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：大型静不定桁架与框架结构呈现复杂的承载特性，冗余矩阵对其分析与设计具有重要价值。根据不同任务需求，需要完整冗余矩阵或仅需其对角线元素。标准计算方法的计算量较大。多数结构属于适度冗余范畴，即静不定次数与所有构件承载模式总数之比小于二分之一。本文提出一种适用于适度冗余系统的冗余贡献闭式表达，该表达式通过基于奇异值分解的冗余矩阵分解方法推导得出。通过多组算例展示了该方法随系统规模增大时的表现，以及在适用情况下随静不定度增加时的计算特性。