Deflections, Vibrations, and Stability of a Pair of Leaning Arches

Abstract

A structure consisting of two arches leaning against each other and attached at their crowns is considered. Such structural units are used in bridges and in frameworks for tents. Their three-dimensional elastic behavior is examined for six types of loads: a concentrated vertical load at the crown, a uniformly distributed vertical load applied over the whole structure or over half of it, a wind load, and uniformly distributed loads acting parallel to the ground and approaching either obliquely or from the side. The arches are semicircular and pinned at the base, and their deflections, vibrations, and stability are investigated for several tilt angles with the use of the finite-element method. Buckling at a bifurcation point occurs for some of the cases involving vertical loads. On the other hand, the two arches may contact each other away from the crown as the load is increased, which reduces the likelihood of instability.