Flexural-torsional Analysis Of Thin-walled Curved Box Girders Considering Shear Lag Effect

With the quickening of the modernization in our country, curved girder bridge has beenwidely applied to adapt to the complex topography. Because of thin-walled box girders’unique characteristics, they have been adopted in the curve girder bridge. While the shear lageffect makes bending torsional analysis of curve box girder complicated. Early researchersoften don’t consider the shear lag effect. Later many scholars began to explore curved boxgirder considered shear lag effect, but ignoring the self-equilibrium condition of the shear lagwarping stress and the effect of secondary shear flow on the restraint torsion, socharacteristics of curve box girder bending and twisting can’t get more objective reflect.Based on the energy variation method, considering shear lag warping line strain energygenerated by the shear lag warping displacement and the buckling strain energy generated bythe new warp generalized displacement, this paper establishes the flexural-torsionaldifferential equations and the corresponding boundary conditions. The derived differentialequations are solved using the Galerkin’s numerical method. The practical formulas for thetwist centre and principal sectoral coordinate of a double-cell box section are derived, whichmakes the bend torsion analysis of curve box girder relatively simplified. Numerical examplesvalidate the method of the paper. First using mathematical software MATLAB is to calculatethe theoretical value. Then utilizing ANSYS software is to get the finite element value. Last,comparing the theoretical values, finite element values and the measured values is to provethe rationality of the method in this paper. Comparison of shear lag warping displacementfunction from three times to two times parabola, and radius of curvature change, width spanratio parameter change, effects on curved box girder. The results show that:(1) Curved box girder control differential equation is established. If neglecting the shearlag deformation and using the first derivative of torsional angle instead of new warpinggeneralized displacement, the equation will become the Vlasov equation. The formulas for thetwist centre and principal sectoral coordinate of a double-cell box section play an importantrole on the simplification of the subsequent calculation process. A plexiglass model of curvebox girder is solved. The result shows the theoretical values are consistent with finite elementvalues and the measured values, which verifies the validity of the method in this paper.(2) When the shear lag warping displacement function from three times to two timesparabola, only the shear lag moment has changes in force on the curved box girder. Eachpoint of normal stress, warping double moment and bending moment are basically unchanged.(3) Because the bending torsion coupling effect, the stress distribution at both side ofcurve box girder cross section is not symmetrical, and the absolute values of the stressdecreases with the increase of radius of curvature. The absolute values of internal force, deflection and torsion angle are also decreased with the increase of radius of curvature. Widespan radio on the influence of the shear lag coefficient than the radius of curvature is a littlebigger. Under uniformly distributed load, the shear lag displacement and warpingdisplacement is zero at the curved box girder cross section. The transformation laws of theabsolute values of stress and internal force along with wide span ratio change are the same asthe radio of curvature change.