The Analysis Of Restrained-torsion Of Curved Box Girders

In order to analyze the mechanical properties of constraint torsion of a curved box girder,based on the relationship between the internal force and elastic deformation of curved box girders,a constrained torsion differential equation of curved box girder was derived and the analytical solutions of internal force,stress and deformation were given by using the initial parameter method.For the straight and curved simply supported box girders with the same span,cross section and the concentrated torque subjected at the mid-span,the differences of constrained torsional mechanical properties between straight and curved simply supported box girders were compared theoretically by calculating.By analyzing the shear stresses and their resultant torques in the cross section of the curved box girder,in this paper,the reasonable calculation method of polar inertia moment of cross section was derived.For the provided simply supported and cantilever box girders,combining with the result of finite element software ANSYS,the influence of different calculation methods of polar inertia moment upon the constrained torsion analysis result of box girder was discussed.In the view of the balance of gravity moment,the calculation formula of plane position of gravity action axis was derived and a equivalent calculation method of gravity action for the curved box girder was proposed.So that a reference was provided for the study of bending and torsion properties of a curved box beam with gravity action.For a concrete curved simply supported box girder,the distributions of constraint torque internal forces and deformation of curved box girder under gravity action was analyzed.On the premise of keeping the span constant,the influence of different curvatures,polar inertia moment calculation methods and the load eccentricity upon the constrained torsional mechanical properties of curved box girder.The study results indicate that:For the straight and curved box girder with the same span and cross section,under the same concentrated torque load in mid-span,the constraint torque internal forces and deformation of curved box girder are greater than the straight box girder.Considering the cantilever slab to calculate the polar inertia moment,the obtained warping stress is more closer to the result of ANSYS shell element than when the cantilever slab is ignored.For the curved simply supported box girder with the concentrated torque load in mid-span,no matter considering the cantilever slab or not,the calculated polar inertia moments have little effect on the generalized warping displacement and torsion angle.Nevertheless the different calculations of polar inertia moment have greater impact on the internal force.The bi-moment of the box girder will be greatly underestimated if the cantilever slab is ignored.For the cantilever box girder,no matter considering the cantilever slab or not,the calculated polar inertia moments have little effect on the torsion angle,but it has obvious effect on the bi-moment.The distribution of bi-moment shows obvious localattenuation phenomenon near the fixed end.The increase of the width of cantilever slab can improve the torsional behavior of cantilever box girder and reduce the torsion at the free end,but it will make the stress redistribute along the beam axis.It is said that at the fixed end and it's adjacent section,the bi-moment and warping stress will increase rapidly.Because the curved box girder is influenced by the structural curvature,the plane position of the gravity action axis is not coincident with the shear center axis.Under the action of gravity,the constraint torsional stress distribution of the inner and outer sides of the cross section is asymmetry.Keeping the span constant,the bending moment,torque and warping bi-moment decrease with the increase of the radius of curvature and the internal forces close to the calculation results of straight box girder under gravity gradually.Structural gravity is the key factor for controlling the torsional internal force and deformation of a curved box girder.The inward eccentricity of the single concentrated force is conducive to reduce the internal force of box girder under constraint torsion.