| With the development of box girder bridges to long cantilever,large web spacing,and thin wall lightness,the mechanical properties and calculation methods have attracted extensive attention of domestic and foreign scholars.The research on shear lag effect of thin-walled box girder has made a lot of achievements in the existing literature,some of which have been incorporated into the bridge design code.However,there is a lack of research on the definition of lateral displacement of the flanges and its influence on static and dynamic characteristics for the box girder with bending deformation.This article is based on the National Nature Fund project(51468032,51508255)and the Lanzhou Jiaotong University Youth Fund project(2018017).Combined with the classical theory of thin-walled box girder and the method of vibration mechanics,this paper theoretically studies the influence of lateral displacement of flanges on the bending static and dynamic characteristics of box girder.The main work and achievements are as follows.(1)The shear lag warping deformation was regarded as an independent deformation state for analyzing,and the additional deflection induced by shear lag effect was chosen as generalized displacement.The warping neutral axis of the cross section was redefined by introducing the three global correction factors for the whole box section,so that the self balance condition of the warping stress and the influence of boundary constraints were fully reflected.Based on the geometric relationship between the warping lateral displacement of the flanges and the additional deflection,the shear lag warping lateral displacement mode of the box girder was defined by combining the condition of deformation continuity.The analytical theory of shear lag effect of box girder considering lateral displacement of the flanges was established by applying the energy variation method.The numerical examples show that the results with the lateral displacement of the flanges are in good agreement with the finite element numerical solution,and the lateral displacement of the flanges has a certain influence on the analysis accuracy of shear lag effect and the additional deflection.(2)Based on the analysis method of bending shear stress of primary beam,the calculation formula of warping shear stress of the box girder was derived by combining the equilibrium differential equation of micro-elements,the condition of displacement coordination and the principle of equal stiffness.The similar relationship between shear stress caused by bending moment,axial force and shear stress distribution mode of shear force were analyzed by starting from the transverse distribution mode of shear stress with all internal forces of variable cross-section box girder.The simplified calculation method of shear stress was established by proposing the concept of conversion shear force on variable cross-section.The numerical examples show that the paper results are in good agreement with the finite element numerical solution,the proportion of warping shear stress in bending shear stress is small,and it satisfies the self balance condition of the section.(3)Based on the analysis theory of shear lag effect of box girder considering lateral displacement of flanges,the additional deflection induced by shear lag effect was chosen as generalized displacement,and the influence of additional deflection on total kinetic energy of box girder was considered.The governing differential equations of bending natural vibration of box girder considering shear deformation and shear lag effect were established by applying the energy variation method.The calculation formulas of natural frequency with shear lag effect,shear deformation and primary beam were derived by combining the characteristic equation of natural vibration and boundary conditions.The frequency parameter solution matrix of the multi-span continuous beam was derived by using the principle of force method and the deformation coordination condition.The distribution of the influence factors of the natural frequency of the three span continuous beam was drawn.The numerical examples show that the bending natural frequencies of box girders with shear lag effect are in good agreement with the finite element numerical solution,the influence of shear deformation on natural frequency is much greater than that of shear lag effect.The shear lag effect should be fully considered for a flat beam.The ratio of side-span to mid-span has a significant effect on the natural frequency of primary beam.the larger the ratio,the weaker the shear deformation.(4)Based on the established analysis theory of free vibration of box girder in this paper,considered the influence of shear lag effect on the dynamic characteristics of box girder.The differential equation and boundary condition of forced vibration of box girder considering shear deformation and shear lag effect was established by applying the energy variation method.When the shear lag effect is neglected,it can be reduced to a differential equation considering shear deformation.The additional deflection of shear lag has obvious advantages over the maximum shear angle difference.It is convenient to analyze the influence of shear lag deflection on the dynamic response of box girder.The numerical example shows that the stress results of considering the lateral displacement of the flanges are in good agreement with the finite element numerical solution.The larger the vibration frequency,the smaller the proportion of warping normal stress in the primary beam,the larger the ratio of shear additional deflection,the smaller the ratio of shear lag additional deflection.The lateral displacement of the flanges has little effect on the stress amplification factor,but the deflection amplification factor has great effect.(5)Based on the established analytical solution of bending static and dynamic characteristics of box girder in this paper,the influence of end restraint condition and corner haunch on the static and dynamic characteristics of box girder was analyzed in detail.The results show that the stronger the end restraint condition,the steeper the distribution curve of shear lag factor,the more flat the deflection curve,and the smaller the dynamic amplification factor.The end restraint condition has a significant effect on the static deflection and dynamic amplification factor of the box girder.It has a little effect on shear lag factor and dynamic amplification factor of simply supported box girder,but the normal stress of upper flanges and the deflection are significant. |
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