A member redundancy index based on distributed static indeterminacy for optimum material distribution for structures with axially loaded members

Abstract

Redundancy analysis in structural systems has been typically approached under particular loading conditions. Structural systems that are found to provide adequate levels of redundancy in light of such an approach may face serious threats resulting from accidental loads. Additionally, determining the degree of redundancy of a system as one unique global information ignores the spatial distribution of the redundancy in that system. Improper distribution of redundancy in the system may lead to the presence of superfluous material in parts of the system. One system measure that has been widely used to gage the level of redundancy in structures is the static indeterminacy. Hence, the redundancy matrix is an excellent tool that provides valuable insight into the distribution of the static indeterminacy among the structural members in the system; independently from any loads applied to the system. One of the essential components in the redundancy matrix is the distributed static indeterminacy. While providing satisfactory levels of redundancy in a system is encouraged, it is also necessary to optimize the material distribution in the system. Having members in the system that are highly, or even completely, redundant indicates an inefficient distribution of material and should be avoided. In this paper, a member redundancy index based on the distributed static indeterminacy is derived. This index can be used to efficiently distribute the material in the system in order to optimize its redundancy distribution.