Analytical solution for quick decision of tied–arch bridge parameters at early-design stage based on Hellinger–Reissner variational method

Abstract

The tied-arch bridge is the combined system of an arch, a beam and suspenders. There have been a few methods applied in the design stage of the analysis of tied-arch bridges including finite element analysis and approximate solutions. The approximate solution based on the Ritz method has been very popular in the analysis of hybrid bridges during the early design stages for its high efficiency. The disadvantage of the Ritz method is that it only directly determines the deformation values while the forces in the structural members should be decided through the obtained deformation values, which highly decreases the accuracy of the force values. Based on the Ritz method, the Hellinger–Reissner (H–R) variational principle is introduced here to improve the approximate solution. It analyzes both the deformation and forces of the tie-arch bridge directly. This is the first time of the application of this method in the analysis of the tied-arch bridges. The advantage of the H–R variational principle is that it provides the forces and deformation values independently and directly which highly enhances the accuracy of the results. For verification, the material properties of the tied-arch bridge of the second-stage project of Line No.1 in Wuhan railway transportation are applied here. And the results from H–R variational method show good agreement with finite element analysis. Hence, the presented method could be a relatively good alternative to use in the early-design stage of the tied-arch bridges.