Dynamic Analysis of Arches Using Lagrangian Approach

Abstract

Research of frequencies and modes of vibration of an arch is pursued, using the method of reducing the structure to a conservative rigid‐elastic system. The role of the reductive matrix of the strain energy is clearly shown. Finally, the loads resulting from earthquakes are investigated using dynamic analysis. It is shown that, when a horizontal earthquake occurs, skew‐symmetric vertical loads are set up; they are more dangerous; for shallow arches, than horizontal loads.