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Mathematical Problems in Engineering
Volume 2014, Article ID 305737, 14 pages
Research Article

Performance-Based Multiobjective Optimal Seismic Retrofit Method for a Steel Moment-Resisting Frame Considering the Life-Cycle Cost

1Department of Architectural Engineering, Yonsei University, 134 Shinchon-dong, Seoul 110-732, Republic of Korea
2Center for Structural Health Care Technology in Buildings, Yonsei University, 134 Shinchon-dong, Seoul 110-732, Republic of Korea
3Chang Minwoo Structural Consultants, 605-8 Yeoksam-Dong, Seoul 135-907, Republic of Korea
4Department of Architecture, Catholic University of Daegu, 13-13 Hayang-ro, Hayang-eup, Gyeongsan-si, Gyeongbuk 712-702, Republic of Korea

Received 17 September 2013; Revised 9 January 2014; Accepted 13 January 2014; Published 25 March 2014

Academic Editor: Pedro Ribeiro

Copyright © 2014 Hyo Seon Park et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This study proposes a performance-based multiobjective optimization seismic retrofit method for steel moment-resisting frames. The brittle joints of pre-Northridge steel moment-resisting frames are retrofitted to achieve ductility; the method involves determining the position and number of connections to be retrofitted. The optimal solution is determined by applying the nondominated sorting genetic algorithm-II (NSGA-II), which acts as a multiobjective seismic retrofit optimization technique. As objective functions, the initial cost for the connection retrofit and lifetime seismic damage cost were selected, and a seismic performance level below the 5% interstory drift ratio was employed as a constraint condition. The proposed method was applied to the SAC benchmark three- and nine-story buildings, and several Pareto solutions were obtained. The optimized retrofit solutions indicated that the lifetime seismic damage cost decreased as the initial retrofit cost increased. Although every Pareto solution existed within a seismic performance boundary set by a constraint function, the seismic performance tended to increase with the initial retrofit cost. Analysis and economic assessment of the relations among the initial retrofit cost, lifetime seismic damage cost, total cost, and seismic performance of the derived Pareto solution allow building owners to make seismic retrofit decisions more rationally.