Approximate Stiffness Matrix for Tapered Beams

Abstract

A method for finding a modified bending stiffness matrix for a member of varying section is presented. The assumption is made that the displacement function for a uniform beam may be used as an approximation to the correct displacement function, thus leading to greater simplicity in the computation, while providing sufficient accuracy for most purposes. It is shown that for two practical applications of the approximate stiffness matrix for tapered beams, economy of effort can be achieved without any great loss of accuracy. For large tapers, the accuracy of the method is acceptable. Even greater accuracy is to be expected for smaller tapers.