VM-WB-MECH-045

VM-WB-MECH-045
Laterally Loaded Tapered Support Structure

Overview

Reference:

Crandall, S. H., & Dahl, N. C. (1959). An Introduction to the Mechanics of Solids (p. 342, problem 7.18). New York, NY: McGraw-Hill Book Co., Inc.

Solver(s): Ansys Mechanical
Analysis Type(s): Static Structural Analysis
Element Type(s): Shell

Test Case

A cantilever beam of thickness t and length has a depth which tapers uniformly from d at the tip to 3d at the wall. It is loaded by a force F at the tip, as shown. Find the maximum bending stress at the mid-length (X = ).

Figure 57: Schematic

Schematic
Schematic

Material PropertiesGeometric PropertiesLoading
Es = 3 x 107 psi
ν s = 0
= 50 in
d = 3 in
t = 2 in
F = 4000 lb (Y direction)

Results Comparison

ResultsTargetMechanicalError (%)
Bending stress at mid length (psi)83338362.10.349