Local Flexibility Coefficients for the Built-In Ends of Beams and Plates

Abstract

The usual methods of structural analysis (including most modern computer methods) are based on the assumption that cross sections remain plane. Consequently local flexibilities at structural discontinuities are not included in these analyses. The present paper considers the effects of local deformations at the built in end of a beam or plate. Influence coefficients are given for the “mean” rotation and deflection due to bending M and shear V acting on the support. The plane strain coefficients also represent limiting solutions for shells with very large diameter to thickness ratios. These “mean” values are defined so that the work done by M and V acting through them is equal to the work done by the corresponding local stresses and deformations acting on the support. Theoretical solutions are obtained for a quarter plane support using DUZ, a finite difference clasticity computer program. The suitability of this method for evaluating local flexibilities at reentrant corners, and the usefulness of the “mean” rotation and deflection values is verified experimentally.