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单跨平面框架结构的动力分析方法有很多种,如取为单自由度的等效静载分析方法,将顶、侧、底荷载分别单独作用进行简单叠加的分析方法以及取顶、侧、底荷载最大值作为静载同时作用的分析方法等。但由于简化的结果都不能反映出结构的真实受力过程和结构内力的实际最大值,仅给出一个很粗糙的近似值。本文利用集中参数法对框架结构按三个自由度分析。可以计算任意已知周边荷载条件下的内力。取结构分别在顶、侧、底荷载单独作用下其对应受荷构件中点产生的位移为基本变量。根据叠加原理、哈密顿原理建立运动微分方程系。求解方程系便可确定框架上任何一点 S 在任一时刻 t 的位移 W(S,t)。用数值积分法求解,找出位移最大值。由微分关系,进而得出最大内力值。最后以浅埋土中单跨框架工事为例,算出结构各特征点上的内力值。并给出一组核爆冲击波作用下土中浅埋框架结构顶、侧、底边端点和中点上的内力系数表。
There are many dynamic analysis methods for a single-span plane frame structure, such as the equivalent static load analysis method taken as a single degree of freedom, and the top, side, and bottom loads acting alone to perform a simple superposition analysis method as well as top, side, and bottom The maximum load is used as the analysis method for simultaneous action of static load. However, because the simplified results do not reflect the actual maximum force of the structure and the actual maximum of the internal force of the structure, only a very rough approximation is given. This paper uses the lumped parameter method to analyze the frame structure with three degrees of freedom. It is possible to calculate the internal forces under any known peripheral load conditions. Take the structure of the top, side, bottom load alone under the load corresponding to the displacement of the load produced by the midpoint of the basic variables. According to the principle of superposition and Hamiltonian principle, the system of motion differential equations is established. Solving equations can determine the displacement W(S,t) of any point S on the frame at any time t. Solve the numerical integration method to find the maximum displacement. From the differential relationship, the maximum internal force value is obtained. Finally, the single-span frame construction in shallow-buried soil is taken as an example to calculate the internal force values at each characteristic point of the structure. A set of internal force coefficients on the top, sides, and bottom edges of shallow frame structures in soil under the action of a nuclear explosion shock wave is presented.