Large statically indeterminate truss and frame structures exhibit complex load-bearing behavior, and redundancy matrices are helpful for their analysis and design. Depending on the task, the full redundancy matrix or only its diagonal entries are required. The standard computation procedure has a high computational effort. Many structures fall in the category of moderately redundant, i.e., the ratio of the statical indeterminacy to the number of all load-carrying modes of all elements is less one half. This paper proposes a closed-form expression for redundancy contributions that is computationally efficient for moderately redundant systems. The expression is derived via a factorization of the redundancy matrix that is based on singular value decomposition. Several examples illustrate the behavior of the method for increasing size of systems and, where applicable, for increasing degree of statical indeterminacy.

翻译：大型超静定桁架与框架结构呈现复杂的承载行为，冗余矩阵对其分析与设计具有重要价值。根据任务需求，可能需要完整的冗余矩阵或仅需其对角元素。标准计算流程的计算量较高。许多结构属于中等冗余范畴，即静不定次数与所有构件全部承载模式数量之比小于二分之一。本文提出一种适用于中等冗余系统的冗余贡献闭式表达式，该表达式通过基于奇异值分解的冗余矩阵因式分解推导得出。通过多个算例展示了该方法随系统规模增大以及（在适用情况下）随静不定次数增大时的表现特征。