Moment Equations for Computer Analysis of Frames

The equilibrium equations of a structure are expressed in terms of joint and floor moments. Because the coefficients of these equations involve only the moment distribution factors at the joints, the method provides a standard approach for all kinds of end conditions and for members with constant as well as variable moments of inertia. The method has particular advantages when used in conjunction with computers, because the coefficient matrix of the moment equations can be generated more readily than similar operations involved in the usual flexibility or stiffness matrix methods. A further advantage of the proposed method is that when the equations are solved, simple application of distribution factors gives the end moments. Using flexibility or stiffness methods, an initial solution must be made for the redundants or displacements, and additional matrix operations are required to determine the moments and shears. Thus, the moment equation method requires less machine time, less storage, and is more readily programmed.