A general characterization of the Hardy Cross method as sequential and multiprocess algorithms

The Hardy Cross method of moment distribution admits, for any problem, an entire family of distribution sequences. Intuitively, the method involves clamping the joints of beams and frames against rotation and balancing moments iteratively, whether consecutively, simultaneously, or in some combination of the two. We present common versions of the moment distribution algorithm and generalizations of them as both sequential and multiprocess algorithms, with the latter exhibiting the full range of asynchronous behavior allowed by the method. We prove, in the limit, that processes so defined converge to the same unique solution regardless of the distribution sequence or interleaving of steps. In defining the algorithms, we avoid overspecifying the order of computation initially using a sequential, nondeterministic process, and then more generally using concurrent processes.