Flexural And Torsional Analysis Of Continuous Box Girder With Special Support Considering Shear Lag Effect

Thin-walled box girder due to its unique properties, has been widely adopted in bridge engineering. The shear lag effect is the most common phenomenon to the box section, which may cause the concrete thin wall box girder crack and even the structural failure if the shear lag effect is ignored. Over the past twenty years, many scholars at home and abroad have done much research on shear lag effect of thin walled box beam, but these studies are mainly for orthogonal box girder rather than skew supported ones. Therefore, this paper analyzes the bending and torsion of continuous box girder taking account of shear lag effect with special supports systematically, and which the results was with an important significance for further studying.This paper considers the shear lag effect based on the theory of elementary beam, and using the cross section displacement model of thin-walled box girder and the torsion warping displacement which takes account of the influence of the two shear flow corresponding to the shear deformation on the warping displacement, thin-walled beam element bending and torsional differential equation are established. Taking the equation homogeneous solution as the displacement function, the elemental shape function matrices relating to thin-walled box girder are derived. Then, elemental bending stiffness matrices and element torsion ones are derived on the basis of the definition of stiffness coefficient. Finally using the concept of elemental stiffness matrix expansion and adding up the two kinds of matrices, the element bending and torsional stiffness matrices are gained. Since the effect of special support is taken into account, the compatibility of displacement of the thin-walled box girder must be established in the supporting coordinate system, which means turning the displacement components in the torque-centroid coordinate system to supporting coordinate system, the coordinate transformation matrices are deduced and the solutions of displacement and stress taking account of the influence of the shear lag effect and special support are obtained in supporting coordinate system.Through the numerical example show the influence of shear lag of different bridge under different loads:simply supported box girder under uniform loads, the influence of shear lag are very small; simply supported beam under concentrated load, the influence of shear lag are more larger than under uniform load; cantilever box girder under uniformly distributed loads, the influence of the shear lag are very large.Several conclusions are drawn as follows by finite element analysis of three span continuous box girder with skew support and the corresponding orthogonal box girder: (1) The stress distribution at the cross section of orthogonal box girder is symmetrical under symmetrical load, and the stress distribution at the cross section of skew support is not symmetrical.(2) Due to the influence of eccentric load, the stress distribution at the cross section of skew box girder and skew box girder is not symmetrical eccentric load, especially the skew box girder, the extent of stress non-homogeneity seems greater. The external reason may be oblique supporting,whereas, the internal reason may involves shear lag warping deformation when deflecting and constrained torsion warping deformation as well as coupling of this two deformations.