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Problem 1 021

This document summarizes the verification of SAP2000 software by analyzing the eigenvalues of a 10-bay, 9-story frame structure. SAP2000 results for the first 3 eigenvalues matched independent results from Bathe and Wilson 1972 and Peterson 1981 with less than 0.1% difference, validating the modal analysis and line mass assignment features of SAP2000.

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100 views2 pages

Problem 1 021

This document summarizes the verification of SAP2000 software by analyzing the eigenvalues of a 10-bay, 9-story frame structure. SAP2000 results for the first 3 eigenvalues matched independent results from Bathe and Wilson 1972 and Peterson 1981 with less than 0.1% difference, validating the modal analysis and line mass assignment features of SAP2000.

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© © All Rights Reserved
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Software Verification

PROGRAM NAME: SAP2000


REVISION NO.: 0

EXAMPLE 1-021
FRAME – BATHE AND WILSON EIGENVALUE PROBLEM

PROBLEM DESCRIPTION
A ten-bay, nine-story, two-dimensional, fixed base frame structure solved in
Bathe and Wilson 1972 is analyzed for the first three eigenvalues. The SAP2000
results are compared with independent results presented in Bathe and Wilson
1981 as well as independent results presented in Peterson 1981.

The material and section properties, and the mass per unit length used for all
members, shown in the figure below, are consistent with those used in the two
above mentioned references.

Important Note: Only bending and axial deformations are considered in the
analysis. Shear deformations are ignored by setting the shear area to 0.

GEOMETRY AND PROPERTIES

9 @ 10' = 90'

10 @ 20' = 200'
Z
Y Material Properties Typical Section Properties
E = 432000 k/ft2 A = 3 ft2
X
Mass per unit length = 3 k-sec/ft2 I = 1 ft4

EXAMPLE 1-021 - 1
Software Verification
PROGRAM NAME: SAP2000
REVISION NO.: 0

TECHNICAL FEATURES OF SAP2000 TESTED


 Modal analysis for eigenvalues
 Line mass assignment to frame objects

RESULTS COMPARISON
SAP2000 results are compared with independent results presented in Bathe and
Wilson 1972 as well as independent results presented in Peterson 1981.

Comparison with Bathe and Wilson 1972

Output Percent
Mode Parameter SAP2000 Independent Difference

1 Eigenvalue 0.589541 0.589541 0%

2 Eigenvalue 5.52696 5.52695 +0.0002%

3 Eigenvalue 16.5879 16.5878 +0.0006%

Comparison with Peterson 1981

Output Percent
Mode Parameter SAP2000 Independent Difference
1 Eigenvalue 0.589541 0.589541 0%

2 Eigenvalue 5.52696 5.52696 0%

3 Eigenvalue 16.5879 16.5879 0%

COMPUTER FILE: Example 1-021

CONCLUSION
The SAP2000 results show an exact comparison with Peterson 1981 and an
acceptable comparison with Bathe and Wilson 1972.

EXAMPLE 1-021 - 2

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