Analytical solutions for thermal effects of suspension bridges based on a surrogate model with longitudinal restraint stiffness

Abstract

Ambient temperature variation has a significant influence on the deformation of main cables and the internal force of towers of long-span suspension bridges. Currently, the finite element method (FEM) is mainly used for these calculations. This paper intends to present an analytical solution of the thermal effects on suspension bridges. First, three typical temperature patterns are defined. Then, a surrogate model is established by replacing the longitudinal restraint stiffness of the main cable and the tower lateral stiffness with a set of equivalent horizontal springs. The stiffnesses of the suspended cables are formulated according to the energy conservation principle, while the tower lateral stiffnesses are obtained by incorporating the pure bending and Euler buckling solutions, namely considering the effect of the axial force placed on the tower top. Following the force equilibrium conditions, two governing equations are built, which can calculate the variations in the longitudinal displacement of the tower top caused by the temperature variation. After that, some other significant thermal effects, such as the horizontal force of the main cable, the sag of the main cable and the bending moment of the tower bottom, are obtained. Finally, the analytical solution is verified through the field test data of the Tsing Ma Bridge in Hong Kong and the FEM results of four typical examples. The proposed surrogate model offers a quick and easy approach for thermal effect analysis with acceptable accuracy. It is helpful to clarify the mechanical nature of temperature effects to facilitate the preliminary bridge design.