In-plane elastic stability of fixed parabolic shallow arches

The nonlinear behavior of fixed parabolic shallow arches subjected to a vertical uniform load is investigated to evaluate the in-plane buckling load. The virtual work principle method is used to establish the non-linear equilibrium and buckling equations. Analytical solutions for the non-linear in-plane symmetric snap-through and antisymmetric bifurcation buckling loads are obtained. Based on the least square method, an approximation for the symmetric buckling load of fixed parabolic arch is proposed to simplify the solution process. And the relation between modified slenderness and buckling modes are discussed. Comparisons with the results of finite element analysis demonstrate that the solutions are accurate. A cable-arch structure is presented to improve the in-plane stability of parabolic arches. The comparison of buckling loads between cable-arch systems and arches only show that the effect of cables becomes more evident with the increase of arch’s modified slenderness. Supported by the National Natural Science Foundation of China (Grant No. 50478075), and Scientific Research Foundation of Graduate School of Southeast University (Grant No. YBJJ0817)