## 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. The technique can be used for nondestructive testing of any structural components that may fail by buckling.

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

${\displaystyle {\frac {d^{4}v}{dx^{4}}}+\alpha ^{2}{\frac {d^{2}}{dx^{2}}}(v-v^{o})=0}$, ${\displaystyle \alpha ^{2}={\frac {P}{EI}}}$

where vo is the initial deflection, and the boundary conditions are

${\displaystyle v(0)=v^{''}(0)=v(L)=v^{''}(L)=0}$

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