Analysis On Restrained Torsion And Distortion Effect Of Thin-walled Box Girders

Box girders are widely used in bridge engineering due to their large torsional rigidity, better adaptability in construction and other advantages. High strength and light weight have increasingly become the main trends of development of box girders construction. For the overall structure of a box girder, torsion and distortion deformation cannot be ignored, and the analysis of restrained torsion and distortion have been a subject that many domestic and foreign scholars extensively attention and study. According to the main problems which analysis on restrained torsion and distortion effect of concrete box girders, restrained torsion and distortion effect of concrete box girders will be in-depth studied by researching object of single box section with inclined webs mainly from the following several aspects in this paper.Aiming at the restrained torsion problems of thin-walled box girders with inclined webs, it is assumed that the shape of the box girder section under load keeps invariant. Based on the theory of free torsion, the shear deformation produced warping torsion is considered. Selecting the new freedom of warping displacement, using the relationship between stress and strain and the warping stress meeting the balance conditions in its own plane, the calculation formulas of restrained torsion warping stress and differential equations are derived, the initial parameter solution is given, in which the torsion angle, warping displacement, torsion bimoment and torsion moment are chosen as the initial parameters. For the geometrical properties in the restrained torsion theory of box girders, by selecting the auxiliary pole, the simple formulas for the twist centre, principal sector coordinate and principal sector moment of inertia of the box section are derived. N umerical examples validate the correctness of the formulas. Based on the formulas derived, the warping bimoment along the curve of torque with the concentrated bending moment at different positions, the influences of the variations of web- inclined angle, cantilever plate width and beam depth on geometrical properties of torsion and warping stress are analyzed in detail.According to the analysis of distortion of thin-walled box girders with inclined webs, selecting the distortion angle of different general angle as distortion displacement, ignoring shear strain produced distortion deformation to establish the relationship between the two components of the distortion angle, the practical formulas for the ratio of corner stress, distortion center and the total potential energy of the system with the distortion effect are derived. The governing differential equation of distortion effect is established by using the principle of minimum potential energy and its initial parameter solution is given, in which the distortion angle, distortion angle variation rate, distortion bimoment and distortion moment are chosen as the initial parameters. A simply supported box-girder model is analyzed and the calculated results are in a good agreement with those provided in other reference literatures. Combined with the numerical example, the influences of the variations of web- inclined angle, cantilever plate width and beam depth on distortional stress are analyzed in detail. A cantilever beam under torsion load and distortion load at the free end is taken as the research object and the calculated results of torsion theory and distortion theory deformation theory are in a good agreement with finite element results and those provided in other references.