Nonlinear Large Deflection-Small Strain Elastic Analysis of Beam-Column with Semirigid Connections

Abstract

The nonlinear large deflection-small strain analysis of a slender beam-column of symmetrical cross section with semirigid connections under end loads (conservative and nonconservative), including the effects of axial load eccentricities and out-of-plumbness, is developed in a simplified manner. Timoshenko's stability functions are utilized in the proposed method which, although approximate, can be used in the stability and nonlinear large deflection-small strain elastic analyses of beam-columns with rigid, semirigid, and simple connections. The proposed method consisting of a single nonlinear equation can also be utilized in the large deflection-small strain inelastic analysis of beam-columns whose connections suffer from flexural degradation or, on the contrary, flexural stiffening. Load results from the proposed method are within 1.5% of the theoretical values up to very large transverse displacements (0.80 times the member span when the changes in the member cord length are taken into account, or 0.30 times the member span when its cord length is assumed to remain constant). The validity and effectiveness of the proposed method and equations are verified against available solutions of large deflection-small strain elastic analysis, including the solution of the classic problem of the “Elastica.”