Comprehensive analysis of stability and strength of thin-walled reinforced concrete elements based on energy approaches
DOI:
https://doi.org/10.26906/znp.2025.65.4197Keywords:
thin-walled reinforced concrete beam, stability of the plane form of bending, energy invariant, torsional stiffness, critical momentAbstract
This work develops and substantiates a comprehensive engineering method for the analysis of thin-walled reinforced concrete beams with a cross-sectional width of b = 40 mm, which unifies the verification of the stability of the plane form of bending and the evaluation of torsional deformability. The relevance of the research is driven by the need to refine the limit states for elements with a depth-to-width ratio of h/b ≈ 5.5, where classical methods fail to fully account for the interaction between flexural and torsional stiffness in the cracked stage. The methodological basis of the study is the energy invariance hypothesis, allowing the replacement of a real cracked reinforced concrete element with an equivalent elastic model accumulating similar potential strain energy. The paper combines a modified Prandtl-Vlasov algorithm for determining the critical buckling moment with an analytical model of torsional compliance accounting for discrete crack distribution. A key feature of the methodology is the detailed consideration of the dowel action of the longitudinal reinforcement, treated as a beam on an elastic foundation, which provides resistance to the mutual shear displacement of crack faces and significantly influences the effective torsional stiffness, GJeff.
A comparative analysis established that increasing the width to 40 mm leads to an almost twofold increase in the out-of-plane moment of inertia, Iy, and the critical moment, Mcr. It is proven that such a change in geometry shifts the structural behavior from the risk zone of sudden (brittle) buckling, characteristic of narrower beams, to the zone of plastic failure along the normal section, where the stability safety factor exceeds unity. Furthermore, adjusted values of the reduction factor, kred, are proposed, accounting for the decreased sensitivity of the wider cross-section to initial geometric imperfections and concrete creep deformations
References
1. Azizov, T. N., & Kochkarov, D. V. (2022). Calculation of statically indeterminate reinforced concrete systems considering crack formation. Bulletin of the National University of Water and Environmental Engineering, 98(2), 39–48. https://doi.org/10.31713/vt220224
2. Azizov, T. N., Orlova, O. V., & Nahaichuk, O. V. (2019). Limits of application of nonlinear calculation methods for composite beams and proposals for their use in construction. Scientific Notes of V. I. Vernadsky Taurida National University. Series: Technical Sciences, 30(69, 2, Part 2), 193–198.
3. Babych, Y. M., & Babych, V. Y. (2017). Calculation and design of reinforced concrete beams (2nd ed., revised and expanded). Rivne: National University of Water and Environmental Engineering.
4. Hudz, S. A., & Hasenko, A. V. (2018). Influence of the stiffness of connected structures on beam stability. In Ways of improving construction efficiency under market relations formation (Issue 35, pp. 114–123). Kyiv: Kyiv National University of Construction and Architecture.
https://doi.org/10.32347/2707-501x.2018.35.114-123
5. State Building Norms of Ukraine DBN B.2.6-98:2009. (2009). Concrete and reinforced concrete structures. Basic provisions.
6. DSTU-N B EN 1992-1-1:2010. (2010). Eurocode 2: Design of concrete structures. Part 1–1: General rules and rules for buildings (EN 1992-1-1:2004, IDT).
7. Kochkarov, D. V. (2017). Engineering methods for calculating statically indeterminate reinforced concrete bar systems. Collection of Scientific Works of the Ukrainian State University of Railway Transport, 170, 98–104. https://doi.org/10.18664/1994-7852.170.2017.111301
8. Melnyk, O. V. (2016). Stiffness and strength of box-shaped reinforced concrete elements with normal cracks under torsional deformation. Uman: Sochinskyi Publishing.
9. Pavlikov, A. M., & Kochkarov, D. V. (2019). Reinforced concrete structures: Practical methods of calculation and design. Poltava: ASMI LLC.
10. Perelmuter, A. V. (2024). Some features of nonlinear calculations in structural design systems. Strength of Materials and Theory of Structures, 113, 183–194. https://doi.org/10.32347/2410-2547.2024.113.183-194
11. Romashko, V. M. (2011). Some features of determining the moment of formation of normal cracks in concrete elements. Resource-Efficient Materials, Structures, Buildings and Constructions, 21, 317–322.
12. Azizov, T., & Pereiras, R. (2022). Consideration of torsional rigidity in the calculation of plates using beam approximation. Sciences of Europe, 1(87), 58–61. https://doi.org/10.24412/3162-2364-2022-87-1-58-61
13. Gvozdev, A. A., & Karpenko, N. I. (1965). Work of reinforced concrete with cracks in a flat stress state. Building Mechanics and Design, 2, 20–23.
14. Kochkarev, D., Azizov, T., & Galinska, T. (2018). Bending deflection reinforced concrete elements determination. MATEC Web of Conferences. https://doi.org/10.1051/matecconf/201823002012
15. McCormac, J. C., & Brown, R. H. (2015). Design of reinforced concrete (10th ed.). Wiley.
16. Timoshenko, S. P., & Goodier, J. N. (1970). Theory of elasticity (3rd ed.). McGraw-Hill.
17. Timoshenko, S. P., & Woinowsky-Krieger, S. (1959). Theory of plates and shells (2nd ed.).
18. McGraw-Hill. Wight, J. K., & MacGregor, J. G. (2011). Reinforced concrete: Mechanics and design. Pearson Education.
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