Simple beams need a nonlinear-displacement analysis even though the magnitude of displacement is small. The reason is that small displacements still significantly change the stiffness of the strip. Initially, the flat strip can resist the load only with bending stiffness. But having deformed a bit, it acquires membrane stiffness. An entirely new mechanism of load support develops because of deformation.

The big trouble with nonlinear-displacement analysis is that it is commonly referred to as "large displacement analysis." This confusing terminology implies that nonlinear-displacement analysis is only necessary for analysis of large displacement. However, the displacements need not be large to require a nonlinear analysis. All that matters is whether or not those displacements significantly modify the stiffness of the analyzed structure.