Steel and Composite Structures

  • 제47권2호
  • /
  • Pages.167-184
  • /
  • 2023
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Seismic retrofit of steel structures with re-centering friction devices using genetic algorithm and artificial neural network

  • Mohamed Noureldin (Department of Global Smart City, Sungkyunkwan University) ;
  • Masoum M. Gharagoz (Department of Global Smart City, Sungkyunkwan University) ;
  • Jinkoo Kim (Department of Global Smart City, Sungkyunkwan University)
  • 투고 : 2021.07.11
  • 심사 : 2023.04.20
  • 발행 : 2023.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this study, a new recentering friction device (RFD) to retrofit steel moment frame structures is introduced. The device provides both self-centering and energy dissipation capabilities for the retrofitted structure. A hybrid performance-based seismic design procedure considering multiple limit states is proposed for designing the device and the retrofitted structure. The design of the RFD is achieved by modifying the conventional performance-based seismic design (PBSD) procedure using computational intelligence techniques, namely, genetic algorithm (GA) and artificial neural network (ANN). Numerous nonlinear time-history response analyses (NLTHAs) are conducted on multi-degree of freedom (MDOF) and single-degree of freedom (SDOF) systems to train and validate the ANN to achieve high prediction accuracy. The proposed procedure and the new RFD are assessed using 2D and 3D models globally and locally. Globally, the effectiveness of the proposed device is assessed by conducting NLTHAs to check the maximum inter-story drift ratio (MIDR). Seismic fragilities of the retrofitted models are investigated by constructing fragility curves of the models for different limit states. After that, seismic life cycle cost (LCC) is estimated for the models with and without the retrofit. Locally, the stress concentration at the contact point of the RFD and the existing steel frame is checked being within acceptable limits using finite element modeling (FEM). The RFD showed its effectiveness in minimizing MIDR and eliminating residual drift for low to mid-rise steel frames models tested. GA and ANN proved to be crucial integrated parts in the modified PBSD to achieve the required seismic performance at different limit states with reasonable computational cost. ANN showed a very high prediction accuracy for transformation between MDOF and SDOF systems. Also, the proposed retrofit showed its efficiency in enhancing the seismic fragility and reducing the LCC significantly compared to the un-retrofitted models.

키워드

과제정보

This study was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1A2C2006631).

참고문헌

  1. Adibia, M., Marefat, M.S., Esmaeily, A., Arani, K.K. and Esmaeily, A. (2017), "Seismic retrofit of external concrete beam-column joints reinforced by plain bars using steel angles prestressed by cross ties", Eng. Struct., 148, 813-828. https://doi.org/10.1016/j.engstruct.2017.07.014.
  2. Afefy, H.M. (2020), "Seismic retrofit of reinforced-concrete coupled shear walls: A review", Pract. Period. Struct. Des. Constr., 25(3), https://doi.org/10.1061/(ASCE)SC.1943-5576.0000489.
  3. AISC-360 (2016), Specification for Structural Steel Buildings, Chicago, USA.
  4. Akin, E., Korkmaz, S.Z., Korkmaz, H.H. and Diri, E. (2016), "Rehabilitation of infilled reinforced concrete frames with thin steel plate shear walls", J. Perform. Constr. Facil., 0(4). https://doi.org/10.1061/(ASCE)CF.1943-5509.0000840.
  5. Aninthaneni, P.K. and Dhakal, R.P. (2017), "Demountable precast concrete frame-building system for seismic regions: conceptual development", J. Arch. Eng., 2 (4), https://doi.org/10.1061/(ASCE)AE.1943-5568.0000275.
  6. Ansys® (2015), Academic Research Mechanical, Release 16.2, Analysis User's Manual, USA.
  7. Arteta, C.A., Carrillo, J., Archbold, J., Gaspar, D., Pajaro, C., Araujo, G. and Mosalam, K.M. (2019), "Response of mid-rise reinforced concrete frame buildings to the 2017 puebla earthquake", Earthq. Spectra., 5(4), 1763-1793. https://doi.org/10.1193/061218EQS144M.
  8. ASCE 41 (2017), Seismic evaluation and retrofit of existing buildings, American Society of Civil Engineers; USA.
  9. Bagheri, H., Hashemi, A. and Yousef-Beik, S.M.M. (2020), "New self-centering tension-only brace using resilient slip-friction joint: experimental tests and numerical analysis", J. Struct. Eng., 146(10), https://doi.org/10.1061/(ASCE)ST.1943-541X.0002789.
  10. Barbagallo, F., Bosco, M., Marino, E.M. and Rossi, P.P. (2018), "Seismic retrofit of braced frame buildings by RC rocking walls and viscous dampers", Earthq. Eng. Struct. Dynam., 47(13), 2682-2707. https://doi.org/10.1002/eqe.3105.
  11. Blebo, F.C. and Roke, D.A. (2018), "Seismic-resistant self-centering rocking core system with buckling restrained columns", Eng. Struct., 173, 372-382. https://doi.org/10.1016/j.engstruct.2018.06.117.
  12. Cao, X., Wu, L. and Li, Z. (2020), "Behaviour of steel-reinforced concrete columns under combined torsion based on ABAQUS FEA", Eng. Struct., 209, 109980. https://doi.org/10.1016/j.engstruct.2019.109980.
  13. Cao, X.Y., Wu, G., Feng, D.C., Wang, Z. and Cui, H.R. (2020), "Research on the seismic retrofit performance of RC frames using SC-PBSPC BRBF substructures", Earthq. Eng. Struct. Dynam., 49(8), 794-816. https://doi.org/10.1002/eqe.3265.
  14. Celik, O.C. and Ellingwood, B.R. (2009), "Seismic risk assessment of gravity load designed reinforced concrete frames subjected to Mid-America ground motions", J. Struct. Eng., 1 5(4), 414-424. http://dx.doi.org/10.1061/(ASCE)0733-9445(2009).
  15. Chancellor, N.B., Eatherton, M.R., Roke, D.A. and Akbas T. (2014), "Self-centering seismic lateral force resisting systems: high-performance structures for the city of tomorrow", Buildings., 4(3), 520-548. https://doi.org/10.3390/buildings4030520.
  16. Choi, H. and Kim, J. (2009), "Evaluation of seismic energy demand and its application on design of buckling-restrained braced frames", Struct. Eng. Mech., 1(1), 93-112. https://doi.org/10.12989/sem.2009.31.1.093
  17. Chowdhury, M.A., Rahmzadeh, A. and Alam, M.S. (2020), "Improving the seismic performance of post-tensioned self-centering connections using SMA angles or end plates with SMA bolts", Smart Mater. Struct., 28(7), https://doi.org/10.1088/1361-665X/ab1ce6.
  18. Cornell, C.A., Jalayer, F., Hamburger, R.O. and Foutch, D.A. (2002), "Probabilistic basis for 2000 SAC federal emergency management agency steel moment frame guidelines", J. Struct. Eng., 128(4), 526-533. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:4(526).
  19. Dong, H., Du, X., Han, Q., Hao, H., Bi, K. and Wang, X. (2017), "Performance of an innovative self-centering buckling restrained brace for mitigating seismic responses, of bridge structures with double column piers", Eng. Struct., 148, 47-62. https://doi.org/10.1016/j.engstruct.2017.06.011.
  20. Elettore, E., Freddi, F., Latour, M. and Rizzano, G. (2021), "Design and analysis of a seismic resilient steel moment resisting frame equipped with damage-free self-centering column bases", J. Constr. Steel Res., 179, 106543. https://doi.org/10.1016/j.jcsr.2021.106543.
  21. Eldin, M. (2007), Application of Recent Techniques of Pushover for Evaluating Seismic Performance of Multistory Buildings, M.Sc. Dissertation, Cairo University, Egypt. https://doi.org/10.13140/RG.2.2.18402.96961.
  22. Eldin, M. (2014), A Simplified Method for Seismic Life-Cycle Cost Estimation of Structures with Application on Sensitivity Analysis, Ph.D. Dissertation, Sungkyunkwan University, Suwon. https://doi.org/10.13140/RG.2.2.11692.08324.
  23. Fajfar, P. (2000), "A nonlinear analysis method for performance based seismic design", Earthq. Eng. Struct. Dynam., 16(3), 573-592. https://doi.org/10.1193/1.1586128.
  24. Fan, X., Xu, L. and Li, Z. (2019), "Seismic performance evaluation of steel frames with pre-pressed spring self-centering braces", J. Constr. Steel Res., 162, https://doi.org/10.1016/j.jcsr.2019.105761.
  25. Fang, C. Wang, W. and Shen, D. (2021), "Development and experimental study of disc spring-based self-centering devices for seismic resilience", J. Struct. Eng., 147(7), https://doi.org/10.1061/(ASCE)ST.1943-541X.0003058.
  26. Farfani, H.A., Behnamfar, F. and Fathollahi, A. (2015), "Dynamic analysis of soil-structure interaction using the neural networks and the support vector machines", Expert Syst. Appl., 42(22), 8971-8981. https://doi.org/10.1016/j.eswa.2015.07.053
  27. FEMA 547 (2006), Techniques for the Seismic Rehabilitation of Existing Buildings, USA.
  28. FEMA P-58-1 (2018), Seismic Performance Assessment of Buildings, 1(2), Applied Technology Council, California, USA.
  29. FEMA P695 (2009), Quantification of Building Seismic Performance Factors, Federal Emergency Management Agency, Washington DC, USA.
  30. Formisano, A., Massimilla, A., Di Lorenzo, G. and Landolfo, R. (2020), "Seismic retrofit of gravity load designed RC buildings using external steel concentric bracing systems", Eng. Failure Anal., 111, 104-485. https://doi.org/10.1016/j.engfailanal.2020.104485.
  31. Fragiadakis, M., Lagaros, N.D. and Papadrakakis, M. (2006), "Performance-based multiobjective optimum design of steel structures considering life-cycle cost", Struct Multidiscip Optimiz, 2, 1-11. https://doi.org/10.1007/s00158-006-0009-y.
  32. Gencturk, B. (2013), "Life-cycle cost assessment of RC and ECC frames using structural optimization", Earthq. Eng. Struct. Dyn., 42, 61-79. https://doi.org/10.1002/eqe.2193.
  33. Gencturk, B. and Elnashai, A.S. (2012), "Life cycle cost considerations in seismic design optimization of structures", In Structural Seismic Design Optimization and Earthquake Engineering: Formulations and Applications., 1-22. https://doi.org/10.4018/978-1-4666-1640-0.ch001.
  34. Gioiella, L., Tubaldib, E., Gara, F., Dezi, L. and Dall'Astaa, A. (2018), "Modal properties and seismic behaviour of buildings equipped with external dissipative pinned rocking braced frames", Eng. Struct., 172, 807-819. https://doi.org/10.1016/j.engstruct.2018.06.043.
  35. Gorgulu, T., Tama, Y.S., Yilmaz, S., Kaplan, H. and Ay, Z. (2012), "Strengthening of reinforced concrete structures with external steel shear walls", J. Constr. Steel Res., 70, 226-235. https://doi.org/10.1016/j.jcsr.2011.08.010.
  36. Guo, T., Wang, J., Song, Y., Xuan, W. and Chen, Y. (2020), "Self-centering cable brace with friction devices for enhancing seismic performance of RC frame structures", Eng. Struct., 207(1), 110187. https://doi.org/10.1016/j.engstruct.2020.110187.
  37. Guo, T., Xu, Z., Song, L., Wang, L. and Zhang, Z. (2017), "Seismic resilience upgrade of RC frame building using self-centering concrete walls with distributed friction devices", J. Struct. Eng., 14 (12), 04017160. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001901.
  38. Huang, L., Zhou, Z., Zhang, Z. and Huang, X. (2018), "Seismic performance and fragility analyses of self-centering prestressed concrete frames with infill walls", J. Earthq. Eng., 25(3), 535-565. https://doi.org/10.1080/13632469.2018.1526142.
  39. ICMS (2019), International Construction Cost Survey, Turner & Townsend. www.turnerandtownsend.com
  40. Javidan, M.M., Eskandari Nasab, M.S., and Kim, J. (2021), "Full-scale tests of two-story RC frames retrofitted with steel plate multi-slit dampers," Steel Compos. Struct., 9(5), 645-664. https://doi.org/10.12989/scs.2021.39.5.645.
  41. Javidan, M.M. and Kim, J. (2022), "A ductile steel damper-brace for low-damage framed structures", Steel Compos. Struct., 44(3), 311-323. https://doi.org/10.12989/scs.2022.44.3.311.
  42. Jeong, S.H. and Elnashai, A.S. (2007), "Probabilistic fragility analysis parameterized by fundamental response quantities", Eng. Struct., 29(6), 1238-1251. https://doi.org/10.1016/j.engstruct.2006.06.026.
  43. Kang, H., Adane, M., Chun, S. and Kim, J. (2022), "Development of seismic retrofit system made of steel frame with vertical slits," Steel Compos. Struct., 44(2), 269-280. https://doi.org/10.12989/scs.2022.44.2.269.
  44. Kam, W.Y., Pampanin, S., Palermo, A. and Carr, A. (2008), "Design procedure and behaviour of advanced flag-shape (AFS) MDOF systems", New Zealand Society of Earthquake Engineering (NZSEE) Conference, Wairakei, New Zealand.
  45. Kari, A., Ghassemieh, M. and Badarloo, B. (2020), "Development and design of a new self-centering energy-dissipative brace for steel structures", J. Intell. Mater. Syst. Struct., 0(6), 924-938. https://doi.org/10.1177/1045389X19828502.
  46. Kucukgoncu, H. and Altun, F. (2020), "The seismic behaviour of RC exterior shear walls used for strengthening of intact and damaged frames", Bull. Earthq. Eng., 18, 3683-3709. https://doi.org/10.1007/s10518-020-00839-7.
  47. Kurosawa, R., Sakata, H., Qu, Z. and Suyama, T. (2019), "Cyclic loading tests on RC moment frames retrofitted by PC frames with mild press joints through RC slabs for connection", Eng. Struct., 197, 109-440. https://doi.org/10.1016/j.engstruct.2019.109440.
  48. Lignos, D.G. and Krawinkler, H. (2011), "Deterioration modeling of steel components in support of collapse prediction of steel moment frames under earthquake loading", J. Struct. Eng., 1 7(11), 1291-1302. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000376
  49. Lin, Y.C., Sause, R. and Ricles, J.M. (2013), "Seismic performance of steel self-centering, moment-resisting frame: hybrid simulations under design basis earthquake", J. Struct. Eng., 1 9(11), https://doi.org/10.1061/(ASCE)ST.1943-541X.0000745.
  50. Liu, C., Junji, S., Kuramoto, H., Takashi T. and Takashi, K. (2016), "Experiment study on RC frame retrofitted by the external structure", Earthq. Eng. Eng. Vib., 15, 563-574. https://doi.org/10.1007/s11803-016-0344-y.
  51. Magliulo, G., Ercolino, M., Petrone, C., Coppola, O. and Manfredi, G. (2014), "The Emilia earthquake: seismic performance of precast reinforced concrete buildings", Earthq Spectra., 0, 891-912. http://doi.org/10.1193/091012EQS285M.
  52. Mathwork (2018), MATLAB ver. R2018b Reference Manual.
  53. Mazza, F. and Mazza, M. (2019), "Seismic retrofit of gravity loads designed r.c. framed buildings combining CFRP and hysteretic damped braces", Bull. Earthq. Eng., 17, 3423-3445. https://doi.org/10.1007/s10518-019-00593-5.
  54. McKenna, F., Fenves, G.L. and Scott, M.H. (2011), Open System for Earthquake Engineering Simulation, Univ. of California, Berkeley, CA, USA.
  55. Michel, C., Karbassib, A. and Lestuzzib, P. (2018), "Evaluation of the seismic retrofit of an unreinforced masonry building using numerical modeling and ambient vibration measurements", Eng. Struct., 158, 124-135. https://doi.org/10.1016/j.engstruct.2017.12.016.
  56. Morkhade, S.G., Shaikh, S., Kumbhar A., Shaikh, A. and Tiwari, R. (2018), "Comparative study of ultimate load for castellated and plain-webbed beams", Int. J. Civil Eng. Technol., 9(8), 1466-1476.
  57. Movaghati, S. and Abdelnaby, A.E. (2021), "Experimental and analytical investigation of improved behavior of existing steel connections by adding self-centering capabilities", J. Build. Eng., 43, 102543. https://doi.org/10.1016/j.jobe.2021.102543.
  58. Naeem, A. and Kim, J. (2018), "Seismic retrofit of a framed structure using damped cable system", Steel Compos. Struct., 29(3), 287-299. https://doi.org/10.12989/scs.2018.29.3.287.
  59. Naeem, A. and Kim, J. (2021), "Seismic retrofit of 3000 kVA power transformer using friction dampers and prestressed tendons", Structures, 2, 641-650. https://doi.org/10.1016/j.istruc.2021.03.029.
  60. Naeem, A., Nour Eldin, M., Kim, J. and Kim, J.W. (2017), "Seismic performance evaluation of a structure retrofitted using steel slit dampers with shape memory alloy bars", Int. J. Steel Struct., 17(4), 1627-1638. https://doi.org/10.1007/s13296-017-1227-4.
  61. Noureldin, M. Kim, J. and Kim, J. (2018), "Optimal distribution of steel slit-friction hybrid dampers based on life cycle cost", Steel Compos Struct., 27(5), 633-646, https://doi.org/10.12989/scs.2018.27.5.633.
  62. Noureldin, M. and Kim, J. (2020), "Parameterized seismic life-cycle cost evaluation method for building structures", J. Struct. Infrastruct. Eng., 17(3), 425-439. https://doi.org/10.1080/15732479.2020.1759656.
  63. Noureldin, M. and Kim, J. (2020), "Seismic fragility evaluation of retrofitted low-rise rc structures", 3rd GeoMEast 2019 International Conference., https://doi.org/10.1007/978-3-030-34252-4_1.
  64. Noureldin, M., Ali, A., Nasab, M.S.E. and Kim, J. (2021a), "Optimum distribution of seismic energy dissipation devices using neural network and fuzzy inference system", Computer-Aided Civil and Infrastruct. Eng., https://doi.org/10.1111/mice.12673.
  65. Noureldin, M., Dereje, A.J. and Kim, J. (2020a), "Seismic retrofit of RC buildings using self-centering PC frames with friction-dampers", Eng. Struct., 208, 109925. https://doi.org/10.1016/j.engstruct.2019.109925.
  66. Noureldin, M., Dereje, A.J. and Kim, J. (2020b), "Seismic retrofit of framed buildings using self-centering PC frames", J. Struct. Eng., 146(10), https://doi.org/10.1061/(ASCE)ST.1943-541X.0002786.
  67. Noureldin, M., Memon, S.A., Gharagoz, M. and Kim, J. (2021b), "Performance-based seismic retrofit of RC structures using concentric braced frames equipped with friction dampers and disc springs", Eng. Struct., 243, 112555, https://doi.org/10.1016/j.engstruct.2021.112555.
  68. Noureldin, M., Ahmed, S. and Kim, J. (2021c), "Self-centering steel slotted friction device for seismic retrofit of beam-column joints", Steel Compos. Struct., 41(1), 13-30. https://doi.org/10.12989/scs.2021.41.1.013.
  69. Noureldin, M., Naeem, A. and Kim, J. (2019), "Life-cycle cost evaluation of steel structures retrofitted with steel slit damper and shape memory alloy-based hybrid damper", Adv. Struct. Eng., 22(1), 3-16. https://doi.org/10.1177/1369433218773487.
  70. Noureldin, M., Naeem, A. and Kim, J. (2019), "Seismic retrofit of a structure using self-centering precast concrete frames with enlarged beam ends", Magazine Concr. Res., 72(22), 1155-1170. https://doi.org/10.1680/jmacr.19.00012.
  71. Noureldin, M., Ali, A., Sim, S. and Kim, J. (2022), "A machine learning procedure for seismic qualitative assessment and design of structures considering safety and serviceability", J. Build. Eng., 50, 104190. https://doi.org/10.1016/j.jobe.2022.104190.
  72. Nzabonimpa, J.D., Hong, W.K. and Kim, J. (2018), "Nonlinear finite element model for the novel mechanical beam-column joints of precast concrete-based frames", Comput. Struct., 189, 31-48. https://doi.org/10.1016/j.compstruc.2017.04.016.
  73. Ozcelik, R., Binici, B. and Kurc, O. (2012), "Pseudo dynamic testing of an rc frame retrofitted with chevron braces", J. Earthq. Eng., 16(4), 515-539. https://doi.org/10.1080/13632469.2011.653297.
  74. PEER (2021), Pacific Earthquake Engineering Research (PEER) Center: NGA Database. www.peer.berkeley.edu
  75. Rafezy, B., Huynh, Q., Gallart, H. and Kheirollahi, M. (2015), "An innovative method for the seismic retrofit of existing steel moment frame structures using side plate technology", Second ATC & SEI Conference on Improving the Seismic Performance of Existing Buildings and Other Structures, San Francisco, California, USA. https://doi.org/10.1061/9780784479728.013.
  76. Roia, D., Gara, F., Balducci, A. and Dezi, L. (2014), "Ambient vibration tests on a reinforced concrete school building before and after retrofit works with external steel 'dissipative towers", Proceedings of the International Conference on Structural Dynamic EURODYN., Porto, Portugal. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002865.
  77. Sarand, N.I. and Jalali, A. (2020), "Evaluation of seismic performance of improved rocking concentrically braced-frames with zipper columns", Periodica Polytechnica Civil Engineering., 64(2), https://doi.org/10.3311/PPci.15052.
  78. Silwal, B., Huang, Q. and Ozbulut, O.E. (2018), "Comparative seismic fragility estimates of steel moment frame buildings with or without superelastic viscous dampers", J. Intell. Mater. Syst. Struct., 29(18), 3598-3613. https://doi.org/10.1177/1045389X18798936.
  79. Soltanzadeh, G., Osman, H.B., Vafaei, M. and Vafaei, Y.K. (2017), "Seismic retrofit of masonry wall infilled RC frames through external post-tensioning", Bull. Earthq. Eng., 16(7), 1-24. https://doi.org/10.1007/s10518-017-0241-4.
  80. Steel Benchmarker, Report #329, (2019), Price History Tables and Charts for, Hot-rolled Band, Cold-rolled Coil, Standard Plate, Rebar, Steel Scrap, www.steelbenchmarker.com.
  81. Takeuchi, T., Yasuda, K. and Iwata, M. (2009), "Seismic retrofit using energy dissipation facades", ATC and SEI Conference on Improving the Seismic Performance of Existing Buildings and Other Structures, San Francisco, California, USA. https://doi.org/10.1061/41084(364)91.
  82. Vahedi, S., Javadi, P. and Hosseini, M.H. (2019), "Seismic evaluation of a nonductile soft-first-story RC building retrofitted with steel-braced frames", J. Perform. Constr. Facil., ASCE, (6), 04019064. https://doi.org/10.1061/(ASCE)CF.1943-5509.0001325.
  83. Veismoradi, S., Yousef-beik, S.M.M., Zarnani, P. and Quenneville, P. (2020), "Seismic retrofit of RC-frames using resilient slip friction joint toggle-bracing system", Proceedings of the 2020 New Zealand Society for Earthquake Engineering Annual Technical Conference, New Zealand. https://repo.nzsee.org.nz/handle/nzsee/1729.
  84. Wang, W., Fang, C., Shen, D., Zhang, R., Ding, J. and Wu, H. (2021), "Performance assessment of disc spring-based self-centering braces for seismic hazard mitigation", Eng. Struct., 242, 112527. https://doi.org/10.1016/j.engstruct.2021.112527.
  85. Wen, Y.K. and Kang, Y.J. (2001), "Minimum building life cycle cost design criteria I: Methodology", J. Struct. Eng. (ASCE)., 127(3), 330-337. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:3(330).
  86. Wolski, M., Ricles, J.M. and Sause, R. (2009), "Experimental study of a self-centering beam-column connection with bottom flange friction device", J. Struct. Eng., 1 5(5), 479-488. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000006.
  87. Wu, H., Zhou, Y. and Liu, W. (2019), "Collapse fragility analysis of self-centering precast concrete walls with different post-tensioning and energy dissipation designs", Bull. Earthq. Eng., 17, 3593-3613. https://doi.org/10.1007/s10518-019-00591-7.
  88. Xu, L., Fan, X. and Li, Z. (2020), "Seismic assessment of buildings with prepressed spring self-centering energy dissipation braces", J. Struct. Eng., 146(2), 04019190. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002493.
  89. Xu, L.H., Fan, X.W. and Li, Z.X. (2016a), "Development and experimental verification of a prepressed spring self-centering energy dissipation brace", Eng Struct., 127, 49-61. https://doi.org/10.1016/j.engstruct.2016.08.043.
  90. Xu, L.H., Fan, X.W. and Li, Z.X. (2016b), "Cyclic behavior and failure mechanism of self-centering energy dissipation braces with pre-pressed combination disc springs", Earthq. Eng. Struct. Dynam., 46(7), 1065-1080. https://doi.org/10.1002/eqe.2844.
  91. Xu, Z.D., Teng, G. and Jie, L. (2020), "Experimental and theoretical study of high energy dissipation viscoelastic dampers based on acrylate rubber matrix", J. Eng. Mech., 146(6), 04020057. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001802.
  92. Zhang, Z., Bi, K., Hao, H., Sheng, P., Feng, L. and Xiao, D. (2020), "Development of a novel deformation-amplified shape memory alloy-friction damper for mitigating seismic responses of RC frame buildings", Eng. Struct., 216, https://doi.org/10.1016/j.engstruct.2020.110751.