Research On Analytic Theory For Distortion Effect Of Thin-walled Box Girders Subjected To Eccentric Vertical Load

With the development of box girders towards to simple single-cell box section with long cantilever slab and large web-spacing,the distortion effect in box girders has been widely concerned by scholars at home and abroad.The requirements of practical and fine analysis for the concrete box girder bridges are added to the Specifications for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts(JTG 3362-2018)in our country.It is clearly proposed that the model of 7 degrees of freedom considering the restraint torsion should be used for the curve box girders and the stress amplification factor is also defined.However,the distortion warping stresses are often greater than the torsion warping stress,so the stress amplification factor included in the influence of distortion warping stress is particularly necessary to optimize the design of box girder bridge.This paper relies on the National Natural Science Foundation of China,Research on the Analytic Theory of Distortion Effect of Thin-wall Box Girders and its Application Based on the Principle of Virtual Work(51968040),and the effects of distortion and lateral bending of thin-walled box girder bridge are studied.The main work and achievements are as follows.The connections and differences of the two different distortion theories,the plate element analysis method,the total potential energy variation method,in the process establishing the distortion control differential equations are analyzed.Then the basic formula for calculating the distortion effect of the box girders is derived using the initial parametric method,which is verified by a model test and some finite element numerical simulations.For the straight-web box girders,it can be proved by the theoretical derivation that the attenuation coefficient calculated by the two different distortion theories is exactly the same.The parameters reflecting distortion characteristics calculated by the plate element analysis are twice the value obtained by the total potential energy variation method and the distortion effect calculated by the two method is totally identical.For the box girders with inclined-webs,the distortion effect calculated by the plate element analysis are larger than the value obtained by the total potential energy variation method.The numerical simulations further reveal the influence of geometric parameters on the distortion effect of thin-walled box girders.Based on the basic principle of the generalized coordinate method,the warping shear flows are expressed by the generalized coordinate and displacement.Then the distortion angles on the section of the box girders caused by the distortion warping stress,distortion shear stress and the external distortion torque are obtained.The distortion differential equation of the thin-wall straight box girders based on the distortion warping shear flow is established by the deformation compatibility condition of the distortion angle.Theoretical analysis proves that for straight-web box girders,the distortion control differential equation calculated by the distortion warping shear flow method is completely consistent with the total potential energy variation method,thus the theory is verified.The elastic relation between the internal force and the displacement of the thin-walled curve box girders considering the influence of constraint torsion and distortion is derived to analyze the influence of curvature on the distortion warping normal stress.The distortion theory of curve box girders based on the distortion shear flow method considering the distortion displacement caused by the coupling effect of bending and distortion is established.On this basis,the idea of the impact line loading is used to solve the distortion effect of the curve box girders.The results show that the distortion theory can correctly reflect the change regulation of distortion warping normal stress of curve box girders,whether for large curvature or small curvature box girders.The numerical simulations further reveal the influence of geometric parameters on the distortion effect of thin-walled curved box girders.The attenuation coefficient resisting distortion is a main index which reflects the ability of the box girders to resist distortion.Based on the theory of elastic support girders,the attenuation coefficient resisting distortion is taken as the characteristic coefficient of the elastic support girder.The external load correction method based on elastic support beam theory is established on the way taking the elastic support reverse force at the section as the actual loading acting on the plane frame or the plate element.When the two ends of the elastic support girders are free boundary conditions,the modified external load can degenerate into the original load.Finite element numerical simulation results shows that the correction method can fully consider the effect of shear deformation under the effect of eccentric load.In order to calculate the transverse internal force considering the distortion deformation of the box girder more accurately,the external load correction method based on the elastic support beam theory is applied to improve the accuracy of the generalized TYL frame analysis method.Moreover,an improved framework model with clear physics concept satisfied a principal that the distortion center always located on the symmetry axis is adopted to establish the transverse internal force analysis theory of box girders.The results of the numerical examples show that the improved transverse internal force analysis method in this paper can better reflect the distribution regularity within all over the span of box girders.The transverse internal force calculated by the improved method are in good agreement with those calculated by ANSYS finite element method,which verified the correctness of the established formula.