Buckling of Column for Various Support Conditions

Description

A column of length 120" is subjected to a compressive normal force. The cross section of the column is an ISO rectangular tube of size: 50 x 30 x 26. Calculate the buckling load for various support conditions.

File Name

Browse to drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\Buckling_6.SLDPRT and open the file.

Mesh Type

Beam mesh.

Material Properties

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

Column Properties

ISO rectangular tube of size: 50 x 30 x 26. Cross sectional area: 0.58 in2; Moments of Inertia: Ix = 0.2792 in4, Iy = 0.1247 in4.

Column Restraints

Four cases are considered for the end restraints:
  • Pinned - Pinned
  • Fixed - Free
  • Fixed - Fixed
  • Fixed - Pinned
At the joint where the force is applied, the translational degree of freedom in the direction of the force is released.

Results

Buckling Load (lb) Theory SOLIDWORKS Simulation
(a) Pinned - Pinned 2,564 2,563.9
(b) Fixed - Free 641 640.96
(c) Fixed - Fixed 10,256 10,255
(d) Fixed - Pinned 5,246 5,245
  • (a) Pinned - pinned column: Pcr = π2E I / L2
  • (b) Fixed - free column: Pcr = π2E I / 4 L2
  • (c) Fixed - fixed column: Pcr = 4 π2E I / L2
  • (d) Fixed - pinned column: Pcr = 2.046 π2E I / L2
where:
  • Pcr = Critical (buckling) load
  • E = Modulus of elasticity
  • I = Smallest moment of inertia of the column's cross section
  • L = Total length of the column

The critical load from SOLIDWORKS Simulation is calculated as:

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

Reference

Gere & Timoshenko, “Mechanics of Materials”, PWS Publishing Company, Boston, MA, pp 755.