Steel moment-resisting frame optimization considering seismic effects and probabilistic constraints

Force-based seismic design, as the conventional earthquake resistant design philosophy, is going to be replaced with probabilistic performance-based design methodology. Through this method, induced damages against various levels of strong ground motions, play a dominant role. Seismic-induced damages are characterized by probabilistic damage functions, namely fragility curves. Fragility curves show the probability of exceeding damage levels (i.e. limit states) conditioned on strong ground motion intensities (i.e. Intensity Measures). Amongst well-known limit states (such as Immediate Occupancy, Life Safety and Collapse Prevention) for which the structure is to be checked, sidesway collapse limit state is of the greatest importance owing to the large amount of triggered losses during past earthquakes. Incremental Dynamic Analysis (IDA) method is the most popular method to achieve fragility curves for variuos limit states. By this methodology, the structure is affected by increasing levels of ensemble of strong ground motions. For each ground motion, the intensity which causes the instability of finite element model of the structure presents the collapse points. Fitting log-normal probability distribution to achieved intensities presents collapse fragility curve. The structure is to be checked against sidesway collapse in such a way that the probability of collapse for design-level seismic hazard is less than the pre-defined allowable probability.        
Optimization of structures is aimed to present the topology, shape of structures and size structural sections in such that minimum target function (mostly structural weight) is achieved, while variuos design constraints are satisfied. Size optimization of structural members has been accomplished through previuos researches applying gravity and equivalent lateral forces. Besides to achieve optimum structures applying realistic effects of earthquakes, number of researches applied time history analysis of structures against one earthquake record or mean of number of earthquake records. To involve effects uncertainties regarding strong ground motions, probabilistic damage margins must be included in optimization constraints. To achieve this goal, in this paper, weight optimization of structres considering probabilistic constraints (represented by target collapse probability) is investigated. To achieve an efficient algorithm, the collapse fragility curve of structure is predicted by trained neural network. The network is trained based on incremental dynamic analysis of simulated models of samped structure. Besides probabilistic constraint regarding collapse probability margin, maximum normal stress and inter-story drift ratio (as deterministic constraints) are involved. Deterministic constraints are calculated by matrix analysis of the structure. Genetic algorithm is applied to solve the optimization problem. Finally, effects of target collapse probability on optimum weight are examined.
Achieved results show that the probabilistic constraint coverns the optimization problem if the target probability of collapse is less than 10%. Beyond this value, deterministic constraints, which are maximum normal stress and interstory drift ratio governs the optimum weight of the sampled structure.