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Journals / El-Cezeri / 2026 / Cilt: 13 Sayı: 2

A New Approach to Determine the Effective Flexural Stiffness of Doubly-Reinforced Beams According to Nonlinear Behavior

Çift Donatılı Kirişlerin Doğrusal Olmayan Davranışına Göre Etkin Eğilme Rijitliğinin Belirlenmesinde Yeni Bir Yaklaşım

Saeid Foroughi(Selcuk University)0000-0002-7556-2118
Bahadır Yüksel(KONYA TEKNİK ÜNİVERSİTESİ)0000-0002-4175-1156
Journal
El-Cezeri
Pages
220–232
Publication Date
2026-05-03
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Analysis results have shown that an important parameter influencing the nonlinear behavior of the sections and the effective stiffness in beams is the reinforcement ratio, which includes concrete strength and compression reinforcement ratios.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Determining the effective stiffness of structural elements made of reinforced concrete with reliability has always been an important subject of research since it provides a reliable estimate of a building's capacity in the case of a seismic event.
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Key Findings & Data:For beam sections, the suggested equation provides values of the effective stiffness coefficient that are reasonably accurate and consistent.
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Conclusion & Impact:Analysis results have shown that an important parameter influencing the nonlinear behavior of the sections and the effective stiffness in beams is the reinforcement ratio, which includes concrete strength and compression reinforcement ratios.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Çift donatılı kiriş · Etkin rijitlik · Moment-eğrilik

Abstract

Determining the effective stiffness of structural elements made of reinforced concrete with reliability has always been an important subject of research since it provides a reliable estimate of a building's capacity in the case of a seismic event. The load-bearing element's design parameters, such as the longitudinal reinforcement ratio and concrete compressive strength, influence the effective stiffness of the cracked section in reinforced concrete structures, even if it is not always constant. In this study, a secure and efficient approach covering all important design parameters is proposed to determine the stiffness coefficient of cracked sections of doubly-reinforced beam models. The proposed equation for the effective stiffness coefficient has been verified by comparisons with moment–curvature relationships and data provided by various researchers and standards, based on numerical results. For beam sections, the suggested equation provides values of the effective stiffness coefficient that are reasonably accurate and consistent. Therefore, it is possible that the results of analytical solutions may differ from each other according to different researchers and standards. Analysis results have shown that an important parameter influencing the nonlinear behavior of the sections and the effective stiffness in beams is the reinforcement ratio, which includes concrete strength and compression reinforcement ratios.

Özet

Betonarme yapı elemanlarının etkin rijitliğinin güvenilir bir şekilde belirlenmesi, sismik bir etki altında binanın kapasitesinin güvenilir bir şekilde tahmin edilmesini sağladığından her zaman önemli bir araştırma konusu olmuştur. Boyuna donatı oranı ve beton basınç dayanımı gibi yük taşıyıcı elemanın tasarım parametreleri, her zaman sabit olmasa bile betonarme yapılarda çatlaklı bölümün etkin rijitliğini etkiler. Bu çalışmada, çift donatılı betonarme kiriş modellerinin çatlamış kesitlerinin rijitlik katsayısının belirlenmesi için tüm önemli tasarım parametrelerini kapsayan, güvenli ve daha hızlı, basit bir denklem önerilmektedir. Etkin rijitlik katsayısı için önerilen tahminler, sayısal sonuçlar temel alınarak çeşitli araştırmacılar ve standartlar tarafından verilen moment–eğrilik ilişkileri ile karşılaştırmalar yapılarak doğrulanmıştır. Kiriş kesitleri için önerilen denklem, makul ölçüde doğru ve tutarlı olan etkili rijitlik katsayısı değerlerini sağlamaktadır. Bu nedenle analitik çözümlerin sonuçları farklı araştırmacılara ve standartlara göre farklılık gösterebilir. Kesitlerin doğrusal olmayan davranışını ve kirişlerdeki etkin rijitliği etkileyen önemli bir parametrenin, beton dayanımı ve basınç donatı oranlarını içeren donatı oranındaki artış olduğu, analiz sonuçlarından elde edilmiştir.

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Cite This Article

Foroughi, S., Yüksel, B. (2026). A New Approach to Determine the Effective Flexural Stiffness of Doubly-Reinforced Beams According to Nonlinear Behavior. El-Cezeri, Cilt: 13 Sayı: 2, 220–232. https://doi.org/10.31202/ecjse.1783406

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References (36)

  1. Kumbasar N., Bending stiffness of reinforced concrete sections, Teknik Dergi, 2015, 26(4), pp. 7265–7278.
  2. Foroughi S. and Yüksel S.B., Moment-curvature and effective section stiffness of reinforced concrete beams, Journal of Polytechnic, 2023, 26(1), pp. 169–177, DOI: 10.2339/politeknik.945426.
  3. Foroughi S., Jamal R. and Yüksel B., Effect of transverse reinforcement and axial load level on curvature ductility and effective section stiffness of reinforced concrete columns, El-Cezeri, 2020, 7(3), pp. 1309–1319, DOI: 10.31202/ecjse.750775.
  4. Caglar N., Demir A., Ozturk H. and Akkaya A., A simple formulation for effective flexural stiffness of circular reinforced concrete columns, Engineering Applications of Artificial Intelligence, 2015, 38, pp. 79–87, DOI: 10.1016/j.engappai.2014.10.011.
  5. Aliasghar-Mamaghani M. and Khaloo A., Effective flexural stiffness of beams reinforced with FRP bars in reinforced concrete moment frames, Journal of Composites for Construction, 2021, 25(1), DOI: 10.1061/(ASCE)CC.1943-5614.0001101.
  6. Celep Z., Nonlinear behavior and analysis of reinforced concrete structural systems: Concepts of Turkish earthquake code (2007), Beta Basım Yayım, 2017, ISBN: 9789752957145. 2017.
  7. Ashour S.A., Effect of compressive strength and tensile reinforcement ratio on flexural behaviour of high strength concrete beams, Engineering Structures, 2000, 22, pp. 413–423, DOI: 10.1016/S0141-0296(98)00135-7.
  8. Paulay T. and Priestley M.J.N., Seismic design of reinforced concrete and masonry buildings, John Wiley & Sons, 1992, DOI:10.1002/9780470172841
  9. Mehanny S.S.F., Kuramoto H. and Deierlein G.G., Stiffness modelling of RC beam-columns for frame analysis, ACI Structural Journal, 2001, 98(2), pp. 215–225, DOI: 10.14359/10190
  10. Panagiotakos T.B. and Fardis M.N., Deformations of reinforced concrete members at yielding and ultimate, ACI Structural Journal, 2001, 98(2), pp. 135–148, DOI: 10.14359/10181
  11. Kumar R. and Singh Y., Stiffness of reinforced concrete frame members for seismic analysis, ACI Structural Journal, 2010, 107(5), pp. 607–615.
  12. Shanfigh P., Hassanpour M., Razavi S.V. and Kobrae M., An investigation of the flexural behaviour of reinforced lightweight concrete beams, International Journal of Physical Sciences, 2011, 6(10), pp. 2414–2421, DOI: 10.5897/IJPS10.550.
  13. Pan Z., Li B. and Lu Z., Effective shear stiffness of diagonally cracked RC beams, Engineering Structures, 2014, 59, pp. 95–103, DOI: 10.1016/j.engstruct.2013.10.023.
  14. Attia M.M., Flexural behavior of strengthened concrete beams with different techniques: Experimental and numerical results, Construction and Building Materials, 2023, 367, 130277, DOI: 10.1016/j.cscm.2023.e01862.
  15. Bashour M., El-Metwally S.E. and Haroun M., Nonlinear behavior study of reinforced concrete coupling beams, Structural Concrete, 2023, 24(4), pp. 2175–2190, DOI: 10.1155/2023/8288308.
  16. El-Gohary H.A., Refined nonlinear estimation of effective flexural rigidity in reinforced concrete beams using curvature integration, Engineering, Technology & Applied Science Research, 2025, 15(2), pp. 13343–13350, DOI: 10.48084/etasr.10503.
  17. Imamović D., Analysing flexural response in RC beams: A closed-form analytical approach integrating moment-curvature and code provisions, Mathematics, 2024, 12(6), 980, DOI: 10.3390/math12213327.
  18. Lofty E.A. and Hassan A.M., Experimental flexural investigation of doubly reinforced concrete beams with hybrid steel truss reinforcement, Innovative Infrastructure Solutions, 2024, 9(1), 27, DOI: 10.1617/s11527-024-02389-9.
  19. Issa M.A.M. and El-Refaie A.A., Performance of doubly reinforced concrete beams with hybrid GFRP–steel reinforcement: Experimental and numerical study, Journal of Building Materials and Structures, 2024, 11(1), pp. 1–15, DOI: 10.1515/jmbm-2022-0308.
  20. Taher H.M.A. and Ali M., Nonlinear finite element analysis of RC beams with different detailing and openings, Civil and Environmental Engineering Reports, 2024, 34(1), pp. 101–116, DOI: 10.1515/eng-2024-0074
  21. Turkish Building Earthquake Code (TBEC), Turkish Building Earthquake Code: Specifications for Building Design under Earthquake Effects, T.C. Bayındırlık ve İskan Bakanlığı, Ankara, 2018.
  22. ASCE/SEI 41-17, Seismic Evaluation and Retrofit of Existing Buildings, Published by The American Society of Civil Engineers, Reston, Virginia, p. 20191-4382, USA, 2017.
  23. ACI 318.,2014. “Building code requirements for reinforced concrete and commentary,” American Concrete Institute Committee, ISBN: 978-0-87031- 930-3.
  24. Eurocode 8., Design of structures for earthquake resistance: Part 3: Assessment and retrofitting of buildings, BS EN 1998-3, CEN, 2005.
  25. Eurocode 8., Design of structures for earthquake resistance: Part 1: General rules, seismic actions and rules for buildings, BS EN 1998-1:2004.
  26. Eurocode 2., Design of concrete structures: Part 1-1: General rules and rules for buildings”, BS EN 1992-1-1:2004.
  27. Avşar Ö., Bayhan B. and Yakut A., Effective flexural rigidities for ordinary reinforced concrete columns and beams, The Structural Design of Tall and Special Buildings, 2014, 23, pp. 463–482, DOI: 10.1002/tal.1056.
  28. Biskinis D.E., Resistance and deformation capacity of concrete members with or without retrofitting, Doctoral Thesis, Civil Engineering Department, University of Patras, Patras, GR. 2007.
  29. Biskinis D.E. and Fardis M.N., Cyclic strength and deformation capacity of RC members, including members retrofitted for earthquake resistance in: Walraven J et al. (ed) 5th International Ph.D. Symposium in Civil Engineering, Balkema, Rotterdam, 2004, pp. 1125–1133.
  30. SAP2000. Structural Software for Analysis and Design, Computers and Structures, Inc, USA.
  31. Micelli F., Candido L., Leone M. and Maria A.A., Effective stiffness in regular reinforced concrete frames subjected to seismic loads, Earthquakes and Structures, 2015, 9(3), pp. 481–501, DOI: 10.12989/eas.2015.9.3.481.
  32. Foroughi S. and Yüksel S.B., Investigation of nonlinear behavior of reinforced concrete columns for different confined concrete models, Politeknik Dergisi, 2022, 25(4), pp. 1447–1462, DOI: 10.2339/politeknik.930774.
  33. Foroughi S. and Yüksel S.B., Investigation of shear strength and deformation capacity models of reinforced concrete circular columns, Turkish Journal of Earthquake Research, 2022, 4(1), pp. 26–41, DOI: 10.46464/tdad.1008476.
  34. Foroughi S., Jamal R. and Yüksel B., Investigation of stress-strain behavior of confined concrete according to TBEC 2018 and Mander model, ECJSE, 2021, 8(1), pp. 363–375, DOI: 10.31202/ecjse.788121.
  35. Mander J.B., Priestley M.J.N. and Park R., Theoretical stress-strain model for confined concrete, Journal of Structural Engineering, 1988, 114(8), pp. 1804–1826, DOI: 10.1061/(ASCE)0733-9445(1988)114:8(1804).
  36. TS500, Requirements for Design and Construction of Reinforced Concrete Structures, Turkish Standards Institute, Ankara, Turkey, 2000.