基于板-梁理论的双轴对称哑铃形钢管混凝土拱弯扭屈曲理论研究

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

现有的理论公式只适用于单一材料构件,无法使用现有的稳定理论解决由不同材料组成的构件,为此,张文福教授在2014年独立提出一种可解决薄壁构件组合扭转和弯扭屈曲的新工程理论,该理论主要采用三种基本假设:刚周边假设、板变形假设、梁变形假设。与传统的Vlasov理论不同,板-梁理论中纵向位移、线性和非线性应变、应变能均可借鉴成熟的Kirchhoff薄板理论和Euler梁理论推导得到,不仅可以解决翘曲无法考虑钢和混凝土不同材料影响的问题,还可以避免假设翘曲函数的随意性带来的争议。为了描述方便,板梁理论中引入了两套坐标系,分别为整体坐标系xyz和局部坐标系nsz,这两套坐标系与Vlasov的坐标类似,均满足右手螺旋法则。整体坐标系的原点与截面形心重合,x、y轴分别为截面的主轴。与Vlasov的曲线坐标系不同,局部坐标系nsz为直角坐标系。原点与每个板件自身的形心重合,s轴与板件的中面重合,n轴与板件中面的法线重合。由n轴转向s轴符合右手螺旋法则,且拇指应该与z轴正方向一致。基于板-梁理论推导双轴对称哑铃形钢管混凝土的截面特性,根据相关假设,建立发生弯扭屈曲的位移场、应变场,推导出总应变能和总初应力势能,进而得出双轴对称哑铃形钢管混凝土截面的抗弯刚度、翘曲刚度和自由扭转刚度,通过算例和有限元分析验证理论公式的正确性。

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.