Abstract
A closed form solution for the exact small deflections of a class of nonprismatic members is presented. Convergence and accuracy studies, carried out in conjunction with a finite element analysis, show the series solution to be rapidly convergent, stable and cost efficient. The solutions are also compared with plane stress finite element studies to assess the range of applicability of the Bernoulli-Euler equations to tapered members. The analytic solution is a powerful tool in that it can be reduced for specific problems or used to form general exact stiffness relations for structural analysis, where one element only is required for each nonprismatic section. Both approaches are demonstrated with examples. The results are compared with cubic finite element studies and again show the accuracy and computational efficiency of the closed form solution.
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