Local Flexibility Coefficients for the Built-in Ends of Beams and Plates Including the Effects of Foundation Fillet Radii

The local deformations at the built-in end of a beam or plate re-entrant corner have considerable influence upon the redundant forces and moments at the juncture, and hence, upon the stresses. The effects of these local flexibilities are quite significant at nozzle-to-vessel intersections, head-to-shell junctures, tubesheet-to-heat exhanger shell junctures, and the like. Methods are available in the literature which permit the incorporation of the additional flexibility of the juncture into a structural analysis, but these methods do not adequately consider the influence of the transition fillet radius. Presented in this paper is the dependency on the fillet radius of the planar flexibility coefficients for the mean rotation and displacement due to bending and shear acting on a quarter-plane support. These relationships are obtained from elastic finite-element analyses of a quarter-plane support and are presented in a form that may be easily incorporated into design methodologies. Also, presented are the stress concentration factors in the fillet and a numerical example illustrating the significance of the results.