Mechanics of Time-Dependent Materials

, Volume 18, Issue 3, pp 589–609 | Cite as

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

  • Ehab HamedEmail author


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.


Beam Concrete Creep Nonlinear Shrinkage Viscoelasticity 


  1. 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) CrossRefGoogle Scholar
  2. 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) CrossRefGoogle Scholar
  3. Balevičius, R., Dulinskas, E.: On the prediction of non-linear creep strains. J. Civ. Eng. Manag. 16(3), 382–386 (2010) CrossRefGoogle Scholar
  4. Bažant, Z.P., Asghari, A.A.: Constitutive law for nonlinear creep of concrete. J. Eng. Mech. Div. 103(1), 113–124 (1977) Google Scholar
  5. Bažant, Z.P., Kim, S.S.: Nonlinear creep of concrete—adaptation and flow. J. Eng. Mech. Div. 105(3), 429–446 (1979) Google Scholar
  6. Bažant, Z.P., Oh, B.H.: Deformation of progressively cracking reinforced concrete beams. ACI J. 81(3), 268–278 (1984) Google Scholar
  7. Bažant, Z.P., Prasannan, S.: Solidification theory for concrete creep: I. Formulation. J. Eng. Mech. 115(8), 1691–1703 (1989) CrossRefGoogle Scholar
  8. 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
  9. Carol, I., Bažant, Z.P.: Viscoelasticity with aging caused by solidification of nonaging constituent. J. Eng. Mech. 119(11), 2252–2269 (1993) CrossRefGoogle Scholar
  10. 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) CrossRefGoogle Scholar
  11. 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) Google Scholar
  12. Cervenka, V., Jendele, L., Cervenka, J.: ATENA Program Documentation, Part 1: Theory. Cervenka Consulting, Prague (2012) Google Scholar
  13. Espion, B.: Long term sustained loading test of reinforced concrete beams. Technical report Brussels, Belgium (1988) Google Scholar
  14. 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) CrossRefGoogle Scholar
  15. 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) zbMATHGoogle Scholar
  16. Gilbert, R.I., Ranzi, G.: Time-Dependent Behaviour of Concrete Structures. Spon, London (2011) Google Scholar
  17. Hamed, E.: Nonlinear creep response of reinforced concrete beams. J. Mech. Mater. Struct. 7(5), 435–460 (2012) CrossRefGoogle Scholar
  18. Leaderman, H.: Elastic and Creep Properties of Filamentous Materials and Other High Polymers. The Textile foundation, Washington (1943) Google Scholar
  19. 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) CrossRefGoogle Scholar
  20. Mazzotti, C., Savoia, M.: Nonlinear creep damage model for concrete under uniaxial compression. J. Eng. Mech. 129(9), 1065–1075 (2003) CrossRefGoogle Scholar
  21. Neville, A.M., Dilger, W.H.: Creep of Concrete: Plain, Reinforced, and Prestressed. North-Holland, Amsterdam (1970) Google Scholar
  22. 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) CrossRefGoogle Scholar
  23. Pipkin, A.C., Rogers, T.G.: A non-linear integral representation for viscoelastic behaviour. J. Mech. Phys. Solids 16(1), 59–72 (1968) CrossRefzbMATHGoogle Scholar
  24. Rots, J.G., de Borst, R.: Analysis of mixed-mode fracture in concrete. J. Eng. Mech. 113(11), 1739–1758 (1987) CrossRefGoogle Scholar
  25. Rusch, H.: Researches toward a general flexural theory for structural concrete. ACI J. Proc. 57, 1–28 (1960) Google Scholar
  26. Santhikumar, S., Karihaloo, B.L., Reid, G.: A model for ageing visco-elastic tension softening material. Mech. Cohes.-Frict. Mater. 3, 27–39 (1998) CrossRefGoogle Scholar
  27. 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
  28. Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis. Springer, Berlin (2002) CrossRefzbMATHGoogle Scholar
  29. 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) CrossRefGoogle Scholar
  30. Washa, G.W., Fluck, P.G.: Plastic flow (creep*) of reinforced concrete continuous beams. ACI J. Proc. 52, 549–561 (1956) Google Scholar
  31. 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

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.University of New South WalesSydneyAustralia

Personalised recommendations