# Study of Redundancy in Near-Ideal Parallel Structural Systems

*by*Rabi S. De, Univ of California, United States,

Ashish Karamchandani, Univ of California, United States,

C. Allin Cornell, Univ of California, United States,

**Abstract:**In this paper the reliability of parallel structural systems is studied in order to begin to understand and quantify the system factors influencing the overload capacity and the redundancy of realistic statically indeterminate structures. Redundancy is defined as the conditional probability of system failure given first failure of any member (it is an inverse measure). In contrast to previous studies of ideal parallel systems, the present study considers unbalanced parallel systems. In an unbalanced system, the ratio of mean member force to mean capacity is different for different members in the intact and in the damaged states of the structure. For a structure that is perfectly balanced in the mean the system effects, inducing redundancy and overload capacity beyond the first member failure, are strictly due to the randomness and uncertainties of the governing variables, i.e., they are probabilistic in origin. In contrast, for a more realistic unbalanced structure, the system effects inducing redundancy are both deterministic and probabilistic in origin. In this study the effect of various parameters, like number of members, postfailure member capacity, excess design capacity, etc., is investigated. Simple approximation is developed for estimation of the probability of failure of complex unbalanced systems. A Reduced Space Monte Carlo Simulation approach has been used for reliability analyses. This proved to be a very efficient technique for the present study.

**Subject Headings:**Structural systems | Failure analysis | Structural reliability | System reliability | Probability | Overloads | Structural failures | Europe | Monaco | Monte Carlo

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