VM-WB-MECH-059

VM-WB-MECH-059
Bending of a Solid Beam (Plane Elements)

Overview

Reference:

Roark, R. J. (1965). Formulas for Stress and Strain (4th ed., pp. 104, 106). New York, NY: McGraw-Hill Book Co., Inc.

Solver(s):

Ansys Mechanical

Analysis Type(s): Static Structural Analysis
Element Type(s): 2-D Plane Stress Shell element

Test Case

A beam of length and height h is built-in at one end and loaded at the free end with:

  • a moment M

  • a shear force F

For each case, determine the deflection δ at the free end and the bending stress σBend at a distance d from the wall at the outside fiber.

Figure 77: Schematic

Schematic

Case 1:

Schematic

Case 2:

Schematic

Material PropertiesGeometric PropertiesLoading
E = 30 x 106 psi
ν = 0.3
= 10 in
h = 2 in
d = 1 in
 Case 1:
M = 2000 ibf-in (Z direction)
Case 2:
F = 300 lb (Y direction)

Analysis

Since the loading is uniform and in one plane, the above problem can be analyzed as a plane stress problem.

Results Comparison

ResultsTargetMechanicalError (%)
Case 1:
Deflection (in)
StressBend (psi)
0.00500
-3000
0.00497
-3015.2
0.502
0.507
Case 2:
Deflection (in)
StressBend (psi)
0.00500
-4050
0.00508
-4057.9
1.694
0.195