Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 6
EXAMPLE 7-001 CABLE – UNIFORM AND TEMPERATURE LOADING PROBLEM DESCRIPTION In this example six cables, each with an undeformed length of 100 feet, and each with a different configuration of supports, are subjected to a 1 kip/ft uniform vertical load (which includes cable self-weight) and a 100 F temperature change. The geometry, properties and loading are as described in Figure 5 of Peyrot and Goulois, 1979 and are reproduced in the following figure. The cable element is used in the SAP2000 model. The support reactions resulting from the prescribed uniform and temperature loads are compared with results presented in Peyrot and Goulois, 1979. In the Sap2000 model cable C1 is modeled and results for cables C2 through C6 are obtained by applying appropriate joint displacement loads to the lower support in the model. The modulus of elasticity, E, is set to 1 k/ft2, the cable area is set to 30,000,000 ft2, and the coefficient of thermal expansion is set to 0.0000065/F. GEOMETRY, PROPERTIES AND LOADING
Z Coordinate in feet
Z
Cable Properties EA = 30,000,000 kips ET = 0.0000065 kips/(ft2-°F) Undeformed Length = 100 ft
90 80 70
Cable Loading Uniform Vertical Load = 1 k/ft Temperature Change = 100 °F
60 50 40 30 20 10 0
C2
C6 0
C3
C4
C5
C1
X 20
40
60
X Coordinate in feet
80
100
Notes 1. Properties and loading shown apply to each of the six cables, C1 to C6. 2. The top and bottom support points of cable C6 both are at X=0 feet.
EXAMPLE 7-001 - 1
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 6
TECHNICAL FEATURES OF SAP2000 TESTED Uniform load applied to cable elements Temperature load applied to cable elements Joint displacement loading Nonlinear static analysis RESULTS COMPARISON The independent results are shown in Figure 5 of Peyrot and Goulois, 1979.
Cable C1
Output Parameter
SAP2000
Independent
Percent Difference
Lower Support X Reaction
4,258,491
4,170,000
+2%
Lower Support Z Reaction
-2,555,045
-2,511,000
+2%
Lower Support X Reaction
504.1
504.0
0%
Lower Support Z Reaction
-328.9
-328.8
0%
Lower Support X Reaction
22.15
22.15
0%
Lower Support Z Reaction
15.73
15.73
0%
Lower Support X Reaction
9.17
9.17
0%
Lower Support Z Reaction
19.24
19.24
0%
Lower Support X Reaction
3.06
3.06
0%
Lower Support Z Reaction
19.93
19.93
0%
Lower Support X Reaction
0.00
0.00
0%
Lower Support Z Reaction
20.02
20.02
0%
C2
C3
C4
C5
C6
COMPUTER FILES: Example 7-001 CONCLUSION The SAP2000 results show an acceptable comparison with the independent results.
EXAMPLE 7-001 - 2