Stiffness compatibility design method for multi‐span concrete rigid‐frame bridges

Abstract Multi‐span rigid‐frame bridges improve durability by eliminating expansion joints and bearings, but their monolithic pier‐girder connections restrain longitudinal deformation and may cause cracking in side‐span piers. This study develops an explicit stiffness‐matching method for the preliminary design of such bridges considering boundary compliance. The effective longitudinal restraint stiffness is first derived using a beam‐spring model that accounts for superstructure rotational restraint and foundation compliance caused by pile‐soil interaction. Analytical equations are then formulated to evaluate service‐stage pier moments under longitudinal braking and temperature actions, with vertical temperature‐gradient effects incorporated through an adjustable temperature amplification factor. Based on these equations, a serviceability‐based design procedure is proposed to reduce the stiffness of selected side‐span piers while maintaining braking resistance through the remaining stiffer interior piers. The accuracy of the analytical moment equations is verified using FE models, and the practical applicability of the stiffness‐matching procedure is supported by comparison with an actual viaduct. The results show that stiffness reduction is mainly required for short‐to‐medium piers, and that temperature‐induced moments exhibit a nonmonotonic variation with pier height. This finding indicates that the governing thermal demand may occur within the short‐pier range rather than at the shortest pier. The proposed method provides a direct and efficient tool for preliminary stiffness allocation and section sizing without repeated FE trial analyses.