Research On Out-of-Plane Buckling Of Circular Arches

At present,out-of-plane buckling of arches accounting for complex boundary condition under a complex load is not clear,especially the out-of-plane buckling of arches accounting for shear deformation is not paid much attention,it makes the using of arch structures leave hidden dangers,and the wide application of arches are restricted.In order to improve the stability theory of an arch,broaden its range of application.In this paper,based on the principle of elastic mechanics,a systematic and innovative research on out-of-plane static and dynamic stability of an arch is developed,which is as follows:(1)Strain functions applying to out-of-plane buckling of circular arches with shear deformation are established.Accurate axial forces and bending moments are solved in the prebuckling analysis.A new out-of-plane buckling energy equation is constructed,and in-plane loads do not directly work during the out-of-plane buckling of an arch.Analytical solutions of the out-of-plane buckling critical load of arches are derived,and the influences of shear deformation and included angle on out-of-plane buckling of arches is analyzed.(2)Mathematical models of complex constraints and complex load conditions of circular arches are established.Axial forces and bending moments in the prebuckling analysis and the out-of-plane critical buckling load are derived,the intrinsic relationship of out-of-plane buckling of arches,in-plane elastic rotational constraints flexibility,load positions,included angles and slenderness ratio are revealed.(3)An analysis method of out-of-plane buckling of an arch in a uniform thermal environment is proposed.Analytical solutions of axial forces,bending moments and the out-of-plane buckling temperature field of circular arches under an external load in a uniform thermal environment are derived,the influences of temperature field on out-of-plane buckling load of arches are studied,the possibility of out-of-plane buckling of an arch in an increase of the temperature field is demonstrated.(4)A method for out-of-plane buckling design of a steel tube concrete(CFST)arch under long term behavior is proposed.With the effects of shrinkage and creep of core concrete,out-of-plane critical buckling load of a concrete filled steel tube arch under an uniformly distributed load or a point load is derived,the relation curve between out-of-plane critical buckling load of an arch and concrete age is obtained,the infulences of the concrete age,load age,slenderness ratio,rise-span ratio and steel content of an arch on the out-of-plane buckling load are analyzed,a design formula of out-of-plane stable ultimately bearing capability of a CFST arch is proposed.(5)Mechanism of parametric resonance instability of an arch is revealed.Mathieu-Hill equations of out-of-plane dynamic instability of an arch are constructed,the dynamic unstable region of parametric resonance of an arch is obtained,the nonlinear vibration and the maximum deformation amplitude are solved while the parameter vibration of an arch happen;the out-of-plane dynamic instability excitation experiment of an arch is completed,out-of-plane dynamic instability region of an arch is drawn,the instability characteristics and the instability mode of an arch are illuminated,The mechanism and the rule of dynamic instability failure of an arch structure are revealed.