# 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

## Comparison

Table 1. Comparison of results
F1 22,100 22,143 0.2% (negligible)
F2 -31,300 -31,315 0.1% (negligible)

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
1 3 TEMP 20 800
2 TEMP 70
PERFORM ANALYSIS
PRINT MEMBER FORCES
FINISH
``````

```   MEMBER END FORCES    STRUCTURE TYPE = TRUSS