ABSTRACT
Consider a perfectly straight, uniform, homogeneous column of flexural rigidity EI, length L which is subjected to an end axial compressive load P . The moment-displacement relation according to the Euler-Bernoulli beam theory is given by
M = −EI d 2w¯
dx¯2 (2.1.1)
in which x¯ is the longitudinal coordinate measured from the column base, w¯ the transverse displacement and M the bending moment. The EulerBernoulli beam theory is based on the assumption that plane normal cross-sections of the beam remain plane and normal to the deflected centroidal axis of the beam, and the transverse normal stresses are negligible (Reddy, 2002).
