Investigation on the vehicle-bridge dynamic interaction considering the vertical curvature of bridge and environmental thermal effects

Abstract

River-crossing bridges often utilise curved design to account for the highway profile change, distribute traffic loads and manage water flow. The vehicle-curved bridge interaction (VBI) is complicated, especially combining with environmental thermal effects. These thermo-mechanical interactions differ substantially from those in straight bridges and warrant detailed study. In this study, a curved bridge is modeled as a Timoshenko beam (TB) with pinned supports at both ends. Governing equations are derived using the four-node isoparametric beam element and cubic polynomial shape function. The vehicle is modelled as a half-car model to account for its bouncing and pitching motions. Thermal effects are represented by a linear temperature gradient through the beam depth, which is converted into equivalent thermal loads. An analytical framework that superimposes moving vehicle loads and thermal loads within the coupled motion equations is developed. The dynamic response of the VBI system is analyzed using a zero-order displacement and velocity overshoot (U₀-V₀) iterative method. The parametric study reveals that: (1) the shear deformation significantly affects high vibration modes; (2) the bridge stiffness increases when the radius of its curvature reduces, which induces the reduction of bridge and vehicle displacement responses; (3) the thermal bending and expansion of the bridge have a large effect on dynamic amplification factor (DAF), while the impact of its curvature on dynamic load coefficient (DLC) becomes dominant for high vehicle speeds. These findings provide valuable insights for the design, analysis, and maintenance of curved bridges operating under combined vehicular and thermal loading conditions.