Nonlinear relations between the beam displacement and generalized strain me
asures, which have basic effects on postbuckling behavior of elastic beams,
are presented. The complex coupling phenomena associated with the higher o
rder strain terms is reviewed for the special case of planar and rectilinea
r pinned-pinned beams. Special consideration was made for the physical assu
mptions used in the various column-beam models. A natural hierarchy results
yielding that all the higher order terms can, for a specific beam formulat
ion, be steadily obtained by dissimilar polynomial approximations of the ge
neralized strains. The asymptotic expansions method and the minimum energy
criterion are used to perform analytical calculation of the postbifurcation
equilibrium path at the neighborhood of a bifurcation point when only a un
ique buckling mode is assumed to occur. As a result. postbuckling branches
are easily obtained even when accounting for both beam centerline extension
al deformation and shear strain. They show that the critical load is scarce
ly affected by the higher order strain terms unlike the postbuckling paths
which are found to be very sensitive to them.