The problem of a low half-sine pinned arch under a quasi-statically applied half-sine load is considered. The low arch is resting on an elastic foundation. Critical loads are obtained by investigating the stability of the equilibrium positions by considering all possible modes of deformation. It is assumed that the behavior of the arch is linearly elastic up to the critical load. The entire range of values for the modulus of the foundation is considered. The results are presented graphically as either critical load (snap-through) or classical buckling load (stable bifurcation) versus the rise parameters for a large number of values of the modulus of foundations. This investigation presents an interesting model for stability studies, because, depending on the value of the rise parameter and the modulus of the foundation, the load-deflection curve exhibits the possibilities of the top-of-the-knee buckling, snap-through buckling through unstable bifurcation, and classical buckling (stable bifurcation).

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