Tip Displacements of a Circular Beam

Description

A circular beam fixed at one end and free at the other end is subjected to a 200 lb force as shown in the figure. Determine the deflections in the X, Y direction. Radius of curvature of the beam = 10". The beam width and thickness are 4" and 1" respectively.

File Name

Browse to drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\Static_3.SLDPRT and open the file.

Study Type

Static.

Mesh Type

Shell mesh.

Shell Parameters

Shell thickness = 1 in - Thin formulation.

Material Properties

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

Results

The UX and UY displacements at the free edge are calculated and compared to analytical values:

Theory SOLIDWORKS Simulation
X Deflection at free edge (UX), inch 0.00712 0.00713
Y Deflection at free edge (UY), inch 0.01 0.01

Analytical Solution

DX = ( 3/4 * π-2)* H R3 / (E *I)

DY = (1/2*H*R3 ) / ( E* I )

where:
  • H: In-plane force
  • R: Radius of curvature of beam
  • E: Modulus of Elasticity
  • w: Beam width
  • t: Beam thickness
  • I: Moment of inertia: w *t3 / 12

Reference

Warren C. Young, “Roark's Formulas for Stress and Strain,” Sixth Edition, McGraw Hill Book Company, New York, 1989.