VM-WB-MECH-030

VM-WB-MECH-030
Bending of Long Plate Subjected to Moment - Plane Strain Model

Overview

Reference:Any standard Strength of Materials book
Solver(s):

Ansys Mechanical

Analysis Type(s):Plane Strain Analysis
Element Type(s):2D Structural Solid

Test Case

A long, rectangular plate is fixed along the longitudinal face and the opposite face is subjected to a moment of 5000 lbf-in about the z-axis. To get accurate results, set the advanced mesh control element size to 0.5 inches.

Find X normal stress at a distance of 0.5 inches from the fixed support. Also find total deformation and reaction moment.

Figure 39: Schematic

Schematic

Material PropertiesGeometric PropertiesLoading
E = 2.9e7 psi
ν = 0.0
Length L = 1000"
Width W = 40"
Thickness T = 1"
Moment M = 5000 lbf-in

Analysis

Since the loading is uniform and in one plane (the x-y plane), the above problem can be analyzed as a plane strain problem. Therefore, the moment applied will be per unit length (5000/1000 = 5 lbf-in). Analysis takes into account the unit length in the z-direction.


Note:  This problem was defined to be solved in the BIN units system. Results should also be viewed in BIN units.


Figure 40: Plane Strain Model (analyzing any cross section (40" x 1") along the length)

Plane Strain Model (analyzing any cross section (40" x 1") along the length)

Results Comparison

ResultsTargetMechanicalError (%)
Normal Stress30300.000
Maximum Normal Stress in the X-Direction (psi)30300.000
Maximum Total Deformation (in)0.1655e-20.16553e-20.018
Total Reaction Moment (lbf-in)-5-50.000