 # V. 2D Plate Thermal Moment and Stress

To find the bending moment due to thermal load through the thickness of a square plate.

## Reference

Timoshenko, S., Strength of Materials, D. Van Nostrand Co., 3rd Edition,1956.

## Problem

Temperature varies 100°F linearly through the thickness of a square plate that is fixed on the edges. Calculate the bending moment on the edges and the maximum bending stress.

 E = 30,000.0 ksi

 α = 70×(10)–7 in/in/°F

 Size = 5 × 5

 Thickness = 0.5 in

 Poisson’s ratio = 0.3 ## Comparison

Table 1. Comparison of results
Moment (in·lb/in) 625.0 625.0 none
Maximum stress (psi) 15,000 15,000 none

Tip: You can copy and paste this content directly into a .std file to run in STAAD.Pro.

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\04 Plates Shells\2D Plate Thermal Moment and Stress.STD is typically installed with the program.

``````STAAD SPACE :THERMAL LOADING OF A PLATE
START JOB INFORMATION
ENGINEER DATE 14-Sep-18
END JOB INFORMATION
*
*  REFERENCE: TIMOSHENKO, S., "STENGTH OF MATERIALS," 3RD EDITION,
*             D. VAN NOSTRAND CO., 1956.
*
UNIT INCHES POUND
JOINT COORDINATES
1 0 0 0; 2 5 0 0; 3 0 5 0; 4 5 5 0;
ELEMENT INCIDENCES SHELL
1 1 2 4 3;
ELEMENT PROPERTY
1 THICKNESS 0.5
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 3e+07
POISSON 0.3
ALPHA 7e-06
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 TO 4 FIXED
LOAD 1 NON UNIFORM HEATING OF THE PLATE
1 TEMP 0 100
PERFORM ANALYSIS
PRINT ELEMENT JOINT STRESSES ALL
FINISH
``````

```   ELEMENT STRESSES    FORCE,LENGTH UNITS= POUN INCH
----------------
STRESS = FORCE/UNIT WIDTH/THICK, MOMENT = FORCE-LENGTH/UNIT WIDTH
ELEMENT  LOAD       SQX        SQY          MX          MY          MXY
VONT       VONB         SX          SY          SXY
TRESCAT    TRESCAB
1      1        -0.00       -0.00     -625.00     -625.00        0.00
15000.00    15000.00        0.00        0.00        0.00
15000.00    15000.00
TOP : SMAX=  -15000.00 SMIN=  -15000.00 TMAX=       0.00 ANGLE= 90.0
BOTT: SMAX=   15000.00 SMIN=   15000.00 TMAX=       0.00 ANGLE= 90.0
JOINT        -0.00       -0.00     -625.00     -625.00        0.00
1      15000.00    15000.00        0.00        0.00        0.00
TOP : SMAX=  -15000.00 SMIN=  -15000.00 TMAX=       0.00 ANGLE= 90.0
BOTT: SMAX=   15000.00 SMIN=   15000.00 TMAX=       0.00 ANGLE= 90.0
JOINT        -0.00       -0.00     -625.00     -625.00        0.00
2      15000.00    15000.00        0.00        0.00        0.00
TOP : SMAX=  -15000.00 SMIN=  -15000.00 TMAX=       0.00 ANGLE= 90.0
BOTT: SMAX=   15000.00 SMIN=   15000.00 TMAX=       0.00 ANGLE= 90.0
JOINT        -0.00       -0.00     -625.00     -625.00       -0.00
4      15000.00    15000.00        0.00        0.00        0.00
TOP : SMAX=  -15000.00 SMIN=  -15000.00 TMAX=       0.00 ANGLE= 90.0
BOTT: SMAX=   15000.00 SMIN=   15000.00 TMAX=       0.00 ANGLE= 90.0
JOINT        -0.00       -0.00     -625.00     -625.00        0.00
3      15000.00    15000.00        0.00        0.00        0.00
TOP : SMAX=  -15000.00 SMIN=  -15000.00 TMAX=       0.00 ANGLE= 90.0
BOTT: SMAX=   15000.00 SMIN=   15000.00 TMAX=       0.00 ANGLE= 90.0
**** MAXIMUM STRESSES AMONG SELECTED PLATES AND CASES ****
MAXIMUM       MINIMUM       MAXIMUM       MAXIMUM       MAXIMUM
PRINCIPAL     PRINCIPAL       SHEAR       VONMISES       TRESCA
STRESS        STRESS        STRESS        STRESS        STRESS
1.500000E+04 -1.500000E+04  1.011339E-03  1.500000E+04  1.500000E+04
PLATE NO.       1             1             1             1             1
CASE  NO.       1             1             1             1             1
```