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BY 4.0 license Open Access Published by De Gruyter Open Access October 27, 2022

Regression dependences in bending reinforced concrete beam with cracks

  • Zhmagul Nuguzhinov , Omirkhan Khabidolda EMAIL logo , Zhetpisbai Bakirov , Syrlybek Zholmagambetov , Alexey Kurokhtin and Daniyar Tokanov


The work is devoted to determining the stress parameters of flexible reinforced concrete beams with cracks. The problem is solved using LIRA-SAPR using beam finite elements, taking into account the nonlinear relationship between deformation and stress in concrete. In the course of solution, a step-by-step loading method is used with the use of an iterative process at each step. To obtain the dependence of the stress parameters on varied factors, a rational planning matrix for a multifactor computer simulation was compiled to determine the stress parameters in bent rectangular reinforced concrete beams with a crack. According to this plan, computer simulations were conducted for concrete beams of C20/25 and B32/40 class. The obtained dependences enable to evaluate the operability of the considered structural elements for both groups of limiting states. They can be used to determine the parameters of fracture mechanics and evaluate the crack resistance of a beam.


[1] Şahmaran M, Li VC. Engineered cementitious composites: can composites be accepted as crack-free concrete? Transp Res Rec. 2010;2164(1):1–8.10.3141/2164-01Search in Google Scholar

[2] Jang SY, Kim BS, Oh BH. Effect of crack width on chloride diffusion coeflcients of concrete by steady-state migration tests. Cement Concr Res. 2011;41(1):9–19.10.1016/j.cemconres.2010.08.018Search in Google Scholar

[3] Otieno MB, Alexander MG, Beushausen HD. Corrosion in cracked and uncracked concrete–influence of crack width, concrete quality and crack reopening. Mag Concr Res. 2010;62(6):393–404.10.1680/macr.2010.62.6.393Search in Google Scholar

[4] Wiktor V, Jonkers HM. Quantification of crack-healing in novel bacteria-based self-healing concrete. Cement Concr Compos. 2011;33(7):763–70.10.1016/j.cemconcomp.2011.03.012Search in Google Scholar

[5] Ohno K, Ohtsu M. Crack classification in concrete based on acoustic emission. Constr Build Mater. 2010;24(12):2339–46.10.1016/j.conbuildmat.2010.05.004Search in Google Scholar

[6] Carpinteri A. Mechanical damage and crack growth in concrete: plastic collapse to brittle fracture. Berlin, Heidelberg: Springer Science & Business Media; 2012.Search in Google Scholar

[7] Wright JR, Rajabipour F, Laman JA, Radlińska A. Causes of early age cracking on concrete bridge deck expansion joint repair sections. Adv Civ Eng. 2014;2014:103421.10.1155/2014/103421Search in Google Scholar

[8] Kagimoto H, Yasuda Y, Kawamura M. ASR expansion, expansive pressure and cracking in concrete prisms under various degrees of restraint. Cement Concr Res. 2014;59:1–15.10.1016/j.cemconres.2014.01.018Search in Google Scholar

[9] Jin L, Zhang R, Du X, Li Y. Investigation on the cracking behavior of concrete cover induced by corner located rebar corrosion. Eng Fail Anal. 2015;52:129–43.10.1016/j.engfailanal.2015.03.019Search in Google Scholar

[10] Li CQ, Yang ST. Prediction of concrete crack width under combined reinforcement corrosion and applied load. J Eng Mech. 2011;137(11):722–31.Search in Google Scholar

[11] Chernin L, Val DV. Prediction of corrosion-induced cover cracking in reinforced concrete structures. Constr Build Mater. 2014;4:1854–69.Search in Google Scholar

[12] Delyavskyy M, Opanasovych V, Bilash O. Bending by concentrated force of a cantilever strip having a through-thickness crack perpendicular to its axis. Appl Sci (Basel). 2020;10(6):20–37.10.3390/app10062037Search in Google Scholar

[13] Mohammadhassani M, Jumaat MZ, Jameel M. Experimental investigation to compare the modulus of rupture in high strength self-compacting concrete deep beams and high strength concrete normal beams. Constr Build Mater. 2012;30:265–73.10.1016/j.conbuildmat.2011.12.004Search in Google Scholar

[14] Amin A, Gilbert RI. Instantaneous crack width calculation for steel fiber-reinforced concrete flexural members. ACI Struct J. 2018;115(2):535–43.10.14359/51701116Search in Google Scholar

[15] Kwan AK, Ma FJ. Crack width analysis of reinforced concrete under direct tension by finite element method and crack queuing algorithm. Eng Struct. 2016;126:618–27.10.1016/j.engstruct.2016.08.027Search in Google Scholar

[16] Ma FJ, Kwan AK. Crack width analysis of reinforced concrete members under flexure by finite element method and crack queuing algorithm. Eng Struct. 2015;105:209–19.10.1016/j.engstruct.2015.10.012Search in Google Scholar

[17] Oliver-Leblond C, Delaplace A, Ragueneau F. Modelling of three-dimensional crack patterns in deep reinforced concrete structures. Eng Struct. 2015;83:176–86.10.1016/j.engstruct.2014.10.040Search in Google Scholar

[18] Tan R, Eileraas K, Opkvitne O, Žirgulis G, Hendriks MA, Geiker M, et al. Experimental and theoretical investigation of crack width calculation methods for RC ties. Struct Concr. 2018;19(5):1436–47.10.1002/suco.201700237Search in Google Scholar

[19] Yang ST, Li KF, Li CQ. Numerical determination of concrete crack width for corrosion-affected concrete structures. Comput Struct. 2018;207:75–82.10.1016/j.compstruc.2017.07.016Search in Google Scholar

[20] Fakhri M, Amoosoltani E, Aliha MR. Crack behavior analysis of roller compacted concrete mixtures containing reclaimed asphalt pavement and crumb rubber. Eng Fract Mech. 2017;180:3–59.10.1016/j.engfracmech.2017.05.011Search in Google Scholar

[21] Yamamoto Y, Nakamura H, Kuroda I, Furuya N. Crack propagation analysis of reinforced concrete wall under cyclic loading using RBSM. Eur J Environ Civ Eng. 2014;18(7):780–92.10.1080/19648189.2014.881755Search in Google Scholar

[22] Deng Z, Wang Y, Yang H, Qian J. Research on crack behavior of recycled concrete beams under short-term loading. KSCE J Civ Eng. 2018;22(5):1763–70.10.1007/s12205-017-0678-7Search in Google Scholar

[23] Salnikov A, Kolchunov V, Yakovenko I. The computational model of spatial formation of cracks in reinforced concrete constructions in torsion with bending. Appl Mech Mater. 2015;725-6:784–9.10.4028/ in Google Scholar

[24] Zhu H. Crack formation of steel reinforced concrete structure under stress in construction period. Frattura Integr Strutt. 2016;36(36):191–200.10.3221/IGF-ESIS.36.19Search in Google Scholar

[25] Khabidolda O, Bakirov ZB, Nuguzhinov ZS, Vatin N. Determining stress intensity factor in bending reinforced concrete beams. Bull Karaganda Univ-Mathemat. 2019;96(4):90–8.10.31489/2019M4/90-98Search in Google Scholar

[26] Nuguzhinov ZS, Bakirov ZB, Kurokhtin AY, Khabidolda O, Nuguzhinova A. Assessment of bending reinforced concrete beams crack resistance. IOP Conf Ser: Mater Sci Eng. 2019;690:012002.10.1088/1757-899X/690/1/012002Search in Google Scholar

[27] Sheng J, Yin SP, Xu SL, Jin ZY. Experimental and theoretical investigations on crack spacing and stiffness of textile-reinforced concrete–strengthened reinforced concrete beams. Adv Struct Eng. 2018;21(11):1696–707.10.1177/1369433218754333Search in Google Scholar

[28] Cohen M, Monteleone A, Potapenko S. Finite element analysis of intermediate crack debonding in fibre reinforced polymer strengthened reinforced concrete beams. Can J Civ Eng. 2018;45(10):840–51.10.1139/cjce-2017-0439Search in Google Scholar

[29] Ma FJ, Kwan AK. Finite element analysis of concrete shrinkage cracks. Adv Struct Eng. 2018;21(10):1454–68.10.1177/1369433217746346Search in Google Scholar

[30] Rossi P, Daviau-Desnoyers D, Tailhan JL. Analysis of cracking in steel fibre-reinforced concrete (SFRC) structures in bending using probabilistic modelling. Struct Concr. 2015; 3(3):381–8.10.1002/suco.201400081Search in Google Scholar

[31] Bykov AA, Matveenko VP, Shardakov IN, Shestakov A. Shock wave method for monitoring crack repair processes in reinforced concrete structure. Mech Solids. 2017;52(4):378–83.10.3103/S0025654417040033Search in Google Scholar

[32] Badiger NS, Malipatil KM. Parametric study on reinforced concrete beam using ANSYS. Civ Environ Res. 2014;6:88–94.Search in Google Scholar

[33] Banjara NK, Ramanjaneyulu K. Experimental and numerical investigations on the performance evaluation of shear deficient and GFRP strengthened reinforced concrete beams. Constr Build Mater. 2017;137:520–34.10.1016/j.conbuildmat.2017.01.089Search in Google Scholar

[34] Dahmani L, Khennane A, Kaci S. Crack identification in reinforced concrete beams using ANSYS software. Strength Mater. 2010;42(2):232–40.10.1007/s11223-010-9212-6Search in Google Scholar

[35] Biolzi L, Cattaneo S. Response of steel fiber reinforced high strength concrete beams: experiments and code predictions. Cement Concr Compos. 2017;77:1–13.10.1016/j.cemconcomp.2016.12.002Search in Google Scholar

[36] Hsu TT. Unified theory of reinforced concrete. London: Routledge; 2017.Search in Google Scholar

[37] Atkinson A, Donev A, Tobias R. Optimum experimental designs, with SAS. Oxford: Oxford University Press; 2007.Search in Google Scholar

[38] Campbell DT, Stanley JC. Experimental and quasi-experimental designs for research. Cambridge: Ravenio Books; 2015.Search in Google Scholar

[39] Kleijnen JP. Regression and Kriging metamodels with their experimental designs in simulation: A review. Eur J Oper Res. 2017;256(1):1–16.10.1016/j.ejor.2016.06.041Search in Google Scholar

[40] Naidu RR, Jampana P, Sastry CS. Deterministic compressed sensing matrices: construction via Euler squares and applications. IEEE Trans Signal Process. 2016;64(14):3566–75.10.1109/TSP.2016.2550020Search in Google Scholar

[41] Zhang L, Huang Q, Lin S, Abdel-Ghaffar K, Blake IF. Quasi-cyclic LDPC codes: an algebraic construction, rank analysis, and codes on Latin squares. IEEE Trans Commun. 2010;58(11):3126–39.10.1109/TCOMM.2010.091710.090721Search in Google Scholar

[42] Marí A, Cladera A, Oller E, Bairan J. Shear design of FRP reinforced concrete beams without transverse reinforcement. Compos B Eng. 2014;57:228–41.10.1016/j.compositesb.2013.10.005Search in Google Scholar

[43] Yuvaraj P, Murthy AR, Iyer NR, Sekar SK, Samui P. Support vector regression based models to predict fracture characteristics of high strength and ultra high strength concrete beams. Eng Fract Mech. 2013;98:29–43.10.1016/j.engfracmech.2012.11.014Search in Google Scholar

[44] Kusuma B. Analytical model for axial stress-strain behavior of welded reinforcement grid confined concrete columns. J Asian Concr Fed. 2015;1:1–10.10.18702/acf.2015.09.1.1Search in Google Scholar

[45] Pudjisuryadi P, Suprobo P. Analytical confining model of square reinforced concrete columns using external steel collars [dissertation]. Surabaya: Petra Christian University; 2013.10.21742/ijiace.2014.1.1.01Search in Google Scholar

[46] Tavio T, Budiantara IN, Kusuma B. Spline nonparametric regression analysis of stress-strain curve of confined concrete. Civ Eng Dimens. 2008;10:14–27.Search in Google Scholar

[47] Slobbe AT, Hendriks MA, Rots JG. Sequentially linear analysis of shear critical reinforced concrete beams without shear reinforcement. Finite Elem Anal Des. 2012;50:108–24.10.1016/j.finel.2011.09.002Search in Google Scholar

[48] Vasudevan G, Kothandaraman S, Azhagarsamy S. Study on non-linear flexural behavior of reinforced concrete beams using ANSYS by discrete reinforcement modeling. Strength Mater. 2013;45(2):231–41.10.1007/s11223-013-9452-3Search in Google Scholar

Received: 2022-02-07
Accepted: 2022-08-26
Published Online: 2022-10-27

© 2022 Zhmagul Nuguzhinov et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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