In-Plane Nonlinear Stability Analysis of Shallow Arches with Elastic Supports

Classical buckling theory has been researched extensively to determine the in-plane buckling behavior of parabolic, circular and catenary arches. To simplify the analyses, several assumptions are made. However, these simplified assumptions are not valid for shallow arches under significant vertical load which are characterized by their high geometric non-linearity. Prebuckling displacements should be accounted for for accurate in-plane buckling analysis of shallow arches. In reality, the supports of arches are not necessarily pin- or fixed-connections. An arch may be supported by elastic foundations or other structural elements that provide elastic restraint at the supports. In this work, elastic foundations are represented by horizontal and rotational springs. These support restraints may have a significant influence on the in-plane buckling behavior. In-plane non-linear stability analysis of shallow arches is performed in this thesis. Energy equations are derived by considering the total potential energy of the arch structure. The vanishing of first variation of total potential energy characterizes the equilibrium state, while the second variation of total potential energy falling to zero represents the transition from a stable state to an unstable state, from which the critical condition may be obtained. Finally, this thesis discusses the effects of horizontal and rotational restraints in calculation of in-plane buckling strength of shallow arches. Several examples are considered to illustrate the application of the theory, presented in this research for general practice.