Transfer Matrix Method For Studying Stability Of Arch Structures

Due to its beautiful shape,reasonable force layout and convenient construction method,the arch is widely used in bridge construction to improve the span capacity of structures.The cable is good of flexibility,it can form a new structure when combined with a arch.This type of structure is full of their advantages and is widely used in large-span structures.In order to find a new way to study the stability of pure arches,cable-arches and through arch bridge,in this paper,based on the buckling differential equation of the circular arch under radial uniform loads,the transfer matrix method is used to solve the eigenvalue buckling problem according to its boundary conditions.Then the in-plane and out-of-plane stability of the pure arch and the cable-arch,and the in-plane stability of the arch bridge are analyzed.The main contents are as follows:(1)The stable concept,categories and solution methods of the arch structure are introduced.At the same time,the in-plane and out-of-plane buckling types of the arch structure are given simultaneously,which lays a foundation for later analysis.(2)In-plane stability of pure arches: Based on the in-plane buckling differential equation of a circular arch under radial uniform load,the transfer matrix method is used to solve the characteristic equation derived according its boundary conditions in order to obtain the in-plane buckling loads.At the same time,by combining the force method and the relationship between the concentrated load applied on the circular arch and its axial force of the arch foot,the transfer matrix method is extended to analyze the in-plane stability of the variable cross-section circular arch subjected to the concentrated load.In addition,ANSYS finite element software is used to establish the model to verify the correctness of the theory and method.Finally,the theoretical method of this paper is used to analyze the parameters of the stability of pure arch.(3)In-plane stability of cable-arches: The in-plane eigenvalue buckling of a cable-arch is discussed by using the above proposed theory and method.Then,It is proved to be of good applicability by the finite element software ANSYS.Finally,the parameter analysis of the stability of the cable-arch is carried out and compared with that of the pure arch.(4)Out-of-plane stability of pure arches and cable-arches: The transfer matrix method is used to solve the out-of-plane buckling differential equations of a circular arch or a cable-arch under radial uniform loads.The characteristic equations of out-of-plane stability of the pure arch and the cable-arch are obtained by combining the boundary conditions.Then the buckling critical loads of the structural roll instability are obtained.At the same time,the relevant parameters of the out-of-plane stability of arches and cable-arches are analyzed by the above proposed method,and compared with the corresponding in-plane stability.(5)In-plane stability of through arch bridges: Firstly,the transfer matrix method is used to solve the tension force of suspenders under the external loads.The tension force of suspenders is regarded as the concentrated force exerted on the arch,and then the axial force at the arch is obtained.By using the relationship between the concentrated load applied on the circular arch and its axial force,the external loads on the beam is transferred to the arch,which is equivalent to the radial uniform load on the arch.Then,the transfer matrix method is used to solve the characteristic equation of the in-plane stability of the arch,then the overall buckling loads of the arch bridge can be obtained.Finally,we can analyze the effects of the relevant parameters of arches,beames and suspenders on the stability.This paper proposed not only the modeling theory for solving the in-plane or out-of-plane eigenvalue buckling of pure arches and cable-arches by transfer matrix method,but also the modeling theory for solving the in-plane buckling of through arch bridges by utilizing the transfer matrix method and the load equivalent relationship.Finally,the related parameters of the stability of the three structures are discussed and some conclusions are drawn that are meaningful for the design and construction of the actual project.