In-Plane Stability of Parabolic Arches

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Abstract
Studies are reported of the response to uniformly distributed loading of parabolic arches of rise equal to a fourth of the span. Base conditions are both fixed and pinned. The distributed loading varies between covering less than half the span to covering the complete span. The numerical studies use a discrete element, large deformation method that enables the prediction of the complete load-deformation history of an elastic arch up to full inversion if necessary. Account is taken of axial as well as flexural strains and, under full span loading published data are confirmed for the load intensities at which equilibrium bifurcation occurs. The significant result is that the intensity of load that can be supported by a fully elastic arch is significantly less than the bifurcation value when approximately three-fourths of the span is loaded. The reduction in load intensity is appreciable for both fixed and pinned arches.

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