Analysis of Suspension Bridges Using Energy Principles

The paper deals with the analysis of suspension bridges using strain energy principles. Interaction between girder and cable is shown to be conveniently treated by means of a Lagrangian multiplier function. The method of calculus of variations is applied to show that the strain energy function, modified by the Lagrangian multiplier, leads to exact equations of equilibrium. Truncated Fourier series representations of the displacements and cable strain increase are used to obtain an approximate solution for a single span bridge. Results are compared with those obtained from the classical deflection theory. Conditions of geometrical compatibility and of equilibrium corresponding to the two theories are investigated and compared. An
improved compatibility condition for the deflection theory is proposed. Finally, both theories are compared with the results from a detailed experimental investigation.

F. Van der Woude