Optimum design and damage control for load sequences

A probabilistic approach to decision-optimal design and damage control is developed for structural systems that can gradually accumulate damage by nonlinear behavior under sequences of dynamic loads, whose occurrence can be idealized by renewal stochastic processes. To minimize consequences and damages during the life cycle of a structure, a damage threshold is established as a measure of damage control. If structural damages are lesser than such a damage threshold the structure is not repaired, otherwise the structure is repaired or rebuilt. The proposed approach is generalized and capable of describing particular cases for the optimization of expected losses. One of them is the well-known case used as a basis for many current design criteria in which it is assumed that the structure is repaired or rebuilt systematically after some damage or failure. The present work extends the ideas and models reported in several seminal papers. However, the proposed approach has the advantage that it takes into account cumulative structural damage over time, allows evaluating objectively the cost of damages and sets an optimum repairing damage threshold. Finally, the probabilistic formulation is illustrated through its application to a building subjected to sequences of earthquakes.