VM-WB-MECH-067

VM-WB-MECH-067
Elongation of a Solid Tapered Bar

Overview

Reference:

Harris, C. O. (1959). Introduction to Stress Analysis (p. 237, problem 4). New York, NY: The Macmillan Co.

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

Test Case

A tapered aluminum alloy bar of square cross-section and length L is suspended from a ceiling. An axial load F is applied to the free end of the bar. Determine the maximum axial deflection δ in the bar and the axial stress σy at mid-length (Y = L/2). Use a global mesh size of 0.5 in.

Figure 89: Problem Sketch

Problem Sketch

Material PropertiesGeometric PropertiesLoading
E = 10.4 x 106 psi
ν = 0.3
L = 10 in
d = 2 in
F = 10000 lbf

Analysis Assumptions and Modeling Notes for Ansys Mechanical

The following figure shows the finite element model in Ansys Mechanical:

Figure 90: Ansys Mechanical Schematic

Ansys Mechanical Schematic

Results Comparison for Ansys Mechanical

ResultsTargetMechanicalError (%)
Directional Deformation Y (in)0.00480770.00482150.287
Normal Stress Y at L/2 (psi)444444630.428