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Modelling of creep in continuous RC beams under high levels of sustained loading

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Abstract

A nonlinear theoretical model is developed in this paper for the long-term analysis of continuous reinforced concrete beams. The model accounts for creep, cracking, nonlinear behaviour in compression, shrinkage, aging, yielding of the reinforcement. The constitutive relations follow the modified principle of superposition, which are presented in the form of nonlinear rheological generalized Maxwell models with strain and time dependent springs and dashpots that account for material nonlinearity and aging of the concrete. The governing equations are presented in an incremental form, and are solved through a step-by-step algorithm in time along with the numerical shooting method for the solution along the beam. An iterative procedure is implemented at each time step for the determination of the rigidities and the creep strains. The capabilities of the model are demonstrated through numerical examples. The results show that creep and shrinkage have various influences on the structural response, and they may decrease the load carrying capacity and the factor of safety of continuous reinforced concrete beams with time.

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References

  • Bacinskas, D., Kaklauskas, G., Gribniak, V., Sung, W.P., Shih, M.H.: Layer model for long-term deflection analysis of cracked reinforced concrete bending members. Mech. Time-Depend. Mater. 16(2), 117–127 (2012)

    Article  Google Scholar 

  • Bakoss, S.L., Gilbert, R.I., Faulkes, K.A., Pilmano, V.A.: Long-term deflections of reinforced concrete beams. Mag. Concr. Res. 34(121), 203–212 (1982)

    Article  Google Scholar 

  • Balevičius, R., Dulinskas, E.: On the prediction of non-linear creep strains. J. Civ. Eng. Manag. 16(3), 382–386 (2010)

    Article  Google Scholar 

  • Bažant, Z.P., Asghari, A.A.: Constitutive law for nonlinear creep of concrete. J. Eng. Mech. Div. 103(1), 113–124 (1977)

    Google Scholar 

  • Bažant, Z.P., Kim, S.S.: Nonlinear creep of concrete—adaptation and flow. J. Eng. Mech. Div. 105(3), 429–446 (1979)

    Google Scholar 

  • Bažant, Z.P., Oh, B.H.: Deformation of progressively cracking reinforced concrete beams. ACI J. 81(3), 268–278 (1984)

    Google Scholar 

  • Bažant, Z.P., Prasannan, S.: Solidification theory for concrete creep: I. Formulation. J. Eng. Mech. 115(8), 1691–1703 (1989)

    Article  Google Scholar 

  • Bažant, Z.P., Wu, S.T.: Rate-type creep law of aging concrete based on Maxwell chain. Mater. Struct. 7(1), 45–60 (1974)

    Google Scholar 

  • Carol, I., Bažant, Z.P.: Viscoelasticity with aging caused by solidification of nonaging constituent. J. Eng. Mech. 119(11), 2252–2269 (1993)

    Article  Google Scholar 

  • Carol, I., Murcia, J.: A model for the non-linear time-dependent behaviour of concrete in compression based on a Maxwell chain with exponential algorithm. Mater. Struct. 22(3), 176–184 (1989)

    Article  Google Scholar 

  • CEB-FIP: Structural concrete. Textbook on behaviour, design and performance. Updated knowledge of the CEB/FIP Model Code 1990. Comite Euro-International du Beton/Federation International de la Precontrainte, Fib-bulletin no. 1, Lausanne, Switzerland (1999)

  • Cervenka, V., Jendele, L., Cervenka, J.: ATENA Program Documentation, Part 1: Theory. Cervenka Consulting, Prague (2012)

    Google Scholar 

  • Espion, B.: Long term sustained loading test of reinforced concrete beams. Technical report Brussels, Belgium (1988)

  • Fernández Ruiz, M., Muttoni, A., Gambarova, P.G.: Relationship between nonlinear creep and cracking of concrete under uniaxial compression. J. Adv. Concr. Technol. 5(3), 383–393 (2007)

    Article  Google Scholar 

  • Findley, W.N., Lai, J.S., Onran, K.: Creep and Relaxation of Nonlinear Viscoelastic Materials (with an Introduction to Linear Viscoelasticity). North-Holland, Amsterdam (1976)

    MATH  Google Scholar 

  • Gilbert, R.I., Ranzi, G.: Time-Dependent Behaviour of Concrete Structures. Spon, London (2011)

    Google Scholar 

  • Hamed, E.: Nonlinear creep response of reinforced concrete beams. J. Mech. Mater. Struct. 7(5), 435–460 (2012)

    Article  Google Scholar 

  • Leaderman, H.: Elastic and Creep Properties of Filamentous Materials and Other High Polymers. The Textile foundation, Washington (1943)

    Google Scholar 

  • Li, Z., Qian, J.: Creep damage analysis and its application to nonlinear creep of reinforced concrete beam. Eng. Fract. Mech. 34(4), 851–860 (1989)

    Article  Google Scholar 

  • Mazzotti, C., Savoia, M.: Nonlinear creep damage model for concrete under uniaxial compression. J. Eng. Mech. 129(9), 1065–1075 (2003)

    Article  Google Scholar 

  • Neville, A.M., Dilger, W.H.: Creep of Concrete: Plain, Reinforced, and Prestressed. North-Holland, Amsterdam (1970)

    Google Scholar 

  • Papa, E., Taliercio, A., Gobbi, E.: Triaxial creep behaviour of plain concrete at high stresses: a survey of theoretical models. Mater. Struct. 31(7), 487–493 (1998)

    Article  Google Scholar 

  • Pipkin, A.C., Rogers, T.G.: A non-linear integral representation for viscoelastic behaviour. J. Mech. Phys. Solids 16(1), 59–72 (1968)

    Article  MATH  Google Scholar 

  • Rots, J.G., de Borst, R.: Analysis of mixed-mode fracture in concrete. J. Eng. Mech. 113(11), 1739–1758 (1987)

    Article  Google Scholar 

  • Rusch, H.: Researches toward a general flexural theory for structural concrete. ACI J. Proc. 57, 1–28 (1960)

    Google Scholar 

  • Santhikumar, S., Karihaloo, B.L., Reid, G.: A model for ageing visco-elastic tension softening material. Mech. Cohes.-Frict. Mater. 3, 27–39 (1998)

    Article  Google Scholar 

  • Smadi, M.M., Slate, F.O., Nilson, A.H.: High-, medium-, and low-strength concretes subject to sustained overloads-strains, strengths, and failure mechanisms. ACI J. Proc. 82, 657–664 (1985)

    Google Scholar 

  • Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis. Springer, Berlin (2002)

    Book  MATH  Google Scholar 

  • Thornton, G.M., Oliynyk, A., Frank, C.B., Shrive, N.G.: Ligament creep cannot be predicted from stress relaxation at low stress: a biomechanical study of the rabbit medial collateral ligament. J. Orthop. Res. 15(5), 652–656 (1997)

    Article  Google Scholar 

  • Washa, G.W., Fluck, P.G.: Plastic flow (creep*) of reinforced concrete continuous beams. ACI J. Proc. 52, 549–561 (1956)

    Google Scholar 

  • Zhou, F.P.: Numerical modelling of creep crack growth and fracture in concrete. In: Localized Damage III: Computer-Aided Assessment and Control. Transaction on Engineering Sciences, vol. 6, pp. 141–148 (1994)

    Google Scholar 

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  1. University of New South Wales, Sydney, NSW, 2052, Australia

    Ehab Hamed

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  1. Ehab Hamed
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Hamed, E. Modelling of creep in continuous RC beams under high levels of sustained loading. Mech Time-Depend Mater 18, 589–609 (2014). https://doi.org/10.1007/s11043-014-9243-7

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  • DOI: https://doi.org/10.1007/s11043-014-9243-7

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