Second-order Analysis Of Tube Structures Considering Shear Lag

The tube structure is suitable for the layout and planning of today's cities,and can also meet people's requirements for space.Therefore,many high-rise buildings tend to tube structure,which is of great significance for the research of tube structure.This paper focuses on the shear lag effect of tube structures.According to different basic assumptions,the influence of shear lag effect on structural displacement and internal force is studied.Firstly,based on the principle of continuity,considering the actual structure and the mechanical characteristics,the frame-tube equivalent continuity of the dense column deep beam is transformed into the equivalent solid web of the orthotropic plate and corner column,and the equivalent continuum mechanical model of the tube structure is established.Secondly,this paper discusses in detail the selection of parameters of the simplified mechanical model,such as length,width,height and wall thickness,as well as the determination of elastic modulus and shear modulus,and clarifies how the internal force of the mechanical model is converted to the actual structure under the action of external forces,and how the displacement is determined.Finally,according to the established mechanical model and the characteristics of stress and deformation,the displacement field under typical stress is assumed,and then the generalized displacement is selected.The displacement at any point of the structure is expressed by the generalized displacement,and then the expression of strain energy is written.The strain energy per unit length is Lagrange function.These functions correspond to the generalized displacement.According to the generalized force corresponding to the generalized displacement,the formerly equation with displacement as unknown variable is transformed into one with displacement and generalized force as unknown variable.This equation is called Hamilton's regular equation.With boundary conditions,the mechanical solution of this equation is obtained.By comparing the mechanical solutions obtained above with the numerical examples in the literature,the correctness and feasibility of the calculation method in this paper are proved.Then,the internal forces and displacements of the structure under different assumptions when shear lag is taken into account,and the effects of compression and bending on the internal forces and displacements of the structure when shear lag is taken into account are studied.In this paper,the mixed energy finite element method is used to calculate the generalized force and displacement of the structure by compiling the MATLAB program.Compared with the example,the calculation result is more accurate.