立柱考虑弹性抗力后临界压力计算问题

The Calculation of Critical Pressure of a Column after Taking into Account Its Elastic Resistance

立柱构件与周围介质(如土体)紧密接触的状态下,当受压变形时则介质也出现相应的弹性抗力。这对于立柱抗压稳定、对临界作用力将产生很大的影响。利用弹性地基梁温克尔假定之弹性抗力原理,推导立柱在轴向力作用下临界力微分方程,建立存在弹性抗力时立柱两端铰接临界压力计算公式。此外一并导出了一端固定一端自由、两端固定、一端固定一端铰接立柱,考虑弹性抗力后的临界力计算公式。为了减少计算工作,只需判断P■(EJkb)^(1/2),当P≤(EJkb)^(1/2)时,无需计算临界压力。当P>(EJkb)^(1/2)时,需要进行稳定分析,即可设计出建筑结构所要求的超强工业构件。

In a state of the column structural component being in close contact with its surrounding medium （for example earth mass）, when deformation is caused by compression, elastic resistance appears in the medium. This will have a significant influence on both the column stability against compression and the critical pressure. The paper has derived the column critical pressure differential equation under axial force and has established the calculation formula of the critical pressure of the hinged column on two ends when the elastic resistance exists using the elastic resistance principle of the elastic foundation beam assumed by Winkler. In addition the paper has also derived the critical pressure calculation formula taking into account the elastic resistance in the case of one end being fixed and the other being free or two ends being fixed or one end being fixed and the other being hinged column. In order to reduce the calculating work only judg-ment is given on P √EJkb, when P≤√EJkb, it is unnecessary to calculate the critical pressure. When P√EJkb, it is necessary to make a stability analysis so that the super structural component required by the building structure could be designed.