Exact snapping loads of a buckled beam under a midpoint force

A buckled beam possesses two stable equilibrium configurations and is a natural bistable device. This paper first derives the exact critical load QcrS for a hinged buckled beam when it is subject to a concentrated force Q   at the midpoint quasi-statically. In the case when the midpoint force is applied suddenly, the exact expression of a conservative dynamic critical load QcrD is derived, which guarantees that snapping will not occur as long as Q is smaller than this value.