Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
EXAMPLE 1-010 FRAME - END OFFSETS EXAMPLE DESCRIPTION This example uses a cantilever beam to test the SAP2000 end offsets. In SAP2000, end offsets may be non-rigid, partially rigid, or fully rigid. The rigidity of the offset is specified by a rigid zone factor. This factor specifies the fraction of the end offset length, measured from the frame element end, that is assumed to be infinitely rigid. The remainder of the end offset, if any, is assumed to have the same flexibility as the beam. Four models are created in this example. The first has no end offset, the second through fourth have an end offset with 0%, 50% and 100% rigidity, respectively. For each model the vertical displacement at the free end of the cantilever is compared with independent hand calculated results. Important Note: Bending and shear deformations are included in the analyses for this example. GEOMETRY, PROPERTIES AND LOADING 10k
12' a
12"
C 18"
Z Y
End offset X
End Offsets Model A: Model B: Model C: Model D:
C
a = 0, no end offset a = 6" end offset, 0% rigid a = 6" end offset, 50% rigid a = 6" end offset, 100% rigid
Section C-C
Material Properties E = 4,320 k/in2 ν = 0.2 G = 1,800 k/in2 Section Properties b = 12 in d = 18 in A = 216 in2 I = 5,832 in4 Av = 180 in2 (shear area)
EXAMPLE 1-010 - 1
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
TECHNICAL FEATURES OF SAP2000 TESTED 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 RESULTS COMPARISON Independent results are hand calculated using the unit load method described on page 244 in Cook and Young 1985. Rigid Zone Model Factor
Output Parameter
SAP2000
Percent Independent Difference
A
N.A.
Uz (free end) in
-0.39951
-0.39951
0%
B
0.0
Uz (free end) in
-0.39951
-0.39951
0%
C
0.5
Uz (free end) in
-0.37523
-0.37523
0%
D
1.0
Uz (free end) in
-0.35197
-0.35197
0%
COMPUTER FILE: Example 1-010a, Example 1-010b, Example 1-010c, Example 1-010d CONCLUSION The SAP2000 results match exactly with the independent results.
EXAMPLE 1-010 - 2
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
HAND CALCULATION
EXAMPLE 1-010 - 3