Abstract
Members of a plane-frame structure may be subjected to a combination of lateral loads, end moments, and axial forces. Analysis of such a structure may be classified as elementary, first-order, or second-order, depending on the load conditions, magnitude of displacements, and method of solution. A numerical procedure is presented for the solution of geometrically nonlinear problems considering second-order effects. After a brief literature review, the paper presents the assumptions pertinent to the research; the relationship between the engineering strain and Green strain tensor considering small strain and moderate to large rotations; finite-element consideration in the derivation of the incremental stiffness matrices using increments of total potential energy and the concepts of a variational method; a procedure for the solution of the nonlinear problems and its algorithm; numerical examples and comparison of the numerical results with published literature; and conclusions and results. The algorithm that is presented is useful in identifying the differences between the first- and second-order analysis of structural systems.
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