Research On Analytic Theory And Its Application For Flexural Anslysis Of Thin-walled Box Girders With Effect Of Shear Deformation

With the development of modern box girder bridges with long cantilever plates,spacing between large webs and thin-walled structures,the spatial mechanical effects caused by the thinning of box girder structures are also more significance.Based on the bending theory of classical thin-walled box girders,and relying on the National Natural Science Foundation of China-“Research on Reasonable Mode of Displacement Function for Shear-lag Warping of Thin-walled Box Girders and Its Application(51268029)”,the aim of this dissertation is to solve the existing problems in the study of flexural space mechanical effects of thin-walled box girders at present.The main contents and results are as follows.(1)This paper takes the representative trapezoidal thin-walled box girder as the analysis object.From the analysis of bending shear flow of thin-wall box girders,combined with the geometric relationship between strain and displacement,the deflection displacement function of thin-walled box girders are theoretically deduced.The shear deformation of the flange and web of the box girder are considered in this function and this displacement function is different from the existing literature for the flexural displacement function of thin-walled box girders.The results of the study indicate that the longitudinal warping displacement distribution of the flange is a quadratic function along the width of the flange when considering the effects of shear deformation.The longitudinal warping displacement distribution of the web is the sum of the first and third order functions along the web height direction when considering the effects of shear deformation.The essence of the shear lag warping displacement function of thin-walled box girders is the flexural displacement function considering only the shear deformation of the upper and lower flange of box girders.(2)The additional deflection caused by the shear deformation is selected as the independent displacement.By defining the shear warping moment,the shear deformation state of the thin-wall box girder is separated from the deflection state of the elementary beam and researched as an independent deformation state.Based on the principle of energy variation,the control differential equation of shear additional deflection is derived and the initial parameter solution of shear additional deflection is given.The results of the example show that the flexural stress of box girders solved by this method is in good agreement with the calculated results of ANSYS space shell element.The shear deformation of the web has little effect on the warping stress of the box girder flange.(3)Based on the expression of shear additional deflection of simple-supported box girder and the boundary continuity condition,a three-shear warping moment method is proposed to solve the flexural stress of continuous box girders with equal section.This method opens up a new way for the flexural analysis of continuous box girders with equal section.Taking the shear additional deflection as an independent displacement,combined with the converted elastic modulus method,a deflection analysis method for concrete box girders considering the effects of shear deformation and creep was proposed.This method not only simplifies the coupling analysis of shear and creep,but also can correspond to the creep analysis of elementary beams,which is convenient for practical engineering applications.The results of the example show that the shear warping moment has a sharp peak at the point of concentrated load and in the point of support in the continuous box girders and decays quickly.When the load is evenly distributed,the shear warping moment distributes evenly and smoothly across the box girder span.(4)Based on the theory of Timoshenko beam,combined with the bending shear stress distribution characteristics of thin-walled box girder,a calculation method for the deflection of box girders ignoring the effect of shear deformation on the flexural displacement distribution function is proposed.Compared with the existing literature methods,this method can solve the deflection displacement of thin-walled box girders considering the effects of full cross-section shear deformation without analyzing the shear lag effect of box girders.The results of the example show that the shear additional deflection calculated by neglecting the effect of shear deformation on the flexural displacement function is slightly larger than the calculation results which considering the effect of shear deformation on the flexural displacement function.Both methods of this paper can solve the box girder deflection with higher accuracy.(5)Based on the deflection displacement function considering the shear deformation of the thin-walled box girders deduced in this paper,the differential equations of the flexural natural vibration frequency of the thin-walled box girder were derived by the Hamilton principle.According to the boundary conditions of differential equations obtained previously,the expression of the flexural natural vibration frequency of simply supported box girder considering the influence of shear deformation is derived by Galerkin's method.Based on the flexural natural frequency formula of simple-supported box girder,the expression of the flexural natural vibration frequency of the continuous box girder is derived by combining with the three-moment equation of the continuous beam.Compared with the existing literature methods,this method not only simplifies the analysis of the flexural natural vibration frequency of box girders,but also eliminates the tedious process of solving high order differential equations.The results of the example show that the calculation results of the flexural natural vibration frequency of the box girders without considering the influence of shear deformation are relatively large.The shear deformation has a great influence on the natural vibration frequency of the box girders and this influence will also increase with the increase of the frequency order of natural vibration.(6)The shear additional deflection and shear generalized rotation angle were chosen as independent degrees of freedom.Based on the analytical theory of this paper,the element stiffness matrix,load vector and mass matrix of the beam segment considering the influence of shear deformation were established.Based on the stiffness matrix of the beam element and the load vector etc.,the finite element technique was used to compile the computer program for solving the internal forces,deformation and natural vibration characteristics of the box girders.In addition to the degree of freedom of the elementary beam,the degree of freedom of the beam element unit node also includes the degree of freedom of the shear additional deflection and its rotation angle.Therefore,the finite beam segment program not only can solve the flexural displacement and internal forces of elementary beams,but also can solve the additional shear displacements and internal forces.It provides an effective way for the deflection analysis of complex continuous box girder structures such as variable cross-sections.(7)Taking the concrete box girder bridges in the actual project as the background,the influence of the shear deformation on the flexural mechanical behavior of the box girder is compared and analyzed using the finite beam segment program of this paper and the finite element entity model of the ANSYS.The influence of section parameters and span variation of the box girder on its amplification factor of stress and deflection was studied.The results show that the stress amplification factor of the box girder has a large value near the position of the concentrated load and near the middle fulcrum and it is relatively small when the load is uniformly distributed.The stress amplification factor of the box girder is greatly affected by the width of the flange,and the larger the span-width ratio is,the smaller the stress amplification factor is.The deflection amplification factor of the box girder is affected not only by the width of the flange but also by the height of the web.With the increase of span-width ratio and span-height ratio of the box girder,the deflection magnification factor decreases continuously.