Finite Difference Methodanalysis Of Curved Girder With Corrugated Steel Webs

Firstly,establishing the coordinate system of thin-walled curved beams by using theRight-handed screw rule. For sections with arbitrary configurations, А. А. Уманский’srestrained torsion theory for closed thin-walled section is applied to determine theprincipal sectorial origins and shear centers, derive the formula for calculating warpdeformation, normal warp stresses, and shear warp stresses. After establishing the relationbetween warp deformation coefficient β′(z) and angle of twist θ(z), the4-order differentialequation of two variables β′(z) and θ(z) is converted into a4-order one of a single variableθ(z) under the condition of the torque L(z) being no more than a binominal of z. The initialparameter approach for4-order differential equation is given to solve the beam subjectedto all kinds of accumulated and distributed twisting moments, this approach is suited for avariety of ordinary boundary conditions.Secondly, For the equations of curved beams can not be decoupled and difficult to getthe analytical solutions, derive the difference scheme of the equation. Equally divided thecorrugated steel webs curved beams into n segments along its central axis, and substituteddisplacement, rotation, and other related elements into equations of the curved beam.Using the boundary conditions to make the differential equations simplify, so as to achievethe purpose of simplifying the calculation process. Applied the MATLAB to calculatevalues in the nodes of the corresponding elements. Then substituted the displacement,angle into equations of bending, Torque and bimoment, calculated the values ofcorresponding nodes.Then, as an example, calculated the deflectiont, rotation, bending momentM xn,torqueL nand bimomentB nin the main span of the Guangzhou Yuwotou Bridge. Theresults showed that thecalculated the deflectiont, rotation, bending momentM xnandbimomentB nof curved beams with corrugated steel webs are symmetrical, but the torqueis antisymmetrical.