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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
A theoretical investigation of box bridge beams is conducted using three methods of analysis, namely, finite element, finite strip and closed cylindrical shell theory. The latter theory allows a rather rapid form of analysis for both plate and cylindrical members for box beams using a computer program.
J.E. Gibson and M.H. Mitwally
Mr. W. J. S. Gover (Redpath Dorrnan Long) : I would like firstly to express some surprise that, on the basis of one worked example and using estimated figures, Mr. Haseltine should come up with so sweeping a statement as 'a steel frame uses considerably more energy than a concrete one'. However, I do not think it serves any useful purpose here to become involved in long arguments about the numbers. Suffice it to say that I and my colleagues in the structural steel industry have considerable reservations about the figures used.