The purpose of the paper is to present an exact analytical solution of a curved beam under thermal load based on the principle of thermal expansion and theory of virtual work. A class of equations for in-plane displacements with three freedom directions and internal forces in the cross-section of curved beams with pinned-pinned ends under thermo load are derived explicitly. In the case of infinite curavature 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. In order to study the temperature effect on a curved bridge, a real multi-span curved bridge subjected to concentrated loads caused by the friction force on the top of bridge piers and thermo load due to temperature difference is analyzed by using the newly derived equations as well as FEM. The agreements further suggest the practicality of the proposed theory. The analytical solutions obtained in this paper would provide a scientific base for further study and design of curved bridges.


Curved beam, as a common structure form, is widely used in many fields, such as civil and mechanical engineering. Thermal effects are commonly found in both mechanical and structural systems. As a general rule, thermal effects in curved beam are much more important for the design of statically indeterminate structures than statically determinate ones. In this paper, the analytical solution of curved beam for in-plane displacements caused by temperature change is derived. Abundance of research references can be found on static and dynamic analysis of spatial curved beam, especially the out-of-plane behaviors. Wu & Howson (2003) studied on out-of-plane responses of curved Timoshenko beam. Gendy & Saleeb introduced the spatial response of curved beams with arbitrary thin-walled cross sections using finite element method.

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