有侧移失稳的Y形柱面内计算长度系数分析

(山东华科规划建筑设计有限公司,山东 聊城 252000)

弹性稳定理论,计算长度系数,位移法,Y形柱,有侧移失稳

Effective length factors for Y-shaped column in-plane with lateral instability
MENG Fan-tao,RUN Xing-qun

(Shandong Huake planning and architectural design CO.,LTD.,Liaocheng 252000,Shandong province,China)

elastic stability theory,effective length factor,displacement method,Y-shaped column,sway buckling

备注

本文依据弹性稳定理论给出了柱脚刚接有侧移失稳的Y形柱弹性稳定方程,并应用MATLAB对方程进行了求解,结果表明,在夹角和上下柱段惯性矩之比相同的情况下,计算长度系数随上下柱段高度之比增大而增大; 在夹角和上下柱段高度之比相同的情况下,计算长度系数随上下柱段惯性矩之比增大而减小; 在上下柱段惯性矩之比和上下柱段高度之比相同的情况下,计算长度系数随夹角增大而增大.数据分析给出了便于工程实用的下段主干计算长度系数的拟合计算式,当夹角小于90°时,该计算式误差在5%以内; 而夹角大于90°且不大于150°时,最大误差为16.25%.最后,通过工程实例验证了本文拟合计算式的精度.

Based on the theory of elastic stability,the elastic stability equation of Y-shaped column rigidly connected with lateral displacement is given.The stability equation is solved by using MATLAB.The results show the effective length coefficient increases with the increase of the height ratio of the upper and lower columns when the angle and the moment of inertia of the upper and lower columns are the same,and the effective length coefficient increases with the ratio of the moment of inertia of the upper and lower columns when the angle and the height ratio of the upper and lower columns are the same.When the ratio of the inertia moment of the upper and lower columns and the ratio of the height of the upper and lower columns are the same,the effective length coefficient increases with the increase of the angle.Through data analysis,the fitting formula of the effective length coefficient of the lower columns is given.When the angle is less than 90°,the error of the fitting formula is less than 5%,and the angle is more than 90° and less than 150°,the maximum error is 16.25%.Finally,the accuracy of the fitting formula is verified by engineering examples.