Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 6
EXAMPLE 1-002 FRAME - TEMPERATURE LOADING EXAMPLE DESCRIPTION The various types of frame temperature loads that can be modeled in SAP2000 are tested in this example using a cantilever beam and a propped cantilever beam. The beam is a 2 inch wide by inch deep rectangular section. In SAP2000, three types of temperature loads can be applied on a frame element: an overall change in temperature; a temperature variation along the element length in the local 1 direction; and a temperature gradient perpendicular to the element length (local 2 or 3 directions). For this example, each of these types of temperature loads is applied separately to both the cantilever beam and the propped cantilever beam. The free-end displacements in the cantilever beam model and the end reaction in the propped cantilever beam model are compared to independent hand calculated results. Important Note: Shear deformations are ignored in this analysis. In SAP2000 this is achieved by setting the property modification factor for shear to 0. GEOMETRY, PROPERTIES AND LOADING 2
10" C
3
3"
Z
X
C
Model A 2"
C
Section C-C C
Material Properties E = 29,000 k/in2 α = 0.0000065 /°F Section Properties A = 6 in2 I = 4.5 in4
Model B
Temperature Loads Load Case 1: Increase of 20 °F Load Case 2: Variation along local 1-axis (X-axis) of 2 °F per inch of element length (20 °F in all) Load Case 3: Gradient along 2-axis (bending about 3-axis) of 20 °F per linear inch (60 °F in 3“ of section height)
EXAMPLE 1-002 - 1
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 6
TECHNICAL FEATURES OF SAP2000 TESTED The specification of Joint patterns The application of Temperature increase Transverse temperature gradient The calculation of Displacements in free expansion Reaction forces in restrained cases caused by temperature loads RESULTS COMPARISON Independent results for load cases 1 and 2 are hand calculated using standard thermal expansion formulas. Results for load case 3 in Model B are hand calculated using Table 3 items 6a and 6c on page 107 in Roark and Young 1975. Model A: Free-End Cantilever Load Case
Output Parameter
SAP2000
Independent
Percent Difference
1
Ux (free end) (in)
0.00130
0.00130
0%
2
Ux (free end) (in)
0.00065
0.00065
0%
3
Uz (free end) (in)
-0.00650
-0.00650
0%
Model B: Propped Cantilever Load Case
Output Parameter
SAP2000
Independent
Percent Difference
1
Fx (at prop) (kips)
-22.62
-22.62
0%
2
Fx (at prop) (kips)
-11.31
-11.31
0%
3
Fz (at prop) (kips)
2.545
2.545
0%
EXAMPLE 1-002 - 2
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 6
COMPUTER FILE: Example 1-002a, Example 1-002b CONCLUSION The SAP2000 results and the independent results match exactly.
EXAMPLE 1-002 - 3
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 6
HAND CALCULATION
EXAMPLE 1-002 - 4
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 6
EXAMPLE 1-002 - 5