Elasto-Dynamic Instability of Shallow Pin-Ended Steel Arches Under Central Step Loading

Abstract

When a shallow steel arch is subjected to in-plane central step loading, the arch will oscillate about an equilibrium position due to the kinetic energy imparted to the arch by the load. If the load is sufficiently large, the motion of the arch may reach an unstable equilibrium configuration that leads to elasto-dynamic instability of the arch. This paper presents a study of the in-plane elasto-dynamic instability of a shallow pin-ended circular arch under central step loading with infinite duration. The principle of conservation of energy is used to establish the criterion for elasto-dynamic instability, and analytical solutions for the lower and upper elasto-dynamic instability loads of the arch are obtained. It is found that the elasto-dynamic instability loads of a shallow pin-ended arch under central step loading with infinite duration are lower than its elasto-static counterparts.