任意线弹性支承的双跨压杆稳定性计算

用初参数法,建立了任意线弹性支承的双跨压杆处于微弯曲平衡状态时,统一的变形方程、静力平衡方程和物理方程.由齐次线性方程组有非零解的条件,导出了临界压力的特征方程.借助软件,对中部铰支的9种完全理想支承的双跨压杆,和一个非完全理想支承的双跨压杆进行了稳定性计算,得到了长度因数与中部支承位置之间的关系,确定了中部支承的最佳位置和最小长度因数,以及最差位置和最大长度因数;同时发现定向-铰支-定向和定向-铰支-自由支承的双跨压杆的长度因数与中部铰支的具体位置无关,其大小依次为1和2.

Calculating stability of double span long column supported by any linear elastic supports

The unified deformation equation, the static equilibrium equations and the constitutive equa- tion were established to double span long column supported by any linear elastic supports in the equilib- rium state of micro bending by the initial parameters method. The characteristic equation of critical force was deduced by the condition of homogeneous linear equations with non-zero solution. The stabil- ity of nine kinds of double span long column supported by ideal hinge support in the central and a doub- le span long column supported by non ideal supports was calculated using software. Finally, the rela- tionship between the factor of length and the position of the central support was obtained~ the best po- sition of the central support and the minimum factor of length ,and the worst position and the maximum factor of length were determined. It is found that the factor of length to the double span long column supported by directional support-hinge support-directional support and directional support-hinge sup- port-free is irrelevant to the specific position of the central support, the values of which are 1 and 2 in order.