Bending of a Cantilever Beam

Description

Calculate the maximum deflection and maximum rotation (θ) of a cantilever beam loaded by a shear force of magnitude 1 lb acting on the free end of the cantilever. The length of the cantilever is 10" and the dimensions of its cross section are 1"X1". The cantilever beam is modeled as two identical cantilevers connected at their common interface with a Bonded contact condition.

File Name

Browse to drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\Static_20.SLDASM and open the file.

Study Type

Static.

Mesh Type

Solid mesh and Beam mesh in separate studies.

Material Properties

Modulus of elasticity = 1 X 106 psi, Poisson's ratio = 0.

Results

 

Theory

SOLIDWORKS Simulation

Solid Mesh

SOLIDWORKS Simulation

Beam Mesh
Displacement at the free end (UX), in -0.004 -0.004 -0.004
Rotation at the free end (RY), rad -0.0006 NA -0.0006

Analytical Solution

Displacement at free end: UX = (2* P*L3 ) / ( 6* E*I )

End rotation: θ = 3 * UX / (2*L)

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