Bending-torsion Coupling Analysis Of Thin-walled Curved Beams Based On Cubic Spline Function

The thin-wall curved beam structure has the characteristics of beautiful shape,strong adaptability to the terrain,saving the building space and so on.It is widely used in modern bridge engineering and highway engineering.But there are phenomena such as shear lag,bending and torsion coupling.It makes the analysis very complicated.Therefore,it is necessary to analyze thin-walled curved beam structure under the bending-torsion coupling.This paper analyzed the coupled bending-torsion problem of thin-walled curved beams without the assumption of plane section and Umanski's assumption of longitudinal warping displacement.The transformed cubic spline function is used to simulate the longitudinal warping displacement.The standard cubic spline function takes the generalized nodal displacement as its parameter.So it is difficult to guarantee the continuity of the displacement at the splitting joints.In this paper,the generalized nodal displacement is replaced by the actual nodal displacement.And the transformed cubic spline function is derived from the standard cubic spline function to simulate the longitudinal displacement.Thus the spline interpolation of the whole section is changed into piecewise spline interpolation on the effect of shear lag,shear stress and warping shear stress.The Hamiltonian dual solution system for the bending-torsion coupling of thin-walled curved beams is established,and the precise integration method is used to calculate it.Unlike the traditional higher-order differential equations,the Hamiltonian dual equation is a first-order differential equation system.The feasibility of this method is verified by examples.This method is used to analyze T-section and box-section curved beams.The last chapter summarizes the influence of width-span ratio,width-thickness ratio,Poisson's ratio and curvature on shear lag effect and bending-torsion coupling effect under various working conditions,which provides design basis for bridge designers.