The Analysis of Certain Interconnected Arch Systems

THIS paper describes a new and very simple method for the analysis of two pinned sinusoidal arch ribs. (Since the difference between a sinusoidal and a parabolic profile of the same rise and span is quite small the theory will apply to parabolic arches with reasonable accuracy.) The analysis shows that the bending moment diagram for an arch rib of this type is obtained by subtracting from the simple span bending moment diagram its first harmonic component. It is also shown that harmonic components of the loading higher than the first produce no horizontal thrust and that a system of arch ribs of negligible torsional stiffness interconnected by cross girders which transmit only vertical forces may be analysed as a flat grid provided that the first harmonic of the simple span bending moment diagram or deflection curve, as the case may be, is omitted. Distribution coefficients for grids have been published previously by the Authors. A worked example of the method of calculation is shown and a confirmatory experiment is described in an Appendix.

A. W. Hendry and L. G. Jaeger