V. Thermal Loading on a Beam
To find the support reactions due to a temperature loads applied on a fixed-fixed beam.
Reference
Hand calculation using the following reference:
Matrix Analysis of Framed Structures, 3rd edition, W.Weaver Jr. & J.M.Gere, Van Nostrand Reinhold, Table B2, Appendix B, p.500
Problem
The beam in the following geometric, load, and section properties: L = 7.5 m, α =
11.7(10)-6/°F,IZ = 5,000 cm4
, E =200 KN/mm2
, A = 50 cm2.
- Case 1: T = 40° F (uniform across section)
- Case 2: T1 = 0° F (below beam), T2 = 50° F (above beam)
Fixed support beam with two different temperature load cases
Comparison
Result Type | Theory | STAAD.Pro | Difference |
---|---|---|---|
Horizontal Reaction at Node A (kN) | 468 | 468 | none |
Moment at Node A (kN·m) | 19.5 | 19.5 | none |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\01 Beams\Thermal Loading on a Beam.STD is typically installed with the program.
STAAD PLANE TEMPERATURE LOAD ON A FIXED-FIXED BEAM
START JOB INFORMATION
ENGINEER DATE 18-Sep-18
END JOB INFORMATION
*
* REFERENCE : MATRIX ANALYSIS OF FRAMED STRUCTURES
* GERE & WEAVER, 3RD EDITION, VAN NOSTRAND REINHOLD
*
* TABLE B-2, APPENDIX B, PAGE 500
*
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 3 0 0; 3 7.5 0 0;
MEMBER INCIDENCES
1 1 2; 2 2 3;
UNIT CM KN
MEMBER PROPERTY AMERICAN
1 2 PRIS AX 50 IZ 5000 YD 30
UNIT METER KN
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 2e+08
POISSON 0.3
ALPHA 1.17e-05
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 FIXED
3 FIXED
LOAD 1
TEMPERATURE LOAD
1 2 TEMP 40
LOAD 2
TEMPERATURE LOAD
1 2 TEMP 0 50
PERFORM ANALYSIS
PRINT SUPPORT REACTION
FINISH