VM11

VM11
Residual Stress Problem

Overview

Reference: S. H. Crandall, N. C. Dahl, An Introduction to the Mechanics of Solids, McGraw-Hill Book Co., Inc., New York, NY, 1959, pg. 234, problem 5.31.
Analysis Type(s): Static, Plastic Analysis (ANTYPE = 0)
Element Type(s): 3D Spar (or Truss) Elements (LINK180)
Input Listing: vm11.dat

Test Case

A chain hoist is attached to the ceiling through three tie rods as shown below. The tie rods are made of cold-rolled steel with yield strength σyp and each has an area A. Find the deflection δ at load F1 when the deflections are elastic in all three rods. When the frame is loaded to F2 (where all three rods become fully plastic), and then unloaded, find the residual stress σr in the central rod.

Figure 14: Residual Stress Problem Sketch

Residual Stress Problem Sketch

Material PropertiesGeometric PropertiesLoading
σyp = 30,000 psi
E = 30 x 106 psi
A = 1 in2
= 100 in
Θ = 30°
F1 = 51,961.5 lb
F2 = 81,961.5 lb

Note:  F1 and F2 values are back-calculated from theoretical relationships.

Analysis Assumptions and Modeling Notes

Automatic load stepping (AUTOTS,ON) is used to obtain the nonlinear plastic solution (load steps 2 and 3).

Results Comparison

TargetMechanical APDL Ratio
Deflection at F1 , in-0.07533-0.075341.000
Stressr , psi-5,650-5,650.34424 [1]1.000

  1. SAXL in element solution printout for element 2.