Abstract

The paper describes a finite element damage model for non linear analysis of concrete or reinforced structures. It is show how can be effectively used to predict local and global damage up to structural failure. Examples of applications of the model to the analysis of different structures such as a nuclear containment shell, a housing building and the domes of St. Mark Basilica are presented.

Abstract

The present work exposes the design of optimization procedures both with the “Particle Swarm Optimization” (PSO) algorithm and the “Genetic Algorithm” (GA) for the design of reinforced concrete frames, making comparisons in cost, weight of the structure and predicted damage. The optimization procedures are built up using the “Idealized Smeared Reinforcement” (ISR) analogy for each element of the structural model frames considered for this work. Two different numerical structural plane-frame models were created for the application and comparison of the performance of the optimization design procedures hereby proposed. The optimization procedures were mono-objective with a cost-objective function, taking on account steel reinforcement and concrete for the cost computation. Two different design approaches were carried on for this work, one proposing asymmetrical reinforcement for columns and the other with symmetrical reinforcement. In order to compute the damage indices considered for this study a non-linear Pushover structural analysis is performed. Results show that asymmetrical reinforcement in columns may reduce concrete volumes, although such reduction in material might not be quite proportional with construction cost, given that asymmetric reinforcement in columns is more expensive than symmetrical, per unit-cost. The bigger the structure, the more likely is to obtain lighter structures by using asymmetrical reinforcement. Regarding damage of the structure, results show that when using asymmetrical reinforcement in columns, it is more likely to obtain smaller values for the expected damage with no great difference on the estimated collapse Safety Factors for the seismic loads. In general, the proposed methodology hereby proposed enhances quite good optima results, requiring only a few adjustments of clash-free and slap reinforcement after the optimization procedure terminates. When designing reinforced concrete frames with asymmetric reinforcement in columns, an increase in construction costs of as much as $25\%$ as that obtained for symmetric reinforcement could be enhanced. In general, with the proposed methodology to optimally design reinforced concrete frames, savings of as much as $20\%$ in construction costs from an initial structural proposal can be reached.