Analytical Solution for In-Plane Displacement of Multi-Span Curved Bridge

Based on the theory of virtual work and principle of thermal elasticity, exact solutions for in-plane displacements of curved beams with pinned-pinned ends are derived explicitly. In the case of infinite limit of radius, these equations coincide with that of the straight beams. Compared with the results of FEM, the analytical solutions by the proposed formulae are accurate. A real multi-span curved bridge subjected to concentrated loads caused by the friction force on the top of piers and thermo load due to temperature difference is analyzed by using the newly derived equations as well as FEM. The agreement further suggests the practicability of the proposed theory. The analytical solutions obtained in this paper would provide a scientific base for further study and design of the curved bridges.