The President 1972-73

Finding the exact solution of boundary and eigenvalue problems in the case where the boundary configuration is not natural to one of the common co-ordinate systems for which the governing partial differential equation can be solved by the standard method of separation of variables is, in general, out of the question. Approximate methods such as finite differences, finite elements, collocation, etc. must be used. It has been shown by several authors that the conformal mapping technique provides a suitable approach for analysing bending, buckling and vibration problems of thin elastic plates.

Continuous composite beams can only be designed by simple plastic theory if the hinges at the supports have adequate rotation capacity. This is often controlled by local buckling of the webs and flanges. Tests to determine the effect of local buckling on the rotation capacity of composite beams under negative bending are described, Comparisons are made with limiting web and flange slenderness ratios currently used in steel design both in Great Britain and in North America. It is found that some of the existing regulations can be applied to composite beams, but that others may be unsafe, for both steel and composite beams. Alternative rules are proposed. J. Jay Climenhaga and R. Paul Johnson

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