Analytical formulas of thermal deformation of suspension bridges

Deformation of a long-span suspension bridge is mainly caused by ambient temperature changes. The temperature-induced deformation of a bridge is usually calculated using complex three-dimensional finite element analysis, the mechanism of which is often unclear. In this study, we derive general, succinct analytical formulas of the thermal deformation of three-span suspension bridges. The deformation of different components is unified into a one-dimensional thermal expansion formula (δL=L_Eθ·δT) by introducing an equivalent length L_E. The sag effect of side-span cables is characterized by the modification coefficients, which demonstrate that the neglect of the sag effect overestimates the thermal deformation. Furthermore, the thermal deformation of the main- and side-span cables and towers is found to interact with each other as a result of the cable tension changes with varying temperature. The analytical formulas are validated using eight long-span suspension bridges including the Akashi Kaikyo bridge, the longest main-span suspension bridge in the world. The closed-form solutions herein also apply to the self-anchored suspension bridges.