In tension a stay is stable except for plastic deformation when the yield stress is passed. In compression another event, buckling, may determine the design limit for load.

The diagram shows a strut of length, L, being loaded in compression by a force, F. The system is stable against small sideways displacements until the force F reaches some critical value:
F_C = {n² p² E A² / 4 L² }
where the rod is assumed to be circular in cross section with an area A. Once F_C is passed, the rod buckles and the section is considered to have failed. The lowest value of F_C is for n = 1.

If the strut is slender enough (i.e. {A/L} is small enough), the buckling force will correspond to a stress, (F_C / A), that is less than the yield stress of the material. For this case, buckling occurs before the elastic limit of the material is reached.

From: Polakowski and Ripling, "Strength and Structure of Engineering Materials," Prentice Hall (1966)