Stress analysis of parabolic arches and their dynamic behavior

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Virginia Polytechnic Institute

This thesis is concerned with both the static and dynamic analysis of parabolic arches. In the dynamic part, special attention is given to the free vibration of such arches.

The following procedure is followed. The loading conditions are assumed and a infinitesimal segment of the arch is taken so as the differential equations relating deflections and slope changes on both ends of the segment are developed. These obtain a set of general equations for elastic parabolic arches.

In dynamics, the equations of general curved structure are developed through considerations of dynamic equilibrium. A sudden removal of loading is assumed to cause the structure to vibrate freely. Then, a method of separating variables for partial differential equations is used to get the equations of deflection components. Each special characteristic function is derived for each special set of boundary conditions so as to get an unlimited number of modes of free vibrations. The Fourier series is employed to determine the coefficients of the dynamic equations, and to get a series-form solution for deflections.

Finally, two numerical examples are given to represent the practical application. Two kinds of parabolic arches, one with two-hinged supports and the other with fixed-ends are considered in each procedure.