基于优化原理框架结构梁柱合理线刚度比研究

Research on reasonable linear stiffness ratio of frames beam to column based on optimal principle

框架结构初步设计中,梁柱截面尺寸估算分别按照梁的跨度及柱所分担的轴力来进行,由此得到结构抗侧刚度并不一定最大。框架柱的抗侧刚度不仅取决于自身的线刚度,还与其两端的框架梁对其约束程度有关,故存在1个合理的框架梁柱线刚度之比,使结构抗侧刚度最大。在保证梁柱材料总量相等的情况下,运用优化原理寻求框架结构等效抗侧刚度的最大值,此时框架结构梁柱线刚度比即为合理值,进而可确定梁柱的合理截面高度,并给出计算图表。算例结果表明,优化后的结构抗侧刚度较优化前明显增加,结构侧移明显减少。该方法简单、实用,可供初步设计使用。

During the primary design of frames, the section sizes are estimated according to the beam span and the axis force bearded by column, but the structural anti - side stiffness will not be the maximum. The structural anti - side stiffness of column lies in not only the linear stiffness of columns, but also the beams restriction degree to the columns. There is a reasonable linear stiffness ratio of frames beam to column, thus the structural anti - side stiffness will be the maximum. On the condition of the equal material quantity, the linear stiffness ratio of frames beam to column is reasonable when the equivalent anti - side stiffness is the maximum by the non - linear optimal principle, and the reasonable section height can also be obtained. Some diagrams were given, and an example was taken to find that the structural anti - side stiffness increased and the lateral displacement decreased obviously after the optimization. It shows that this method is accurate, convenient and applicable to the preliminary stage of design.