Nonlinear Buckling Mechanism of an Arch Subjected to a Symmetrically-placed Point Load

Abstract

The aim of this study is to devive an analytical solution to predict the buckling load of the thin-walled arch under a point load at mid-span position. A deflection function and the energy method are adopted to build the nonlinear equilibrium formulae, by solving which, the analytical solution is expressed explicitly. Subsequently, a numerical simulation is established to track the load-displacement paths of equilibrium. The simulation results indicate the load drops significantly after its maxima (critical buckling load) and follows multiple branches characterized by load limits and displacement limits. A comparison is taken between the numerical and analytical results, and a good accordance is depicted. Moreover, parameters that may affect the buckling load are analyzed, with the inclusion of rotational stiffness supports, the central angle, as well as the normalized thickness on the load capacity. Finally, both the proposed theoretical formule and simulation results agree excellently with the test results and other closed-form expressions published elsewhere.