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Ankastre Mesnetli Petek Kirişlerin Optimizasyonu

Year 2025, Volume: 10 Issue: 1, 1 - 8, 24.07.2025

Marwan Abdulkareem Shakir Albayati , Ahmad Reshad Noori , Aylin Ece Kayabekir

https://doi.org/10.19072/ijet.1642459

Abstract

Petek kirişler, estetik açıdan çekici tasarımları, farklı geometrik şekilleri, çevre dostu olmaları ve zaman, maliyet ve performans açısından ekonomik avantajları nedeniyle çeşitli alanlarda giderek artan ilgi görmektedir. Bu kirişler özellikle ağırlıklarını arttırmadan eğilmeye karşı direnç gösterme konusunda mükemmeldir. Bu çalışmada, petek kirişlerin performansı, amaç fonksiyonu olarak temsil edilen maksimum düşey sapma ile optimize edilmiştir. Bu, üç optimizasyon algoritması kullanılarak kesitin optimal boyutlarının belirlenmesiyle elde edilir: Gri Kurt Optimizasyonu (GWO), Parçacık Sürü Optimizasyonu (PSO) ve Diferansiyel Evrim (DE). Bu çalışma petek kirişler için üç farklı malzeme türüne odaklanmaktadır: S235, S255 ve S355. Sonuçlar, PSO ve DE algoritmalarının çok benzer sonuçlar ürettiğini, GWO algoritmasının ise biraz farklı sonuçlar verdiğini ortaya çıkardı. Genel olarak, üç algoritmanın tümü, PSO ve DE algoritmalarını çok az fark bir şekilde tercih ederek, mühendislik uygulamalarında iyi bir yetenek sergilemektedir.

Keywords

Petek kiriş maksimum düşey yer değiştirme gri kurt optimizasyonu (GWO) parçacık sürüsü optimizasyonu (PSO) diferansiyel evrim (DE)

References

  • [1] Erdal, F. (2017). A firefly algorithm for optimum design of new-generation beams. Engineering Optimization, 49(6), 915-931.
  • [2] Sorkhabi, R. V., Naseri, A., & Naseri, M. (2014). Optimization of the castellated beams by particle swarm algorithms method. APCBEE procedia, 9, 381-387
  • [3] Kaveh, A., & Shokohi, F. (2016). Application of grey wolf optimizer in design of castellated beams. Asian Journal of Civil Engineering, 17(5), 683-700.
  • [4] Kaveh, A., Almasi, P., & Khodagholi, A. (2023). Optimum design of castellated beams using four recently developed meta-heuristic algorithms. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 47(2), 713-725.
  • [5] Mashayekhi, M. R., & Mosayyebi, S. (2023). A new hybrid Harris hawks optimization (HHO) and particle swarm optimization (PSO) algorithm for the design of castellated beams. Asian Journal of Civil Engineering, 24(7), 2121-2139.
  • [6] Muro, C., Escobedo, R., Spector, L., & Coppinger, R. P. (2011). Wolf-pack (Canis lupus) hunting strategies emerge from simple rules in computational simulations. Behavioural processes, 88(3), 192-1.
  • [7] Mohan, S. C., Maiti, D. K., & Maity, D. (2013). Structural damage assessment using FRF employing particle swarm optimization. Applied Mathematics and Computation, 219(20), 10387-10400.
  • [8] Deng, W., Shang, S., Cai, X., Zhao, H., Song, Y., & Xu, J. (2021). An improved differential evolution algorithm and its application in optimization problem. Soft Computing, 25, 5277-5298.
  • [9] Sorkhabi, R. V., Naseri, A., & Naseri, M. (2014). Optimization of the castellated beams by particle swarm algorithms method. APCBEE procedia, 9, 381-387.
  • [10] Barkiah, I., & Darmawan, A. R. (2021). Comparison behavior of flexural capacity castellated beam of hexagonal opening with circle opening. Internatıonal journal of civil engineering and technology (IJCIET), 12(8).
  • [11] Elaiwi, S. S. (2019). Analysis and design of castellated beams. Doctoral dissertation. University of Plymouth.United Kingdom.
  • [12] de Oliveira, J. P., Cardoso, D. C. T., & Sotelino, E. D. (2019). Elastic flexural local buckling of Litzka castellated beams: Explicit equations and FE parametric study. Engineering Structures, 186, 436-445.
  • [13] Pachpor, P. D., Gupta, L. M., Deshpande, N. V., & Bedi, K. (2011). Parameteric study of castellated Beam. Advanced Materials Research, 163, 842-845.
  • [14] Kshirsagar, V. V., & Parekar, S. R. (2018). Behaviour of castellated beams with and without stiffeners-A review. Behaviour, 5(04).
  • [15] Mezher, N. A. M., Noori, A. R., & Ertürkmen, D. (2023). Influence of the web opening shapes on the bending and free vibration responses of castellated steel beams. International Journal of Engineering Technologies IJET, 8(2), 83-100.
  • [16] Doori, S., & Noori, A. R. (2021). Finite element approach for the bending analysis of castellated steel beams with various web openings. ALKÜ Fen Bilimleri Dergisi, 3(2), 38-49.
  • [17] Ertürkmen, D., & Noori, A. R. (2023). Sonlu elemanlar yöntemi ile eğri eksenli petek kirişlerin eğilme analizi. Çukurova Üniversitesi Mühendislik Fakültesi Dergisi, 38(1), 73-84.
  • [18] Yang XS. 2008. Nature-Inspired Metaheuristic Algorithms. Luniver Press: Bristol.
  • [19] Yang, X. S. (2010). Firefly algorithm, Levy flights and global optimization. In Research and development in intelligent systems XXVI: Incorporating applications and innovations in intelligent systems XVII Springer London (pp. 209-218).
  • [20] Yang, X. S., & Hossein Gandomi, A. (2012). Bat algorithm: a novel approach for global engineering optimization. Engineering computations, 29(5), 464-483.
  • [21] Hashim, N. S., & De’nan, F. (2024). The magnitude of stress concentration of I-beam with web opening because of lateral-torsional buckling effects. World Journal of Engineering, 21(2), 386-397.
  • [22] Boyer, J. P. (1964). Castellated beams-new developments. AISC Engineering Journal, 1(3), 104.
  • [23] Mohebkhah, A., & Showkati, H. (2005). Bracing requirements for inelastic castellated beams. Journal of Constructional Steel Research, 61(10), 1373-1386.
  • [24] Durif, S., & Bouchair, A. (2012). Behavior of cellular beams with sinusoidal openings. Procedia engineering, 40, 108-113.
  • [25] Yuan, W. B., Yu, N. T., Bao, Z. S., & Wu, L. P. (2016). Deflection of castellated beams subjected to uniformly distributed transverse loading. International Journal of Steel Structures, 16, 813-821.
  • [26] Deshmukh, M. N., & Kasnale, A. (2019). Behaviour of Castellated Beam with Coupled Stiffener. Behaviour, 6(06).
  • [27] Kang, L., Hong, S., & Liu, X. (2021). Shear behaviour and strength design of cellular beams with circular or elongated openings. Thin-Walled Structures, 160, 107353.
  • [28] Ferreira, F. P. V., Martins, C. H., & De Nardin, S. (2020). Advances in composite beams with web openings and composite cellular beams. Journal of Constructional Steel Research, 172, 106182.
  • [29] Demirdjian, S. (1999). Stability of castellated beam webs. Master Thesis, Department of Civil Engineering and Applied Mechanics, McGill University, Canada.
  • [30] Megharief, J. D. (1997). Behavior of composite castellated beams. Master Thesis, Department of Civil Engineering and Applied Mechanics, McGill University, Canada.
  • [31] Kshirsagar, V. V., & Parekar, S. R. (2018). Behaviour of castellated beams with and without stiffeners-A review. Behaviour, 5(04).
  • [32] Morkhade, S. G., Shirke, T., Mansuke, A., Chavan, M. U., & Gupta, L. M. (2021). Experimental and analytical investigation of castellated steel beams with varying openings eccentricity. Journal of the Institution of Engineers (India): Series A, 102(2), 479-488.
  • [33] Verweij, J. G. (2010). Cellular beam-columns in portal frame structures. Master Thesis, Delft University of Technology, Delft, The Netherlands.
  • [34] Panedpojaman, P., Thepchatri, T., & Limkatanyu, S. (2014). Novel design equations for shear strength of local web-post buckling in cellular beams. Thin-walled structures, 76, 92-104.
  • [35] Grilo, L. F., Fakury, R. H., & de Souza Veríssimo, G. (2018). Design procedure for the web-post buckling of steel cellular beams. Journal of Constructional Steel Research, 148, 525-541.
  • [36] Tsavdaridis, K. D., & D'Mello, C. (2011). Web buckling study of the behaviour and strength of perforated steel beams with different novel web opening shapes. Journal of constructional steel research, 67(10), 1605-1620.
  • [37] Erdal, F., & Saka, M. P. (2013). Ultimate load carrying capacity of optimally designed steel cellular beams. Journal of constructional steel research, 80, 355-368.
  • [38] Mirjalili, S. M. S. M., Mirjalili, S. M., & Lewis, A. (2014). Grey Wolf Optimizer Adv Eng Softw 69: 46–61. ed.
  • [39] Temür, R., Kayabekir, A. E., Bekdas, G., & Nigdeli, S. M. (2018). Grey wolf optimizer based design of reinforced concrete retaining walls considering shear key. International Journal of Theoretical and Applied Mechanics, 3.
  • [40] P. Fourie, A. Groenwold, The particle swarm optimization in topology optimization, in: Fourth World Congress of Structural and Multidisciplinary Optimization, 2001, p. 154.
  • [41] P. Fourie, A. Groenwold, The particle swarm optimization algorithm in size and shape optimization, Struct. Multidiscip. Optim. 23 (2002) 259–267.
  • [42] Das, S., Mullick, S. S., & Suganthan, P. N. (2016). Recent advances in differential evolution–an updated survey. Swarm and evolutionary computation, 27, 1-30.
  • [43] Mashayekhi, M. R., & Mosayyebi, S. (2023). A new hybrid Harris hawks optimization (HHO) and particle swarm optimization (PSO) algorithm for the design of castellated beams. Asian Journal of Civil Engineering, 24(7), 2121-2139.
  • [44] Hieu, N. T., & Tuan, V. A. (2018). Weight optimization of composite cellular beam based on the differential evolution algorithm. Journal of Science and Technology in Civil Engineering (JSTCE)-HUCE, 12(5), 28-38.
  • [45] Abbass, H. A., Sarker, R., & Newton, C. (2001, May). PDE: a Pareto-frontier differential evolution approach for multi-objective optimization problems. In Proceedings of the 2001 congress on evolutionary computation (IEEE Cat. No. 01TH8546) (Vol. 2, pp. 971-978). IEEE.
  • [46] Kayabekir, A. E., Nigdeli, S. M., & Bekdaş, G. (2023). The Development of Hybrid Metaheuristics in Structural Engineering. In Hybrid Metaheuristics in Structural Engineering: Including Machine Learning Applications (pp. 17-34). Cham: Springer Nature Switzerland.
  • [47] Kayabekir, A. E., Nigdeli, S. M., & Bekdaş, G. (2023). The Development of Hybrid Metaheuristics in Structural Engineering. In Hybrid Metaheuristics in Structural Engineering: Including Machine Learning Applications (pp. 17-34). Cham: Springer Nature Switzerland.
  • [48] Albayati, M. A. S., & Noorı, A. R. (2024). Üç Farklı Metasezgisel Algoritma Kullanılarak Petek Kirişlerin Yer Değiştirme Optimizasyonu. Çukurova Üniversitesi Mühendislik Fakültesi Dergisi, 39(4), 979-990.

Optimization of Fixed Supported Castellated Steel Beams

Year 2025, Volume: 10 Issue: 1, 1 - 8, 24.07.2025

Marwan Abdulkareem Shakir Albayati , Ahmad Reshad Noori , Aylin Ece Kayabekir

https://doi.org/10.19072/ijet.1642459

Abstract

Castellated beams have garnered increasing attention in various fields due to their aesthetically appealing design, diverse geometric shapes, environmental friendliness, and economic advantages in terms of time, cost, and performance. These beams particularly excel in resisting bending without increasing their weight. The novelty of this paper, is to optimize the performance of castellated beams by maximum vertical deflection, represented as the objective function. This is achieved by determining the optimal dimensions of the cross-section using three optimization algorithms: Gray Wolf Optimization (GWO), Particle Swarm Optimization (PSO), and Differential Evolution (DE). This study focuses on three different types of material for castellated beams: S235, S255, and S355. The results revealed that the PSO and DE algorithms produce very similar outcomes, while the GWO algorithm shows slightly different results. Overall, all three algorithms demonstrate good capability in engineering applications, with a slight preference for the PSO and DE algorithms.

Keywords

Castellated beam maximum vertical displacement gray wolf optimization (GWO) particle swarm optimization (PSO) differential evolution (DE)

References

  • [1] Erdal, F. (2017). A firefly algorithm for optimum design of new-generation beams. Engineering Optimization, 49(6), 915-931.
  • [2] Sorkhabi, R. V., Naseri, A., & Naseri, M. (2014). Optimization of the castellated beams by particle swarm algorithms method. APCBEE procedia, 9, 381-387
  • [3] Kaveh, A., & Shokohi, F. (2016). Application of grey wolf optimizer in design of castellated beams. Asian Journal of Civil Engineering, 17(5), 683-700.
  • [4] Kaveh, A., Almasi, P., & Khodagholi, A. (2023). Optimum design of castellated beams using four recently developed meta-heuristic algorithms. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 47(2), 713-725.
  • [5] Mashayekhi, M. R., & Mosayyebi, S. (2023). A new hybrid Harris hawks optimization (HHO) and particle swarm optimization (PSO) algorithm for the design of castellated beams. Asian Journal of Civil Engineering, 24(7), 2121-2139.
  • [6] Muro, C., Escobedo, R., Spector, L., & Coppinger, R. P. (2011). Wolf-pack (Canis lupus) hunting strategies emerge from simple rules in computational simulations. Behavioural processes, 88(3), 192-1.
  • [7] Mohan, S. C., Maiti, D. K., & Maity, D. (2013). Structural damage assessment using FRF employing particle swarm optimization. Applied Mathematics and Computation, 219(20), 10387-10400.
  • [8] Deng, W., Shang, S., Cai, X., Zhao, H., Song, Y., & Xu, J. (2021). An improved differential evolution algorithm and its application in optimization problem. Soft Computing, 25, 5277-5298.
  • [9] Sorkhabi, R. V., Naseri, A., & Naseri, M. (2014). Optimization of the castellated beams by particle swarm algorithms method. APCBEE procedia, 9, 381-387.
  • [10] Barkiah, I., & Darmawan, A. R. (2021). Comparison behavior of flexural capacity castellated beam of hexagonal opening with circle opening. Internatıonal journal of civil engineering and technology (IJCIET), 12(8).
  • [11] Elaiwi, S. S. (2019). Analysis and design of castellated beams. Doctoral dissertation. University of Plymouth.United Kingdom.
  • [12] de Oliveira, J. P., Cardoso, D. C. T., & Sotelino, E. D. (2019). Elastic flexural local buckling of Litzka castellated beams: Explicit equations and FE parametric study. Engineering Structures, 186, 436-445.
  • [13] Pachpor, P. D., Gupta, L. M., Deshpande, N. V., & Bedi, K. (2011). Parameteric study of castellated Beam. Advanced Materials Research, 163, 842-845.
  • [14] Kshirsagar, V. V., & Parekar, S. R. (2018). Behaviour of castellated beams with and without stiffeners-A review. Behaviour, 5(04).
  • [15] Mezher, N. A. M., Noori, A. R., & Ertürkmen, D. (2023). Influence of the web opening shapes on the bending and free vibration responses of castellated steel beams. International Journal of Engineering Technologies IJET, 8(2), 83-100.
  • [16] Doori, S., & Noori, A. R. (2021). Finite element approach for the bending analysis of castellated steel beams with various web openings. ALKÜ Fen Bilimleri Dergisi, 3(2), 38-49.
  • [17] Ertürkmen, D., & Noori, A. R. (2023). Sonlu elemanlar yöntemi ile eğri eksenli petek kirişlerin eğilme analizi. Çukurova Üniversitesi Mühendislik Fakültesi Dergisi, 38(1), 73-84.
  • [18] Yang XS. 2008. Nature-Inspired Metaheuristic Algorithms. Luniver Press: Bristol.
  • [19] Yang, X. S. (2010). Firefly algorithm, Levy flights and global optimization. In Research and development in intelligent systems XXVI: Incorporating applications and innovations in intelligent systems XVII Springer London (pp. 209-218).
  • [20] Yang, X. S., & Hossein Gandomi, A. (2012). Bat algorithm: a novel approach for global engineering optimization. Engineering computations, 29(5), 464-483.
  • [21] Hashim, N. S., & De’nan, F. (2024). The magnitude of stress concentration of I-beam with web opening because of lateral-torsional buckling effects. World Journal of Engineering, 21(2), 386-397.
  • [22] Boyer, J. P. (1964). Castellated beams-new developments. AISC Engineering Journal, 1(3), 104.
  • [23] Mohebkhah, A., & Showkati, H. (2005). Bracing requirements for inelastic castellated beams. Journal of Constructional Steel Research, 61(10), 1373-1386.
  • [24] Durif, S., & Bouchair, A. (2012). Behavior of cellular beams with sinusoidal openings. Procedia engineering, 40, 108-113.
  • [25] Yuan, W. B., Yu, N. T., Bao, Z. S., & Wu, L. P. (2016). Deflection of castellated beams subjected to uniformly distributed transverse loading. International Journal of Steel Structures, 16, 813-821.
  • [26] Deshmukh, M. N., & Kasnale, A. (2019). Behaviour of Castellated Beam with Coupled Stiffener. Behaviour, 6(06).
  • [27] Kang, L., Hong, S., & Liu, X. (2021). Shear behaviour and strength design of cellular beams with circular or elongated openings. Thin-Walled Structures, 160, 107353.
  • [28] Ferreira, F. P. V., Martins, C. H., & De Nardin, S. (2020). Advances in composite beams with web openings and composite cellular beams. Journal of Constructional Steel Research, 172, 106182.
  • [29] Demirdjian, S. (1999). Stability of castellated beam webs. Master Thesis, Department of Civil Engineering and Applied Mechanics, McGill University, Canada.
  • [30] Megharief, J. D. (1997). Behavior of composite castellated beams. Master Thesis, Department of Civil Engineering and Applied Mechanics, McGill University, Canada.
  • [31] Kshirsagar, V. V., & Parekar, S. R. (2018). Behaviour of castellated beams with and without stiffeners-A review. Behaviour, 5(04).
  • [32] Morkhade, S. G., Shirke, T., Mansuke, A., Chavan, M. U., & Gupta, L. M. (2021). Experimental and analytical investigation of castellated steel beams with varying openings eccentricity. Journal of the Institution of Engineers (India): Series A, 102(2), 479-488.
  • [33] Verweij, J. G. (2010). Cellular beam-columns in portal frame structures. Master Thesis, Delft University of Technology, Delft, The Netherlands.
  • [34] Panedpojaman, P., Thepchatri, T., & Limkatanyu, S. (2014). Novel design equations for shear strength of local web-post buckling in cellular beams. Thin-walled structures, 76, 92-104.
  • [35] Grilo, L. F., Fakury, R. H., & de Souza Veríssimo, G. (2018). Design procedure for the web-post buckling of steel cellular beams. Journal of Constructional Steel Research, 148, 525-541.
  • [36] Tsavdaridis, K. D., & D'Mello, C. (2011). Web buckling study of the behaviour and strength of perforated steel beams with different novel web opening shapes. Journal of constructional steel research, 67(10), 1605-1620.
  • [37] Erdal, F., & Saka, M. P. (2013). Ultimate load carrying capacity of optimally designed steel cellular beams. Journal of constructional steel research, 80, 355-368.
  • [38] Mirjalili, S. M. S. M., Mirjalili, S. M., & Lewis, A. (2014). Grey Wolf Optimizer Adv Eng Softw 69: 46–61. ed.
  • [39] Temür, R., Kayabekir, A. E., Bekdas, G., & Nigdeli, S. M. (2018). Grey wolf optimizer based design of reinforced concrete retaining walls considering shear key. International Journal of Theoretical and Applied Mechanics, 3.
  • [40] P. Fourie, A. Groenwold, The particle swarm optimization in topology optimization, in: Fourth World Congress of Structural and Multidisciplinary Optimization, 2001, p. 154.
  • [41] P. Fourie, A. Groenwold, The particle swarm optimization algorithm in size and shape optimization, Struct. Multidiscip. Optim. 23 (2002) 259–267.
  • [42] Das, S., Mullick, S. S., & Suganthan, P. N. (2016). Recent advances in differential evolution–an updated survey. Swarm and evolutionary computation, 27, 1-30.
  • [43] Mashayekhi, M. R., & Mosayyebi, S. (2023). A new hybrid Harris hawks optimization (HHO) and particle swarm optimization (PSO) algorithm for the design of castellated beams. Asian Journal of Civil Engineering, 24(7), 2121-2139.
  • [44] Hieu, N. T., & Tuan, V. A. (2018). Weight optimization of composite cellular beam based on the differential evolution algorithm. Journal of Science and Technology in Civil Engineering (JSTCE)-HUCE, 12(5), 28-38.
  • [45] Abbass, H. A., Sarker, R., & Newton, C. (2001, May). PDE: a Pareto-frontier differential evolution approach for multi-objective optimization problems. In Proceedings of the 2001 congress on evolutionary computation (IEEE Cat. No. 01TH8546) (Vol. 2, pp. 971-978). IEEE.
  • [46] Kayabekir, A. E., Nigdeli, S. M., & Bekdaş, G. (2023). The Development of Hybrid Metaheuristics in Structural Engineering. In Hybrid Metaheuristics in Structural Engineering: Including Machine Learning Applications (pp. 17-34). Cham: Springer Nature Switzerland.
  • [47] Kayabekir, A. E., Nigdeli, S. M., & Bekdaş, G. (2023). The Development of Hybrid Metaheuristics in Structural Engineering. In Hybrid Metaheuristics in Structural Engineering: Including Machine Learning Applications (pp. 17-34). Cham: Springer Nature Switzerland.
  • [48] Albayati, M. A. S., & Noorı, A. R. (2024). Üç Farklı Metasezgisel Algoritma Kullanılarak Petek Kirişlerin Yer Değiştirme Optimizasyonu. Çukurova Üniversitesi Mühendislik Fakültesi Dergisi, 39(4), 979-990.
There are 48 citations in total.

Details

Primary Language English
Subjects Structural Engineering
Journal Section Makaleler
Authors

Marwan Abdulkareem Shakir Albayati

Ahmad Reshad Noori

Aylin Ece Kayabekir

Early Pub Date May 5, 2025
Publication Date July 24, 2025
Submission Date February 18, 2025
Acceptance Date April 9, 2025
Published in Issue Year 2025 Volume: 10 Issue: 1

Cite

APA Albayati, M. A. S., Noori, A. R., & Kayabekir, A. E. (2025). Optimization of Fixed Supported Castellated Steel Beams. International Journal of Engineering Technologies IJET, 10(1), 1-8. https://doi.org/10.19072/ijet.1642459
AMA Albayati MAS, Noori AR, Kayabekir AE. Optimization of Fixed Supported Castellated Steel Beams. IJET. July 2025;10(1):1-8. doi:10.19072/ijet.1642459
Chicago Albayati, Marwan Abdulkareem Shakir, Ahmad Reshad Noori, and Aylin Ece Kayabekir. “Optimization of Fixed Supported Castellated Steel Beams”. International Journal of Engineering Technologies IJET 10, no. 1 (July 2025): 1-8. https://doi.org/10.19072/ijet.1642459.
EndNote Albayati MAS, Noori AR, Kayabekir AE (July 1, 2025) Optimization of Fixed Supported Castellated Steel Beams. International Journal of Engineering Technologies IJET 10 1 1–8.
IEEE M. A. S. Albayati, A. R. Noori, and A. E. Kayabekir, “Optimization of Fixed Supported Castellated Steel Beams”, IJET, vol. 10, no. 1, pp. 1–8, 2025, doi: 10.19072/ijet.1642459.
ISNAD Albayati, Marwan Abdulkareem Shakir et al. “Optimization of Fixed Supported Castellated Steel Beams”. International Journal of Engineering Technologies IJET 10/1 (July 2025), 1-8. https://doi.org/10.19072/ijet.1642459.
JAMA Albayati MAS, Noori AR, Kayabekir AE. Optimization of Fixed Supported Castellated Steel Beams. IJET. 2025;10:1–8.
MLA Albayati, Marwan Abdulkareem Shakir et al. “Optimization of Fixed Supported Castellated Steel Beams”. International Journal of Engineering Technologies IJET, vol. 10, no. 1, 2025, pp. 1-8, doi:10.19072/ijet.1642459.
Vancouver Albayati MAS, Noori AR, Kayabekir AE. Optimization of Fixed Supported Castellated Steel Beams. IJET. 2025;10(1):1-8.

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