Extrapolation Techniques for Buckling Loads

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Abstract
The Southwell, Modified and Massey extrapolation techniques are derived for a doubly symmetric beam with a transverse force applied at an eccentricity to the shear center. A finite element algorithm which takes into account small initial geometric imperfections is presented using simple matrix algebra. The load vs. deflection path for elastic cases, can be traced for beams with varying kinematic boundaries, loadings, and distributions of small initial geometric imperfections. Comparison of the Southwell, Modified, and Massey Plots are made using finite element results for the problem of an I‐section cantilever beam with a concentrated end load applied at the bottom flange. The Southwell Plot appears to be superior as a nondestructive procedure for the determination of the buckling load.

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