Simultaneous joint balancing(SJB)processes or consecutive joint balancing(CJB)processes are balancing processes for the moment distribution method.Based on the equilibrium equations of moments at joints by the matrix displacement method,the iteration formulations were formed to solve the weighted rotations for both processes.According to both solution procedures,the following were proven:(1)the system of equations solved by both processes were identical with the system of the equilibrium equations for the moments of the joints;(2)SJB process and CJB process adopted the incremental Jacobi method and the incremental Gauss-Seidel method respectively to solve the system of equations,and the incremental Jacobi method and the incremental Gauss-Seidel method were consistent with the Jacobi method and the Gauss-Seidel method respectively;(3)the moments at the ends of all the members solved by both processes were identical with the moments figured out by the slope-deflection equation.They demonstrated that the unknowns solved by the moment distribution method were the weighted rotations whose weights were the total stiffness factors at the joints with opposite signs.A weighted rotation equaled the sum of the unbalanced moments of the joint in the iterations of all the cycles.
关键词
力矩分配法/雅可比法/高斯-赛德尔法/矩阵位移法
Key words
moment distribution method/simultaneous joint balancing process/consecutive joint balancing process/Jacobi method/Gauss-Seidel method/matrix displacement method
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