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The search for a bona fide robustness index to quantify the system performance upon unexpected disturbances has been a continuous research effort. Previous studies have largely neglected to reflect...

Design optimization of building structures under progressive collapse threats is a challenging problem. This is not only because the progressive collapse is a system failure phenomenon involving complicated material and geometrical nonlinearities, but also because the extremely low probability and the much larger uncertainty associated with the initiating events that trigger such a failure could render most risk reduction strategies economically unjustified, should the conventional risk-neutral decision making approach be followed. Facing these challenges, this paper presents an innovative two-stage optimization method for progressive collapse design of reinforced concrete frame structures. The first, tactical stage involves a bi-objective optimization that maximizes the structural robustness while minimizing the total additional reinforcement beyond the conventional design. This stage of optimization results in a Pareto efficiency frontier between the increase in longitudinal reinforcement and structural robustness, which is measured by a new risk-based robustness index. At each efficiency point, the optimal allocation of reinforcement across the beams affected by a column removal scenario is determined. The second, strategic stage includes a descriptive decision making module based on the cumulative prospect theory (CPT) in order to characterize the bounded rationality of a decision maker when facing large uncertainty. Based on an empirically calibrated CPT model, the study finds that the threshold for the probability of initiating event below which no additional investment is justified for progressive collapse design is pushed to the lower end of the empirical incidence rate. This is completely in contrast to previous research results based on the risk-neutral argument. Using a multi-storey plane frame for illustration, the study also clearly shows that the Alternate Path Method following the linear static procedure is not efficient from a purely engineering perspective. When the decision maker’s risk attitude is considered, the APM design is found to be unduly conservative.

O presente trabalho visa analisar o comportamento estrutural de vigas de concreto armado em flexão, por meio de uma modelagem discreta de fratura com o uso de interfaces coesivas. Avaliou-se, neste estudo, a influência da utilização de elementos de interface entre todos os elementos de concreto da malha de elementos finitos, representando o dano de forma generalizada. Desta forma, é possível analisar desde a alteração na resposta estrutural por meio do gráfico entre força aplicada e deslocamento no centro do vão das vigas, bem como o surgimento e propagação de fissuras ao longo de todo o comprimento das mesmas. Foram utilizadas também leis específicas para simular o comportamento de aderência entre o concreto e o aço através de elementos de aderência. O trabalho envolveu o estudo de diferentes situações, a partir da simulação de vigas com diversas configurações, sendo analisada também a sensibilidade do modelo às variações dos parâmetros de entrada, que abrangem as propriedades dos materiais e os parâmetros numéricos do modelo coesivo utilizado. Os resultados mostraram que metodologia utilizada é capaz de representar importantes fenômenos como a perda de rigidez associada a fissuração no concreto, além de reproduzir a fissuração de maneira adequada destes elementos estruturais. The aim of this work is to analyze the structural behavior of reinforced concrete beams in bending, by means of a discrete modeling using cohesive interfaces. It was evaluated the influence of using interface elements between all concrete elements of the finite element mesh, representing the damage in all the structural element. From that, it is possible to analyze the alteration on the structural behavior on the applied load versus midspan deflection of the beams, as well as the propagation of cracks along the beam length. It was also used specific laws to simulate the adherence between the concrete and steel bars. The work involved the study of the sensibility of the model to the variations of the input parameters, which included the material properties and the numeric parameters of the proposed model. The results showed that the methodology used is capable of representing important phenomena like the rigidity loss associated to the concrete cracking, as well as reproducing the cracking itself accordingly.