风吸力作用下仅考虑扭转约束的Z形和C形檩条弹性弯扭屈曲

Elastic Stability of Cold-formed Z & C Purlins Under Wind Suction Considering the Effects of Torsional Restraint

采用开口薄壁构件理论,在忽略屋面板对檩条侧向约束的条件下,根据上翼缘受扭转约束简支檩条的线性总势能方程,应用变分法推导无支撑Z形和C形檩条在风吸力作用下的扭转角及位移表达式。考虑屈曲前应力在檩条弯扭屈曲变形过程中产生的非线性应变能,根据其弯扭总势能方程,采用势能驻值原理推导无支撑Z形和C形檩条的临界弯矩表达式。扭转角、位移和临界弯矩表达式与采用ANSYS板壳单元建模的计算结果对比,吻合较好,表明理论公式精度较高,可用于工程设计。

Based on the buckling theory of thin-walled members and the total potentials of cold-formed Z and C purlins whose lateral restraints are ignored,the formulae of rotation and lateral displacement of the purlins were obtained under wind suction on the principle of variation. Considering the nonlinear strain energy generated during flexural-torsional buckling by the stress before buckling,the expression of critical moment of Z and C purlins was obtained on the basis of stationary value of total potential energy. The rotation,lateral displacement and buckling moment were compared with numerical results using shell elements of ANSYS and found to be in excellent agreement with ANSYS.