Probabilistic Assessment of Bending Strength of Statically Indeterminate Reinforced Concrete Beams

Document Type : Original Article

Author

Faculty of Civil Engineering, University of Architecture Ho Chi Minh City, HCMC, Vietnam

Abstract

This paper presents a reliability analysis of a two-span reinforced concrete beam, taking into account of random variations in cross-sectional dimensions, area and position of reinforcement for sagging and hogging bending moments, material strengths, loads and model uncertainties. In addition, the limit state functions for the statically indeterminate beam were derived; considering the static equilibrium requirement after the moments were redistributed as well as the codified allowable limit for the adjusted moment at each beam section. A large number of Monte Carlo simulations were performed in which the basic variables were modeled with normal, lognormal and Gumbel distributions. When the elastic moment distribution was used in evaluating the beam reliability, the two-span beam behaved as a series system with three critical nodes located at the interior support and midspan sections. The probability that the system had at least one overloaded node was greater than the failure probability of an individual node. However, considering moment redistribution made it possible to reduce the amount of reinforcement whilst maintaining the reliability of the beam. When the reinforcement area was reduced by 26% at the support section or 14% at the midspan sections, the failure probability was predicted to be 6.90´10-5, which is deemed acceptable for a 50 year reference period.

Keywords

Main Subjects


  1. EN 1992-1-1:2004, “Eurocode 2 - Design of Concrete Structures, Part 1-1: General Rules and Rules for Buildings”, Brussels, European Committee for Standardization, (2004).
  2. ISO 2394:2015, “General principles on reliability for structures”, Geneva, International Standards Organization, (2015).
  3. Melchers, R.E. and Beck, A.T., “Structural reliability analysis and prediction”, New Jersey, John Wiley & Sons, (2018).
  4. EN 1990:2002, “Eurocode - Basis of structural design”, Brussels, European Committee for Standardization, (2005).
  5. Ghanooni-Bagha, M., Shayanfar, M.A., Reza-Zadeh, O. and Zabihi-Samani, M., "The effect of materials on the reliability of reinforced concrete beams in normal and intense corrosions", Maintenance and Reliability, Vol. 19, No. 3, (2017), 393-402, doi: 10.17531/ein.2017.3.10.
  6. Shahnewaz, M., Rteil, A. and Alam, M.S., "Shear strength of reinforced concrete deep beams–a review with improved model by genetic algorithm and reliability analysis", Structures, Vol. 23, (2020), 494-508, doi: 10.1016/j.istruc.2019.09.006.
  7. Fadaee, M.J. and Dehghani, H., "Reliability-based torsional design of reinforced concrete beams strengthened with CFRP laminate", International Journal of Engineering, Transactions A: Basics, Vol. 26, No. 10, (2013), 1103-1110, doi: 10.5829/idosi.ije.2013.26.10a.01.
  8. Khmil, R., Tytarenko, R., Blikharskyy, Y. and Vegera, P., "Development of the procedure for the estimation of reliability of reinforced concrete beams, strengthened by building up the stretched reinforcing bars under load", Eastern-European Journal of Enterprise Technologies, Vol. 5, No. 7, (2018), 32-42, doi: 10.15587/1729-4061.2018.142750.
  9. Arshian, A.H. and Morgenthal, G., "Probabilistic assessment of the ultimate load-bearing capacity in laterally restrained two-way reinforced concrete slabs", Engineering Structures, Vol. 150, (2017), 52-63, doi: 10.1016/j.engstruct.2017.07.035.
  10. Heidari, M., Robert, F., Lange, D. and Rein, G., "Probabilistic study of the resistance of a simply-supported reinforced concrete slab according to Eurocode parametric fire", Fire Technology, Vol. 55, No. 4, (2019), 1377-1404, doi: 10.1007/s10694-018-0704-4.
  11. Shahpari, A. and Yazdani, A., "The use of monte-carlo simulations in seismic hazard analysis in Tehran and surrounding areas", International Journal of Engineering, Transactions C: Aspects, Vol. 25, No. 2, (2012), 159-166, doi: 10.5829/idosi.ije.2012.25.02c.9.
  12. Razmkhah, M.H., Kouhestanian, H., Shafaei, J., Pahlavan, H. and Shamekhi Amiri, M., "Probabilistic seismic assessment of moment resisting steel buildings considering soft-story and torsional irregularities", International Journal of Engineering, Transactions B: Applications, Vol. 34, No. 11, (2021), 2476-2493, doi: 10.5829/IJE.2021.34.11B.11.
  13. Scott, R. and Whittle, R., "Moment redistribution effects in beams", Magazine of Concrete Research, Vol. 57, No. 1, (2005), 9-20, doi: 10.1680/macr.2005.57.1.9.
  14. Do Carmo, R.N. and Lopes, S.M., "Ductility and linear analysis with moment redistribution in reinforced high-strength concrete beams", Canadian Journal of Civil Engineering, Vol. 32, No. 1, (2005), 194-203, doi: 10.1139/l04-080.
  15. Lou, T., Peng, C., Karavasilis, T.L., Min, D. and Sun, W., "Moment redistribution versus neutral axis depth in continuous PSC beams with external CFRP tendons", Engineering Structures, Vol. 209, (2020), 109927, doi: 10.1016/j.engstruct.2019.109927.
  16. Farouk, M.A. and Khalil, K.F., "New analytical method for computing moment redistribution in RC beams under concentrated load", Australian Journal of Structural Engineering, Vol. 22, No. 2, (2021), 120-139, doi: 10.1080/13287982.2021.1912518.
  17. Sturm, A.B., Visintin, P. and Oehlers, D.J., "Closed‐form expressions for predicting moment redistribution in reinforced concrete beams with application to conventional concrete and ultrahigh performance fiber reinforced concrete", Structural Concrete, Vol. 21, No. 4, (2020), 1577-1596, doi: 10.1002/suco.201900498.
  18. 18. Jukić, M., Brank, B. and Ibrahimbegović, A., “Embedded discontinuity finite element formulation for failure analysis of planar reinforced concrete beams and frames”, Engineering Structures, Vol. 50, (2013), 115-125, doi: 10.1016/j.engstruct.2012.07.028.
  19. Earij, A., Alfano, G., Cashell, K. and Zhou, X., “Nonlinear three–dimensional finite–element modelling of reinforced–concrete beams: Computational challenges and experimental validation”, Engineering Failure Analysis, Vol. 82, (2017), 92-115, doi: 10.1016/j.engfailanal.2017.08.025.
  20. Słowik, M., 2019. The analysis of failure in concrete and reinforced concrete beams with different reinforcement ratio. Archive of Applied Mechanics, Vol. 89, No. 5, (2019), 885-895. doi: 10.1007/s00419-018-1476-5.
  21. AS 3600:2018, “Concrete Structures”, Sydney, Standards Australia Limited, (2018).
  22. CSA A23.3:2019, “Design of Concrete Structures”, Rexdale, Canadian Standards Association, (2019).
  23. ACI 318-19, “Building Code Requirements for Structural Concrete and Commentary”, Michigan, American Concrete Institute, (2019).
  24. Markova, J., Sousa, M., Dimova, S., Athanasopoulou, A., Iannaccone, S. and Pinto, A., “Reliability of structural members designed with the Eurocodes NDPs selected by EU and EFTA member states”, EUR 29410 EN Publication by European commission and joint research centre, (2018).
  25. Hibbeler, R.C., “Structural analysis”, 10th ed, Upper Saddle River, Pearson Prentice Hall, (2017).
  26. MathWorks, “MATLAB R2015a”, Massachusetts, The MathWorks Inc., (2015).
  27. 27. Ehsani, R., Sharbatdar, M.K. and Kheyroddin, A., “Ductility and moment redistribution capacity of two-span RC beams”, Magazine of Civil Engineering, Vol. 90, No. 6, (2019), 104-118. doi: 10.18720/MCE.90.10.