Exact Bernoulli-Euler static stiffness matrix for a range of tapered beam-columns

The static stiffnesses for torsional and flexural deformation of a tapered beam under axial loading are determined analytically, extending the Bernoulli-Euler/Bessel-function approach of Banerjee and Williams (1985). The derivation of the expressions is explained in detail, and numerical results for sample problems are presented in tables and shown to be in excellent agreement with those obtained using stepped beams of 400 or 500 elements.