基于屈曲模态的弹性压弯构件平面内二阶弯矩计算

CALCULATION OF SECOND-ORDER IN-PLANE BENDING MOMENT OF ELASTIC COMPRESSION-BENDING MEMBERS BASED ON BUCKLING MODES

目前,对于一般情形,结构工程师缺乏简便可靠的手段计算钢结构构件的二阶效应,采用大挠度大变形的直接分析法成为唯一选择。该文从一般情形的等截面等轴力压弯构件平面内受力的基本方程出发,证明了其屈曲模态的正交性以及各种可能平衡状态的稳定性,并首次采用屈曲模态分解法,得到了构件二阶效应的屈曲模态级数解。更进一步,结合构件屈曲荷载的分布规律,给出了实用的构件平面内二阶弯矩的估算方法,对典型受力状态的构件进行了算例验证,并对极端情况下的误差进行了分析。该文提出的屈曲模态分解法用于计算构件的二阶效应时,仅需利用其一阶分析结果、一阶屈曲模态和一阶屈曲荷载,简便可靠,可供工程师在计算钢结构构件平面内二阶弯矩时参考。

For a more common situation,in order to estimate the in-plane second-order effect of the elastic members under compressing,there seems no convenient and accountable method other than the complicated direct analysis method is available.Based on the differential equation of the in-plane second-order effect of a constant-section column under a uniform axial compression,the orthogonality relation of its buckling modes is proved,and the stability of all possible equilibrium states is discussed.Furthermore,the in-plane second-order effect is adopted by buckling modal series method for the first time,and its accuracy is demonstrated by several typical situations.For the computational complexity and awful accuracy of some specific situation,a simplified method is proposed in which only the first order in-plane result and the axial force and the deform shape of its first buckling mode are required.And the efficiency and accuracy of this new method are evaluated by several typical situations.