
Buckling
A
failure mode that must be taken into account when components are used
in compression is buckling. The diagram shows a strut that is long compared
to its diameter. The two ends of the strut can rotate but are constrained
to stay on the same vertical line. A load, F, applied to the strut causes
an initial elastic response, the strut decreasing in length as the load is increased
in accordance with Hooke's law. As the load F is increased one of two
outcomes may result. If the rod remains stable against buckling (remains straight)
the yield stress, s_{y}, of the material
may be passed and the strut will deform plastically and retain a deformed length
when the force is removed. For a slender rod it is more probable that
the rod deflects elastically in a transverse direction when a force F_{Cr} = p^{2}EI/L^{2} is reached, where
E is Young's modulus, I the geometric moment of inertia, and L the length of
the strut. Provided the transverse deformation does not cause the material to
plastically deform, removal of the load in this buckling case will cause the
strut to return to its initial length and shape. In general, for a slender
strut the stress at which buckling occurs is lower than s_{y} and this is the limiting strength factor in compression
loading. 









