Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 1
EXAMPLE 1-019 FRAME – BUCKLING OF A RIGID FRAME PROBLEM DESCRIPTION A one-story, one-bay, two-dimensional frame is subjected to an axial force, P, at the top of each column. The buckling load for this configuration is calculated and compared with independent results calculated using formulas derived in Timoshenko and Gere 1961. Several SAP2000 models are used. Each model is identical, except for the discretization of the three frame objects. Important Note: Only buckling in the XZ plane is considered. The frame is assumed to be braced against bucking in the YZ plane. This is achieved by making only the Ux, Uz and Ry degrees of freedom active in the analysis. Important Note: Only bending deformations are considered in the analysis. Shear and axial deformations are ignored. In SAP2000 this is achieved by setting the property modification factor for area to 100,000 and setting the property modification factor for shear area to 0. GEOMETRY, PROPERTIES AND LOADING P
Material Properties E = 29,900 k/in2
P
Z 14 4"
Y X
Section Properties W8X31 A= 9.12 in2 I = 110 in4
Frame Object Discretization Model A: 1 frame element per frame object Model B: 2 frame elements per frame object Model C: 4 frame elements per frame object
144"
TECHNICAL FEATURES OF SAP2000 TESTED Buckling analysis of a rigid frame Automatic frame subdivision
EXAMPLE 1-019 - 1
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 1
RESULTS COMPARISON Independent results are calculated using formulas presented in Article 2.4 on pages 62 through 66 in Timoshenko and Gere 1961.
Model
Output Parameter
SAP2000
Independent
Percent Difference
A 1 element per object
Buckling Load (kips)
280.98
280.19
+0.28%
B 2 elements per object
Buckling Load (kips)
280.24
280.19
+0.02%
C 4 elements per object
Buckling Load (kips)
280.19
280.19
0%
COMPUTER FILES: Example 1-019a, Example 1-019b, Example 1-019c CONCLUSION The SAP2000 results show an acceptable comparison with the independent results. As the discretization increases the SAP2000 result converges to the independent result.
EXAMPLE 1-019 - 2
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 1
HAND CALCULATION
EXAMPLE 1-019 - 3