An analytically improved four-stage model for single-lap torqued bolted joints accounting for preload relaxation

The bolted joint is a vital connection type in aerospace, shipping, mechanics, and other fields. The bolt preload always exists and is standardly specified due to the tightening of the bolts, which would significantly influence the joint’s mechanical properties because of the preload relaxation. However, the vast majority of extant theoretical models of bolt joints do not account for this influence. In this study, the mechanism of preload relaxation in a single-lap bolted joint subjected to static tension is investigated. An improved analytical four-stage model is then proposed, which can predict the load–displacement curves of bolted joints with the preload relaxation for various initial bolt preloads, bolt-hole clearances, and materials with varying component thicknesses. The load–displacement curves predicted by the improved four-stage model demonstrate that due to preload relaxation, the slope of the joint load–displacement curve decreases in the first, second, and fourth stages, and the turning points of each stage would be moved back accordingly. The improved model enables the structural engineers to precisely determine the effects of various sensitivity factors on the bolted joint. The results indicate that a higher initial bolt preload, a thinner joint, and the combination of high stiffness bolts and low stiffness plates would result in a more pronounced preload relaxation.