Jordan Journal of Civil Engineering

Automated seismic design of planar frames blending structural reliability and heuristic optimization


Laureen Nicole Carvajal-Oyaga; Laura Valentina Ni�o-Sep�lveda; David Cotes-Prieto; Iv�n Cotes;


This study presents a robust reinforced concrete planar frame (RCPF) automated design procedure incorporating reliability analysis (RA) and heuristic optimization (HO). The state limit function selected corresponds to the story drift. In order to reduce the computational burden and make a real-life practical application, the response surface method (RSM) was employed to obtain state limit function. Then, two methods, the Hasofer-Lind and Rackwitz-Fiessler (HL-RF) and the Monte Carlo simulation (MCS) were applied to determine the reliability index 𝛽. The story drift limit state (SDLS) was evaluated using linear elastic analysis, in a five stories and three spans RCPF under gravitational and seismic loads, included all sway special moments frames constrains, in accordance with the Colombian code for seismic-resistant buildings (NSR-10). The weight of the RCPF was minimized employing particle swarm optimization (PSO) and genetic algorithm (GA) considering as discrete variables its cross-sections and longitudinal reinforcement. Two optimization scenarios, developed in the software MATLAB� 2019b were considered: (i) including a minimum 𝛽 as a design constrain (ii) without including a minimum 𝛽 as a design constrain. For scenario (i) compressive strength of concrete and seismic load were considered as the random variables. The results show an increase in the weight of the RCPF for scenario (i) of 11.63% (HL-RF) and 16.89% (MCS) when compared to scenario (ii). Nonetheless, 𝛽 values for scenario (i) were 1.534 (HL-RF) and 1.713 (MCS) which were significantly higher than 0.065, 𝛽 value for scenario (ii). In conclusion, in all design examples, achieving satisfactory security levels (𝛽) means an increase in the cross sectional areas of the RCPF beyond NSR-10 minimal requirements. Finally, from the structural security point of view, the presented procedure permits to carried out rapid RCPF designs incorporating RA and HO in satisfactory computational times.


Reinforced concrete structures, Heuristic optimization, Particle swarm optimization, Genetic algorithm, Reliability index, Response surface method, HL-RF method, Monte Carlo simulation.