sectional shapes may be specified for analysis.These include rolled steel shapes, user specified prismatic shapes etc.. Fig.1.6 shows local axis system(s) for these shapes.


Figure 1.4 : Reverse Cylindrical Coordinate System

1.5.2 Local Coordinate SystemA local coordinate system is associated with each member. Each axis ofthe local orthogonal coordinate system is also based on the right hand rule.Fig. 1.5 shows a beam member with start joint 'i' and end joint 'j'. Thepositive direction of the local x-axis is determined by joining 'i' to 'j' andprojecting it in the same direction. The right hand rule may be applied toobtain the positive directions of the local y and z axes. The local y and z-axes coincide with the axes of the two principal moments of inertia. Notethat the local coordinate system is always rectangular.

A wide range of cross-sectional shapes may be specified for analysis.These include rolled steel shapes, user specified prismatic shapes etc.. Fig.1.6 shows local axis system(s) for these shapes.

Section 1 1-7

Figure 1.5

Section 1 1-7

Figure 1.5


Local axis for different cross-sectionsFigure 1.6

NOTE: The local x-axis of the above sections are going into the paper


Local axis for different cross-sectionsFigure 1.6

NOTE: The local x-axis of the above sections are going into the paper

Section 1 1-9

Local Axis Systemfor different cross sections when the SET Z UP command is specified.

Local X axis goes into the page.

Section 1 1-9

Local Axis Systemfor different cross sections when the SET Z UP command is specified.

Local X axis goes into the page.


1.5.3 Relationship Between Global & LocalCoordinates

Since the input for member loads can be provided in the local andglobal coordinate system and the output for member-end-forces isprinted in the local coordinate system, it is important to know therelationship between the local and global coordinate systems. Thisrelationship is defined by an angle measured in the followingspecified way. This angle will be defined as the beta () angle.For offset members the beta angle/reference point specificationsare based on the offset position of the local axis, not the jointpositions.

Beta AngleWhen the local x-axis is parallel to the global Y-axis, as in thecase of a column in a structure, the beta angle is the angle throughwhich the local z-axis has been rotated about the local x-axis froma position of being parallel and in the same positive direction ofthe global Z-axis.

When the local x-axis is not parallel to the global Y-axis, the betaangle is the angle through which the local coordinate system hasbeen rotated about the local x-axis from a position of having thelocal z-axis parallel to the global X-Z plane and the local y-axis inthe same positive direction as the global Y-axis. Figure 1.7 detailsthe positions for beta equals 0 degrees or 90 degrees. Whenproviding member loads in the local member axis, it is helpful torefer to this figure for a quick determination of the local axissystem.

Reference PointAn alternative to providing the member orientation is to input thecoordinates (or a joint number) which will be a reference pointlocated in the member x-y plane but not on the axis of the member.



1.5.3 Relationship Between Global & LocalCoordinates

Since the input for member loads can be provided in the local andglobal coordinate system and the output for member-end-forces isprinted in the local coordinate system, it is important to know therelationship between the local and global coordinate systems. Thisrelationship is defined by an angle measured in the followingspecified way. This angle will be defined as the beta () angle.For offset members the beta angle/reference point specificationsare based on the offset position of the local axis, not the jointpositions.

Beta AngleWhen the local x-axis is parallel to the global Y-axis, as in thecase of a column in a structure, the beta angle is the angle throughwhich the local z-axis has been rotated about the local x-axis froma position of being parallel and in the same positive direction ofthe global Z-axis.

When the local x-axis is not parallel to the global Y-axis, the betaangle is the angle through which the local coordinate system hasbeen rotated about the local x-axis from a position of having thelocal z-axis parallel to the global X-Z plane and the local y-axis inthe same positive direction as the global Y-axis. Figure 1.7 detailsthe positions for beta equals 0 degrees or 90 degrees. Whenproviding member loads in the local member axis, it is helpful torefer to this figure for a quick determination of the local axissystem.

Reference PointAn alternative to providing the member orientation is to input thecoordinates (or a joint number) which will be a reference pointlocated in the member x-y plane but not on the axis of the member.


Section 1 1-11From the location of the reference point, the programautomatically calculates the orientation of the member x-y plane.

>k2, or k1+k2 k1, A=1and hence, 1/(1-A) =1/0. Thus, huge variations in stiffnesses ofadjacent members are not permitted. Artificially high E or Ivalues should be reduced when this occurs.

Math precision errors are also caused when the units of lengthand force are not defined correctly for member lengths,member properties, constants etc.

Users also have to ensure that the model defined represents onesingle structure only, not two or more separate structures. Forexample, in an effort to model an expansion joint, the user mayend up defining separate structures within the same input file.Multiple structures defined in one input file can lead to grosslyerroneous results.

1.18.2 Second Order AnalysisSTAAD offers the capability to perform second order stabilityanalyses. Two methods are available - a simplified method calledP-Delta Analysis and an elaborate method called Non LinearAnalysis. Both methods are explained below.

1.18.2.1 P-Delta AnalysisStructures subjected to lateral loads often experience secondaryforces due to the movement of the point of application of verticalloads. This secondary effect, commonly known as the P-Deltaeffect, plays an important role in the analysis of the structure. InSTAAD, a unique procedure has been adopted to incorporate theP-Delta effect into the analysis. The procedure consists of thefollowing steps:

Seesection 5.37

Seesection 5.37

Section 1 1-592) Math precision

A math precision error is caused when numerical instabilitiesoccur in the matrix decomposition (inversion) process. One of theterms of the equilibrium equation takes the form 1/(1-A), whereA=k1/(k1+k2); k1 and k2 being the stiffness coefficients of twoadjacent members. When a very "stiff" member is adjacent to avery "flexible" member, viz., when k1>>k2, or k1+k2 k1, A=1and hence, 1/(1-A) =1/0. Thus, huge variations in stiffnesses ofadjacent members are not permitted. Artificially high E or Ivalues should be reduced when this occurs.

Math precision errors are also caused when the units of lengthand force are not defined correctly for member lengths,member properties, constants etc.

Users also have to ensure that the model defined represents onesingle structure only, not two or more separate structures. Forexample, in an effort to model an expansion joint, the user mayend up defining separate structures within the same input file.Multiple structures defined in one input file can lead to grosslyerroneous results.

1.18.2 Second Order AnalysisSTAAD offers the capability to perform second order stabilityanalyses. Two methods are available - a simplified method calledP-Delta Analysis and an elaborate method called Non LinearAnalysis. Both methods are explained below.

1.18.2.1 P-Delta AnalysisStructures subjected to lateral loads often experience secondaryforces due to the movement of the point of application of verticalloads. This secondary effect, commonly known as the P-Deltaeffect, plays an important role in the analysis of the structure. InSTAAD, a unique procedure has been adopted to incorporate theP-Delta effect into the analysis. The procedure consists of thefollowing steps:

Seesection 5.37

Seesection 5.37


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

2) Primary deflections are then combined with the originallyapplied loading to create the secondary loadings. The loadvector is then revised to include the secondary effects.

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

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

4) Element/Member forces and support reactions are calculatedbased on the new deflections.

It may be noted that this procedure yields very accurate resultswith all small displacement problems. STAAD allows the user togo through multiple iterations of the P-Delta procedure ifnecessary. The user is allowed to specify the number of iterationsbased on the requirement. To set the displacement convergencetolerance, enter a SET DISP f command before the JointCoordinates. If the change in displacement norm from one iterationto the next is less than f then it is converged.

The P-Delta analysis is recommended by several design codes suchas ACI 318, LRFD, IS456-1978, etc. in lieu of the momentmagnification method for the calculation of more realistic forcesand moments.

P-Delta effects are calculated for frame members and plateelements only. They are not calculated for solid elements. P-Deltaand Nonlinear analysis is restricted to structures where members


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

2) Primary deflections are then combined with the originallyapplied loading to create the secondary loadings. The loadvector is then revised to include the secondary effects.

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

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

4) Element/Member forces and support reactions are calculatedbased on the new deflections.

It may be noted that this procedure yields very accurate resultswith all small displacement problems. STAAD allows the user togo through multiple iterations of the P-Delta procedure ifnecessary. The user is allowed to specify the number of iterationsbased on the requirement. To set the displacement convergencetolerance, enter a SET DISP f command before the JointCoordinates. If the change in displacement norm from one iterationto the next is less than f then it is converged.

The P-Delta analysis is recommended by several design codes suchas ACI 318, LRFD, IS456-1978, etc. in lieu of the momentmagnification method for the calculation of more realistic forcesand moments.

P-Delta effects are calculated for frame members and plateelements only. They are not calculated for solid elements. P-Deltaand Nonlinear analysis is restricted to structures where members

Section 1 1-61and plate elements carry the vertical load from one structurelevel to the next.

1.18.2.2 Non Linear AnalysisSTAAD also offers the capability to perform non-linear staticanalysis based on geometric non-linearity. The non-linear analysisalgorithm incorporates both member geometric stiffnesscorrections and secondary loadings.

Non linear analysis methodology is generally adopted forstructures subject to large displacements. As large displacementsgenerally result in significant movement of the point of applicationof loads, consideration of secondary loadings becomes animportant criteria. In addition, geometric stiffness corrections areapplied to take into consideration the modified geometry. Since thegeometric stiffness corrections are based on generateddisplacements, they are different for different load cases. Thismakes the non-linear analysis option load dependent. The STAADnon-linear analysis algorithm consists of the following steps :

1) First, primary displacements are calculated for the appliedloading.

2) Stiffness corrections are applied on the member/plate elementstiffness matrices based on observed displacements. Newglobal stiffness matrix is assembled based on revisedmember/element stiffness matrices using updated jointcoordinates.

3) Load vectors are revised to include the secondary effects dueto primary displacements.

4) The new set of equations are solved to generate newdisplacements.

5) Element/Member forces and support reactions are calculatedfrom these new displacements.

6) The STAAD non-linear analysis algorithm allows the user togo through multiple iterations of the above procedure. Thenumber of iterations may be specified by the user based on the

Seesection 5.37

Section 1 1-61and plate elements carry the vertical load from one structurelevel to the next.

1.18.2.2 Non Linear AnalysisSTAAD also offers the capability to perform non-linear staticanalysis based on geometric non-linearity. The non-linear analysisalgorithm incorporates both member geometric stiffnesscorrections and secondary loadings.

Non linear analysis methodology is generally adopted forstructures subject to large displacements. As large displacementsgenerally result in significant movement of the point of applicationof loads, consideration of secondary loadings becomes animportant criteria. In addition, geometric stiffness corrections areapplied to take into consideration the modified geometry. Since thegeometric stiffness corrections are based on generateddisplacements, they are different for different load cases. Thismakes the non-linear analysis option load dependent. The STAADnon-linear analysis algorithm consists of the following steps :

1) First, primary displacements are calculated for the appliedloading.

2) Stiffness corrections are applied on the member/plate elementstiffness matrices based on observed displacements. Newglobal stiffness matrix is assembled based on revisedmember/element stiffness matrices using updated jointcoordinates.

3) Load vectors are revised to include the secondary effects dueto primary displacements.

4) The new set of equations are solved to generate newdisplacements.

5) Element/Member forces and support reactions are calculatedfrom these new displacements.

6) The STAAD non-linear analysis algorithm allows the user togo through multiple iterations of the above procedure. Thenumber of iterations may be specified by the user based on the

Seesection 5.37


requirement. It may be noted, however, that multiple iterationsmay increase the computer resource requirements andexecution time substantially.

Note : The following points may be noted with respect to the non-linear analysis facility -

1) Since the procedure is load dependent, the user is required touse the SET NL and CHANGE commands properly. The SETNL command must be provided to specify the total number ofprimary load cases. The CHANGE command should be used toreset the stiffness matrices after each load case.

2) As the geometric corrections are based on displacements, allloads that are capable of producing significant displacementsmust be part of the load case(s) identified for non-linearanalysis.

3) To set the displacement divergence tolerance, enter a SETDISP f command before the Joint Coordinates. If anydisplacement on any iteration exceeds f , then the solution isdiverging and is terminated. The default value for f is thelargest of the total width, height, or depth of the structuredivided by 120.

P-Delta and Nonlinear analysis is restricted to structures wheremembers or plates carry the axial load from one structure level tothe next.

1.18.2.3 Multi-Linear Analysis

When soil is to be modeled as spring supports, the varying resistanceit offers to external loads can be modeled using this facility, such aswhen its behavior in tension differs from its behavior incompression. Stiffness-Displacement characteristics of soil can berepresented by a multi-linear curve. Amplitude of this curve willrepresent the spring characteristic of the soil at differentdisplacement values. The load cases in a multi-linear spring analysismust be separated by the CHANGE command and PERFORMANALYSIS command. The SET NL command must be provided to


requirement. It may be noted, however, that multiple iterationsmay increase the computer resource requirements andexecution time substantially.

Note : The following points may be noted with respect to the non-linear analysis facility -

1) Since the procedure is load dependent, the user is required touse the SET NL and CHANGE commands properly. The SETNL command must be provided to specify the total number ofprimary load cases. The CHANGE command should be used toreset the stiffness matrices after each load case.

2) As the geometric corrections are based on displacements, allloads that are capable of producing significant displacementsmust be part of the load case(s) identified for non-linearanalysis.

3) To set the displacement divergence tolerance, enter a SETDISP f command before the Joint Coordinates. If anydisplacement on any iteration exceeds f , then the solution isdiverging and is terminated. The default value for f is thelargest of the total width, height, or depth of the structuredivided by 120.

P-Delta and Nonlinear analysis is restricted to structures wheremembers or plates carry the axial load from one structure level tothe next.

1.18.2.3 Multi-Linear Analysis

When soil is to be modeled as spring supports, the varying resistanceit offers to external loads can be modeled using this facility, such aswhen its behavior in tension differs from its behavior incompression. Stiffness-Displacement characteristics of soil can berepresented by a multi-linear curve. Amplitude of this curve willrepresent the spring characteristic of the soil at differentdisplacement values. The load cases in a multi-linear spring analysismust be separated by the CHANGE command and PERFORMANALYSIS command. The SET NL command must be provided to

Section 1 1-63specify the total number of primary load cases. There may not beany PDELTA, NONLINEAR, dynamic, or TENSION/COMPRESSION member cases. The multi-linear spring commandwill initiate an iterative analysis which continues to convergence.

1.18.2.4 Tension / Compression Only Analysis

When some members or support springs are linear but carry onlytension (or only compression), then this analysis may be used. Thisanalysis is automatically selected if any member or spring has beengiven the tension or compression only characteristic. This analysis isan iterative analysis which continues to convergence. Any member/spring that fails its criteria will be inactive (omitted) on the nextiteration. Iteration continues until all such members have the properload direction or are inactive (default iteration limit is 10).

This is a simple method that may not work in some cases becausemembers are removed on interim iterations that are needed forstability. If instability messages appear on the 2nd and subsequentiterations that did not appear on the first cycle, then do not use thesolution. If this occurs on cases where only springs are thetension/compression entities, then use multi-linear spring analysis.

The load cases in a tension/compression analysis must be separatedby the CHANGE command and PERFORM ANALYSIS command.The SET NL command must be provided to specify the total numberof primary load cases. There may not be any Multi-linear springs,NONLINEAR, or dynamic cases.

Section 1 1-63specify the total number of primary load cases. There may not beany PDELTA, NONLINEAR, dynamic, or TENSION/COMPRESSION member cases. The multi-linear spring commandwill initiate an iterative analysis which continues to convergence.

1.18.2.4 Tension / Compression Only Analysis

When some members or support springs are linear but carry onlytension (or only compression), then this analysis may be used. Thisanalysis is automatically selected if any member or spring has beengiven the tension or compression only characteristic. This analysis isan iterative analysis which continues to convergence. Any member/spring that fails its criteria will be inactive (omitted) on the nextiteration. Iteration continues until all such members have the properload direction or are inactive (default iteration limit is 10).

This is a simple method that may not work in some cases becausemembers are removed on interim iterations that are needed forstability. If instability messages appear on the 2nd and subsequentiterations that did not appear on the first cycle, then do not use thesolution. If this occurs on cases where only springs are thetension/compression entities, then use multi-linear spring analysis.

The load cases in a tension/compression analysis must be separatedby the CHANGE command and PERFORM ANALYSIS command.The SET NL command must be provided to specify the total numberof primary load cases. There may not be any Multi-linear springs,NONLINEAR, or dynamic cases.


1.18.2.5 Non Linear Cable/Truss Analysis(available in limited form)

When all of the members, elements and support springs are linearexcept for cable and/or preloaded truss members, then this analysistype may be used. This analysis is based on applying the load insteps with equilibrium iterations to convergence at each step. Thestep sizes start small and gradually increase (15-20 steps is thedefault). Iteration continues at each step until the change indeformations is small before proceeding to the next step. If notconverged, then the solution is stopped. The user can then selectmore steps or modify the structure and rerun.

Structures can be artificially stabilized during the first few loadsteps in case the structure is initially unstable (in the linear, smalldisplacement, static theory sense).

The user has control of the number of steps, the maximum number ofiterations per step, the convergence tolerance, the artificialstabilizing stiffness, and the minimum amount of stiffness remainingafter a cable sags.

This method assumes small displacement theory for allmembers/trusses/elements other than cables & preloaded trusses.The cables and preloaded trusses can have large displacement andmoderate/large strain. Cables and preloaded trusses may carrytension and compression but cables have a reduced E modulus if notfully taut. Pretension is the force necessary to stretch the cable/trussfrom its unstressed length to enable it to fit between the two endjoints. Alternatively, you may enter the unstressed length for cables.

The current nonlinear cable analysis procedure can result incompressive forces in the final cable results. The procedure wasdeveloped for structures, loadings, and pretensioning loads that willresult in sufficient tension in every cable for all loading conditions.The possibility of compression was considered acceptable in theinitial implementation because most design codes strongly

See sections5.30, 5.37,1.11


1.18.2.5 Non Linear Cable/Truss Analysis(available in limited form)

When all of the members, elements and support springs are linearexcept for cable and/or preloaded truss members, then this analysistype may be used. This analysis is based on applying the load insteps with equilibrium iterations to convergence at each step. Thestep sizes start small and gradually increase (15-20 steps is thedefault). Iteration continues at each step until the change indeformations is small before proceeding to the next step. If notconverged, then the solution is stopped. The user can then selectmore steps or modify the structure and rerun.

Structures can be artificially stabilized during the first few loadsteps in case the structure is initially unstable (in the linear, smalldisplacement, static theory sense).

The user has control of the number of steps, the maximum number ofiterations per step, the convergence tolerance, the artificialstabilizing stiffness, and the minimum amount of stiffness remainingafter a cable sags.

This method assumes small displacement theory for allmembers/trusses/elements other than cables & preloaded trusses.The cables and preloaded trusses can have large displacement andmoderate/large strain. Cables and preloaded trusses may carrytension and compression but cables have a reduced E modulus if notfully taut. Pretension is the force necessary to stretch the cable/trussfrom its unstressed length to enable it to fit between the two endjoints. Alternatively, you may enter the unstressed length for cables.

The current nonlinear cable analysis procedure can result incompressive forces in the final cable results. The procedure wasdeveloped for structures, loadings, and pretensioning loads that willresult in sufficient tension in every cable for all loading conditions.The possibility of compression was considered acceptable in theinitial implementation because most design codes strongly

See sections5.30, 5.37,1.11

Section 1 1-65recommend cables to be in tension to avoid the undesirabledynamic effects of a slack cable such as galloping, singing, orpounding. The engineer must specify initial preloading tensionswhich will ensure that all cable results are in tension. In additionthis procedure is much more reliable and efficient than generalnonlinear algorithms. To minimize the compression the SAGMINinput variable can be set to a small value such as 0.01, however thatcan lead to a failure to converge unless many more steps arespecified and a higher equilibrium iteration limit is specified.SAGMIN values below 0.70 generally requires some adjustments ofthe other input parameters to get convergence.

Currently the cable and truss are not automatically loaded byselfweight, but the user should ensure that selfweight is applied inevery load case. Do not enter component load cases such as windonly; every case must be realistic. Member loads will be lumped atthe ends for cables and trusses. Temperature load may also beapplied to the cables and trusses. It is OK to break up thecable/truss into several members and apply forces to the intermediatejoints. Y-up is assumed and required.

The member force printed for the cable is Fx and is along the chordline between the displaced positions of the end joints.

The analysis sequence is as follows:1. Compute the unstressed length of the nonlinear members based

on joint coordinates, pretension, and temperature.2. Member/Element/Cable stiffness is formed. Cable stiffness is

from EA/L and the sag formula plus a geometric stiffness basedon current tension.

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

4. Perform equilibrium iterations to adjust the change in directionsof the forces in the nonlinear cables, so that the structure is instatic equilibrium in the deformed position. If force changes aretoo large or convergence criteria not met within 15 iterationsthen stop the analysis.

Section 1 1-65recommend cables to be in tension to avoid the undesirabledynamic effects of a slack cable such as galloping, singing, orpounding. The engineer must specify initial preloading tensionswhich will ensure that all cable results are in tension. In additionthis procedure is much more reliable and efficient than generalnonlinear algorithms. To minimize the compression the SAGMINinput variable can be set to a small value such as 0.01, however thatcan lead to a failure to converge unless many more steps arespecified and a higher equilibrium iteration limit is specified.SAGMIN values below 0.70 generally requires some adjustments ofthe other input parameters to get convergence.

Currently the cable and truss are not automatically loaded byselfweight, but the user should ensure that selfweight is applied inevery load case. Do not enter component load cases such as windonly; every case must be realistic. Member loads will be lumped atthe ends for cables and trusses. Temperature load may also beapplied to the cables and trusses. It is OK to break up thecable/truss into several members and apply forces to the intermediatejoints. Y-up is assumed and required.

The member force printed for the cable is Fx and is along the chordline between the displaced positions of the end joints.

The analysis sequence is as follows:1. Compute the unstressed length of the nonlinear members based

on joint coordinates, pretension, and temperature.2. Member/Element/Cable stiffness is formed. Cable stiffness is

from EA/L and the sag formula plus a geometric stiffness basedon current tension.

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

4. Perform equilibrium iterations to adjust the change in directionsof the forces in the nonlinear cables, so that the structure is instatic equilibrium in the deformed position. If force changes aretoo large or convergence criteria not met within 15 iterationsthen stop the analysis.


5. Go to step 2 and repeat with a greater percentage of the appliedload. The nonlinear members will have an updated orientationwith new tension and sag effects.

6. After 100% of the applied load has converged then proceed tocompute member forces, reactions, and static check. Note thatthe static check is not exactly in balance due to thedisplacements of the applied static equivalent joint loads.

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

Also for cables and preloaded trusses:1. Do not use Member Offsets.2. Do not include the end joints in Master/Slave command.3. Do not connect to inclined support joints.4. Y direction must be up.5. Do not impose displacements.6. Do not use Support springs in the model.7. Applied loads do not change global directions due to

displacements.8. Do not apply Prestress load, Fixed end load.9. Do not use Load Combination command to combine cable

analysis results. Use a primary case with Repeat Load instead.

1.18.3 Dynamic AnalysisCurrently available dynamic analysis facilities include solution ofthe free vibration problem (eigenproblem), response spectrumanalysis and forced vibration analysis.

Solution of the EigenproblemThe eigenproblem is solved for structure frequencies and modeshapes considering a diagonal, lumped mass matrix, with massespossible at all active d.o.f. included. Two solution methods may be

See sections5.30,5.32.10, 5.34


5. Go to step 2 and repeat with a greater percentage of the appliedload. The nonlinear members will have an updated orientationwith new tension and sag effects.

6. After 100% of the applied load has converged then proceed tocompute member forces, reactions, and static check. Note thatthe static check is not exactly in balance due to thedisplacements of the applied static equivalent joint loads.

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

Also for cables and preloaded trusses:1. Do not use Member Offsets.2. Do not include the end joints in Master/Slave command.3. Do not connect to inclined support joints.4. Y direction must be up.5. Do not impose displacements.6. Do not use Support springs in the model.7. Applied loads do not change global directions due to

displacements.8. Do not apply Prestress load, Fixed end load.9. Do not use Load Combination command to combine cable

analysis results. Use a primary case with Repeat Load instead.

1.18.3 Dynamic AnalysisCurrently available dynamic analysis facilities include solution ofthe free vibration problem (eigenproblem), response spectrumanalysis and forced vibration analysis.

Solution of the EigenproblemThe eigenproblem is solved for structure frequencies and modeshapes considering a diagonal, lumped mass matrix, with massespossible at all active d.o.f. included. Two solution methods may be

See sections5.30,5.32.10, 5.34

Section 1 1-67used: the subspace iteration method for all problem sizes(default for all problem sizes), and the optional determinant searchmethod for small problems.

Mass ModelingThe natural frequencies and mode shapes of a structure are theprimary parameters that affect the response of a structure underdynamic loading. The free vibration problem is solved to extractthese values. Since no external forcing function is involved, thenatural frequencies and mode shapes are direct functions of thestiffness and mass distribution in the structure. Results of thefrequency and mode shape calculations may vary significantlydepending upon the mass modeling. This variation, in turn, affectsthe response spectrum and forced vibration analysis results. Thus,extreme caution should be exercised in mass modeling in adynamic analysis problem.

In STAAD, all masses that are capable of moving should bemodeled as loads applied in all possible directions of movement.Even if the loading is known to be only in one direction there isusually mass motion in other directions at some or all joints andthese mass directions (loads in weight units) must be entered tobe correct. Joint moments that are entered will be considered to beweight moment of inertias (force-length2 units).

Please enter selfweight, joint and element loadings in globaldirections with the same sign as much as possible so that themasses do not cancel each other.

Member/Element loadings may also be used to generate jointtranslational masses. Note that member end joint moments that aregenerated by the member loading (including concentratedmoments) are discarded as irrelevant to dynamics. Enter massmoments of inertia, if needed, at the joints as joint moments.

STAAD uses a diagonal mass matrix of 6 lumped mass equationsper joint. The selfweight or uniformly loaded member is lumped50% to each end joint without rotational mass moments of inertia.

Section 1 1-67used: the subspace iteration method for all problem sizes(default for all problem sizes), and the optional determinant searchmethod for small problems.

Mass ModelingThe natural frequencies and mode shapes of a structure are theprimary parameters that affect the response of a structure underdynamic loading. The free vibration problem is solved to extractthese values. Since no external forcing function is involved, thenatural frequencies and mode shapes are direct functions of thestiffness and mass distribution in the structure. Results of thefrequency and mode shape calculations may vary significantlydepending upon the mass modeling. This variation, in turn, affectsthe response spectrum and forced vibration analysis results. Thus,extreme caution should be exercised in mass modeling in adynamic analysis problem.

In STAAD, all masses that are capable of moving should bemodeled as loads applied in all possible directions of movement.Even if the loading is known to be only in one direction there isusually mass motion in other directions at some or all joints andthese mass directions (loads in weight units) must be entered tobe correct. Joint moments that are entered will be considered to beweight moment of inertias (force-length2 units).

Please enter selfweight, joint and element loadings in globaldirections with the same sign as much as possible so that themasses do not cancel each other.

Member/Element loadings may also be used to generate jointtranslational masses. Note that member end joint moments that aregenerated by the member loading (including concentratedmoments) are discarded as irrelevant to dynamics. Enter massmoments of inertia, if needed, at the joints as joint moments.

STAAD uses a diagonal mass matrix of 6 lumped mass equationsper joint. The selfweight or uniformly loaded member is lumped50% to each end joint without rotational mass moments of inertia.


The other element types are integrated but roughly speaking theweight is distributed equally amongst the joints of the element.

The members/elements of finite element theory are simplemathematical representations of deformation meant to apply over asmall region. The FEA procedures will converge if you subdividethe elements and rerun; then subdivide the elements that havesignificantly changed results and rerun; etc. until the key resultsare converged to the accuracy needed.

An example of a simple beam problem that needs to subdivide realmembers to better represent the mass distribution (and the dynamicresponse and the force distribution response along members) is asimple floor beam between 2 columns will put all of the mass onthe column joints. In this example, a vertical ground motion willnot bend the beam even if there is a concentrated force (mass) atmid span.

In addition, the dynamic results will not reflect the location ofa mass within a member (i.e. the masses are lumped at thejoints). This means that the motion, of a large mass in themiddle of a member relative to the ends of the member, is notconsidered. This may affect the frequencies and mode shapes.If this is important to the solution, split the member into two.Another effect of moving the masses to the joints is that theresulting shear/moment distribution is based as if the masseswere not within the member. Note also that if one end of amember is a support, then half of the that member mass islumped at the support and will not move during the dynamicresponse.

Damping ModelingDamping may be specified by entering values for each mode, orusing a formula based on the first two frequencies, or by usingcomposite modal damping. Composite modal damping permitscomputing the damping of a mode from the different dampingratios for different materials (steel, concrete, soil). Modes thatdeform mostly the steel would have steel damping ratio, whereas


The other element types are integrated but roughly speaking theweight is distributed equally amongst the joints of the element.

The members/elements of finite element theory are simplemathematical representations of deformation meant to apply over asmall region. The FEA procedures will converge if you subdividethe elements and rerun; then subdivide the elements that havesignificantly changed results and rerun; etc. until the key resultsare converged to the accuracy needed.

An example of a simple beam problem that needs to subdivide realmembers to better represent the mass distribution (and the dynamicresponse and the force distribution response along members) is asimple floor beam between 2 columns will put all of the mass onthe column joints. In this example, a vertical ground motion willnot bend the beam even if there is a concentrated force (mass) atmid span.

In addition, the dynamic results will not reflect the location ofa mass within a member (i.e. the masses are lumped at thejoints). This means that the motion, of a large mass in themiddle of a member relative to the ends of the member, is notconsidered. This may affect the frequencies and mode shapes.If this is important to the solution, split the member into two.Another effect of moving the masses to the joints is that theresulting shear/moment distribution is based as if the masseswere not within the member. Note also that if one end of amember is a support, then half of the that member mass islumped at the support and will not move during the dynamicresponse.

Damping ModelingDamping may be specified by entering values for each mode, orusing a formula based on the first two frequencies, or by usingcomposite modal damping. Composite modal damping permitscomputing the damping of a mode from the different dampingratios for different materials (steel, concrete, soil). Modes thatdeform mostly the steel would have steel damping ratio, whereas

Section 1 1-69modes that mostly deform the soil, would have the soildamping ratio.

Response Spectrum AnalysisThis capability allows the user to analyze the structure for seismicloading. For any supplied response spectrum (either accelerationvs. period or displacement vs. period), joint displacements,member forces, and support reactions may be calculated. Modalresponses may be combined using one of the square root of thesum of squares (SRSS), the complete quadratic combination(CQC), the ASCE4-98 (ASCE), the Ten Percent (TEN) or theabsolute (ABS) methods to obtain the resultant responses. Resultsof the response spectrum analysis may be combined with theresults of the static analysis to perform subsequent design. Toaccount for reversibility of seismic activity, load combinations canbe created to include either the positive or negative contribution ofseismic results.

Response Time History AnalysisSTAAD is equipped with a facility to perform a response historyanalysis on a structure subjected to time varying forcing functionloads at the joints and/or a ground motion at its base. This analysisis performed using the modal superposition method. Hence, all theactive masses should be modeled as loads in order to facilitatedetermination of the mode shapes and frequencies. Please refer tothe section above on "mass modeling" for additional informationon this topic. In the mode superposition analysis, it is assumed thatthe structural response can be obtained from the "p" lowest modes.The equilibrium equations are written as

>P@^[` >F@^[` >N@^[` ^3`

W

... ... (1)

Using the transformation

{ } { }L

L

S

L

T[ = =

See section5.32.10

See Sections5.31.6 and5.32.10.2

Section 1 1-69modes that mostly deform the soil, would have the soildamping ratio.

Response Spectrum AnalysisThis capability allows the user to analyze the structure for seismicloading. For any supplied response spectrum (either accelerationvs. period or displacement vs. period), joint displacements,member forces, and support reactions may be calculated. Modalresponses may be combined using one of the square root of thesum of squares (SRSS), the complete quadratic combination(CQC), the ASCE4-98 (ASCE), the Ten Percent (TEN) or theabsolute (ABS) methods to obtain the resultant responses. Resultsof the response spectrum analysis may be combined with theresults of the static analysis to perform subsequent design. Toaccount for reversibility of seismic activity, load combinations canbe created to include either the positive or negative contribution ofseismic results.

Response Time History AnalysisSTAAD is equipped with a facility to perform a response historyanalysis on a structure subjected to time varying forcing functionloads at the joints and/or a ground motion at its base. This analysisis performed using the modal superposition method. Hence, all theactive masses should be modeled as loads in order to facilitatedetermination of the mode shapes and frequencies. Please refer tothe section above on "mass modeling" for additional informationon this topic. In the mode superposition analysis, it is assumed thatthe structural response can be obtained from the "p" lowest modes.The equilibrium equations are written as

>P@^[` >F@^[` >N@^[` ^3`

W

... ... (1)

Using the transformation

{ } { }L

L

S

L

T[ = =

See section5.32.10

See Sections5.31.6 and5.32.10.2


Equation 1 reduces to "p" separate uncoupled equations of theform

W5TTTLL

LLLLL

=++ where is the modal damping ratio and the naturalfrequency for the ith mode.

These are solved by the Wilson- method which is anunconditionally stable step by step scheme. The time step for theresponse is chosen as 0.1 T where T is the period of the highestmode that is to be included in the response. The qis are substitutedin equation 2 to obtain the displacements {x} at each time step.

Time History Analysis for a Structure Subjectedto a Harmonic Loading

A Harmonic loading is one in which can be described using thefollowing equation

WVLQ)W)

+=

In the above equation,

F(t) = Value of the forcing function at any instant of time "t"F0 = Peak value of the forcing function

= Frequency of the forcing function = Phase Angle

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


Equation 1 reduces to "p" separate uncoupled equations of theform

W5TTTLL

LLLLL

=++ where is the modal damping ratio and the naturalfrequency for the ith mode.

These are solved by the Wilson- method which is anunconditionally stable step by step scheme. The time step for theresponse is chosen as 0.1 T where T is the period of the highestmode that is to be included in the response. T

technical reference 2002

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