V. Axial Forces in a Plane Frame 2
To find member forces due to a thermal load in a plane truss.
Reference
Gere J. M., and Timoshenko, S. P., Mechanics of Materials, 2nd Edition, PWS Engineering, p.21, Problem 2.6 - 23.
Problem
A symmetric, three-bar truss ABCD undergoes a temperature increase of 20°C in the two outer bars and 70°C in the middle bar. Calculate the forces F1 and F2 in the bars.
E = 200 GPa |
α = 14( 10)-6 / °C |
A = 900 mm2 |
Plane truss subject to differential thermal loading
Comparison
Result Type | Theory | STAAD.Pro | Difference |
---|---|---|---|
F1 | 22,100 | 22,143 | 0.2% (negligible) |
F2 | -31,300 | -31,315 | 0.1% (negligible) |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\02 Trusses\Axial Forces in a Plane Frame 2.STD is typically installed with the program.
STAAD TRUSS :A PLANE TRUSS
START JOB INFORMATION
ENGINEER DATE 18-Sep-18
END JOB INFORMATION
*
* REFERENCE: MECHANICS OF MATERIALS, GERE AND TIMOSHENKO, 2ND EDITION
* PWS ENGINEERING, PAGE 121, PROBLEM 2.6-23
*
UNIT METER NEWTON
JOINT COORDINATES
1 -2.12132 2.12132 0; 2 0 2.12132 0; 3 2.12132 2.12132 0; 4 0 0 0;
MEMBER INCIDENCES
1 1 4; 2 2 4; 3 3 4;
UNIT MMS NEWTON
MEMBER PROPERTY AMERICAN
1 TO 3 PRIS AX 900
UNIT METER NEWTON
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 2e+11
POISSON 0.29542
ALPHA 1.4e-05
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 TO 3 PINNED
LOAD 1 TEMPERATURE LOAD
TEMPERATURE LOAD
1 3 TEMP 20 800
2 TEMP 70
PERFORM ANALYSIS
PRINT MEMBER FORCES
FINISH
STAAD Output
MEMBER END FORCES STRUCTURE TYPE = TRUSS ----------------- ALL UNITS ARE -- NEWT METE (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 1 1 -22142.72 0.00 0.00 0.00 0.00 0.00 4 22142.72 0.00 0.00 0.00 0.00 0.00 2 1 2 31314.54 0.00 0.00 0.00 0.00 0.00 4 -31314.54 0.00 0.00 0.00 0.00 0.00 3 1 3 -22142.72 0.00 0.00 0.00 0.00 0.00 4 22142.72 0.00 0.00 0.00 0.00 0.00