Buckling of a Quarter Ring Under a Radial Force

Description

A quarter ring has a radius of 5" , a width of 1", and a thickness of 0.1". The quarter ring is supported symmetrically. Find the buckling load applied radially as shown.

File Name

Browse to drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\Buckling_2.SLDPRT and open the file.

Mesh Type

Shell mesh.

Shell Parameters

Shell thickness = 0.1" - Thin formulation.

Material Properties

Modulus of elasticity = 1 X 107 psi.

Results

    Buckling Load (per arc length) (lbs/in)
Theory 26.66
SOLIDWORKS Simulation (Shell mesh) High 26.66
Draft 26.67
The theoretical value is calculated from Donnell approximation as: Pcr = 4EI / R3 = 26.66 lb/in, where:
  • Pcr = Critical (buckling) force
  • E = Modulus of elasticity
  • I = Moment of inertia of the cross section of the shell
  • R = Radius

The critical load from SOLIDWORKS Simulation is calculated as:

Pcr = (Applied force)*(Buckling load factor)

Reference

Brush, D. O., and Almroth, B. O., "Buckling of Bars, Plates, and Shells," McGraw-Hill Inc., New York, 1975, p. 139.