ÇELİK LİFLİ BETONARME KİRİŞLERİN EĞİLME DAVRANIŞININ MODELLENMESİ

Abstract

Bu çalışmada, büyük ölçekli ve çelik lif takviyeli betonarme kirişlerin eğilme davranışının modellenmesi incelenmiştir. Araştırmada, Değiştirilmiş Basınç Alanları Teorisi’ ne (DBAT) dayanan doğrusal olmayan bir sonlu elemanlar yöntemi (DOSE) ile analitik bir yöntem kullanılmıştır. Analiz yöntemlerinde çelik liflerin betonarme çekme dayanımına katkısı farklı yaklaşımlarla modellemiştir. İlk yaklaşımda lifli betonun artık çekme dayanımı çatlak genişliği ile ilişkilendirilmiş ve DBAT tabanlı DOSE yöntemine uyarlanmıştır. Analitik yöntemde ise artık çekme dayanımı çatlak genişliğinden bağımsız olarak kabul edilmiştir. Söz konusu analiz yöntemlerinin performansları literatürden seçilen deneysel bir çalışma üzerinde incelenmiştir. Deneysel çalışmada, değişken oranlarda boyuna donatı ve lif içeriğine sahip dört metre uzunluğundaki beş adet betonarme kirişin dört nokta eğilme testleri gerçekleştirilmiştir. Sonuçlar, DBAT tabanlı DOSE yönteminin, seçilen yükleme ve sınır koşullarında büyük ölçekli betonarme eleman davranışını (yük taşıma kapasitesi, çatlak profilleri ve eğilme rijitliği gibi) başarıyla temsil ettiğini göstermiştir. Diğer yandan, analitik metodun, yük taşıma kapasitesini donatı ve lif oranından bağımsız olarak her zaman daha düşük tespit ettiğini ortaya koymuştur. Bu yöntemdeki hata oranının büyük ölçüde çekme donatısı oranına bağlı olduğu açıkça ortaya konmuştur.

Keywords

• Çelik Lifli Betonarme
• Çelik Lif Katkısının Analitik Modellenmesi
• Sonlu Elemanlar Analizi
• Çelik Lifli Betonarme Kiriş Eğilme Davranışı.

MODELING THE BENDING BEHAVIOR OF STEEL FIBER-REINFORCED CONCRETE BEAMS

Abstract

In this study, modeling of the bending behavior of large-scale steel fiber-reinforced concrete beams (SFRC) was investigated using the Modified Compression Field Theory (MCFT) based non-linear finite element (NLFE) method and an analytical method. The two analysis methods included different modeling approaches for the contribution of steel fibers to the tensile strength of reinforced concrete. In the first approach, the residual tensile strength of fibrous concrete was related to the crack width and adopted into the MCTF-based NLFE method. However, the residual tensile strength was free from the crack width in the second approach, which was employed in the analytical method. The capabilities of the mentioned analysis methods were investigated on an experimental study selected from the literature. The experimental study included the four-point bending tests of five four-meter-long simply supported SFRC beams having various ratios of longitudinal reinforcement and fiber content. Results revealed that the MCTF-based NLFE method performed superior in representing the large-scale member responses (such as load-carrying capacity, crack profiles, and flexural stiffness) for the selected loading and boundary conditions while the simplified analytical tool was found to be always conservative in the determination of strength regardless of conventional reinforcement and fiber ratio. However, the rate of error was apparently proven to be highly dependent on the tensile reinforcement ratio.

Keywords

• Steel Fiber-Reinforced Concrete (SFRC)
• Analytical Modeling of Steel Fiber Contribution
• Finite Element Analysis
• Bending Behavior of SFRC Beams.

References

1. American Concrete Institute (ACI) 224R-01, 2001. Control of Cracking in Concrete Structures.
2. Amin A, Foster SJ., 2016. Shear strength of steel fibre reinforced concrete beams with stirrups. Engineering Structures, 111, 323-332.
3. American Concrete Institute (ACI) 544.4R-18, 2018. Guide to Design with Fiber-Reinforced Concrete. Michigan, USA.
4. Arslan G, Keskin RSO, Ulusoy S., 2017. An experimental study on the shear strength of SFRC beams without stirrups”. Journal of Theoretical and Applied Mechanics, 55(4), 1205-1217
5. American Concrete Institute (ACI 544.4R-88), 1988. Design considerations for steel fiber reinforced concrete. Michigan, USA.
6. Campione G., 2008. Simplified flexural response of steel fiber-reinforced concrete beams. Journal of Materials in Civil Engineering, 20(4), 283-293.
7. Collins MP., Mitchell D., 1997. Prestressed concrete structures. Toronto, Canada, Response Publications,
8. Comité Euro International du Béton (CEB/FIP), 1987. Model Code for Concrete Structures, CEB-FIP International Recommendations, Third Edition, Paris, France, 348 pp.

9. Elsaigh WA, Kearsley EP, Robberts JM., 2011. Modeling the behavior of steel-fiber reinforced concrete ground slabs II: Development of slab model. Journal of Transportation Engineering, 137(12), 889-896.
10. EN 1992-1-1:2004, 2004. Eurocode 2: Design of Concrete Structures – Part 1-1: General Rules and Rules for Buildings, 226 pp.
11. Hameed R, Sellier A, Turatsinze A, Duprat F., 2013. Flexural behavior of reinforced fibrous concrete beams: experiments and analytical modelling. Pakistan Journal of Engineering and Applied Sciences, 13, 19-28.
12. Hadi MN., Elbasha N., 2007. Effects of tensile reinforcement ratio and compressive strength on the behavior of over-reinforced helically confined HSC beams. Construction and Building Materials, 21(2):269–76.
13. Hognested E., 1951. Study of combined bending and axial load in reinforced concrete members. Urbana: University of Illinois Engineering Experiment Station, Bulletin series no. 399.
14. Lantsoght EOL., 2018. How do steel fibers improve the shear capacity of reinforced concrete beams without stirrups?. Composites Part B: Engineering, 175.
15. Leutbecher T, Fehling E., 2008. Crack width control for combined reinforcement of rebars and fibers exemplified by ultra-high-performance concrete. Fib Task Group 8.6 Ultra High-Performance Fibre Reinforced Concrete (UHPFRC), 1-28.
16. Lee SC, Cho JY, Vecchio J., 2013. Simplified diverse embedment model for steel fiber-reinforced concrete elements in tension. ACI Materials Journal, 110(4), 403-412.
17. Lee SC, Cho JY, Vecchio FJ., 2016. Analysis of steel fiber-reinforced concrete elements subjected to shear. ACI Structural Journal, 113(2), 275-285.
18. Lee SC, Oh JH, Cho JY., 2015. Compressive Behavior of Fiber-Reinforced Concrete with End-Hooked Steel Fibers. Materials, 8, 1442-1458.
19. Mahmood SMF, Agarwal A, Foster SJ, Valipour H., 2018. Flexural performance of steel fibre reinforced concrete beams designed for moment redistribution. Engineering Structures, 177, 695-706.
20. MATLAB. Programming Software. The MathWorks Inc.
21. Marti P, Pfyl T, Sigrist V, Ulaga T., 1999. Harmonized test procedures for steel fiber reinforced concrete. Materials Journal, 96(6), 676-685.
22. Meda A., Plizzari G, 2004. New design approach for steel fiber-reinforced concrete slabs-on-ground based on fracture mechanics. ACI Structural Journal, 101(3), 298-303..
23. Meda A, Minelli F, Plizzari GA., 2012. Flexural behavior of RC beams in fibre reinforced concrete. Composites Part B: Engineering, 43, 2930-2937.
24. Naaman AE., 2003. Strain hardening and deflection hardening fiber reinforced cement composites. Fourth International Workshop on High Performance Fiber Reinforced Cement Composites, Ann Arbor-USA, 95-113.
25. Palermo, D., Vecchio, F. J., 2004. Compression Field Modeling of Reinforced Concrete Subjected to Reversed Loading: Verification. ACI Structural Journal, 101(2).
26. Plizzari GA, Tiberti G., 2006. Steel fibers as reinforcement for precast tunnel segments. Tunnelling and Underground Space Technology, 21(3-4), 438-439.
27. Saatci S, Batarlar B., 2017. Çelik fiber katkılı etriyesiz betonarme kirişlerin davranışı. Journal of the Faculty of Engineering and Architecture of Gazi University, 32(4), 1143-1154.
28. Shin SW, Ghosh SK, Moreno J., 1989. Flexural ductility of ultra-high-strength concrete members. ACI Structural Journal, 86(4):394–400.
29. Susetyo J, Gauvreau P, Vecchio FJ., 2013. Steel fiber-reinforced concrete panels in shear: analysis and modeling. ACI Structural Journal, 110(2), 285-295.
30. Turkish Standard (TS 500), 2000. Requirements for design and construction of reinforced concrete structures. Ankara, Türkiye.
31. Valle M, Buyukozturk O., 1993. Behaviour of fiber reinforced high-strength concrete under direct shear. Materials Journal, 90(2), 122-133.
32. Vecchio FJ., Palermo D., 2000. NLFEARC: look Both Ways Before Crossing. ACI Fall 2000 Convention.
33. Vecchio FJ., Collins MP., 1986. The Modified Compression Field Theory for reinforced concrete elements subjected to shear. ACI Journal, 83(2), 219-231.
34. Vecchio FJ., 2000. Analysis of shear-critical reinforced concrete beams. ACI Structural Journal, 97(1), 102-110.
35. Vecchio, F. J., Wong, P., S., 2002. VecTor2 & FormWorks User’s Manual
36. Vecchio, F. J., 2002. Contribution of Nonlinear Finite-Element Analysis to Evaluation of Two Structural Concrete Failures, Journal of Performance of Constructed Facilities,16,110-115.
37. Voo JYL, Foster SJ., 2003. Variable engagement model for fibre reinforced concrete in tension. School of civil and environmental Engineering, The University of New South Wales, Sydney, Australia, UNICIV Report, NO. R-420.
38. Xu C, Cao PZ, Wu K, Lin SQ, Yang DG., 2019. Experimental investigation of the behavior composite steel-concrete composite beams containing different amounts of steel fibres and conventional reinforcement. Construction and Building Materials, 202, 23-36.
39. Yaylaci, M., 2016. The investigation crack problem through numerical analysis. Structural Engineering and Mechanics, 57(6), 1143-1156.
40. Yaylaci, M., 2022. Simulate of edge and an internal crack problem and estimation of stress intensity factor through finite element method. Advances in Nano Research , 12(4), 405-414.
41. Yoo DY., Yoon YS., 2015. Structural performance of ultra-high-performance concrete beams with different steel fibers. Engineering Structures, 102:409–23.
42. Zhang, Z., 2020. Finite Element Modelling of Ultra-High Performance Fibre Reinforced Concrete. MSc. Thesis, Graduate Department of Civil Engineering, University of Toronto.