One-step moment distribution, plane frames.
The conventional moment distribution method is revitalized with a new approach which requires only one-cycle of balance and carry-over and no iteration. For a continuous beam, the method begins by assuming the value of the balancing moment, say x, at the first joint. By invoking the moment equilibrium condition successively from the first towards the last joints, balancing and carry-over moments at other joints can be determined in terms of the unknown x without iteration. By means of moment equilibrium of the last joint, the unknown x can be solved exactly, regardless of the number of spans, and the final moment distribution of the whole structure can be easily obtained. Further, for multi-bay, single story frames, the analysis is carried out without the need to separate the analysis into two stages as in conventional MDM, and the final exact moments are found by solving two unknowns only, regardless of the number of bays. As such, the revitalized MDM is particularly advantageous for solving continuous beams and single-story frames with large number of spans or bays. Five examples are given herein to demonstrate the procedures and efficiency of the proposed method.
IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE)
Kong, J.,& Wong, S. H. (2018). Revitalizing the moment distribution method: A fast and exact analysis of multibay, multi-story frames.. IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE), 15 (5), 15-24. http://dx.doi.org/10.9790/1684-1505041524