RELIABILITY BASED RISK OPTIMIZATION

Abstract eng:
Reliability-Based Risk Optimization (RBRO) aims at the optimum level of safety to be achieved in a given structural design in order to minimize total expected costs or maximize the expected profit to be obtained with the designed structure. RBRO is as a tool for decision making in the presence of uncertainty. It can be used to establish the optimum levels of safety, maintenance, inspections and quality control to be performed in a given structural system, in order to maximize the expected profit. RBRO has been advocated as a means to achieve optimum reliability in future revisions of current structural design codes, which so far have mainly been calibrated to maintain safety levels of previous codes. In this paper, RBRO is used to find the optimal safety coefficient in order to minimize the total expected cost of structural systems. The problem is formulated in the partial safety factor format used in current design codes, with an additional partial factor introduced to serve as optimization variable. The expected cost of failure (or risk) is defined as the product of a limit state exceedance probability by a limit state exceedance cost. These costs include costs of repairing, rebuilding, and paying compensation for injury and loss of life. The total expected failure cost is the sum of individual expected costs over all failure modes. The procedure is applied in the design of a steel frame communications tower, subject to extreme storm and tornado wind loads. The study shows that when non-structural terms dominate design costs (e.g., in residential or office buildings) it is not too costly to over-design; this observation is in agreement with the observed practice for non-optimized structural systems. In this situation, it is much easier to lose money by under-design. When structural material cost is a significant part of design cost (e.g. concrete dam or bridge), one is likely to lose significant money by over-design. In this situation, a risk optimization analysis is highly recommended. The study shows that optimum reliability is strongly dependant on limit state exceedance consequences. This may represent different optimum levels for the different parties involved, and lead to a multi-objective optimization. It can also be the case, however, that a multi-objective problem only arises because risk is not properly understood and hence not properly dealt with by the parties involved. Finally, the study also shows that under time-varying loads like tornados, the optimum reliability is strongly dependent on the selected design life.

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