Analytical Method For Dynamic Response Of Steel-Concrete Composite Beams Based On Shear Beam Theory

The steel-concrete composite beam is the structure which is composed of concrete slab and steel beam through shear connectors and can be stressed as a whole.Because it is widely used in the construction of high-speed railway bridges,its dynamic performance analysis is very important.However,at present,the basic assumptions of the dynamic analysis theory of steel-concrete composite beams are not clear.In some theories,too many parameters are considered to make the calculation inefficient.Some other theories consider too few parameters to make the calculation not accurate enough.This paper focuses on the dynamic analysis theory and method of steel-concrete composite beams and studies the shear slips,shear deformation,rotary inertia,and other related structural and material influence factors upon the dynamic performance of steel-concrete composite beams.The main work and research results are as follows:(1)The basic theoretical assumptions for dynamic analysis of steel-concrete composite beams are perfected.Based on the Timoshenko composite beam theory with the assumption of independent shear angles of sub beams,considering the effects of shear slip,shear deformation and rotary inertia,the differential equations of motion of steel-concrete composite beams are derived.The analytical methods for calculating the dynamic characteristics of steel-concrete composite beams under typical boundary conditions(clamped-free,pinned-pinned,clamped-pinned and clamped-clamped)are presented.The Euler-Bernoulli composite beam theory,Timoshenko composite beam theory with the assumption of identical shear angles of sub beams and Timoshenko composite beam theory with the assumption of independent shear angles of sub beams are compared and discussed,which shows the rationality and necessity of the third theory.It is clear that shear deformation and shear slips should be considered in the dynamic analysis of steel-concrete composite beams,but the rotary inertia can be ignored.Finally,the basic assumptions of Shear composite beam theory,which is more suitable for dynamic analysis of steel-concrete composite beams,are summarized and put forward.Based on Shear composite beam theory,the dynamic analysis method of continuous steel-concrete composite beams is proposed,which provides a theoretical and methodological basis for exploring the influence factors affecting the dynamic performance of steel-concrete composite beams.(2)The relevant factors influencing the dynamic performance of steel-concrete composite beams are explored.Numerical examples are used to analyze the influence of structural and material parameters of composite beams on their dynamic properties.The dimensionless section composite connection coefficient related to the stiffness of shear connector is proposed,α~*=KL~2/EA.And the limit values ofα~*are given.After reaching the limit value,the influence of shear slips is no longer considered.whether the influence of shear deformation is considered or not,the limit values ofα~*can be used to design the shear connectors of steel-concrete composite beams in engineering.Based on the analytical expression of natural frequency of simply supported steel-concrete composite beams,an approximate analytical expression of natural frequency of steel-concrete composite beams under other typical boundary conditions is proposed,which can be used to quickly calculate the natural frequency of composite beams in engineering.The effects of structural and material parameters on the dynamic response of steel-concrete composite beams under moving loads are studied.The results show that the shear deformation has little effect on the shear slips but has a greater effect on the vertical displacement.The relationship between the dynamic amplification factors of shear slips and vertical displacement are uncertain.(3)An analytical method for analyzing the dynamic behavior of steel-concrete composite beams is proposed.Based on Shear composite beam theory,the dynamic stiffness matrix method for analyzing the dynamic characteristics of steel-concrete composite beams with axially variable bending stiffness is proposed.To enhance the numerical stability of the method,the coefficient matrix method is further proposed.In the derivation of the two methods,the solution of the differential equation of motion is used instead of the approximate function,and the approximate displacement field or force field is not introduced.Therefore,the calculation results are exact,and the calculation accuracy is not limited by the number of divided elements.The orthogonality condition of the mode shape is derived,and the analytical solution for dynamic response of the steel-concrete composite beam under dynamic load is derived by using the mode shape orthogonality and the modal superposition method.In particular,the analytical expression for dynamic response of simply supported steel-concrete composite beams under a moving concentrated load is given.The results of theoretical analysis show that the analytical solution for dynamic response of simply supported steel-concrete composite beams is the same as that of ordinary simply supported beams,only the expression of natural frequency is different.(4)The application of Shear composite beam theory and related analytical methods in the dynamic analysis of high-speed railway steel-concrete composite bridges is realized.The vehicle bridge coupling analysis model of steel-concrete composite beam is established and solved by the intersystem iteration method.The response of the bridge subsystem is solved by the Shear composite beam theory and related analytical methods proposed in this paper.The dynamic performance of a high-speed railway steel-concrete composite bridge is analyzed.The results show that the shear deformation cannot be ignored in the dynamic analysis of steel-concrete composite girder bridges.Attention should be paid to the dynamic performance analysis of shear connectors.The Shear composite beam theory and related dynamic analysis methods proposed in this paper can be used for the dynamic analysis of high-speed railway steel-concrete composite bridges and have obvious advantages in calculation accuracy.In this paper,there are 89 figures,18 tables,148 equations and 157 references.