Effect of axial strain on postbuckling behavior of slanted elastic columns

Abstract

The purpose of this thesis is to investigate the load-displacement characteristics of a pinned-end axially-loaded column including the effect of axial strain. The buckling and post-buckling behavior of the column is investigated utilizing a nonlinear theory of large deflection analogous to the "elastica problem" of classical nonlinear elasticity.

The minimum potential theorem of variational calculus is utilized to obtain the nonlinear differential equations of equilibrium. Numerical solutions of the problem are obtained using an "Intermediate Theory" which combines the potential energy function together with the Rayleigh-Ritz method to produce a set of nonlinear algebraic equations which are solved by numerical iterative techniques. The results of the "Intermediate Theory" are compared with the classical nonlinear differential equation solutions in order to justify the adequacy of the approximate procedure. The problem of the vertical column is examined as a first step to justify the latter considerations. The entire mathematical process is then used to investigate the behavior of a slanted column where the axial force does not align with the column axis.