EVALUATION OF DEFLECTION PERFORMANCE OF SIZING-OPTIMIZED COLD-FORMED STEEL BEAMS WITH VARIOUS CROSS-SECTIONS

Öz

Strength-based optimization of cold-formed steel (CFS) sections is a common strategy to enhance material efficiency, but it often results in slender profiles where serviceability performance is a concern. This study investigates the deflection performance of three distinct CFS profiles—a lipped channel, an unlipped channel, and a built-up I-section—after they were sizing-optimized (via parametric scaling) for strength limit states according to AISI S100-16. The final optimized dimensions for both secondary beams and girders were evaluated against the serviceability criteria of the International Building Code. A numerical analysis based on the conjugate beam method was employed, which accurately accounts for the variable effective moment of inertia along the beams’ spans. The results demonstrate that all six optimized sections comfortably satisfy the deflection limits for both live load (L) and total load (D+L) conditions. A comparative analysis revealed that while the lipped channel section was the most materially efficient, it exhibited greater, though still acceptable, deflections compared to the heavier unlipped and I-sections. This study contributes by quantitatively demonstrating that CFS beams optimized solely for AISI S100-16 strength limits can inherently satisfy IBC serviceability criteria, confirming the viability of this optimization approach in practical floor design. The findings confirm that a well-executed strength optimization does not compromise serviceability and that the lipped channel section provides an optimal balance between material economy and structural performance for the floor system studied.

Anahtar Kelimeler

• Cold-Formed Steel
• Deflection
• Serviceability Limit State
• Section Optimization
• Effective Moment of Inertia

Çeşitli Enkesitli Boyut Optimizasyonu Yapılmış Soğukta Şekil Verilmiş Çelik Kirişlerin Sehim Performansının Değerlendirilmesi

Öz

Soğukta şekil verilmiş çelik (SŞVÇ) kesitlerin dayanım esaslı optimizasyonu, malzeme verimliliğini artırmak için yaygın bir stratejidir, ancak bu durum genellikle kullanılabilirlik performansının kritik hale geldiği narin profillerle sonuçlanır. Bu çalışma, AISI S100-16’ya göre dayanım sınır durumları için (parametrik ölçeklendirme yoluyla) boyut optimizasyonu yapıldıktan sonra üç farklı SŞVÇ profilinin— dudaklı C, dudaksız C ve birleşik I-kesit—sehim performansını incelemektedir. Hem tali kirişler hem de ana kirişler için optimizasyon sonucu elde edilen boyutlar, Uluslararası Yapı Yönetmeliği’nin kullanılabilirlik kriterlerine göre değerlendirilmiştir. Kirişlerin açıklıkları boyunca değişken olan etkin atalet momentini hassas bir şekilde hesaba katan, eşlenik kiriş yöntemine dayalı sayısal bir analiz gerçekleştirilmiştir. Sonuçlar, altı optimize edilmiş kesitin tamamının hem hareketli yük (L) hem de toplam yük (D+L) koşulları için sehim sınırlarını rahatlıkla sağladığını göstermektedir. Yapılan karşılaştırmalı analizde, dudaklı C kesitinin malzeme açısından en verimli olmasına rağmen, daha ağır olan dudaksız C ve I-kesitlere kıyasla daha büyük, ancak yine de kabul edilebilir, sehimler oluşturduğu görülmüştür. Bu çalışma, yalnızca AISI S100-16 dayanım sınırlarına göre optimize edilmiş SŞVÇ kirişlerin, IBC kullanılabilirlik kriterlerini kendiliğinden karşılayabildiğini kantitatif olarak göstererek bu optimizasyon yaklaşımının pratik döşeme tasarımındaki uygulanabilirliğini doğrulamaktadır. Bulgular, etkin bir dayanım optimizasyonunun kullanılabilirliği tehlikeye atmadığını ve dudaklı C kesitinin, incelenen döşeme sistemi için malzeme ekonomisi ve yapısal performans arasında en uygun dengeyi sağladığını doğrulamaktadır.

Anahtar Kelimeler

• Soğukta Şekil Verilmiş Çelik
• Sehim
• Kullanılabilirlik Sınır Durumu
• Kesit Optimizasyonu
• Etkin Atalet Momenti

Kaynakça

1. AbouHamad, M., & Abu-Hamd, M. (2019). Framework for construction system selection based on life cycle cost and sustainability assessment. Journal of Cleaner Production, 241, 118397. https://doi.org/10.1016/j.jclepro.2019.118397
2. Thirunavukkarasu, K., Kanthasamy, E., Gatheeshgar, P., Poologanathan, K., Rajanayagam, H., Suntharalingam, T., & Dissanayake, M. (2021). Sustainable performance of a modular building system made of built-up cold-formed steel beams. Buildings, 11(10), 460. https://doi.org/10.3390/buildings11100460
3. Liang, H., Roy, K., Fang, Z., & Lim, J. B. P. (2022). A critical review on optimization of cold-formed steel members for better structural and thermal performances. Buildings, 12(1), 34. https://doi.org/10.3390/buildings12010034
4. Sheta, A., Ma, X., Zhuge, Y., ElGawady, M. A., Mills, J. E., Singh, A., & Abd-Elaal, E.-S. (2021). Structural performance of novel thin-walled composite cold-formed steel/PE-ECC beams. Thin-Walled Structures, 162, 107586. https://doi.org/10.1016/j.tws.2021.107586
5. Marrone, G., Imperadori, M., & Sesana, M. M. (2023). Life-cycle assessment of light steel frame buildings: A systematic literature review. In Life-Cycle of Structures and Infrastructure Systems (pp. 2405–2412). CRC Press. https://doi.org/10.1201/9781003323020-293
6. Tavares, V., Soares, N., Raposo, N., Marques, P., & Freire, F. (2021). Prefabricated versus conventional construction: Comparing life-cycle impacts of alternative structural materials. Journal of Building Engineering, 41, 102705. https://doi.org/10.1016/j.jobe.2021.102705
7. Lawson, R. M., & Richards, J. (2010). Modular design for high-rise buildings. Proceedings of the Institution of Civil Engineers - Structures and Buildings, 163(3), 151–164. https://doi.org/10.1680/stbu.2010.163.3.151
8. Schafer, B. W. (2011). Cold‐formed steel structures around the world. Steel Construction, 4(3), 141–149. https://doi.org/10.1002/stco.201110019

9. Rukavina, M. J., Skejić, D., Kralj, A., Ščapec, T., & Milovanović, B. (2022). Development of lightweight steel framed construction systems for nearly-zero energy buildings. Buildings, 12(7), 929. https://doi.org/10.3390/buildings12070929
10. Ádány, S., & Schafer, B. W. (2008). A full modal decomposition of thin-walled, single-branched open cross-section members via the constrained finite strip method. Journal of Constructional Steel Research, 64(1), 12–29. https://doi.org/10.1016/j.jcsr.2007.04.004
11. Peng, Z., Yang, Y., Zhang, L., Xiong, W., & Cai, Y. (2025). A review on the buckling behavior of cold-formed thin-walled steel members. Mechanics of Solids, 60(2), 1469–1484. https://doi.org/10.1134/S0025654425600710
12. Ayhan, D., & Schafer, B. W. (2015). Cold-formed steel member bending stiffness prediction. Journal of Constructional Steel Research, 115, 148–159. https://doi.org/10.1016/j.jcsr.2015.07.004
13. Rasmussen, K. J. R. (2023). Stiffness reduction of cold-formed steel structures subject to sectional buckling and yielding. Journal of Structural Engineering, 149(11). https://doi.org/10.1061/JSENDH.STENG-12655
14. Mojtabaei, S. M., Hajirasouliha, I., & Becque, J. (2021a). Optimized design of cold‐formed steel elements for serviceability and ultimate limit states. Ce/Papers, 4(2–4), 481–486. https://doi.org/10.1002/cepa.1319
15. Mojtabaei, S. M., Ye, J., & Hajirasouliha, I. (2019). Development of optimum cold-formed steel beams for serviceability and ultimate limit states using Big Bang-Big Crunch optimisation. Engineering Structures, 195, 172–181. https://doi.org/10.1016/j.engstruct.2019.05.089
16. Gossen, P. A. (n.d.). Stiffness versus strength. https://www.structuremag.org/article/stiffness-versus-strength/
17. Lim, J. B. P., & Nethercot, D. A. (2003). Serviceability design of a cold-formed steel portal frame having semi-rigid joints. Steel and Composite Structures, 3(6), 451–474. https://doi.org/10.12989/scs.2003.3.6.451
18. Phan, D. T., Lim, J. B. P., Tanyimboh, T. T., Lawson, R. M., Xu, Y., Martin, S., & Sha, W. (2013). Effect of serviceability limits on optimal design of steel portal frames. Journal of Constructional Steel Research, 86, 74–84. https://doi.org/10.1016/j.jcsr.2013.03.001
19. Ye, J., Hajirasouliha, I., Becque, J., & Pilakoutas, K. (2016a). Development of more efficient cold-formed steel channel sections in bending. Thin-Walled Structures, 101, 1–13. https://doi.org/10.1016/j.tws.2015.12.021
20. Leng, J., Guest, J. K., & Schafer, B. W. (2011). Shape optimization of cold-formed steel columns. Thin-Walled Structures, 49(12), 1492–1503. https://doi.org/10.1016/j.tws.2011.07.009
21. Parastesh, H., Mohammad Mojtabaei, S., Taji, H., Hajirasouliha, I., & Bagheri Sabbagh, A. (2021). Constrained optimization of anti-symmetric cold-formed steel beam-column sections. Engineering Structures, 228, 111452. https://doi.org/10.1016/j.engstruct.2020.111452
22. Parastesh, H., Hajirasouliha, I., Taji, H., & Bagheri Sabbagh, A. (2019). Shape optimization of cold-formed steel beam-columns with practical and manufacturing constraints. Journal of Constructional Steel Research, 155, 249–259. https://doi.org/10.1016/j.jcsr.2018.12.031
23. Mojtabaei, S. M., Becque, J., & Hajirasouliha, I. (2021b). Structural size optimization of single and built-up cold-formed steel beam-column members. Journal of Structural Engineering, 147(4). https://doi.org/10.1061/(ASCE)ST.1943-541X.0002987
24. Ye, J., Hajirasouliha, I., Becque, J., & Eslami, A. (2016b). Optimum design of cold-formed steel beams using Particle Swarm Optimisation method. Journal of Constructional Steel Research, 122, 80–93. https://doi.org/10.1016/j.jcsr.2016.02.014
25. Fourie, P. C., & Groenwold, A. A. (2002). The particle swarm optimization algorithm in size and shape optimization. Structural and Multidisciplinary Optimization, 23(4), 259–267. https://doi.org/10.1007/s00158-002-0188-0
26. Gatheeshgar, P., Poologanathan, K., Gunalan, S., Nagaratnam, B., Tsavdaridis, K. D., & Ye, J. (2020). Structural behaviour of optimized cold‐formed steel beams. Steel Construction, 13(4), 294–304. https://doi.org/10.1002/stco.201900024
27. Svanberg, K. (1987). The method of moving asymptotes—a new method for structural optimization. International Journal for Numerical Methods in Engineering, 24(2), 359–373. https://doi.org/10.1002/nme.1620240207
28. Phan, D. T., Mojtabaei, S. M., Hajirasouliha, I., Ye, J., & Lim, J. B. P. (2020). Coupled element and structural level optimisation framework for cold-formed steel frames. Journal of Constructional Steel Research, 168, 105867. https://doi.org/10.1016/j.jcsr.2019.105867
29. Akchurin, D., Ding, C., Xia, Y., Blum, H., Schafer, B. W., & Li, Z. (2022). Optimization of cold-formed steel members considering reduced stiffness and strength due to cross-sectional instabilities. Proceedings of the Structural Stability Research Council-Proceedings of the 2022 Annual Stability Conference, Denver, CO, USA, 22–25.
30. Akchurin, D., Ding, C., Xia, Y., Blum, H. B., Schafer, B. W., & Li, Z. (2023). Instability-driven family optimization of cold-formed steel lipped-channel cross-sections with strength and stiffness constraints. Thin-Walled Structures, 192, 111118. https://doi.org/10.1016/j.tws.2023.111118
31. Ayhan, D., & Schafer, B. W. (2012). Characterization of moment-rotation response of cold-formed steel beams. Annual Stability Conference, Structural Stability Research Council.
32. American Iron and Steel Institute. (2022). North American specification for the design of cold-formed steel structural members (AISI S100-16 (2020) w/S3-22). https://www.buildusingsteel.org/wp-content/uploads/2023/06/AISI-S100-16-2020-wS3-22.pdf
33. Mahar, A. M., Jayachandran, S. A., & Mahendran, M. (2022). Design of locally buckling cold-formed steel built-up columns formed by unlipped channel sections. Thin-Walled Structures, 174, 109132. https://doi.org/10.1016/j.tws.2022.109132
34. Schafer, B. W. (2019). Advances in the direct strength method of cold-formed steel design. Thin-Walled Structures, 140, 533–541. https://doi.org/10.1016/j.tws.2019.03.001
35. Phan, D. K., & Rasmussen, K. J. R. (2019). Flexural rigidity of cold-formed steel built-up members. Thin-Walled Structures, 140, 438–449. https://doi.org/10.1016/j.tws.2019.03.051
36. Deng, F., He, Y., Deng, L., & Zhong, W. (2022). Experimental and numerical study on the flexural behavior of cold-formed steel multi-limb built-up section beams. Buildings, 12(10), 1639. https://doi.org/10.3390/buildings12101639
37. Rasmussen, K. J. R., Khezri, M., Zhang, H., & Schafer, B. W. (2025). Recent research on built-up cold-formed steel structures. Thin-Walled Structures, 215, 113546. https://doi.org/10.1016/j.tws.2025.113546
38. Ananthi, G. B. G., Srivardhini, M. S., & Deepak, M. S. (2024). Optimization of cold-formed steel perforated sections subjected to bending (pp. 343–361). https://doi.org/10.1007/978-3-031-72527-2_27
39. Abdel-Rahman, N., & Sivakumaran, K. S. (1998). Effective design width for perforated cold-formed steel compression members. Canadian Journal of Civil Engineering, 25(2), 319–330. https://doi.org/10.1139/cjce-25-2-319
40. International Codes Council. (2018). International Building Code. https://www.iccsafe.org/products-and-services/i-codes/2018-i-codes/ibc/
41. American Society for Testing and Materials. (2019). Standard specification for carbon structural steel (ASTM A36/A36M-19). https://store.astm.org/a0036_a0036m-19.html
42. İnşaat Mühendisleri Odası. (2017). Yapı malzemeleri ve yapı kısımlarının birim hacim ağırlıkları [Unit volume weights of building materials and building parts]. https://www.imo.org.tr/resimler/dosya_ekler/f7deb880ca6b4b7_ek.pdf
43. Özçe Demir Çelik. (2014). Galvanizli / trapez sac boyutları ve ağırlıkları [Galvanized / trapezoidal sheet dimensions and weights]. https://www.ozcedemir.com.tr/galvanizli_saclar-s59.html
44. Celep, Z. (2022). Betonarme yapılar [Reinforced concrete structures] (12th ed.). Zekai Celep.
45. Türk Standartları Enstitüsü. (2024). Yapı elemanlarının boyutlandırılmasında alınacak yüklerin hesap değerleri (TS 498/T3) [Calculation values of loads to be taken in the dimensioning of building elements (TS 498/T3)]. https://intweb.tse.org.tr/Standard/Standard/Standard.aspx?081118051115108051104119110104055047105102120088111043113104073100097112047071071086090066043110
46. American Society of Civil Engineers. (2022). Minimum design loads and associated criteria for buildings and other structures (ASCE/SEI 7-22). https://ascelibrary.org/doi/book/10.1061/9780784415788
47. Bischoff, P. H. (2005). Reevaluation of Deflection Prediction for Concrete Beams Reinforced with Steel and Fiber Reinforced Polymer Bars. Journal of Structural Engineering, 131(5), 752–767. https://doi.org/10.1061/(ASCE)0733-9445(2005)131:5(752)