Equivalent Stiffness—Flexibility Matrices for Series, Parallel and Closed—Loop Systems
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Quite often, in practice, systems contain series and parallel connected members or closed loops. Such special arrangements of members occur, for instance, in building structures, pipe lines, continuous bridges, etc. The analysis of these systems, then, can be expedited and the results may be improved if they are replaced (theoretically) by a single member with an equivalent flexibility (stiffness). In doing this, with the exception of the end points, all the intermediate nodal points will be eliminated. This in turn reduces the size of the overall stiffness (flexibility) matrix of the entire system.
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