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对门式刚架中工字楔形柱平面内稳定作了理论分析和探讨,推导了基于结构力学意义上柱的平面内一阶线弹性稳定性方程,对两端简支情况给出了平面内稳定长度系数的高精度近似解析解。给出了其他可能的近似支撑情况的边界条件,对4种支撑情况给出了平面内长度系数的表和相应的修正公式。对于一般意义上柱的平面内长度系数给出了力学近似简化模型,并给出了符合一定条件的柱的长度系数的一种计算方法。另外,文章导出的一个微分方程解析解为推导工字楔形单元在压力作用下的转角位移方程提供了依据,即为二阶线弹性分析工字形变截面构件提供了理论依据。
Based on the structural mechanics, the first-order linear elastic stability equation in the plane of column is deduced, and the in-plane stability is given for the simple support at both ends High Accuracy Approximate Analytic Solution of Length Coefficient. The boundary conditions of other possible approximate support cases are given, and the tables of the in-plane length coefficients and the corresponding correction formulas are given for the four support cases. A simplified model of mechanics approximation is given for the in-plane length coefficient of a column in general sense. A calculation method for the length coefficient of a column which satisfies certain conditions is given. In addition, an analytic solution of differential equation derived from the article provides a basis for deriving the angular displacement equation of I-shaped wedges under pressure, which provides a theoretical basis for second-order linear analysis of I-shaped members.