Abstract
This paper studies the optimization process through the metaheuristic algorithm known as Simulated Annealing (SA) applied to a dissipative system formed by Buckling-Restrained Braces (BRBs) to improve the seismic behavior of existing RC framed buildings. The optimization algorithm is aimed at finding the solution with the minimum cost of the dissipative structure. During the process different aspects such as the distribution of the BRBs in the frame, the use of either short or long core BRBs, and other geometrical characteristics of the core were simultaneously considered. The seismic performance of all proposed designs was evaluated using the Capacity Spectrum Method. The SA algorithm was implemented in Matlab, creating a link between it and OpenSees, to allow the transfer of information during the optimization process. The use of both platforms proved to be efficient in the optimization of complex structures using metaheuristic algorithms. The results indicate that the proposed procedure is capable to find solutions with a significant saving of materials, used in the dissipative structure (up to 65%), compared to the solution obtained by a design method specialized in this kind of systems.
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References
Abedini H, Hoseini Vaez SR, Zarrineghbal A (2020) Optimum design of buckling-restrained braced frames. Structures 25:99–112. https://doi.org/10.1016/j.istruc.2020.03.004
Aguaguiña M, Zhou Y, Zhou Y (2020) Data supporting the development of loading protocols for seismic qualification of BRBs considering global performance requirements. Data Brief. https://doi.org/10.1016/j.dib.2019.104803
Aguirre N, Hurtado J (2008) Robust stochastic optimal control of seismically excited buildings. Comput Struct Dynamics Earthq Eng 1:507–529. https://doi.org/10.1201/9780203881637.ch32
AlHamaydeh M, Abed F, Mustapha A (2016) Key parameters influencing performance and failure modes for BRBs using nonlinear FEA. J Constr Steel Res 116:1–18. https://doi.org/10.1016/j.jcsr.2015.08.038
ASCE/SEI 4–17 (2017) Seismic evaluation and retrofit of existing buildings. American Society of Civil Engineers. Reston, EE. UU. https://doi.org/10.1061/9780784414859
ATC-40 (1996) Seismic evaluation and retrofit of concrete building. Report No. ATC–40. Applied Technology Council. California, EE. UU
Balling RJ, Balling LJ, Richards PW (2009) Design of buckling-restrained braced frames using nonlinear time history analysis and optimization. J Struct Eng 135(5):461–468. https://doi.org/10.1061/(asce)st.1943-541x.0000007
Blum C, Roli A (2003) Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Comput Surv 35:268–308. https://doi.org/10.1145/937503.937505
CDHCM (2020) La Comisión de Derechos Humanos de la Ciudad de México y la reconstrucción. Línea de base de indicadores. Comisión de Derechos Humanos de la Ciudad de México. Ciudad de México, México
Coello CA, Christiansen AD (2000) Multiobjective optimization of trusses using genetic algorithms. Comput Struct 75(6):647–660. https://doi.org/10.1016/S0045-7949(99)00110-8
Coello CC, Hernández FS, Farrera FA (1997) Optimal design of reinforced concrete beams using genetic algorithms. Expert Syst Appl 12(1):101–108. https://doi.org/10.1016/S0957-4174(96)00084-X
Degertekin SO, Saka MP, Hayalioglu MS (2008) Optimal load and resistance factor design of geometrically nonlinear steel space frames via tabu search and genetic algorithm. Eng Struct 30(1):197–205. https://doi.org/10.1016/j.engstruct.2007.03.014
Dillen W et al (2020) Optimization in a realistic structural engineering context: redesign of the market hall in Ghent. Eng Struct 228:111473. https://doi.org/10.1016/j.engstruct.2020.111473
Eurocode UNE-EN (1998) Eurocode 8: Design of structures for earthquake resistance
Farhat F, Nakamura S, Takahashi K (2009) Application of genetic algorithm to optimization of buckling restrained braces for seismic upgrading of existing structures. Comput Struct 87(1–2):110–119. https://doi.org/10.1016/j.compstruc.2008.08.002
Fleischer, M. (1995) Simulated annealing: past, present and future. In: Proceedings of the 1995 winter simulation conference
Ghowsi AF, Sahoo DR, Kumar PCA (2020) Cyclic tests on hybrid buckling-restrained braces with Fe-based SMA core elements. J Constr Steel Res 175:106323. https://doi.org/10.1016/j.jcsr.2020.106323
Granville V, Rasson JP, Krivánek M (1994) Simulated annealing: a proof of convergence. IEEE Trans Pattern Anal Mach Intell 16(6):652–656. https://doi.org/10.1109/34.295910
Guerrero H et al (2016a) A method for preliminary seismic design and assessment of low-rise structures protected with buckling-restrained braces. Eng Struct 123:141–154. https://doi.org/10.1016/j.engstruct.2016.05.015
Guerrero H et al (2017) Evaluation of the economic benefits of using buckling-restrained braces in hospital structures located in very soft soils. Eng Struct 136:406–419. https://doi.org/10.1016/j.engstruct.2017.01.038
Guerrero H, Ji T, Escobar J (2016b) Experimental studies of a steel frame model with and without buckling-restrained braces. Revista De Ingeniería Sísmica 95:33–52. https://doi.org/10.18867/ris.95.338
Hashemi S et al (2022) Multi-objective optimal design of SC-BRB for structures subjected to different near-fault earthquake pulses. Structures 36:1021–1031
Hoveidae N et al (2015) Numerical investigation of seismic behavior of short-core all-steel buckling restrained braces. J Constr Steel Res 114:89–99. https://doi.org/10.1016/j.jcsr.2015.06.005
Hoveidae N (2019) Numerical investigation of seismic response of hybrid buckling restrained braced frames. Periodica Polytechnica Civil Engineering 63(1):130–140. https://doi.org/10.3311/PPci.12040
Hoveidae N, Radpour S (2021) A novel all-steel buckling restrained brace for seismic drift mitigation of steel frames bulletin of earthquake engineering. Springer, Netherlands
Hoveidae N, Radpour S (2021b) Performance evaluation of buckling-restrained braced frames under repeated earthquakes. Bull Earthq Eng 19(1):241–262. https://doi.org/10.1007/s10518-020-00983-0
Kaveh A et al (2010) Performance-based seismic design of steel frames using ant colony optimization. J Constr Steel Res 66(4):566–574. https://doi.org/10.1016/j.jcsr.2009.11.006
Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680. https://doi.org/10.1126/science.220.4598.671
Mahrenholtz C et al (2014) Retrofit of reinforced concrete frames with buckling-restrained braces. Earthq Eng Struct Dyn 1(056):1–6. https://doi.org/10.1002/eqe.2458
Martínez FJ et al (2010) Heuristic optimization of RC bridge piers with rectangular hollow sections. Comput Struct 88(5–6):375–386. https://doi.org/10.1016/j.compstruc.2009.11.009
MathWorks Inc (2020) Matlab and Optimization Toolbox. EE. UU
Medina J (2001) Estimation of incident and reflected waves using simulated annealing. J Waterw Port Coast Ocean Eng 127:213–221
Minafò G, Camarda G (2022) An open-source GA framework for optimizing the seismic upgrading design of RC frames through BRBs. Eng Struct 251:113508. https://doi.org/10.1016/j.engstruct.2021.113508
Mirtaheri M et al (2011) Experimental optimization studies on steel core lengths in buckling restrained braces. J Constr Steel Res 67(8):1244–1253. https://doi.org/10.1016/j.jcsr.2011.03.004
Moreschi LM, Singh MP (2003) Design of yielding metallic and friction dampers for optimal seismic performance. Earthq Eng Struct Dynam 32(8):1291–1311. https://doi.org/10.1002/eqe.275
Mortezagholi MH, Zahrai SM (2020) Analytical and numerical studies on reducing lateral restraints in conventional and all steel buckling restrained braces. J Build Eng. https://doi.org/10.1016/j.jobe.2020.101513
NTC-04 (2004) Complementary norms for seismic design, Mexico City Government. Mexico City, Mexico
NTC-17 (2017) Complementary norms for seismic design, Mexico City Government. Mexico City, Mexico
OpenSees (2021) Command Manual. Available at: https://opensees.berkeley.edu/wiki/index.php/OpenSees_User (Accessed, 8 May 2021)
Pandikkadavath MS, Sahoo DR (2016) Analytical investigation on cyclic response of buckling-restrained braces with short yielding core segments. Int J Steel Struct 16:1273–1285. https://doi.org/10.1007/s13296-016-0083-y
Papavasileiou GS, Charmpis DC (2016) Seismic design optimization of multi-storey steel-concrete composite buildings. Comput Struct 170:49–61. https://doi.org/10.1016/j.compstruc.2016.03.010
PEER (2006) OpenSees, open source finite element platform for earthquake engineering simulations. University of California, Berkeley, Pacific Earthquake Engineering Research Center
Rezazadeh F, Talatahari S (2019) Seismic energy-based design of BRB frames using multi-objective vibrating particles system optimization. Structures 24:227–239. https://doi.org/10.1016/j.istruc.2020.01.006
Ruiz SE et al (2020) BRB retrofit of mid-rise soft-first-story RC moment-frame buildings with masonry infill in upper stories. J Buil Eng 38:101783. https://doi.org/10.1016/j.jobe.2020.101783
Sarno L, Manfredi G (2012) Experimental tests on full: scale RC unretrofitted frame and retrofitted with buckling— restrained braces. Earthq Eng Struct Dynam 41:315–333
SASID (2017) Sistema de Acciones Sísmicas para Diseño, Gobierno de la Ciudad de México. Available at: https://sasid.unam.mx/webNormasCDMX/default.aspx Accessed 8, May 2021
Scott, M. H. (2011) Numerical integration options for force-based beam-column element in OpenSees, pp. 1–7. Available at: https://opensees.berkeley.edu/wiki/images/a/ab/IntegrationTypes.pdf Accessed 8, May 2021
Scott MH, Fenves GL (2006) Plastic hinge integration methods for force-based beam-column elements. J Struct Eng 132(2):244–252. https://doi.org/10.1061/(asce)0733-9445(2006)132:2(244)
Scott MH, Ryan KL (2013) Moment-rotation behavior of force-based plastic hinge elements. Earthq Spectra 29(2):597–607. https://doi.org/10.1193/1.4000136
Seo H, Kim J, Kwon M (2018) Optimal seismic retrofitted RC column distribution for an existing school building. Eng Struct 168:399–404. https://doi.org/10.1016/j.engstruct.2018.04.098
Sörensen K (2013) Metaheuristics-the metaphor exposed. Int Trans Oper Res 22:3–18. https://doi.org/10.1111/itor.12001
De Stefani L, Scotta R, Lazzari M (2015) Optimal design of seismic retrofitting of RC frames with eccentric steel bracing. Bull Earthq Eng 13(2):613–633. https://doi.org/10.1007/s10518-014-9633-x
Sutcu F, Takeuchi T, Matsui R (2014) Seismic retrofit design method for RC buildings using buckling-restrained braces and steel frames. J Constr Steel Res 101:304–313. https://doi.org/10.1016/j.jcsr.2014.05.023
Takeuchi T et al (2008) Estimation of cumulative deformation capacity for buckling restrained braces placed in frames. J Struct Eng 134:822–831. https://doi.org/10.3130/aijs.71.155_2
Teran-Gilmore A, Virto-Cambray, N (2010) Preliminary design of low-rise buildings stiffened with buckling-restrained braces by a displacement-based approach. In: Proceedings of the 9th U.S. National and 10th Canadian Conference on Earthquake Engineering Compte Rendu de la 9ième Conférence Nationale Américaine et 10ième Conférence Canadienne de Génie Parasismique. Toronto, Canada. doi: https://doi.org/10.1193/1.3054638.
Tremblay R et al (2006) Seismic testing and performance of buckling-restrained bracing systems. Can J Civ Eng 33:183–198. https://doi.org/10.1139/l05-103
United Nations (2021) Sustainable Development. Available at: https://www.un.org/sustainabledevelopment/es/ Accessed 20, Jul 2021
Urrego, O. (1994) Elección del mejor arreglo de disipadores en un marco plano. UNAM, México
Winker P, Maringer D (2007) The threshold accepting optimization algorithm in economics and statistics. In: Kontoghiorghes EY, Gatu C (eds) Optimization, econometric and financial analysis. Advances in computational management science, Springer, Berlin, Heidelberg
Yepes V et al (2008) A parametric study of optimum earth-retaining walls by simulated annealing. Eng Struct 30(3):821–830. https://doi.org/10.1016/j.engstruct.2007.05.023
Zhang HY, Zhang LJ (2017) Tuned mass damper system of high-rise intake towers optimized by improved harmony search algorithm. Eng Struct 138:270–282. https://doi.org/10.1016/j.engstruct.2017.02.011
Zou XK et al (2007) Multiobjective optimization for performance-based design of reinforced concrete frames. J Struct Eng 133(10):1462–1474. https://doi.org/10.1061/(asce)0733-9445(2007)133:10(1462)
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The first author would like to thank Consejo Nacional de Ciencia y Tecnología (CONACyT) and the Fiidem alliance for the scholarship that allowed the development of the present research project.
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Velasco, L., Hospitaler, A. & Guerrero, H. Optimal design of the seismic retrofitting of reinforced concrete framed structures using BRBs. Bull Earthquake Eng 20, 5135–5160 (2022). https://doi.org/10.1007/s10518-022-01394-z
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DOI: https://doi.org/10.1007/s10518-022-01394-z