Exact static and dynamic critical loads of a sinusoidal arch under a point force at the midpoint

This paper derives the exact static and dynamic critical loads for a pinned sinusoidal arch under a concentrated force at the midpoint. For quasi-static loading, the exact critical load can be derived analytically when the rise parameter h   is greater than 4.81. In the case when the concentrated force is applied suddenly, exact dynamic critical load can be formulated when the equilibrium configurations P12± exist.