空间直梁传递矩阵的物理意义推导法

Physical meaning method for deriving transfer matrix of space straight beams

基于传递矩阵中各元素的物理意义,采用单元基本计算体系,利用平衡条件和虚功原理推导了考虑弯矩、剪切和轴力影响的空间弹性直梁在无外荷载及各种外荷载作用下的传递矩阵,并针对实例,对所推导公式进行编程运算,得到示例桥梁关键截面的内力。将计算结果与有限元法计算结果进行比较,二者吻合良好,表明推导方法可行。该方法避免了初参数法的繁琐,概念清晰,求解简便,并可以应用到其他结构在不同荷载情况下传递矩阵的推导。

Based on the physical meanings of the elements in transfer matrix,with the basic computing system of the unit,spatial transfer matrix of the elastic beam under all kinds of external loads was deduced by balance equations and the principle of virtual work.The derived formula considers the effects of bending moment,shear and axial force.A practical project was taken as a case for calculation by the traditional finite element method and the spatial transfer matrix formula method.The comparison of the in-ternal force in key sections of the example bridge calculated by the two different methods shows that,the spatial transfer matrix formula is correct and the physical meaning method is efficient.This method avoids the cumbersome of the initial parameter meth-od,has a clear concept and is easy to solve,and can be applied to the derivation of other structures under different loads.