Bending of a Solid Beam

Description

A 10" long cantilever beam has a rectangular cross section of 1" width and 2" height. Find the deflection of the free end under the effect of the following loads:
  • An end moment of 2000 in-lb, and
  • A shear force of 300 lbs.

File Name

Browse to drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\Static_16.SLDPRT and open the file.

Study Type

Static.

Mesh Type

Solid mesh and Beam mesh in separate studies.

Meshing Parameters

Use a Global Size of 2 in for Solid mesh.

Material Properties

Modulus of elasticity = 3 X 107 psi, Poisson's ratio = 0.

Results

Y-displacement at the free end (UY), in

Theory

SOLIDWORKS Simulation

Solid Mesh

SOLIDWORKS Simulation

Beam Mesh
End moment (Moment Study) 0.005 0.005006 0.005
Shear force (Force Study) 0.005 0.005093 0.005

Analytical Solution

wy = (2* P*L3 ) / ( 6* E*I ) (Force Study)

wy = (M* L2 ) / (2* E*I ) (Moment Study)

where:
  • P: Shear force
  • M: End moment
  • L: Beam length
  • E: Modulus of elasticity
  • I: Area moment of inertia

Reference

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