Theoritical Study of Flexural-Torsional Buckling of Biaxial Symmetric Dumbbell-Shaped CFST Arches Based on Plate-Beam Theory

The existing theoretical formulas are only applicable to single-material components, and the existing stability theory cannot be used to solve components composed of different materials. Therefore, Professor Wenfu Zhang independently proposed a new engineering theory that can solve the combined torsion and flexural-torsional buckling of thin-walled members in 2014. The theory mainly adopts three basic assumptions:rigid periphery assumption, plate deformation assumption, beam deformation assumption. Different from the traditional Vlasov theory, the longitudinal displacement, linear and nonlinear strain, and strain energy in the plate-beam theory can be derived from the mature Kirchhoff thin plate theory and Euler beam theory. It can not only solve the problem of warpage that cannot consider the influence of different materials of steel and concrete, but also avoid the controversy caused by the arbitrariness of assuming the warpage function.
For the convenience of description, two sets of coordinate systems are introduced in the plate-beam theory, namely the global coordinate system xyz and the local coordinate system nsz. These two sets of coordimate systems are similar to the Vlasov coordinates, and both satisty the right-handed spiral rule.The origin of the global coordinate system coincides with the centroid of the section, and the x and y axes are the main axes of the section, respectively. Unlike Vlasov curvilinear coordinate system, the local coordinate system nsz is a rectangular coordinate system. The origin coincides with the centroid of each plate, the s-axis coincides with the mid-plane of the plate, and the n-axis coincides with the normal to the mid-plane of the plate. Turning from the n-axis to the s-axis conforms to the right-hand screw rule, and the thumb should be aligned with the positive z-axis.
Based on the plate-beam theory, the cross-sectional properties of the biaxially symmetric dumbbell-shaped CFST section are deduced, and the displacement field and strain field for bending-torsional buckling are established according to related assumptions, and the total strain energy and total initial stress potential energy are derived. Furthermore, the bending stiffness, warping stiffness and free torsion stiffness of the biaxially symmetric dumbbell-shaped concrete-filled steel tube section are obtained, and the correctness of the theoretical formula is verified through calculation examples and finite element analysis.