论文部分内容阅读
众所周知稳定分析的矩阵位移法是由一级和二级刚度矩阵组成总刚度矩阵。前者是不考虑柱轴向荷载的一般刚度矩阵,本文采用所谓“单向传递无剪力二次分配法”(以后均称“简单分析方法”)去快速精确计算;后者是考虑刚架变形,在柱顶(或各层柱顶)轴向荷载偏离作用下的几何刚度矩阵,这种由于柱轴向力 P 侧向偏离△的影响,叫做 P—△影响,这种偏离的 P·△力偶矩产生柱剪力增量,而此柱剪力增量又产生侧向位移的增量,如此反复循环增长,逐渐收敛的关系经研究是等比级数关系。设此等比级数的公比为 q_1,(i 代表第 i 层间编号)当 q_i≥1时,此 i 层间柱的侧移等比级数是发散的,此时即可得到 i 层间柱顶轴向荷载的临界值 P_(cr)的概数,设在单位干扰力作用下,当层间柱顶无轴向荷载时,(荷载参数为零)刚架的侧移为δ_o,而当层间柱顶有轴向荷载,荷载参数为 P 时,刚架的侧移为δ,则δ_o/δ表示对应各个不同荷载参数 P 时刚架的侧移刚度。本文很方便迅速试算各个荷载参数后,绘成δ_o/δ和荷载参数 P 之间的关系曲线图,从而迅速定出 P_(cr)临界荷载值。本文贡献是把两种孤立方法联系起来,首次合并应用于求高层建筑刚架弹性稳定的临界荷载的计算中。本文的研究对弹性稳定临界荷载的快速计算有所帮助,它可以用简单的计算器计算,即就是对二十层或三十层的楼房建筑刚架去解算这个问题,也是很方便的,并得到相当满意的结果。此外,本文还包含单跨高层建筑刚架侧向位移的快速计算方法,计算精度也相当高。
It is well known that the matrix displacement method for stability analysis consists of a total stiffness matrix consisting of first- and second-order stiffness matrices. The former is a general stiffness matrix that does not consider the axial load of the column. In this paper, the so-called “unidirectional transfer no-shear secondary distribution method” (hereinafter referred to as the “simple analysis method”) is used to calculate quickly and accurately; the latter is to consider the rigid frame deformation. At the top of the column (or at the top of each column), the axial stiffness of the column is deviated from the geometrical stiffness matrix. This is due to the influence of the lateral deflection Δ of the column’s axial force P, called the P-Δ effect. This deviation P·△ Coupled moments generate column shear increments, and the increase in column shear increases the lateral displacement. As a result of repeated cycles of growth, the relationship of gradual convergence has been studied in terms of geometric progression. Let this ratio series have a common ratio of q_1, (i denotes the number between the i-th floor). When q_i ≥ 1, the i-story column is divergent with respect to the side-shift series, and the i-layer can be obtained at this time. The critical value of the critical value P_(cr) of the axial load on the top of the stud is set under the action of the unit disturbing force. When there is no axial load on the top of the column, (the load parameter is zero) the lateral displacement of the rigid frame is δ_o. When the top of the column has axial load and the load parameter is P, the lateral displacement of the rigid frame is δ. Then δ_o/δ represents the stiffness of the rigid frame when corresponding to different load parameters P. In this paper, it is convenient to quickly test the load parameters, draw the relationship curve between δ_o/δ and the load parameter P, so as to quickly determine the critical load value of P_(cr). The contribution of this paper is to link the two isolated methods together for the first time in the calculation of the critical load for the elastic stability of the rigid frame of a high-rise building. The study in this paper is helpful for the rapid calculation of the elastic stability critical load. It can be calculated with a simple calculator, that is, it is also very convenient to solve this problem for a twenty-story or thirty-story building construction frame. And get quite satisfactory results. In addition, this paper also includes a quick calculation method for the lateral displacement of a single-span high-rise building rigid frame, and the calculation accuracy is also quite high.