On the nonunique equilibrium states of a shallow arch subjected to a uniform lateral load

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Abstract
Using the exact solutiom of a shallow elastic arch clamped at both ends and subjected to a uniform lateral load, it is shown that, in addition to the equilibrium states usually discussed in the literature, also other equilibrium states, which correspond to higher modes of deformation, do exist. It is shown that there exist only a finite number of equilibrium branches which correspond to these higher modes, the number depending upon the shallowness of the arch. A number of graphs are presented which demonstrate these findings. The paper concludes with the proof that all states of equilibrium which correspond to the branches of higher order are unstable.

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