Sidesway Analysis of Unsymmetrical Multi-storey Frames by a Modified Method of Moment Distribution

For the analysis of statically indeterminate framed structures the Cross method of moment distribution is the most widely used, especially in the English-speaking world. Its ease of computation and rapidity of application in analysing structures with non-translatory joints are beyond dispute, but when problems arise where sidesway occurs a prohibitive increase of computational labour is often the result. The fact that on the one hand most designers have aversion to such computational labour and on the other hand approximate analyses are inevitably unreliable, renders it desirable to develop an adequate method of analysis. Since a great proportion of engineers have already acquired mastery over the moment distribution technique, a modification of the above method, rather than its substitution by an entirely new method, would thus seem preferable. It is proposed to put forward in this paper a modified method of moment distribution in which sidesway can be automatically allowed for without employing the temporary support device. The procedure of the proposed method is as follows :-
(a)Under a system& of loading (Fig. 4), the joints of the frame are locked against rotation but remain free to move laterally. Locking moments are thus induced at the joints.
(b)One of the joints is then released and is thus subjected to both rotation and translation. The unbalanced moment is distributed among adjacent members in proportion to their modified stiffness factors.
(c)The rotation and translation of the released joint result in deflecting other members than the adjacent ones (Fig. 3a, joint A). The induced moments are obtained by multiplying the distributed moments by corresponding modified carry-over factors.

Lloyd C.P. Yam