On Moment Distribution Method, Kani Method and Slope-Deflection Method

摘要

This paper clarified the following. 1. So called "Kani method" is a kind of slope-deflection methods, i.e; every process of Kani Method can be explained by the slope-deflection method which is solved by Iteration. In the Iteration process of the slope-deflection method, calculating a joint rotation angle moment φ_i is none the less computing the fixed moment of jolnt i in the Kani method except some multiplier, and in the same process, computing a deflection angle moment ψ is not more than calculating the corresponding storey moment of Kani method except some multiplier. Mathematically, Kani method and the slope-deflection method solved by Iteration are identical. 2. Ordinary Cross method is also a kind of slope-deflection methods, which solved by Iteration. In the latter process we construct the equations like followings (c.f. Fig. 2)(数式については省略)　Instead of the equations (1), solving two systems of equations (3) and (4) separately by Iteration, then this process is identical with the ordinary moment distribution method. Solving equation (3) by Iteration corresponds to solving the problem by the ordinary moment distribution method in which the given loads act no joint movement occurs. Solving equations(4) by Iterstion is the same process in the ordinary moment distribution method where some horizontal forces act and some joint movements occur and no given load acts. 3. Explaining the both of Kani method and ordinary moment distribution method by the slope-deflection method, as above, it is easy to understand the differences between Kani method and the ordinary moment distribution method. For example, speed of convergence of ordinary moment distribution method is cleary more rapid than that of Kani method, because of the small number of arguments. In the former case, however, the processes of moment distribution and balancing must be repeated some definite number of times and then balancing the horizontal forces are necessary. So, problem of "Which method is superior one" is not determined.