Software Verification

PROGRAM NAME: SAP2000

REVISION NO.: 6

EXAMPLE 2-013
SHELL –TEMPERATURE LOAD THAT IS CONSTANT THROUGH SHELL THICKNESS

PROBLEM DESCRIPTION
In this example a rectangular plate with irregularly shaped elements is subjected
to a temperature increase of 100 °F that is constant through the thickness of the
plate. The geometry and properties for the plate are the same as those described
for the patch test in MacNeal and Harder 1985. Joint displacements and stresses
resulting from the temperature load are compared with hand calculated results.

Two different models are created for this example. The models are identical,
except for the joint restraints. Model A has a fixed restraint at joint 1, thus
allowing free expansion of the plate. Model B has pinned restraints at the four
corner joints (joints 1, 2, 7 and 8), thus restraining the temperature expansion.

GEOMETRY, PROPERTIES AND LOADING

0.24"
Joint Coordinates (inches)
Joint X Y Z
2 8
4 1 0 0 0
4 6 2 0 0.12 0
3 0.04 0.02 0
0.12"

1 5
3 4 0.08 0.08 0
Y 5 0.18 0.03 0
3 2 5
Z 1 7 6 0.16 0.08 0
7 0.24 0 0
1 - Joint number 8 0.24 0.12 0
X
1 - Area object number
Material Properties Section Properties Loading
E = 1,000,000 lb/in2 Thickness = 0.001 in Temp raised 100 °F
ν = 0.25
Joint Restraint
γ = Coeff. thermal exp.
= 5.5E-06 Model A: Joint 1 has Ux, Uy, Uz, Rx , Ry and Rz restrained
Model B: Joints 1, 2, 7 and 8 have Ux, Uy and Uz restrained

EXAMPLE 2-013 - 1
 Software Verification
PROGRAM NAME: SAP2000
REVISION NO.: 6

TECHNICAL FEATURES OF SAP2000 TESTED

 Temperature loading for shell elements

RESULTS COMPARISON
The independent results are hand calculated based on Equation 1.3.4 on page 9 in
Cook and Young 1985. The results for the thin plate option and the thick plate
option are presented separately.

Thin Plate Option

Output Percent
Model Parameter SAP2000 Independent Difference
Ux (jt 8) in 0.000132 0.000132 0%
A
Uy (jt 8) in 0.000066 0.000066 0%
Free
expansion σxx (jt 8) lb/in2 0 0 0%
σyy (jt 8) lb/in2 0 0 0%
Ux (jt 8) in 0 0 0%
B Uy (jt 8) in 0 0 0%
Restrained σxx (jt 8) lb/in2 -733.33 -733.33 0%
σyy (jt 8) lb/in2 -733.33 -733.33 0%

EXAMPLE 2-013 - 2
 Software Verification
PROGRAM NAME: SAP2000
REVISION NO.: 6

Thick Plate Option

Output Percent
Model Parameter SAP2000 Independent Difference
Ux (jt 8) in 0.000132 0.000132 0%
A
Uy (jt 8) in 0.000066 0.000066 0%
Free
expansion σxx (jt 8) lb/in2 0 0 0%
σyy (jt 8) lb/in2 0 0 0%
Ux (jt 8) in 0 0 0%
B Uy (jt 8) in 0 0 0%
Restrained σxx (jt 8) lb/in2 -733.33 -733.33 0%
σyy (jt 8) lb/in2 -733.33 -733.33 0%

COMPUTER FILES: Example 2-013a-thick, Example 2-013a-thin;

Example 2-013b-thick, Example 2-013b-thin

CONCLUSION
The SAP2000 results show an exact comparison with the independent results for
both the thin plate option and the thick plate option.

EXAMPLE 2-013 - 3
 Software Verification
PROGRAM NAME: SAP2000
REVISION NO.: 6

HAND CALCULATION

EXAMPLE 2-013 - 4