Continuous Method of Suspension Bridge Analysis

A general formulation of a deflection theory is presented which is based on a continuous mathematical model. The problem is treated as a nonlinear boundary-value problem for ordinary differential equations. Because of its nonlinear character, the Newton-Raphson procedure is applied in a function space. Each linear solution within the Newton-Raphson solution is a linear boundary-value problem which is solved as sets of linear initial-value problems. Serious numerical difficulties are encountered in solving these initial-value problems, as well as the methods employed in overcoming these difficulties. The method presented differs substantially from the classical continuous deflection theory in that horizontal cable displacements are admitted, which eliminates the need for any explicit cable condition of compatibility. In addition, nonlinear terms in the cable equations of equilibrium are fully taken into account. Example problems are presented and the results are compared with the results of a discrete formulation by the writers. Conclusions are drawn concerning the effect of hanger elongations.