Analysis Of In-plane Stability Of Arch Considering The Limited Axial Stiffness

As an ancient structure in the form, arch has been widely used in the engineering practice for the advantages of good mechanics performance, elegant appearance and relatively good economic indicators. Compared to the straight beam element, arch support will produce horizontal thrust to turn the moment caused by external load into axial force under the vertical load, therefore,as a component mainly bear axial force, the problem of stability becomes the key to the design of arch. The out-plane stability of arches can be strengthened by setting enough lateral supports or through the mutual constraints between themselves, while arch is usually lack of in-plane supports for its large span, which makes it hard to guarantee the in-plane stability of arch. Therefore, the in-plane stability of arch becomes the key to the design of arch. Many scholars at home and abroad has done a lot of researches on the stability theory of arch and has carried out different conclusions based on different assumptions, however, seeing that the stability of arch is affected by many factors and is hard to study, there is no complement and uniform design theory of in-plane stability of arch so far.Compared to the previous study, most classical analytic solutions of in-plane critical buckling load of arch are produced by taking the hypothesis of neglecting the influence of axial compression. In order to get a closer in-plane buckling load of arch to the engineering practice, based on the classical analytic solution of Timoshenko and considering the axial stiffness as well, this work derived the antisymmetric critical buckling load formula of arch subjected to radial-uniformly-distributed load by the means of equilibrium method. Through the model establishment of circular arch and geometric nonlinear analysis in the large general finite element program STRAND7, the finite element solution of circular arch considering the axial compressive deformation are obtained, and by the comparison with the critical buckling load formula deduced by equilibrium method, the accuracy of critical buckling load formula has been verified.Except for circular arch, parabolic arch and catenary arch are also common used in th eengineering practice. Many scholars have done plenty of researches on them and come up with different conclusions.On the basis of the circular arch, this work spreads the search for the critical buckling load of pure pressure circular arch to parabolic arch and catenary arch. Considering the complexity of theoretical derivation, this work utilizes the finite element program to establish calculation model and do geometric nonlinear analysis, and compare the results with the classical solution of Timoshenko.To search for a formula of critical buckling load which is more common used for the engineering practice, lots of analysis of arch with the only difference of rise-span ratio are done, and finally the critical buckling load formula,which is associated with the axial stiffness and the rise-span ratio,of parabolic arch and catenary arch with the axial compressive deformation taken into consideration are derived.