Calculating Factors of Safety and Margins of Safety from Interaction Equations for Preloaded Bolts

This report presents the derivation of the factored interaction equations for preloaded bolts in two- or three-dimensional space. This is an extension of the previous work of the first author which covered factored interaction equations consisting of load or stress-ratios which were either solely constant or solely varying quantities. The factored interaction equations for preloaded bolts consist of an axial load-ratio that is a combination of a constant quantity, preload and thermal load at preload, and a varying quantity, tensile and bending loads, and was not covered under the previous work. Two forms of the factored interaction equations for preloaded bolts, arising from two perspectives, are presented and compared. Closed form solutions for the tensile, shear, and bending loads as functions of the other concurrent loads that produces zero margin of safety are presented.