VM3

VM3
Thermally Loaded Support Structure

Overview

Reference:	S. Timoshenko, Strength of Material, Part I, Elementary Theory and Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, pg. 30, problem 9.
Analysis Type(s):	Static, Thermal Stress Analysis (ANTYPE = 0)
Element Type(s):	3D Spar (or Truss) Elements (LINK180)
Input Listing:	vm3.dat

Test Case

Find the stresses in the copper and steel wire structure shown below. The wires have a cross-sectional area of A. The structure is subjected to a load Q and a temperature rise of ΔT after assembly.

Figure 4: Support Structure Problem Sketch

Material Properties

Geometric Properties

E_c = 16 x 10⁶ psi

α_c = 92 x 10^-7 in/in-°F

E_s = 30 x 10⁶ psi

α_s = 70 x 10^-7 in/in-°F

A = 0.1 in²

Q = 4000 lb

ΔT = 10°F

Analysis Assumptions and Modeling Notes

Length of wires (20 in.), spacing between wires (10 in.), and the reference temperature (70°F) are arbitrarily selected. The rigid lower beam is modeled by nodal coupling.

Results Comparison

	Target	Mechanical APDL	Ratio
Stress in steel, psi	19,695.	19,695.	1.000
Stress in copper, psi	10,152.	10,152.	1.000