Southwell plot

The Southwell plot is a graphical method of determining experimentally a structure's critical load, without needing to subject the structure to near-critical loads.^[1] The technique can be used for nondestructive testing of any structural elements that may fail by buckling

Critical load

Southwell Plot.

Consider a simply supported beam under a compressive load P. The differential equation of equilibrium is

Southwell plots v/P against v and obtains P₁=P_critical=P_c from the slope of the predicted straight line graph.^[3]

This analysis was done for a specific point on a simply supported beam, but the concept can be extended to arbitrary structures. With any problem whose mathematical analog is the same fourth order ordinary differential equation as above, with similar boundary conditions, the first eigenvalue of the associated homogenous problem can be obtained from the slope of the graph. Therefore, a point of large deflection can be chosen, and it does not need to be the center of a simply supported beam