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.
Model
Comparison
Table 1. Comparison of results
Result Type |
Theory |
STAAD.Pro
|
Difference |
Moment (in·lb/in) |
625.0 |
625.0 |
none |
Maximum stress (psi) |
15,000 |
15,000 |
none |
STAAD Output
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