VM-WB-MECH-044

VM-WB-MECH-044
Thermally Loaded Support Structure

Overview

Reference:	Timoshenko, S. (1955). Strength of Material, Part I: Elementary Theory and Problems (3rd ed., pp. 30, problem 9). New York, NY: Ds. Van Nostrand Co., Inc.
Solver(s):	Ansys Mechanical
Analysis Type(s):	Linear Thermal Stress Analysis
Element Type(s):	Beam

Test Case

An assembly of three vertical wires has a rigid horizontal beam on which a vertically downward force Q is acting. Length of the wires is 20 in, the spacing between the wires is 10 in and the reference temperature is 70 °F. The entire assembly is subjected to a temperature rise of ΔT. Find the stresses in the copper and steel wire of the structure shown below. The wires have a cross-sectional area of A.

Figure 56: Schematic

Material Properties

Geometric Properties

VMSIM044_material_rigid:

E_r = 3e16 psi

ν_r = 0

VMSIM044_material_copper:

E_c = 1.6e7 psi

ν_c = 0

α_c = 9.2e-6 / °F

VMSIM044_material_steel:

E_s = 3e7 psi

ν_s = 0

α_s = 7e-6 / °F

A = 0.1 in²

Q = 4000 lb (Y direction)

ΔT = 10 °F

Results Comparison

Results	Target	Mechanical	Error (%)
Stress in steel (psi)	19695	19695	0.00
Stress in copper (psi)	10152	10152	0.00