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

Table 1. Comparison of results
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