Exact solution for in-plane displacement of redundant curved beam

Abstract

Early theoretical research of curved beams dates back to 1980s (Zhao et al. 2006). Analytical solutions of internal forces and deformations were derived (Heins 1981, Yao 1989) for plane curved beams with constant curvature under out-of-plane loads, based on traditional mechanics of structures, in which the coupling of flexure and torsion was taken into account. Further, Tufekci and Dogruer (2006) obtained the exact solution of out-of-plane problems of a plane arch with varying curvature and cross section. Along with the development of the study, some theoretical results for plane curved beams have been applied in the design of curved bridges (Sun 1995). Nevertheless, the in-plane problems of curved beams have not been studied widely. Much less research could be found in related Criterion and Standards. In order to investigate the reason of in-plane damage happened in curved bridges in recent years, Li et al. (2007) and Li and Zhao (2008) presented the solution of the displacement of the plane curved beams subjected to an in-plane load and a changed temperature by using structural mechanics method. The method brings some errors for application without considering the effects of the transverse shear deformation and torsion-related warping. The purpose of this study is to give the exact solution of curved beams stressed by the centripetal force of vehicles running along the bridge in plane, including the contribution of transverse shear deformation effect. The accuracy and efficiency of the theory are demonstrated by comparing the analytical solutions with the results obtained by structural mechanics method. Finally particular