| In view of the shear lag problem in thin-walled box girders,the energy variational method is usually used to analyze the problem,and the core of this method is the selection of the shear lag warping displacement function.Most literatures assume the form of warpage displacement function,but do not give theoretical derivation.In this paper,the problem of shear lag is solved by the warping displacement function derived from theory.(1)Based on the abstract expression of longitudinal displacement function,the corresponding governing differential equation is derived by using energy variational method.By analyzing the form of the differential equation,the warping displacement function about the hyperbolic cosine form is constructed.Then the warping displacement function is modified by shear deformation and axial self-balance,and the correction coefficient of boundary constraint influence of cantilever plate is introduced.(2)The shear lag problem of the thin-walled box girder is deduced based on the energy variational principle,taking the maximum shear angle difference of the wing plate and the additional deflection caused by shear lag as the generalized displacement,and considering the influence of the shear deformation of the web.The results show that when the shear force is linearly distributed along the span,the web shear deformation has no effect on the normal bending stress of the flange of box girder,but it has an effect on the deflection of the beam,and the shear lag effect has an effect on both.When analyzing the shear lag problem,the shear lag deformation state can be regarded as a basic and independent deformation state,which is analyzed separately.(3)Two types of box beam sections are selected,that is,the rectangular section with the cantilever plate width equal to half of the width of the top plate and the trapezoidal section with the cantilever plate width not equal to half of the width of the top plate.Based on the numerical results of finite element method,the correction coefficient of the boundary constraint influence of cantilever plate is determined to be 1.5 when calculating with this method.By comparing the examples,the influence of the correction coefficient of the boundary constraint on the deflection of cantilever plate can be neglected,and the effect on the stress of the lower wing(bottom plate)is relatively small,but the effect on the stress of the upper wing is relatively large,and the influence on the cantilever plate is more significant than that on the top plate.(4)According to the method presented in this paper,the simple supported beam and cantilever beam examples are solved,and the results are compared with those obtained by ANSYS modeling.The calculation results show that the results obtained by the method are in good agreement with the ANSYS results,and reflect the stress distribution of cantilever plate more truthfully,thus verifying the rationality of the analysis method in this paper.The effect of shear deformation on the deflection of box girder is more significant than that of shear lag effect.For simple-supported beams,the deflection of elementary beams,the additional deflection of shear deformation and the additional deflection of shear lag all show the law of decreasing from midspan to fulcrums on both sides.For cantilever beams,the additional deflection of elementary beams,shear deformation and the additional deflection of shear lag all show the law of increasing from fixed end to free end.(5)The shear lag coefficients of simply supported beams and cantilever beams are analyzed and solved.The results show that the shear lag effect of simply supported beams under concentrated load is more significant than that under uniform load.For cantilever beams,the shear lag effect is more significant under uniform load than under concentrated load.For the cantilever box girder with uniform load,the “negative shear lag effect” will appear near the cantilever end,and the closer to the cantilever end,the more obvious the negative shear lag effect of the wing. |
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