The limit state of a compressed-stretched flexible rod

One of the most important design problems is reducing the weight of a structure without performance degradation. As a rule, calculations at the design stage are performed for the maximum load expected during the life cycle of the product. However, the loads over the operation time may exceed design values (e.g., because of the earthquake). In this case, the limit state design can prevent catastrophic failure and, at the same time, provide a more efficient construction. The problem of determining the maximum load for a compressed-stretched rod is considered. The limit load applied to a flexible compressed straight rod causes its buckling. When both ends of the rod are fixed, it becomes a compressed-stretched statically indeterminate rod. This paper deals with a uniform rod of constant cross-section made of an ideal elastic-plastic material under a longitudinal force. The Euler formulation of an elastic state is involved. It is shown that, depending on the applied longitudinal force, the limit load is determined by an elastic or approximate elastoplastic solution, or by a limit state solution for a short rod.

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