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Verification Manual | Part II, Simulation Descriptions |

DSVM29

Elasto-Plastic Analysis of a Rectangular Beam

Overview

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Reference:Timoshenko S., Strength of Materials, Part II, Advanced Theory and Problems, Third Edition, Article 64, pp. 349
Analysis Type(s):Static Plastic Analysis
Element Type(s):Solid

Test Case

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A rectangular beam is loaded in pure bending. For an elastic-perfectly-plastic stress-strain behavior, show that the beam remains elastic at M = Myp = σypbh2 / 6 and becomes completely plastic at M = Mult = 1.5 Myp. To get accurate results, set the advanced mesh control element size to 0.5 inches.

Figure 29.1  Stress-Strain Curve

Figure 29.2  Schematic

Material Properties
E = 3e7 psi
ν = 0.0
σyp = 36000 psi
Geometric Properties
Length L = 10”
Width b = 1”
Height h = 2”
Loading
M = 1.0 Myp to 1.5 Myp
(Myp = 24000 lbf - in)

Analysis

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The load is applied in three increments: M1 = 24000 lbf-in, M2 = 30000 lbf-in, and M3 = 36000 lbf-in.

Results Comparison

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M/MypTargetDSError (%)
 StateEquivalent Stress (psi)StateEquivalent Stress (psi) 
1fully elastic36000fully elastic360590.164
1.25elastic-plastic36000elastic-plastic362880.800
1.5plasticsolution not convergedplasticsolution not converged-

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