Abstract
Starting from the principle of virtual forces (PVF), one devises a flexibility-type method to obtain, based on the Timoshenko beam theory (TBT), exact expressions for the structural properties of nonprismatic frame elements. One adopts polynomials of different orders to interpolate the sectional rigidity values over the elements and employs exact Timoshenko’s shape functions for evaluating deformation-dependent structural properties, such as geometric stiffness. In this respect, we present a mathematically formal process to obtain the changes in the preexisting element forces needed to calculate geometric stiffnesses. The procedure adopted in this paper easily allows one to include higher-order nonlinear terms in the analysis. Robustness of the proposed formulation is observed by conducting geometrically nonlinear analyses of 2D semirigid steel frames possessing nonprismatic members. General nonlinear curves describing the semirigid connections may be easily incorporated into the analysis.
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