Keywords: optimum design, reinforced concrete buildings, life-cycle cost, minimum torsional response.

Three design philosophies for the design of reinforced concrete buildings are considered in this study. In the first one the initial construction cost is considered as the objective function to be minimized, the second one is formulated as a minimization problem of the torsional responses while a combined formulation is also examined as the third design approach. According to the first approach the torsional behaviour is minimized by considering the minimization distance of the mass center and rigidity centre while in the second one this is achieved by minimizing the eccentricity between the mass center and the strength center. This is a reliable way to assess, in terms of their efficiency, torsionally unbalanced structures. Seismic design codes enforce a number of recommendations in order to deal with torsionally unbalanced structures. On the other hand, new design concepts have been proposed taking into account the nonlinear behavior of the structure in more than one earthquake intensity levels. This design philosophy is denoted as performance based design (PBD). The influence of large eccentricities of the rigidity and strength centres in relation to the mass center is assessed with respect to the seismic response of buildings. In particular, various structural optimum design formulations are assessed with respect to the minimum torsional response in three hazard levels (frequent, occasional and rare) and with respect to the total life-cycle cost.

In all formulations that are examined in this work the design variables are divided in two categories: topology design variables corresponding to the topology or layout of the columns and shear walls of the building and sizing design variables corresponding to the dimensions of the cross sections. The formulation of the optimization problem incorporates both code demands and architectural constraints. The optimizer is based on evolutionary algorithms, while the optimum designs obtained, with the various formulations of the problem, are assessed with respect to both initial and limit-state dependent costs taking into consideration the behavior of the structure during its life time. In this paper it is shown that designs obtained according to the minimum eccentricity of the rigidity centre formulation behave well in frequent (50/50 hazard level) and occasional (10/50 hazard level) earthquakes, while designs obtained according to the minimum eccentricity of the strength centre formulation behave well in rare (2/50 hazard level) events. Designs based on a combined formulation seem to behave equally well in the three hazard levels examined.

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