An iterative method for analyzing statically indeterminate beams and frames. Developed by Hardy Cross, it involves successively locking and unlocking joints to distribute moments until equilibrium is reached. It was a standard hand-calculation technique before the widespread use of computers for structural analysis, simplifying complex problems into a series of arithmetic steps based on member stiffness and carry-over factors.
The Moment Distribution 方法 is a displacement method of analysis that was revolutionary for its time, as it allowed engineers to solve complex indeterminate structures without solving large systems of simultaneous equations. The process begins by assuming all joints are fixed against rotation and calculating the ‘fixed-end moments’ caused by external loads on the members.
The core of the method is an iterative process of ‘balancing’ the joints. At each joint, the unbalanced moment (the sum of fixed-end moments) is distributed among the connecting members according to their relative rotational stiffness. A portion of this distributed moment, known as the ‘carry-over moment’ (typically half the value), is then transferred to the far end of the member. This process is repeated, moving from joint to joint, with the unbalanced moments becoming progressively smaller in each cycle. The iteration continues until the moments are balanced to a desired degree of accuracy, at which point the final end moments for all members are determined by summing the initial fixed-end moments and all subsequent distributed and carry-over moments.
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