Buckling of a Frame

Description

Two parallel sides of a 100" square frame are loaded axially as shown. The frame has a uniform square cross section of 1"X1". Find the symmetrical buckling load in the plane of the frame.

File Name

Browse to drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\Buckling_1.SLDPRT and open the file.

Mesh Type

Shell mesh.

Shell Parameters

Shell thickness = 1" - Thin formulation.

Material Properties

Modulus of elasticity = 1 X 107 psi.

Modeling Hints

A quarter of the frame is modeled due to double symmetry and only the symmetrical modes are considered.

Results

    Buckling Load (lbs)
Theory 1372
SOLIDWORKS Simulation High 1392
Draft 1421
The theoretical value is calculated from: Pcr = 16.47EI/ L2 = 1372.45, where:
  • Pcr = Critical (buckling) force
  • E = Modulus of elasticity
  • I = Moment of inertia of the cross section
  • L = Length of the frame side

The critical load from SOLIDWORKS Simulation is calculated as:

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

Reference

Timoshenko, S. P. and Gere J. M., “Theory of Elastic Stability,” McGraw-Hill Book Co., New York, 1961.