VM16

VM16
Bending of a Solid Beam (Plane Elements)

Overview

Reference:

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

Analysis Type(s):

Static Analysis (ANTYPE = 0)

Element Type(s):

2D Structural Solid Elements (PLANE42)

2D 4 Node structural elements(PLANE182)

Input Listing:

vm16.dat

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 σ_Bend a distance d from the wall at the outside fiber.

Figure 20: Bending of a Solid Beam with Plane Elements Problem Sketch

Material Properties

Geometric Properties

E = 30 x 10⁶ psi

υ = 0.0

= 10 in

h = 2 in

d = 1 in

Case 1, M = 2000 in-lb

Case 2, F = 300 lb

Analysis Assumptions and Modeling Notes

The stiffness matrix formed in the first load step is also used in the second load step (automatically determined by Mechanical APDL). The end moment is represented by equal and opposite forces separated by a distance h. The bending stress is obtained from face stresses on element 1.

Results Comparison

		Target	Mechanical APDL	Ratio
PLANE42
Case 1	Deflection, in	0.00500	0.00500	1.000
Case 1	Stress_Bend , psi	3000	3000[1]	1.000
Case 2	Deflection, in	0.00500	0.00505	1.010
Case 2	Stress_Bend , psi	4050	4050[1]	1.000
PLANE182
Case 1	Deflection, in	0.00500	0.00500	1.000
Case 1	Stress_Bend , psi	3000	3000	1.000
Case 2	Deflection, in	0.00500	0.00505	1.010
Case 2	Stress_Bend , psi	4050	4050	1.000

S(PAR) in face printout for element 1 in element solution printout.