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A Methodology for Fast and Accurate Analytical Fragility Analysis of Linear Structural Systems during Wind Storms: ALFA

Yıl 2023, Cilt: 39 Sayı: 3, 508 - 520, 31.12.2023

Öz

Wind-storms are extremely destructive natural disasters that cause structural damage, and consequently severe personal injuries and casualties. To reduce these injuries and casualties, risk assessment of existing structures and improvement of building design regulations have become important. To assess the risk of structural systems during wind storms, analytical fragility analysis is a recently developed method by providing conditional failure probabilities for the structural systems. However, the analytical fragility analysis requires extensive computational time and effort which makes it infeasible for large scale structures. This proposed paper develops a new methodology (Analytical Linear Fragility Analysis: ALFA) to simplify and to expedite the analytical fragility analysis for linear structural systems without compromising accuracy. ALFA is exemplified by obtaining the fragility curves of 70 different multi-degree of freedom (MDOF) linear mass-column systems subjected to varying wind loading conditions. The fragility curves of the same mass-column systems were also obtained using Monte-Carlo (MC) based brute-force methodology, which is a commonly used computationally expensive method in literature, and results are compared. This comparison yields the conclusion that ALFA is 240 times faster than the brute-force one, without losing accuracy. Moreover, ALFA can be utilized for improvement of performance-based design specifications and for the preliminary risk assessment of nonlinear structural systems.

Teşekkür

The author of this paper would like to express his appreciation to Dr. Hatice Sinem Sas for her help on proofreading for the draft of the paper.

Kaynakça

  • [1] J.Y. Lee, B.R. Ellingwood, A decision model for intergenerational life-cycle risk assessment of civil infrastructure exposed to hurricanes under climate change, Reliab. Eng. Syst. Saf. 159 (2017) 100–107. doi:10.1016/j.ress.2016.10.022.
  • [2] M.O. Amini, J.W. van de Lindt, Quantitative Insight into Rational Tornado Design Wind Speeds for Residential Wood-Frame Structures Using Fragility Approach, J. Struct. Eng. 140 (2014) 1–15. doi:10.1061/(asce)st.1943-541x.0000914.
  • [3] S. Cao, J. Wang, Statistical Summary and Case Studies of Strong Wind Damage in China, J. Disaster Res. 8 (2013) 1096–1102.
  • [4] K. Lee, D. Rosowsky, Synthetic hurricane wind speed records: development of a database for hazard analyses and risk studies, Nat. Hazards Rev. (2007) 1–30. doi:10.1061/(ASCE)1527-6988(2007)8:2(23).
  • [5] M.G. Stewart, Cyclone damage and temporal changes to building vulnerability and economic risks for residential construction, J. Wind Eng. Ind. Aerodyn. 91 (2003) 671– 691. doi:10.1016/S0167-6105(02)00462-2.
  • [6] J. Shanmugasundaram, S. Arunachalam, S. Gomathinayagam, N. Lakshmanan, P. Harikrishna, Cyclone damage to buildings and structures - a case study, in: J. Wind Eng. Ind. Aerodyn., 2000: pp. 369–380. doi:10.1016/S0167-6105(99)00114-2.
  • [7] B. Gardiner, P. Berry, B. Moulia, Review: Wind impacts on plant growth, mechanics and damage, Plant Sci. 245 (2016) 94–118. doi:10.1016/j.plantsci.2016.01.006.
  • [8] C. Ciftci, S.R. Arwade, B. Kane, S.F. Brena, Analysis of the probability of failure for open-grown trees during wind storms, Probabilistic Eng. Mech. 37 (2014) 41–50. doi:10.1016/j.probengmech.2014.04.002.
  • [9] A.C. Khanduri, G.C. Morrow, Vulnerability of buildings to windstorms and insurance loss estimation, J. Wind Eng. Ind. Aerodyn. 91 (2003) 455–467. doi:10.1016/S0167- 6105(02)00408-7.
  • [10] T.W. Schmidlin, Human fatalities from wind-related tree failures in the United States, 1995-2007, Nat. Hazards. 50 (2009) 13–25. doi:10.1007/s11069-008-9314-7.
  • [11] D.O. Prevatt, J.W. van de Lindt, E.W. Back, A.J. Graettinger, S. Pei, W. Coulbourne, R. Gupta, J. Darryl, A. Duzgun, Making the Case for Improved Structural Design: Tornado Outbreaks of 2011, Leadersh. Manag. Eng. 12 (2012) 254–270.
  • [12] Y. Tamura, Wind-Induced Damage To Building and Disaster Risk Reduction, in: 17th Asia-Pacific Conf. Wind Eng., Taipei, Taiwan, 2009.
  • [13] K.H. Lee, D. V. Rosowsky, Fragility assessment for roof sheathing failure in high wind regions, Eng. Struct. 27 (2005) 857–868. doi:10.1016/j.engstruct.2004.12.017.
  • [14] J.W. van de Lindt, T.N. Dao, Performance-Based Wind Engineering for Wood-Frame Buildings, J. Struct. Eng. 135 (2009) 169–177. doi:10.1061/(ASCE)0733- 9445(2009)135:2(169).
  • [15] A. Quilligan, A. O’Connor, V. Pakrashi, Fragility analysis of steel and concrete wind turbine towers, Eng. Struct. 36 (2012) 270–282. doi:10.1016/j.engstruct.2011.12.013.
  • [16] V. Sim, W.Y. Jung, Comparison of Wind Fragility for Window System in the Simplified 10 and 15-Story Building Considering Exposure Category, World Acad. Sci. Eng. Technol. 10 (2016) 1627–1641.
  • [17] J.R. McDonald, K.C. Mehta, J.E. Minor, Tornado-resistant design of nuclear power-plant structures, Nucl. Saf. 15 (1974) 432–439.
  • [18] R.P. Kennedy, C.A. Cornell, R.D. Campbell, S. Kaplan, H.F. Perla, PROBABILISTIC SEISMIC SAFETY STUDY OF AN EXISTING NUCLEAR POWER PLANT., Nucl. Eng. Des. 59 (1980) 315–338. doi:10.1016/0029-5493(80)90203-4.
  • [19] S. Kaplan, H.F. Perla, D.C. Bley, A Methodology for Seismic Risk Analysis of Nuclear Power Plants, Risk Anal. 3 (1983) 169–180. doi:10.1111/j.1539-6924.1983.tb00118.x.
  • [20] G.C. Marano, R. Greco, M. Mezzina, Stochastic approach for analytical fragility curves, KSCE J. Civ. Eng. 12 (2008) 305–312. doi:10.1007/s12205-008-0305-8.
  • [21] J.W. Van de Lindt, D. V Rosowsky, Strength-based reliability of wood shearwalls subject to wind load, J. Struct. Eng. 131 (2005) 359–363. doi:Doi 10.1061/(Asce)0733- 9445(2005)131:2(359).
  • [22] B.R. Ellingwood, D. V Rosowsky, Y. Li, J.H. Kim, Fragility Assessment of Light-Frame Wood Construction Subjected to Wind and Earthquake Hazards, J. Struct. Eng. 130 (2004) 1921–1930. doi:10.1061/(ASCE)0733-9445(2004)130:12(1921).
  • [23] D. V. Rosowsky, B.R. Ellingwood, Performance-Based Engineering of Wood Frame Housing: Fragility Analysis Methodology, J. Struct. Eng. 128 (2002) 32–38. doi:10.1061/(ASCE)0733-9445(2002)128:1(32).
  • [24] A. Singhal, A.S. Kiremidjian, Method for Probabilistic Evaluation of Seismic Structural Damage, J. Struct. Eng. 122 (1996) 1459–1467. doi:10.1061/(ASCE)0733- 9445(1996)122:12(1459).
  • [25] Y. Pan, A.K. Agrawal, M. Ghosn, Seismic fragility of continuous steel highway bridges in New York state, J. Bridg. Eng. 12 (2007) 689–699. doi:Doi 10.1061/(Asce)1084- 0702(2007)12:6(689).
  • [26] D. Karmakar, S. Ray-Chaudhuri, M. Shinozuka, Finite element model development, validation and probabilistic seismic performance evaluation of Vincent Thomas suspension bridge, Struct. Infrastruct. Eng. 11 (2015) 223–237. doi:10.1080/15732479.2013.863360.
  • [27] B. Sun, Y. Zhang, D. Dai, L. Wang, J. Ou, Seismic fragility analysis of a large-scale frame structure with local nonlinearities using an efficient reduced-order Newton-Raphson method, Soil Dyn. Earthq. Eng. 164 (2023) 107559.
  • [28] W.-S. Yun, H.J. Ham, H.-J. Kim, S. Lee, Evaluation of Extreme Wind Fragility of Balcony Window Systems in Apartments, J. Archit. Inst. Korea Struct. Constr. 31 (2015) 3–11.
  • [29] M. Rota, A. Penna, C.L. Strobbia, Processing Italian damage data to derive typological fragility curves, Soil Dyn. Earthq. Eng. 28 (2008) 933–947. doi:10.1016/j.soildyn.2007.10.010.
  • [30] P. Gehl, J. Douglas, D.M. Seyedi, Influence of the Number of Dynamic Analyses on the Accuracy of Structural Response Estimates, Earthq. Spectra. 31 (2013) 97–113. doi:10.1193/102912EQS320M.
  • [31] S.H. Jeong, A.S. Elnashai, Probabilistic fragility analysis parameterized by fundamental response quantities, Eng. Struct. 29 (2007) 1238–1251. doi:10.1016/j.engstruct.2006.06.026.
  • [32] M. Shinozuka, M.Q. Feng, J. Lee, T. Naganuma, Statistical Analysis of Fragility Curves, J. Eng. Mech. 126 (2000) 1224–1231. doi:10.1061/(ASCE)0733- 9399(2000)126:12(1224).
  • [33] K.R. Karim, F. Yamazaki, A simplified method of constructing fragility curves for highway bridges, Earthq. Eng. Struct. Dyn. 32 (2003) 1603–1626. doi:10.1002/eqe.291.
  • [34] D. Straub, A. Der Kiureghian, Improved seismic fragility modeling from empirical data, Struct. Saf. 30 (2008) 320–336. doi:10.1016/j.strusafe.2007.05.004.
  • [35] M.G. Sfahani, H. Guan, Y.C. Loo, Seismic reliability and risk assessment of structures based on fragility analysis - A review, Adv. Struct. Eng. 18 (2015) 1653–1669.
  • [36] H.A. Panofsky, J.A. Dutton, Atmospheric Turbulence: Models and Methods for Engineering Applications, John Wiley and Sons Ltd, New York, 1984.
  • [37] A.K. Chopra, Dynamics of Structure: Theory and Applications to Earthquake Engineering, Pearson/Prentice Hall, New Jersey, 2007.
  • [38] A.G. Davenport, The spectrum of horizontal gustiness near the ground in high winds, Q. J. R. Meteorol. Soc. 87 (1961) 194–211. doi:10.1002/qj.49708737208.
  • [39] M. Shinozuka, G. Deodatis, Simulation of Stochastic Processes by Spectral Representation, Appl. Mech. Rev. 44(4) (1991) 191–204. doi:10.1115/1.3119501.
  • [40] A. Nataf, Détermination des distributions de probabilités dont les marges sont données, Comptes Rendus l’Académie Des Sci. 225 (1962) 42–43.

Rüzgar Fırtınaları Sırasında Lineer Yapısal Sistemlerin Hızlı ve Doğru Analitik Kırılganlık Analizi için Bir Metodoloji

Yıl 2023, Cilt: 39 Sayı: 3, 508 - 520, 31.12.2023

Öz

Rüzgar fırtınaları, yapısal hasara ve sonuç olarak ciddi kişisel yaralanmalara ve kayıplara neden olan son derece yıkıcı doğal afetlerdir. Bu yaralanma ve can kayıplarını azaltmak için mevcut yapıların risk değerlendirmesi ve bina tasarım yönetmeliklerinin iyileştirilmesi önem kazanmıştır. Rüzgar fırtınaları sırasında yapısal sistemlerin riskini değerlendirmek için, analitik kırılganlık analizi, yapısal sistemler için koşullu arıza olasılıkları sağlayarak son zamanlarda geliştirilen bir yöntemdir. Bununla birlikte, analitik kırılganlık analizi, büyük ölçekli yapılar için uygulanamaz hale getiren kapsamlı hesaplama zamanı ve çabası gerektirir. Önerilen bu makale, doğruluktan ödün vermeden doğrusal yapısal sistemler için analitik kırılganlık analizini basitleştirmek ve hızlandırmak için yeni bir metodoloji (Analitik Lineer Kırılganlık Analizi: ALFA) geliştirmektedir. ALFA, değişen rüzgar yükü koşullarına maruz kalan 70 farklı çok serbestlik dereceli (MDOF) lineer kütle kolon sisteminin kırılganlık eğrilerinin elde edilmesiyle örneklenmiştir. Literatürde hesaplama açısından pahalı bir yöntem olan Monte-Carlo (MC) tabanlı kaba kuvvet metodolojisi kullanılarak aynı kütle-kolon sistemlerinin kırılganlık eğrileri de elde edilmiş ve sonuçlar karşılaştırılmıştır. Bu karşılaştırma, ALFA'nın kesinliği kaybetmeden kaba kuvvetten 240 kat daha hızlı olduğu sonucunu verir. Ayrıca ALFA, performansa dayalı tasarım özelliklerinin iyileştirilmesi ve doğrusal olmayan yapısal sistemlerin ön risk değerlendirmesi için kullanılabilir.

Kaynakça

  • [1] J.Y. Lee, B.R. Ellingwood, A decision model for intergenerational life-cycle risk assessment of civil infrastructure exposed to hurricanes under climate change, Reliab. Eng. Syst. Saf. 159 (2017) 100–107. doi:10.1016/j.ress.2016.10.022.
  • [2] M.O. Amini, J.W. van de Lindt, Quantitative Insight into Rational Tornado Design Wind Speeds for Residential Wood-Frame Structures Using Fragility Approach, J. Struct. Eng. 140 (2014) 1–15. doi:10.1061/(asce)st.1943-541x.0000914.
  • [3] S. Cao, J. Wang, Statistical Summary and Case Studies of Strong Wind Damage in China, J. Disaster Res. 8 (2013) 1096–1102.
  • [4] K. Lee, D. Rosowsky, Synthetic hurricane wind speed records: development of a database for hazard analyses and risk studies, Nat. Hazards Rev. (2007) 1–30. doi:10.1061/(ASCE)1527-6988(2007)8:2(23).
  • [5] M.G. Stewart, Cyclone damage and temporal changes to building vulnerability and economic risks for residential construction, J. Wind Eng. Ind. Aerodyn. 91 (2003) 671– 691. doi:10.1016/S0167-6105(02)00462-2.
  • [6] J. Shanmugasundaram, S. Arunachalam, S. Gomathinayagam, N. Lakshmanan, P. Harikrishna, Cyclone damage to buildings and structures - a case study, in: J. Wind Eng. Ind. Aerodyn., 2000: pp. 369–380. doi:10.1016/S0167-6105(99)00114-2.
  • [7] B. Gardiner, P. Berry, B. Moulia, Review: Wind impacts on plant growth, mechanics and damage, Plant Sci. 245 (2016) 94–118. doi:10.1016/j.plantsci.2016.01.006.
  • [8] C. Ciftci, S.R. Arwade, B. Kane, S.F. Brena, Analysis of the probability of failure for open-grown trees during wind storms, Probabilistic Eng. Mech. 37 (2014) 41–50. doi:10.1016/j.probengmech.2014.04.002.
  • [9] A.C. Khanduri, G.C. Morrow, Vulnerability of buildings to windstorms and insurance loss estimation, J. Wind Eng. Ind. Aerodyn. 91 (2003) 455–467. doi:10.1016/S0167- 6105(02)00408-7.
  • [10] T.W. Schmidlin, Human fatalities from wind-related tree failures in the United States, 1995-2007, Nat. Hazards. 50 (2009) 13–25. doi:10.1007/s11069-008-9314-7.
  • [11] D.O. Prevatt, J.W. van de Lindt, E.W. Back, A.J. Graettinger, S. Pei, W. Coulbourne, R. Gupta, J. Darryl, A. Duzgun, Making the Case for Improved Structural Design: Tornado Outbreaks of 2011, Leadersh. Manag. Eng. 12 (2012) 254–270.
  • [12] Y. Tamura, Wind-Induced Damage To Building and Disaster Risk Reduction, in: 17th Asia-Pacific Conf. Wind Eng., Taipei, Taiwan, 2009.
  • [13] K.H. Lee, D. V. Rosowsky, Fragility assessment for roof sheathing failure in high wind regions, Eng. Struct. 27 (2005) 857–868. doi:10.1016/j.engstruct.2004.12.017.
  • [14] J.W. van de Lindt, T.N. Dao, Performance-Based Wind Engineering for Wood-Frame Buildings, J. Struct. Eng. 135 (2009) 169–177. doi:10.1061/(ASCE)0733- 9445(2009)135:2(169).
  • [15] A. Quilligan, A. O’Connor, V. Pakrashi, Fragility analysis of steel and concrete wind turbine towers, Eng. Struct. 36 (2012) 270–282. doi:10.1016/j.engstruct.2011.12.013.
  • [16] V. Sim, W.Y. Jung, Comparison of Wind Fragility for Window System in the Simplified 10 and 15-Story Building Considering Exposure Category, World Acad. Sci. Eng. Technol. 10 (2016) 1627–1641.
  • [17] J.R. McDonald, K.C. Mehta, J.E. Minor, Tornado-resistant design of nuclear power-plant structures, Nucl. Saf. 15 (1974) 432–439.
  • [18] R.P. Kennedy, C.A. Cornell, R.D. Campbell, S. Kaplan, H.F. Perla, PROBABILISTIC SEISMIC SAFETY STUDY OF AN EXISTING NUCLEAR POWER PLANT., Nucl. Eng. Des. 59 (1980) 315–338. doi:10.1016/0029-5493(80)90203-4.
  • [19] S. Kaplan, H.F. Perla, D.C. Bley, A Methodology for Seismic Risk Analysis of Nuclear Power Plants, Risk Anal. 3 (1983) 169–180. doi:10.1111/j.1539-6924.1983.tb00118.x.
  • [20] G.C. Marano, R. Greco, M. Mezzina, Stochastic approach for analytical fragility curves, KSCE J. Civ. Eng. 12 (2008) 305–312. doi:10.1007/s12205-008-0305-8.
  • [21] J.W. Van de Lindt, D. V Rosowsky, Strength-based reliability of wood shearwalls subject to wind load, J. Struct. Eng. 131 (2005) 359–363. doi:Doi 10.1061/(Asce)0733- 9445(2005)131:2(359).
  • [22] B.R. Ellingwood, D. V Rosowsky, Y. Li, J.H. Kim, Fragility Assessment of Light-Frame Wood Construction Subjected to Wind and Earthquake Hazards, J. Struct. Eng. 130 (2004) 1921–1930. doi:10.1061/(ASCE)0733-9445(2004)130:12(1921).
  • [23] D. V. Rosowsky, B.R. Ellingwood, Performance-Based Engineering of Wood Frame Housing: Fragility Analysis Methodology, J. Struct. Eng. 128 (2002) 32–38. doi:10.1061/(ASCE)0733-9445(2002)128:1(32).
  • [24] A. Singhal, A.S. Kiremidjian, Method for Probabilistic Evaluation of Seismic Structural Damage, J. Struct. Eng. 122 (1996) 1459–1467. doi:10.1061/(ASCE)0733- 9445(1996)122:12(1459).
  • [25] Y. Pan, A.K. Agrawal, M. Ghosn, Seismic fragility of continuous steel highway bridges in New York state, J. Bridg. Eng. 12 (2007) 689–699. doi:Doi 10.1061/(Asce)1084- 0702(2007)12:6(689).
  • [26] D. Karmakar, S. Ray-Chaudhuri, M. Shinozuka, Finite element model development, validation and probabilistic seismic performance evaluation of Vincent Thomas suspension bridge, Struct. Infrastruct. Eng. 11 (2015) 223–237. doi:10.1080/15732479.2013.863360.
  • [27] B. Sun, Y. Zhang, D. Dai, L. Wang, J. Ou, Seismic fragility analysis of a large-scale frame structure with local nonlinearities using an efficient reduced-order Newton-Raphson method, Soil Dyn. Earthq. Eng. 164 (2023) 107559.
  • [28] W.-S. Yun, H.J. Ham, H.-J. Kim, S. Lee, Evaluation of Extreme Wind Fragility of Balcony Window Systems in Apartments, J. Archit. Inst. Korea Struct. Constr. 31 (2015) 3–11.
  • [29] M. Rota, A. Penna, C.L. Strobbia, Processing Italian damage data to derive typological fragility curves, Soil Dyn. Earthq. Eng. 28 (2008) 933–947. doi:10.1016/j.soildyn.2007.10.010.
  • [30] P. Gehl, J. Douglas, D.M. Seyedi, Influence of the Number of Dynamic Analyses on the Accuracy of Structural Response Estimates, Earthq. Spectra. 31 (2013) 97–113. doi:10.1193/102912EQS320M.
  • [31] S.H. Jeong, A.S. Elnashai, Probabilistic fragility analysis parameterized by fundamental response quantities, Eng. Struct. 29 (2007) 1238–1251. doi:10.1016/j.engstruct.2006.06.026.
  • [32] M. Shinozuka, M.Q. Feng, J. Lee, T. Naganuma, Statistical Analysis of Fragility Curves, J. Eng. Mech. 126 (2000) 1224–1231. doi:10.1061/(ASCE)0733- 9399(2000)126:12(1224).
  • [33] K.R. Karim, F. Yamazaki, A simplified method of constructing fragility curves for highway bridges, Earthq. Eng. Struct. Dyn. 32 (2003) 1603–1626. doi:10.1002/eqe.291.
  • [34] D. Straub, A. Der Kiureghian, Improved seismic fragility modeling from empirical data, Struct. Saf. 30 (2008) 320–336. doi:10.1016/j.strusafe.2007.05.004.
  • [35] M.G. Sfahani, H. Guan, Y.C. Loo, Seismic reliability and risk assessment of structures based on fragility analysis - A review, Adv. Struct. Eng. 18 (2015) 1653–1669.
  • [36] H.A. Panofsky, J.A. Dutton, Atmospheric Turbulence: Models and Methods for Engineering Applications, John Wiley and Sons Ltd, New York, 1984.
  • [37] A.K. Chopra, Dynamics of Structure: Theory and Applications to Earthquake Engineering, Pearson/Prentice Hall, New Jersey, 2007.
  • [38] A.G. Davenport, The spectrum of horizontal gustiness near the ground in high winds, Q. J. R. Meteorol. Soc. 87 (1961) 194–211. doi:10.1002/qj.49708737208.
  • [39] M. Shinozuka, G. Deodatis, Simulation of Stochastic Processes by Spectral Representation, Appl. Mech. Rev. 44(4) (1991) 191–204. doi:10.1115/1.3119501.
  • [40] A. Nataf, Détermination des distributions de probabilités dont les marges sont données, Comptes Rendus l’Académie Des Sci. 225 (1962) 42–43.

Ayrıntılar

Birincil Dil İngilizce
Konular İnşaat Yapım Mühendisliği, Kırılma Mekaniği
Bölüm Makaleler
Yazarlar

Cihan ÇİFTÇİ

Erken Görünüm Tarihi 31 Aralık 2023
Yayımlanma Tarihi 31 Aralık 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 39 Sayı: 3

Kaynak Göster

APA ÇİFTÇİ, C. (2023). A Methodology for Fast and Accurate Analytical Fragility Analysis of Linear Structural Systems during Wind Storms: ALFA. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, 39(3), 508-520.
AMA ÇİFTÇİ C. A Methodology for Fast and Accurate Analytical Fragility Analysis of Linear Structural Systems during Wind Storms: ALFA. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi. Aralık 2023;39(3):508-520.
Chicago ÇİFTÇİ, Cihan. “A Methodology for Fast and Accurate Analytical Fragility Analysis of Linear Structural Systems During Wind Storms: ALFA”. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi 39, sy. 3 (Aralık 2023): 508-20.
EndNote ÇİFTÇİ C (01 Aralık 2023) A Methodology for Fast and Accurate Analytical Fragility Analysis of Linear Structural Systems during Wind Storms: ALFA. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi 39 3 508–520.
IEEE C. ÇİFTÇİ, “A Methodology for Fast and Accurate Analytical Fragility Analysis of Linear Structural Systems during Wind Storms: ALFA”, Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, c. 39, sy. 3, ss. 508–520, 2023.
ISNAD ÇİFTÇİ, Cihan. “A Methodology for Fast and Accurate Analytical Fragility Analysis of Linear Structural Systems During Wind Storms: ALFA”. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi 39/3 (Aralık 2023), 508-520.
JAMA ÇİFTÇİ C. A Methodology for Fast and Accurate Analytical Fragility Analysis of Linear Structural Systems during Wind Storms: ALFA. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi. 2023;39:508–520.
MLA ÇİFTÇİ, Cihan. “A Methodology for Fast and Accurate Analytical Fragility Analysis of Linear Structural Systems During Wind Storms: ALFA”. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, c. 39, sy. 3, 2023, ss. 508-20.
Vancouver ÇİFTÇİ C. A Methodology for Fast and Accurate Analytical Fragility Analysis of Linear Structural Systems during Wind Storms: ALFA. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi. 2023;39(3):508-20.

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