Structural buckling 01: square column

Steel column with a square cross section.

Case Description

A solid steel column has a square cross section, is fully fixed at one end, and free at the other end. The column is subjected to a unit load at the free end. Therefore, the resultant buckling multiplier equals the critical buckling load. The result of interest is the lowest (fundamental) buckling mode.

Dimensions

• Cross Section = 25 mm x 25 mm
• Length = 1 m

Study Type

• Structural Buckling

Mesh Parameters

• Mesh Type = Solid, Tetrahedral
• Mesh Size = 8 mm, absolute
• Element Order = Parabolic

Material Properties

• Modulus of Elasticity = 2.1 x 105 MPa
• Poisson's Ratio = 0.3

Constraint

• Fully Fixed (X, Y, and Z) at the bottom (–Z end)

Loads

• 1 N Force at the top (+Z end)

Comparison of Results

The critical buckling load for Mode 1 equals the buckling multiplier times the applied load of 1.0 N.

Reference

Timoshenko, S. and Gere, J. M., Theory of Elastic Stability, 3rd Edition. New York: McGraw-Hill Book Co., Inc., 1970.