Buckling of Columns with Variable Cross Sections

Description

A long column consists of two portions each with a constant cross section. Both cross sections are squares with sides 1" and 0.795" with the thicker portion in the bottom. The thicker portion is fixed at its base and a force of 100 lbs is applied to the free end of the thinner portion. The lengths of the thicker and thinner portions are 60" and 40" respectively. Calculate the buckling load of the column.

File Name

Browse to drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\Buckling_5.SLDPRT and open the file.

Mesh Type

Solid mesh and Beam mesh in separate studies.

Material Properties

Modulus of elasticity = 3X107 psi, Poisson's ratio = 0.3.

Results

  Critical (Buckling) Load
Theory 530.00
SOLIDWORKS Simulation - Solid Mesh 531.62
SOLIDWORKS Simulation - Beam Mesh 534.96
The buckling load is calculated as: Pcr = 2.12 EI2/L2, where:
  • Pcr = Critical (buckling) force
  • E = Modulus of elasticity
  • I2 = Moment of inertia of the cross section of the thicker portion of the column
  • L = Total length of the column

The critical load from SOLIDWORKS Simulation is calculated as:

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

Reference

Wang, C. T., “Applied Elasticity,” McGRaw-Hill Book Company, New York, 1953, pp 231.