Theoretical Analysis of Suspension Bridges

The analysis of suspension bridges is a typical problem of structural frames that are associated with large deflections that play an important part in the behavior of the frame. Theoretical and practical treatises on suspension bridges were developed by many authors. Their attempt to idealize the problem to make it suitable for hand calculations has exposed these solutions to criticism. A systematic method is introduced for the analysis of suspension bridges based on the finite deflection theory and the n-dimensional generalization of the Newton-Raphson process for solving the simultaneous nonlinear equations. The basic assumptions are reported and the application of the Newton-Raphson process is examined. A derivation is given for the tangent stiffness matrix of a structural frame at a state of deformation. The analysis for two problems, a cable and a trussed girder, is given to introduce the application of the new approach. The concept of the tangent stiffness matrix is a new technique for rapid convergence of the analysis. The method is general and of particular interest for the analysis of the suspension bridges under construction conditions. It is also suitable for electronic computers.