VM-WB-MECH-085

VM-WB-MECH-085
Bending of a Composite Beam

Overview

Reference:

Roark.R.J. & Young.W.C. (1975). Formulas for Stress and Strain. New York, NY: McGraw-Hill Book Co., Inc.

Solver(s):

Ansys Mechanical

Analysis Type(s): Static Analysis
Element Type(s): Solid

Test Case

A beam of length  and width w made up of two layers of different materials is subjected to a uniform rise in temperature from Tref to To, and a bending moment My at the free-end. Ei and α i correspond to the Young's modulus and thermal coefficient of expansion for layer i, respectively.

Determine the free-end displacement δ (in the Z-direction) and the X-direction stresses at the top and bottom surfaces of the layered beam.

This problem is also presented in

VM144

in the Mechanical APDL Verification Manual.

Figure 112: Schematic

Schematic

Material PropertiesGeometric PropertiesLoading

MAT1:

E1 = 1.2 x 106 psi
α 1 = 1.8 x 10-4 in/in/°F

MAT2:

E2 = 0.4 x 106 psi
α 2 = 0.6 x 10-4 in/in/°F

 = 8 in

w = 0.5 in

t1 = 0.2 in

t2 = 0.1 in

To = 100°F

Tref = 0°F

My = 10.0 in-lb

Results Comparison

ResultsTargetMechanicalError (%)

Displacement, in

0.8320.8320

StressxTOP, psi

1730.61730.60

StressxBOT, psi

2257.62257.60