爆炸荷载作用下承重柱的弹性动力响应分析

THE LINEAR DYNAMIC RESPONSES OF COLUMNS SUBJECTED TO BLAST LOADS

为了建立爆炸荷载作用下承重柱构件的弹性动力响应分析方法,进一步奠定研究承重柱非线性抗爆响应和破坏形态的理论基础,该文将承重柱简化为承受轴向荷载的约束梁构件,并基于经典Timoshenko梁理论,通过建立等效频率矩阵、等效荷载向量矩阵以及修正的等效质量矩阵,采用变量分离法联立方程求解,推导出承受恒定轴力的Timoshenko梁在任意横向爆炸荷载作用下的弹性动力响应的解析解;并以此弹性解析方法为基础,进一步分析讨论了爆炸荷载作用下,长细比、初始轴向应变、端部约束条件及荷载参数等因素对承重柱弹性动态响应的影响,研究结果对钢柱或钢筋混凝土柱(RC柱)的抗爆分析与设计有参考作用。

The motivation of this paper is to predict linear responses of explosion-loaded columns, and lay the theoretical foundation for the further investigation on the non-linear responses and damage modes of columns subjected to explosion loads. The column was simplified as an axially loaded beam, and an analytical solution on the linear responses of axially loaded Timoshenko beams subjected to arbitrary transverse dynamic loads was presented theoretically. The equivalent matrix of frequency, loads and modified equivalent matrix of mass were established according to the Timoshenko＇s beam theory and the method of separation-variables. Furthermore, the influences of parameters such as length-depth ratio, initial axial compressive strain, boundary constraints and blast loads on the responses of the columns were discussed, based on the proposed solution. The analytical results and conclusions were helpful to the analysis and design of explosion-loaded steel or RC columns.