Zhi-Qi He

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.

Strut‐and‐tie modeling (STM) is commonly employed in the design of multiple pile caps in bridge structures. However, the construction of the model can be complicated by manual and experience‐related challenges. Based on load‐path modeling (LPM), this study presents analytical solutions for solving the elastic stress distribution in multiple‐pile caps with various structural configurations. This is accomplished by employing the transparent LPM approach that combines graphical and analytical features. It is found that the LPM is able to capture the distribution of transverse tensile stresses in the bottom region of multiple‐pile caps. At the same time, direct equations are developed to calculate the resultant transverse tension forces in multiple‐pile caps. The LPM results can be used as a quantitative basis for constructing strut‐and‐tie models. Finally, a worked example is provided to show the efficiency of the proposed LPM.

The steel–concrete hybrid girder bridge structure is a combination of steel and concrete members in the direction of the bridge length. In long-span segmental concrete box girder bridges, the utilization of lightweight steel girders in the middle portion of the main span would greatly reduce the bridge self-weight while decreasing concrete creep and shrinkage effects. A critical parameter in the design of hybrid girder bridges is the rational length of the steel portion as a part of the main span (in other words, the rational location of the steel–concrete connection). Based on the concept of system equivalence, the steel–concrete hybrid system is equivalent to a full-concrete system with a reasonable span arrangement. The governing condition of the equivalence is that both systems have the same magnitude of self-weight hogging bending moments over the piers. Applying the system equivalence method, the rational length ratio of the steel portion to the main span (ξ) is explicitly solved, and its relationship with the length ratio of side span to main span (λ) is established. Finally, the proposed analytical approach is validated by five case studies, indicating that it is an effective and efficient method for the preliminary design of hybrid girder bridges.