Warping Displacement Model Research For Shear Lag Effect Of Tin-walled Box Girder

Thin-walled box girder bridge structure is widely used. When symmetrical box girder isbending, the shear deformation of the wing makes a lateral bending of the uneven distributionof normal stresses, we call that the presence of shear lag comes. If we ignore this phenomenonwill underestimate the actual stress generated box girder structure, it will make the structureunsafe. Thin-walled box girder as a classic topic in bridge design and analysis should not beoverlooked. The initial study, Reissner used the principle of minimum potential energyanalysis of shear lag effect of box girder biaxial symmetrical rectangular cross-section,assumed the wing warping displacement function along the longitudinal as transversedistribution parabola.But there is no theoretical basis for this assumption. In this paper, theresearch bending shears flow of ’flange plate’, which is caused by ’in-plane shear deformation’and ’vertical shear’. Theoretically justify the shear lag warping displacement function isparabola. This paper based on the original literature on displacement function parabola. Witha self-balancing axial force correction function for the condition to get a more accuratecalculation of the value of the stress, and shear lag effect caused by the additional deflectionflange plate instead of the traditional way under the maximum shear angle difference ormaximum vertical displacement difference as generalized displacement. And with the energycalculus of variations method to establish control of fourth-order differential equations toobtain the calculation method for solving the shear lag stress, and compared the results withANSYS model to verify the correctness of the method and formula. And create ANSYSmodels mode with different load, support conditions and cross-section, making theapplication of this method and formulas more universal.This paper studies the following aspects:1. Theoretically justify the shear lag warping displacement function to determine theform of warping displacement function under conditions of axial force to considerself-balancing.2. With the additional deflection due to shear lag effect, instead of flange plate ofmaximum shear corner poor or maximum vertical displacement difference as generalizeddisplacement. Based on the energy calculus of variations method establish differentialequations. In order to study a new calculation method of the shear lag effect of stresscombined with numerical examples to prove its correctness and accuracy.3. As the examples show special boundary conditions, and therefore the stress cantileverplate with the model error is large, so this paper are two options for correction method tocorrect it. Combined with an example, compare the two correction methods to select the mostappropriate method to correct the shear lag warping displacement function. 4. Most of the literature in the study of shear lag problem, the displacement functions areselected according to the aspect ratio of the square of the board to fix the function, in order tobetter respond to stress situations, but some literature selection and the area is proportional tothe ratio correction function. This paper aims to compare specific examples illustrate the kindof correction method is more in line with the actual stress.5. In this paper, the study used two box girder forms of a rectangular cross section and atrapezoidal cross-section. Cantilever beam and simply support beam, two forms of support, aswell as uniform load and concentration of these two bearer form, after comparing examples,this paper to get proof the research method has universal applicability.