[1] AISC 341-10 - American Institute of Steel Construction. Seismic Provisions for Structural Steel Buildings. 2010.
[2] Fema P. 58-1, Seismic performance assessment of buildings volume 1-methodology. Appl Technol Counc Calif Redw City 2012.
[3] Simpson BG, Mahin SA. Experimental and numerical investigation of strongback braced frame system to mitigate weak story behavior. J Struct Eng 2018;144:4017211. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001960.
[4] Toorani A, Gholhaki M, Vahdani R. The investigation into the effect of consecutive earthquakes on the strongback bracing system. Structures, vol. 24, Elsevier; 2020, p. 477–88. https://doi.org/10.1016/j.istruc.2020.01.018.
[5] Lai J-W, Mahin SA. Strongback system: A way to reduce damage concentration in steel-braced frames. J Struct Eng 2015;141:4014223.
[6] Simpson B, Mahin S. Design development of a four-story Strongback braced frame. Key Eng Mater 2018;763:1050–7. https://doi.org/10.4028/www.scientific.net/KEM.763.1050.
[7] Bagley JD. The behavior of adaptive systems which employ genetic and correlation algorithms: technical report 1967.
[8] Goldberg DE. Genetic algorithms as a computational theory of conceptual design. Appl. Artif. Intell. Eng. VI, Springer; 1991, p. 3–16.
[9] Wu S-J, Chow P-T. Integrated discrete and configuration optimization of trusses using genetic algorithms. Comput Struct 1995;55:695–702.
[10] Rafiq MY, Southcombe C. Genetic algorithms in optimal design and detailing of reinforced concrete biaxial columns supported by a declarative approach for capacity checking. Comput Struct 1998;69:443–57.
[11] Kameshki ES, Saka MP. Optimum design of nonlinear steel frames with semi-rigid connections using a genetic algorithm. Comput Struct 2001;79:1593–604.
[12] Balling RJ, Briggs RR, Gillman K. Multiple optimum size/shape/topology designs for skeletal structures using a genetic algorithm. J Struct Eng 2006;132:1158–65. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:7(1158).
[13] Cui H, An H, Huang H. Truss topology optimization considering local buckling constraints and restrictions on intersection and overlap of bar members. Struct Multidiscip Optim 2018;58:575–94. https://doi.org/10.1007/s00158-018-1910-x.
[14] Rao GV. Optimum designs for transmission line towers. Comput Struct 1995;57:81–92. https://doi.org/10.1016/0045-7949(94)00597-V.
[15] Hasançebi O. Adaptive evolution strategies in structural optimization: Enhancing their computational performance with applications to large-scale structures. Comput Struct 2008;86:119–32. https://doi.org/10.1016/j.compstruc.2007.05.012.
[16] Geem ZW, Kim JH, Loganathan GV. A new heuristic optimization algorithm: harmony search. Simulation 2001;76:60–8.
[17] Kaveh A, Talatahari S. Particle swarm optimizer, ant colony strategy and harmony search scheme hybridized for optimization of truss structures. Comput Struct 2009;87:267–83. https://doi.org/10.1016/j.compstruc.2009.01.003.
[18] Jahankhani E, Asadollahfardi G, Samadi A. Toward sustainable water quality monitoring systems using particle swarm, Ant Colony, and Tabu Search optimization methods. Qual Quant 2024;58:2957–77. https://doi.org/10.1007/s11135-023-01781-x.
[19] Panian L, Bucci N, Janhunen B. BRBM frames: An improved approach to seismic-resistant design using buckling-restrained braces. Improv. Seism. Perform. Exist. Build. Other Struct. 2015, 2015, p. 632–43. https://doi.org/10.1061/9780784479728.052.
[20] Laghi V, Palermo M, Gasparini G, Trombetti T. Strong-back system coupled with framed structure to control the building seismic response. J Civ Environ Eng 2017;7:1–7. https://doi.org/10.4172/2165-784x.1000274.
[21] Laghi V, Palermo M, Gasparini G, Silvestri S, Trombetti T. Strongback system to enhance the building seismic response of framed structures. Atti Del XVII Convegno ANIDIS L’ingegneria Sismica Ital Pist 17-21 Settembre 2017-(Studi Tema Di Internet Ecosyst 2017:72–81.
[22] Liu J. Steel Structures Research Update: Strongback Steel-Braced Frames for Improved Seismic Behavior in Buildings. Eng J 2017;54:297–308. https://doi.org/10.62913/engj.v54i4.1120.
[23] Palermo M, Laghi V, Gasparini G, Trombetti T. Coupled response of frame structures connected to a strongback. J Struct Eng 2018;144:4018148. https://doi.org/10.1061/(asce)st.1943-541x.0002134.
[24] Talley PC. Capacity design methods for strongback braced frames 2018.
[25] Lin J-L, Kek M-K, Tsai K-C. Stiffness configuration of strongbacks to mitigate inter-story drift concentration in buildings. Eng Struct 2019;199:109615. https://doi.org/10.1016/j.engstruct.2019.109615.
[26] Faramarzi MS, Taghikhany T. Direct performance-based seismic design of strongback steel braced systems. Structures, vol. 28, Elsevier; 2020, p. 482–95. https://doi.org/10.22060/ceej.2025.23688.8197.
[27] Simpson BG. Higher‐mode force response in multi‐story strongback‐braced frames. Earthq Eng Struct Dyn 2020;49:1406–27. https://doi.org/10.1002/eqe.3310.
[28] Jahangir H, Bagheri M. Evaluation of seismic response of concrete structures reinforced by shape memory alloys. Int J Eng 2020;33:410–8. https://doi.org/10.5829/IJE.2020.33.03C.05.
[29] Jahangir H, Bagheri M, Delavari SMJ. Cyclic behavior assessment of steel bar hysteretic dampers using multiple nonlinear regression approach. Iran J Sci Technol Trans Civ Eng 2021;45:1227–51. https://doi.org/10.1007/s40996-020-00497-4.
[30] Faramarzi MS, Taghikhany T. A comparative performance-based seismic assessment of strongback steel braced frames. J Build Eng 2021;44:102983. https://doi.org/10.1016/j.jobe.2021.102983.
[31] Astudillo B, Panian L, Simpson B. Design and Performance Comparison of Strongback Systems and Typical Chevron BRB Frames. 12th Natl Conf Earthq Eng 2022.
[32] Abolghasemi S, Wierschem NE, Denavit MD. Impact of strongback on structure with varying damper and stiffness irregularity arrangements. J Constr Steel Res 2024;213:108333. https://doi.org/10.1016/j.jcsr.2023.108333.
[33] Soleymani A, Saffari H. A novel hybrid strong-back system to improve the seismic performance of steel braced frames. J Build Eng 2024;84:108482. https://doi.org/10.1016/j.jobe.2024.108482.
[34] Gholhaki M, Gorji Azandariani M, Hooshdar Rostami A, Rezaifar O. Seismic Retrofit and Strengthening of Reinforced Concrete Moment Frames with Strongback-Braced System. Pract Period Struct Des Constr 2024;29:4024005. https://doi.org/10.1061/PPSCFX.SCENG-1407.
[35] Ghasemi Jouneghani H, Nouri Y, Mortazavi M, Haghollahi A, Memarzadeh P. Seismic performance factors of elliptic-braced frames with rotational friction dampers through IDA. Pract Period Struct Des Constr 2024;29:4024070. https://doi.org/10.1061/PPSCFX.SCENG-1540.
[36] Ghasemi Jouneghani H, Nouri Y, Memarzadeh P, Haghollahi A, Hemati E. Seismic performance and failure mechanisms evaluation of multi-story elliptic and mega-elliptic bracing frames: Experimental and numerical investigation. Structures 2024;70:107658. https://doi.org/https://doi.org/10.1016/j.istruc.2024.107658.
[37] Saffarzadeh K, Saffari H, Soleymani A. Development of loading protocols for different structural systems. Innov Infrastruct Solut 2025;10:1–19. https://doi.org/10.1007/s41062-025-02340-z.
[38] Nouri Y, Jouneghani HG, Haghollahi A, Memarzadeh P, Hemati E. Experimental and numerical study of seismic performance and failure mechanisms of multi-story elliptic and Quasi-X braced resisting frames. Results Eng 2025;26:105657. https://doi.org/https://doi.org/10.1016/j.rineng.2025.105657.
[39] Nouri Y, Ghasemi Jouneghani H, Shirkhani A, Hemati E, Hemati SA, Hajirasouliha I. Seismic retrofit of steel moment frames with arc and ring yielding dampers: A probabilistic loss assessment using FEMA P-58. Structures 2025;76:108898. https://doi.org/https://doi.org/10.1016/j.istruc.2025.108898.
[40] FEMA P. 695; Federal Emergency Management Agency (FEMA). Quantif Build Seism Perform Factors Appl Technol Counc Washington, DC, USA 2009.
[41] Jouneghani HG, Nouri Y, Roudbaraki R, Haghollahi A, Hemati E. Evaluating seismic performance factors of mega elliptic-braced moment resisting frames (MEL BRFs) with FEMA P695 methodology. J Build Eng 2025;111:113511. https://doi.org/https://doi.org/10.1016/j.jobe.2025.113511.
[42] PayamiFar T, Sojoudizadeh R, Azizian H, Rahimi L. Seismic Optimization of Steel Mega‐Braced Frame With Improved Prairie Dog Metaheuristic Optimization Algorithm. Struct Des Tall Spec Build 2025;34:e2207. https://doi.org/10.1002/tal.2207.
[43] No S. 2800 (2015) of Iranian Code of Practice for Seismic Resistance Design of Buildings 2015.
[44] Prestandard F. commentary for the seismic rehabilitation of buildings (FEMA356). Washington, DC Fed Emerg Manag Agency 2000;7:518.