Software Verification - CSI...

Software Verification

PROGRAM NAME: SAP2000

REVISION NO.: 14

METHODOLOGY - 1

METHODOLOGY

A comprehensive series of test problems, or examples, designed to test the various elements, analysis features, and design algorithms of the program were created. The

results produced by SAP2000 were compared to independent sources, such as hand calculated results, theoretical or published results, or results obtained from other

structural/finite element programs. The comparison of the SAP2000 results with results obtained from independent sources is provided in tabular form as part of each example.

Many different equation solver options are available in SAP2000. The different solver

options typically give identical results for most of the analysis examples. For a few numerically sensitive problems the different solver options may give slightly different

results. The results presented in this document are those obtained using the Advanced equation solver running as a separate 32bit process on an Intel(R) Core(TM) i7 CPU with the Windows 7 Professional 64-bit operating system.

ACCEPTANCE CRITERIA The comparison of the SAP2000 validation and verification example results with

independent results is typically characterized in one of the following three ways.

Exact: There is no difference between the SAP2000 results and the independent results within the larger of the accuracy of the typical SAP2000 output and the

accuracy of the independent result.

Acceptable: For force, moment and displacement values, the difference between

the SAP2000 results and the independent results does not exceed five percent (5%). For internal force and stress values, the difference between the SAP2000 results and the independent results does not exceed ten percent (10%). For

experimental values, the difference between the SAP2000 results and the independent results does not exceed twenty five percent (25%).

Unacceptable: For force, moment and displacement values, the difference between the SAP2000 results and the independent results exceeds five percent (5%). For internal force and stress values, the difference between the SAP2000

results and the independent results exceeds ten percent (10%). For experimental values, the difference between the SAP2000 results and the independent results

exceeds twenty five percent (25%).



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METHODOLOGY - 2

The percentage difference between results is typically calculated using the following formula:

Percent Difference =SAP2000 Result

Independent Result-1

SAP2000 Result

Independent Result-1100

SUMMARY OF EXAMPLES

The example problems are categorized into nine groups based on the structural elements used or design type in the example. Table 1 defines the nine groups, illustrates the example problem numbering system used for each group, and identifies the summary

table used for each group.

TABLE 1: GROUPING OF EXAMPLE PROBLEMS

Group Structural

Elements Tested Example Numbering Summary

Table

1 Frame 1-001, 1-002, … , 1-xxx Table 2-1

2 Shell 2-001, 2-002, … , 2-xxx Table 2-2

3 Plane 3-001, 3-002, … , 3-xxx Table 2-3

4 Asolid 4-001, 4-002, … , 4-xxx Table 2-4

5 Solid 5-001, 5-002, … , 5-xxx Table 2-5

6 Link 6-001, 6-002, … , 6-xxx Table 2-6

7 Cable 7-001, 7-002, … , 7-xxx Table 2-7

8 Steel Frame Code Name Ex### Table 2-8

9 Concrete Frame Code Name Ex### Table 2-9

As shown in Table 1, Tables 2-1 through 2-9 summarize the validation and verification

examples for each of the nine categories. Tables 2-1 through 2-9 include the example number, the problem title, a summary of the program features tested and the method of independent verification.



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TABLE 2-1: SUMMARY OF GROUP 1 (FRAME) EXAMPLES

Exam. No. Problem Title Program Features Tested

Method of Independent Verification

1-001 General Loading

Calculation and application of Self load Projected, uniformly distributed load

Application of Uniformly distributed load in global coordinates Uniformly distributed load in frame object local

coordinates Trapezoidal and triangular distributed load on

frames Joint moments and forces

Static analysis of frames under all of these loading types

Hand calculation using the unit load method described on page 244 in Cook and Young 1985.

1-002 Temperature Loading

The specification of Joint patterns

The application of Temperature increase Transverse temperature gradient

The calculation of Displacements in free expansion Reaction forces in restrained case caused by

temperature loads

Hand calculation using standard thermal expansion formulas and using Table 3 items 6a and 6c on page 107 in Roark and Young 1975.

1-003 Distributed and Concentrated Moments

The application of Distributed moments (uniform, trapezoidal,

triangular) to frame objects Concentrated moments to frame objects

Hand calculation using equation 8.1.3 on page 284 in Cook and Young 1985.

1-004 Rotated Local Axes

Frame local axes rotated from global axes Use of AISC sections

Hand calculation using the beam deflection formulas in Table 3 item 1a and Table 3 item 2a on pages 96 and 98, respectively, in Table 3 in Roark and Young 1975.

1-005 Displacement Loading

Settlement of support in frame structures Rotation of support in frame structures Settlement of support with linear (translational) spring Rotation of support with rotational spring Skewed supports Skewed support settlement


1-006

Non-Prismatic Sections and Automatic Frame Subdivision

Structural behavior of a non-prismatic frame section Self weight calculations Linear variation of section area Linear, parabolic and cubic variation of moment of

inertia Linear variation of section torsional constant

Automatic frame subdivision




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1-007 End Releases

The end releases in a frame element, including Axial release Shear release Bending release

The related frame static analysis

Hand calculation using basic statics.

1-008 Partial Fixity End Releases

The partial fixity end releases in a frame element, including Shear partial fixity Bending partial fixity

The application of gravity load to a frame object


1-009 Prestress Applied To Frame Objects

Prestress tendon with parabolic tendon profile and different eccentricities at the two ends

Prestress tendon modeled usings loads Prestress tendon modeled as elements Prestress losses

Hand calculation using basic principles and the unit load method described on page 244 in Cook and Young 1985.

1-010 End Offsets

The use of end offsets in frames, including Non-rigid offsets Partially rigid offsets Fully rigid offsets

The effect of end offsets on the frame static analysis results


1-011 Insertion Point Cardinal point Joint offsets

Hand calculation using statics.

1-012

No Tension and No Compression Frame Objects

Tension and compression limits for frame objects End releases

Hand calculation using the unit load method described on page 244 in Cook and Young 1985 together with statics.

1-013

Simply Supported Beam on Elastic Foundation

Frame line spring assignments Static analysis of beam on elastic foundation Automatic frame subdivision

Hand calculated using formulas presented in Problem 3 on page 23 of Timoshenko 1956.

1-014 Eigenvalue Problem

Eigenvalue analysis of a frame with unequal moment of inertia values (I22 ≠ I33) for bending modes

Automatic frame subdivision

Hand calculation based on formulas presented on page 313 of Clough and Penzien 1975.



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1-015 Steady State Harmonic Loads

Steady state analysis of frame systems Time history analysis of frame systems with periodic

loading Line mass assignment to frame objects Automatic frame subdivision

Comparison with illustrative example 20.2 on page 434 of Paz 1985.

1-016

Tension Stiffening Using P-Delta Analysis

P-Delta force assignment to frame objects Nonlinear static analysis using the P-Delta option Automatic frame subdivision

Hand calculation using equation 23 on page 28 and equations 43 and 45 on page 43 of Timoshenko 1956.

1-017 Vibration of a String Under Tension

Static nonlinear analysis using the P-Delta option to provide tension stiffening

Modal analysis of frame for eigenvalues

Hand calculation using vibration theory presented on pages 506 though 510 of Kreyszig 1983.

1-018

Bending, Shear and Axial Deformations in a Rigid Frame

Calculation of bending, shear and axial deformations in a rigid frame

Frame property modification factors


1-019 Buckling of a Rigid Frame

Buckling analysis of a rigid frame Automatic frame subdivision

Hand calculation using formulas presented in Article 2.4 on pages 62 though 66 of Timoshenko and Gere 1961.

1-020

Response Spectrum Analysis of a Two-Dimensional Rigid Frame

Modal analysis of frame for eigenvalues and time periods

Response spectrum analysis Joint masses

Comparison with example 13.11 on page 521 of Chopra 1995.

1-021

Bathe and Wilson Eigenvalue Problem

Modal analysis for eigenvalues Line mass assignment to frame objects

Comparison with results published in Bathe and Wilson 1972 and comparison with results from another computer program published in Peterson 1981.



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1-022

Two-Dimensional Moment Frame with Static and Dynamic Loads

Diaphragm constraint Joint force assignments Joint mass assignments Modal analysis for eigenvalues Response spectrum analysis Modal time history analysis for base excitation Direct integration time history analysis for base

excitation

Comparison with results from another computer program published by Engineering/Analysis and Computers/ Structures International.

1-023 ASME Eigenvalue Problem

Three-dimensional frame analysis Modal analysis using eigenvectors Joint mass assignments

Comparison with results from another computer program published in Peterson 1981 and in DeSalvo and Swanson 1977.

1-024

Response Spectrum Analysis of a Three-Dimensional Moment Frame

Three-dimensional frame analysis Modal analysis using eigenvectors Rigid diaphragm constraint Joint mass assignments Response spectrum analysis

Comparison with results from another computer program published in Peterson 1981.

1-025

Response Spectrum Analysis of a Three-Dimensional Braced Frame

Three-dimensional frame analysis Modal analysis using eigenvectors Rigid diaphragm constraint Joint mass assignments Response spectrum analysis

Comparison with results from another computer program published in Peterson 1981.

1-026 Moment and Shear Hinges

Static nonlinear analysis of a frame structure using moment and shear hinges

Hand calculation using the unit load method described on page 244 in Cook and Young 1985 together with basic deflection formulas and superposition.

1-027 Construction Sequence Loading

Nonlinear static analysis using the construction sequence loading option

Frame end releases

Hand calculation using the unit load method described on page 244 in Cook and Young 1985 together with basic deflection formulas.



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1-028 Large Axial Displacements

Static nonlinear analysis of frame structure with large axial displacements using the SAP2000 P-Delta plus large displacements option

Frame end releases


1-029 Large Bending Displacements

Static nonlinear analysis of frame structure with large bending displacements using the SAP2000 P-Delta plus large displacements option

Hand calculation and Equation 4 in Article 7.1 of Chapter 7 on page 91 of Roark and Young 1975.

1-030 Moving Loads Moving load case Multi-step static load case for vehicles

Comparison with results published in Appendix A of AASHTO 1990 and hand calculation.



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TABLE 2-2: SUMMARY OF GROUP 2 (SHELL) EXAMPLES

Exam. No.

Problem Description Program Features Tested


2-001 Patch Test With Prescribed Displacements

Membrane analysis using shell elements Plate bending analysis using shell elements

Thin-plate option Thick-plate option

Joint displacement loading

Hand calculation based theory in Timoshenko and Goodier 1951 and Timoshenko and Woinowsky-Krieger 1959. Results also published in MacNeal and Harder 1985.

2-002 Straight Beam with Static Loads

Membrane analysis using shell elements Plate bending analysis using shell elements Effect of shell element aspect ratio Effect of geometrical distortion of shell element from

rectangular Joint force loading

Hand calculation using the unit load method described on page 244 in Cook and Young 1985 and using formulas from Roark and Young 1975. Results also published in MacNeal and Harder 1985.

2-003 Curved Beam with Static Loads

Membrane analysis using shell elements Plate bending analysis using shell elements Joint force loading

Hand calculation using the unit load method described on page 244 in Cook and Young 1985. Results also published in MacNeal and Harder 1985.

2-004 Twisted Beam with Static Loads

Membrane analysis using shell elements Plate bending analysis using shell elements Joint force loading


2-005 Rectangular Plate with Static Loads

Plate bending analysis using shell elements Uniform load applied to shell elements Joint force loading

Hand calculation based theory in Timoshenko and Woinowsky-Krieger 1959. Results also published in MacNeal and Harder 1985.



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METHODOLOGY - 9


Exam. No.



2-006 Scordelis-Lo Roof with Static Loads

Three-dimensional analysis using shell elements Self weight applied to shell elements Gravity load applied to shell elements Uniform load applied to shell elements

Some results published in MacNeal and Harder 1985. Other results scaled from plotted results in Zienkiewicz 1977 that were calculated using theory presented in Scordelis and Lo 1964.

2-007

Hemispherical Shell Structure with Static Loads

Three-dimensional analysis using shell elements Joint local axes Joint force loads

Results published in MacNeal and Harder 1985.

2-008 Cantilever Plate Eigenvalue Problem

Eigenvalue analysis using shell elements Area object mass assignment Area object automatic mesh Area object stiffness modifiers

Hand calculation using Table 7.7 on page 7-30 of Harris and Crede 1976.

2-009 Plate on Elastic Foundation

Plate bending analysis using shell elements Area object spring assignment Joint force loads

Hand calculation using equation 185 on page 275 of Timoshenko and Woinowsky-Krieger 1959.

2-010 Cylinder with Internal Pressure

Three-dimensional analysis using shell elements Surface pressure load applied to shell elements Joint local axes

Hand calculation using item 1b in Table 29 on page 448 of Roark and Young 1975.

2-011

ASME Cooling Tower Problem with Static Wind Pressure

Three-dimensional analysis using shell elements Joint patterns Shell element surface pressure load using joint

pattern

Results scaled from plotted results in Zienkiewicz 1977 that were calculated using theory presented in Albasiny and Martin 1967.

2-012

Plate Bending when Shear Deformations Are Significant

Plate bending analysis of shell elements when shear deformations are significant

Area object stiffness modifiers Frame distributed loads

Results published in example shown on page 376 of Roark and Young 1975.



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Exam. No.



2-013

Temperature Load that Is Constant Through Shell Thickness

Temperature loading for shell elements

Hand calculation using equation 1.3.4 on page 9 of Cook and Young 1985.

2-014

Temperature Gradient Through Shell Thickness

Temperature gradient loading for shell elements Area object local axes Joint local axes

Hand calculation using formulas presented in item 8e of Table 24 on page 361 of Roark and Young 1975.

2-015 Orthotropic Plate

Plate bending analysis of shells Orthotropic material properties Area object stiffness modifiers

Hand calculated using theory presented in Chapter 6 of Ugural 1981.

2-016 Out-of-Plane Buckling

Buckling analysis of shells Automatic area meshing (N x N) with added restraints Joint springs Frame property modifiers Frame distributed load Frame automatic subdivide at intermediate joints

Hand calculated using theory presented in Timoshenko and Gere 1961.

2-017 In-Plane Buckling

Buckling analysis of shells Joint force loads Active degrees of freedom

Hand calculated using equation 2-4 on page 48 of Timoshenko and Gere 1961.

2-018 Large Axial Displacements

Static nonlinear analysis of shell structure with large axial displacements using the SAP2000 P-Delta plus large displacements option

Joint constraints


2-019 Large Bending Displacements

Static nonlinear analysis of shell structure with large bending displacements using the SAP2000 P-Delta plus large displacements option

Automatic area meshing

Hand calculation and Equation 4 in Article 7.1 of Chapter 7 on page 91 of Roark and Young 1975.

2-020 Prestress Applied to Area Objects


Prestress tendon modeled using loads and applied to area objects

Prestress tendon modeled as elements and applied to area objects

Prestress losses




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TABLE 2-3: SUMMARY OF GROUP 3 (PLANE) EXAMPLES

Exam. No.




Membrane analysis using plane stress elements Incompatible bending mode option for plane elements Joint displacement loading

Hand calculation based theory in Timoshenko and Goodier 1951. Results also published in MacNeal and Harder 1985.


Membrane analysis using plane elements Effect of plane element aspect ratio Effect of geometrical distortion of plane element from

rectangular Joint force loading

Hand calculation using the unit load method described on page 244 in Cook and Young 1985 and using formulas from Roark and Young 1975. Results also published in MacNeal and Harder 1985.


Membrane analysis using plane stress elements Joint force loading


3-004 Thick-Walled Cylinder

Analysis using plane stress elements Analysis using plane strain elements Plane surface pressure load

Hand calculation based on theory in Timoshenko 1956 and based on formulas in Roark and Young 1975. Results also published in MacNeal and Harder 1985.

3-005 Pore Pressure Pore pressure loading for planes Joint pattern

Hand calculation using basic principles.



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METHODOLOGY - 12

TABLE 2-4: SUMMARY OF GROUP 4 (ASOLID) EXAMPLES

Exam. No.



4-001

Soil Supporting Uniformly Loaded Circular Footing

Analysis using asolid elements Asolid surface pressure load Incompatible bending modes for asolid objects

Hand calculation based on data presented in Poulos and Davis 1974.


Analysis using asolid elements Asolid surface pressure load

Hand calculation based on theory in Timoshenko 1956. Results also published in MacNeal and Harder 1985.

4-003 Rotating Annular Disk

Analysis using asolid elements Asolid rotate load

Hand calculation based on equations presented in Item 8 on page 567 of Roark and Young 1975.

4-004 Pore Pressure Pore pressure loading for asolids Joint pattern




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METHODOLOGY - 13

TABLE 2-5: SUMMARY OF GROUP 5 (SOLID) EXAMPLES

Exam. No.




Patch test using solid elements Joint displacement loading

Results also published in MacNeal and Harder 1985.


Solid object bending with and without the incompatible modes option

Effect of solid object aspect ratio Effect of geometrical distortion of solid object from a

cube Joint force loading



Solid object bending with the incompatible bending modes option

Joint force loading


5-004 Twisted Beam with Static Loads

Solid object bending and twist with the incompatible bending modes option

Joint force loading


5-005 Rectangular Plate with Static Loads

Plate bending analysis using solid elements Surface pressure load applied to solid objects Joint force loading

Hand calculation based theory in Timoshenko and Woinowsky-Krieger 1959. Results also published in MacNeal and Harder 1985.



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Exam. No.



5-006 Scordelis-Lo Roof with Static Loads

Three-dimensional analysis using solid objects Self weight applied to solid objects Gravity load applied to shell objects

Some results published in MacNeal and Harder 1985. Other results scaled from plotted results in Zienkiewicz 1977 that were calculated using theory presented in Scordelis and Lo 1964.

5-007

Hemispherical Dome Structure with Static Loads

Three-dimensional analysis using solid elements Joint force loads

Results published in MacNeal and Harder 1985.


Analysis using solid elements Solid surface pressure load Joint local axes

Hand calculation based on theory in Timoshenko 1956. Results also published in MacNeal and Harder 1985.

5-009 Prestress Applied to Solid Objects


Prestress tendon modeled using loads and applied to solid objects

Prestress tendon modeled as elements and applied to solid objects

Prestress losses


5-010 Buckling Buckling analysis of solids Joint force loads Active degrees of freedom

Hand calculation using equation 2-4 on page 48 of Timoshenko and Gere 1961.

5-011 Temperature Load

Temperature loading for solid elements

Hand calculation using equation 1.3.4 on page 9 of Cook and Young 1985.

5-012 Plate on Elastic Foundation

Plate bending analysis using solid elements Solid object surface spring assignment Solid object automatic mesh Joint force loads

Hand calculation using equation 185 on page 275 of Timoshenko and Woinowsky-Krieger 1959.



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Exam. No.



5-013 Pore Pressure Pore pressure loading for solids Solid local axis assignments Joint pattern




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TABLE 2-6: SUMMARY OF GROUP 6 (LINK) EXAMPLES

Exam. No.



6-001 Linear Link with Ramp Loading

Linear links Modal load case for eigenvectors Modal time history load case Direct integration time history load case Ramp loading

Hand calculation using theory presented in section 4.5 on pages 126 through 129 of Chopra 1995.

6-002 Multi-linear Elastic Link

Multi-linear links Displacement-controlled nonlinear static analysis

Comparison with defined link force-deformation characteristics.

6-003 Gap Element

Gap element links Force-controlled nonlinear static analysis Nonlinear modal time history analysis Nonlinear direct time history analysis Frame point loads Joint force loads Joint mass assignments Ramp loading for time histories


6-004 Hook Element Hook element links Force-controlled nonlinear static analysis Frame temperature loads

Hand calculation using standard thermal expansion formulas.

6-005

Damper Element Under Harmonic Loading

Damper element links Linear link elements Nonlinear modal time history analysis Nonlinear direct integration time history analysis Joint force loads

Hand calculation using equation 3.2.6 on page 70 in Chopra 1995.

6-006

SUNY Buffalo Damper with Linear Velocity Exponent

Damper links with linear velocity exponents Frame end length offsets Joint mass assignments Modal analysis for ritz vectors Linear modal time history analysis Nonlinear modal time history analysis Linear direct integration time history analysis Nonlinear direct integration time history analysis Generalized displacements

Comparison with experimental results from shake table tests published in Section 5, pages 61 through 73, of Scheller and Constantinou 1999.

6-007

SUNY Buffalo Damper with Nonlinear Velocity Exponent

Damper links with nonlinear velocity exponents Frame end length offsets Joint mass assignments Modal analysis for ritz vectors Nonlinear modal time history analysis Nonlinear direct integration time history analysis Generalized displacements




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TABLE 2-6: SUMMARY OF GROUP 6 (LINK) EXAMPLES

Exam. No.



6-008 Plastic Wen Link

Plastic Wen links Displacement-controlled nonlinear static analysis Link local axis assignments Link gravity load


6-009 Plastic Kinematic Link

Plastic kinematic links Displacement-controlled nonlinear static analysis Link gravity load


6-010

SUNY Buffalo Eight-Story Building with Rubber Isolators

Rubber isolator links Linear links Zero-length, two-joint link elements Diaphragm constraints Modal analysis for ritz vectors Nonlinear modal time history analysis Nonlinear direct integration time history analysis Generalized displacements

Comparison with results from the computer program 3D-BASIS-ME (see Tsopelas, Constantinou and Reinhorn 1994) published in Section 2, pages 5 through 23, of Scheller and Constantinou 1999.

6-011

SUNY Buffalo Seven-Story Building with Friction Pendulum Isolators

Friction pendulum link elements Damper link elements Zero-length, two-joint link elements Diaphragm constraints Frame end length offsets Modal analysis for ritz vectors Nonlinear modal time history analysis Nonlinear direct integration time history analysis Joint masses


6-012 Frequency Dependent Links

Frequency dependent links Steady state analysis

Hand calculation using formulas and theory presented in section 3.2 on pages 68 through 69 of Chopra 1995.



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TABLE 2-7: SUMMARY OF GROUP 7 (CABLE) EXAMPLES

Exam. No.



7-001 Uniform and Temperature Loading

Uniform load applied to cable elements Temperature load applied to cable elements Joint displacement loading Nonlinear static analysis

Comparison with results published in Figure 5 of Peyrot and Goulois, 1979.

7-002 Uniform and Concentrated Loading

Uniform load applied to cable elements Concentrated load applied to cable elements Response combination results Nonlinear static analysis

Comparison with results published in Section 4.6.2, Table 4.2, of Tibert, 1999.

7-003 Prestressed Cable Net

Uniform load applied to cable nets Concentrated load applied to cable nets Nonlinear static analysis

Comparison with results published in Section 4.6.3, Table 4.4, of Tibert, 1999.



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TABLE 2-8: SUMMARY OF GROUP 8 (STEEL FRAME DESIGN) EXAMPLES

Design Code Examples Program Features Tested


AISC 360-05

Ex001 Ex002

Bending of a wide flange member Compression of a built-up wide flange member

Examples F.1-2a and E.2 of AISC Design Examples, Vol. 13.

AISC 360-10

Ex001 Ex002


Examples F.1-2a and E.2 of AISC Design Examples, Vol. 13.

AISC ASD-89

Ex001 Ex002

Bending of a wide flange member Compression of a wide flange member

Example 3 of Allowable Stress Design Manual of Steel Construction, 9th Ed.

AISC LRFD-93

Ex001 Ex002

Bending of a wide flange member Combined compression and biaxial bending of a wide

flange member

Examples 5.1 and 6.2 of LRFD Manual of Steel Construction, 2nd Ed.

AS 4100-1998

Ex001 Ex002 Ex003

Compression of a wide flange member Bending of a wide flange member Combined compression and bending of a wide flange

member

Hand calculations.

BS 5950-2000

Ex001 Ex002

Bending of a wide flange member Combined compression and bending of a square tube

member

Hand calculations and Example 15 of SCI Publication P326.

CSA S16-09

Ex001 Ex002

Bending of a wide flange member Combined compression and bending of a wide flange

member

Examples 1, 2, and 3 of the Handbook of Steel Construction to CSA S16-01.

CSA S16-14

Ex001 Ex002


member

Examples 1, 2, and 3 of the Handbook of Steel Construction to CSA S16-01.

EN 3-2005 Ex001 Ex002 Ex003

Combined compression and bending of a wide flange member


member

Hand calculations.

IS 800-2007

Ex001 Ex002 Ex003

Compression of a wide flange member Bending of a wide flange member Combined compression and biaxial bending of a wide

flange member

Hand calculations.



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TABLE 2-8: SUMMARY OF GROUP 8 (STEEL FRAME DESIGN) EXAMPLES



KBC 2009 Ex001 Ex002


Hand calculations.

NTC 2008 Ex001 Ex002



Hand calculations.

NZS 3404-1997

Ex001 Ex002 Ex003

Compression of a wide flange member Bending of wide flange member Combined compression and bending of a wide flange

member

Hand calculations.



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TABLE 2-9: SUMMARY OF GROUP 9 (CONCRETE FRAME DESIGN) EXAMPLES



ACI 318-08

Ex001 Ex002

Shear reinforcement design of a rectangular beam Flexural reinforcement design of a rectangular beam P-M interaction check of a rectangular column

Hand calculations.

ACI 318-11

Ex001 Ex002


Hand calculations.

ACI 318-14

Ex001 Ex002


Hand calculations.

AS 3600-2009

Ex001 Ex002

Shear reinforcement design of a T-beam Flexural reinforcement design of a T-beam P-M interaction check of a rectangular column

Hand calculations.

BS 8110-1997

Ex001 Ex002


Hand calculations.

CSA A23.3-04

Ex001 Ex002


Hand calculations.

CSA A23.3-14

Ex001 Ex002


Hand calculations.

EN 2-2004 Ex001 Ex002


Hand calculations.

IS 456-2000

Ex001 Ex002


Example 1 from SP-16 Design Aids for Reinforced Concrete and hand calculations.

KBC 2009 Ex001 Ex002


Hand calculations.

NTC 2008 Ex001 Ex002


Hand calculations.

NZS 3101-2006

Ex001 Ex002


Hand calculations.

RCDF 2004

Ex001 Ex002


Hand calculations.



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TABLE 2-9: SUMMARY OF GROUP 9 (CONCRETE FRAME DESIGN) EXAMPLES



SS CP 65-1999

Ex001 Ex002


Example 3.4 of Chanakya Arya, Design of Structural Elements and hand calculations.

TS 500-2000

Ex001 Ex002


Hand calculations.



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MATRIX OF PROGRAM FEATURES COVERED IN EXAMPLES This section presents tables illustrating which element assignments, including loads, and

which load case types are addressed in each of the analysis examples. Table 3 shows the contents of the matrix tables.

TABLE 3: CONTENTS OF MATRIX TABLES

Features Table

Joint assignments including loads Table 4-1

Frame object assignments including loads Table 4-2

Area object assignments including loads Table 4-3

Solid object assignments including loads Table 4-4

Link object assignments including loads Table 4-5

Cable object assignment including loads Table 4-6

Load case types Table 4-7

As illustrated in Table 3, the program features matrices are presented in tables 4-1

though 4-6. These tables are shown on the following pages.



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TABLE 4-1: JOINT ASSIGNMENT MATRIX

Joint Assignments Example Problems

Restraints Most

Constraints 1-022, 1-024, 1-025, 2-018, 6-010, 6-011

Springs 1-005, 2-016

Masses 1-020, 1-022, 1-023, 1-024, 1-025, 6-003, 6-006, 6-007, 6-011

Local axes 1-005, 2-007, 2-010, 2-014, 5-008

Panel zones

Joint patterns 1-002, 2-011, 3-005, 4-004, 5-013

Joint forces

1-001, 1-003, 1-004, 1-006, 1-010, 1-011, 1-012, 1-016, 1-019, 1-022, 1-026, 1-027, 1-028, 1-029, 2-002, 2-003, 2-004, 2-005, 2-007, 2-009, 2-017, 3-002, 3-003, 5-003, 5-004, 5-005, 5-012, 6-003, 6-005

Joint displacements 1-005, 2-001, 3-001



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TABLE 4-2: FRAME OBJECT ASSIGNMENT MATRIX

Frame Assignments Example Problems

Non-prismatic section 1-006

Frame property modifiers 1-001, 1-002, 1-004, 1-005, 1-006, 1-013, 1-014, 1-018, 1-020, 1-021, 1-024, 2-016

End releases 1-007, 1-012, 1-028

Partial fixity 1-008

Local axes 1-004

End length offsets 1-010, 6-006, 6-007, 6-011

Insertion point 1-011

Prestress definition 1-009

P-Delta force 1-016

Tension/compression limits 1-012

Hinges 1-026

Line springs 1-013

Line mass 1-015, 1-021

Automatic frame subdivide 1-006, 1-013, 1-014, 1-015, 1-017, 1-019, 2-016

Gravity load 1-008

Point load 1-001, 1-004, 1-007, 1-011, 1-013, 6-003

Distributed load 1-001, 1-003, 1-008, 1-015, 1-016, 1-018, 2-012, 2-016

Temperature load 1-002, 6-004

Prestress load 1-009

Frame self weight 1-006, 1-009



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TABLE 4-3: AREA OBJECT TYPE AND ASSIGNMENT MATRIX

Area Type and Assignments Example Problems

Shell type area object 2-001 through 2-020

Plane type area object 3-001 through 3-005

Asolid type area object 4-001 through 4-004

Stiffness modifiers 2-008, 2-012, 2-015

Local axes 2-014

Area springs 2-009

Area Mass 2-008

Automatic area mesh 2-008, 2-016, 2-019

Gravity load (all) 2-006

Uniform load (shell) 2-005, 2-006

Uniform load to frames (shell)

Surface pressure (all) 2-010, 2-011,3-004, 4-001, 4-002

Pore pressure (plane, asolid) 3-005, 4-004

Temperature load (all) 2-013, 2-014

Rotate load (asolid) 4-003

Wind pressure coefficients (shell)

General prestress applied to area objects

2-020



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TABLE 4-4: SOLID OBJECT ASSIGNMENT MATRIX

Solid Assignments Example Problems

Local axes 5-013

Surface springs 5-012

Automatic solid mesh 5-012

Gravity load 5-006

Surface pressure load 5-005, 5-008

Pore pressure load 5-013

Temperature load 5-011

General prestress applied to solid objects

5-009



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METHODOLOGY - 28

TABLE 4-5: LINK OBJECT TYPE AND ASSIGNMENT MATRIX

Link Type and Assignments Example Problems

Linear link 6-001, 6-005, 6-010

Multilinear elastic link 6-002

Gap (compression only) link 6-003

Hook (tension only) link 6-004

Damper link 6-005, 6-006, 6-007, 6-011

Plastic (Wen) link 6-008

Plastic (kinematic) link 6-009

Rubber isolator link 6-010

Friction isolator link 6-011

Frequency dependent link 6-012

Local axes 6-008

Gravity load 6-008, 6-009

TABLE 4-6: CABLE OBJECT TYPE AND ASSIGNMENT MATRIX Link Type and Assignments Example Problems

Cable element 7-001, 7-002

Cable net 7-003

Rubber isolator link 6-010

Friction isolator link 6-011

Frequency dependent link 6-012

Uniform load 7-001, 7-002

Temperature load 7-001



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METHODOLOGY - 29

TABLE 4-7: LOAD CASE TYPE MATRIX

Load case type Example Problems

Linear static Most

Multi-step static 1-030

Nonlinear static 1-012, 1-016, 1-017, 1-026, 6-002, 6-003, 6-004, 6-008, 6-009, 7-001, 7-002, 7-003

Nonlinear static with construction sequence loading

1-027

Nonlinear static with large displacements

1-028, 1-029, 2-018, 2-019

Modal for eigenvectors 1-014, 1-017, 1-020, 1-021, 1-022, 1-023, 1-024, 1-025, 2-008 6-001

Modal for ritz vectors 6-006, 6-007, 6-010, 6-011

Response spectrum 1-020, 1-022, 1-024, 1-025

Linear transient modal time history

1-022, 6-001, 6-006

Linear periodic modal time history

1-015

Nonlinear transient modal time history

6-003, 6-005, 6-006, 6-007, 6-010, 6-011

Linear direct integration time history

1-022, 6-001, 6-006

Nonlinear direct integration time history

6-003, 6-005, 6-006, 6-007, 6-010, 6-011

Moving load 1-030

Buckling 1-019, 2-016, 2-017, 5-010

Steady state 1-015, 6-012

Power spectral density

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