Buckling Instability

When a strut is loaded in compression it may be unable to support the applied load and fail by Buckling rather than by Plastic Deformation. The buckling process involves the
primary elastic response of the uniaxially loaded strut
that at some critical load is followed by the secondary buckling behavior. This is illustrated in the diagram in terms of the transverse displacement, w, of the strut.

From: Brush & Almroth, "Buckling of Bars,
Plates, and Shells," McGraw Hill (1975)

In the elastic range there is no transverse displacement and the strut remains straight. At the Euler buckling load, P = p² EI/ L² , the strut becomes unstable and if the load is kept constant the transverse displacement goes to infinity (the strut collapses)!