Restrained Torsion Analysis Of Box Girder With Corrugated Steel Webs

Firstly, using the assumption that the displacements are small, and that, the Hooke’s law is valid, for girders with arbitrary single-or multi-cell cross section subjected only to twisting moments, the shear flow and the section warp, together with the angle of twist θ(z), are analyzed, and the inertia moment of pure torsion is deduced accordingly. Then, for sections with arbitrary configurations, A. A. Уманский’s restrained torsion theory for closed thin-walled section is applied to determine the principal sectorial origins and shear centers, derive the formula for calculating warp deformation, normal warp stresses, and shear warp stresses. After establishing the relation between warp deformation coefficient β’(z) and angle of twist θ(z), the4-order differential equation of two variables β’(z) and θ(z) is converted into a4-order one of a single variable6(z) under the condition of the torque L(z) being no more than a binominal of z (This is usually the case used in practice). Following this, the initial parameter approach for4-order differential equation is given to solve the beam subjected to all kinds of accumulated and distributed twisting moments, this approach is suited for a variety of ordinary boundary conditions. A rectangular box girder with uniform thickness is taken to verify the validity of this approach. Primarily, an arbitrary sectorial origin and an arbitrary center of twist are selected, auxilliary sectorial coordinates are calculated. After this, by multiplying-graph method, the principal center of twist and principal sectorial origin are found, and the principal sectorial coordinates and all sorts of sectorial properties of the section are consequentially determined. Under the actions of uniformly distributed twisting moment and accumulated twisting moment, the restrained torsion equation is solved respectively. From the solution, the law of angle of twist θ(z),warping coefficient β’(z), bimoment B(z), torque Z(z), and bending-twisting moment M(?)(z) versus length z, and the law of warping u(z, s), normal warping stresses σ(?)(z, s), and shear warping stress τ(?)(z, s) over each cross section are obtained. Comparison between the results and documents concerned shows that the approach is exactly correct and entirely precise.Having ensured the validity and feasibility of the approach and the procedure, an analysis of the middle span of a practical47m+91.5m+47m continuous box girder with corrugated web is fulfilled. According to the principle that the corrugated steel web and concrete web have same bearing capacity for total shear force, the thickness of steel web is converted into equivalent thickness of concrete. Meeting the demands of present Chinese General Code for Design of Highway Bridges and Culverts (JTG D60-2004), the maximum vertical forces (inducing the bending moments) and maximum torques (inducing the twisting moments) are determined for one to four lanes respectively. Considering that only the restrained torsion are to be analyzed in this dissertation, the2-lanes action is chosen as object of analysis due to the2-lanes twisting moment being the largest one among the four groups of data. Following this, the restraint torsional equation is solved under uniformly distributed loads and under accumulative load. From the solution, the variational law of the angle of twist6(z), warping coefficientt β(z),bimoment B(z), torque L(z), and bending-twisting moment M(?)(z) along longitudinal direction z, and for several typical sections, the variational law of warping displacement u(z, s), normal warping stress σ(?)(z, s), shear warping stress τ(?)(z, s) over each section are obtained.