用共旋坐标有限元法分析高层建筑框架结构的二阶效应

虽然分析平面框架二次效应的方法早在20世纪80年代就已提出,但其中许多工作过分复杂或简单,值得改进.采用共旋坐标法准确地导出了平面梁单元发生大转动小应变时的单元切线刚度矩阵,并利用该单元切线刚度矩阵的列式和Newton-Raphson迭代法开发了1个FORTRAN程序NPFSAP,从而获得了高层框架结构二阶效应的高精度数值解,由此发现高层建筑的二次效应与水平荷载的关系不明显,但建筑物刚度越小,竖向荷载越大,建筑物层数越多,二次效应越明显.提出了1个高层框架中柱二次效应的计算公式,为工程设计人员提供了准确计算框架弯矩的办法.

Co-rotational Procedures for Finite Element Analysis of Second-order Effects of Tall Building Frame Structures

Although methods for the second-order effects of plane frames were developed in the 1980s, much of this early work was surprisingly sophisticated or simplified and, it is worth re-visiting. Starting from the geometric and physical relations of the plane frame, this work has successfully applied co-rotational procedure to derive non-linear tangent stiffness matrix of plane beam element in large but small-strained rotational displacement. A non-linear finite element iteration procedure is thus established by the Newton-Raphson technique, and a corresponding Fortran program NPFSAP has been tumed out. Numerical results of high accuracy for the second-order effects of tall building steel frame structures are thus obtained. Computations indicate that tall building frames are surprisingly sensitive to second-order effects and that these effects are irrelevant to the lateral building loads but become more significant with the decrease of building stiffness, and increase of vertical loadings and building stories. Furthermore, a calculate formula of second-order effects for middle column is presented for engineering designers to accurately calculate the frame moments.