Modeling of Externally Prestressed Beams until Fracture in Non Linear Elasticity

Abstract:

In this paper, we present an analytical model to analyze reinforced and prestressed concrete beams loaded in combined bending, axial load and shear, in the frame of non linear elasticity. In this model, the equilibrium of the beam is expressed by solving a system of equations, governing beams equilibrium, based on the stiffness matrix of the beam, which connects the load vector to the node displacements vector of the beam. It is built from the stiffness matrix of the section which takes into account a variation of the shearing modulus (depending on the shear variation) instead of assuming a constant shearing modulus as in linear elasticity. For the internal tendons, the stiffness matrix is completed by the terms due to the prestress effect in flexural equilibrium and by the balancing of one part of the shear by the transverse component of the force in the inclined cables.

• Periodical: Applied Mechanics and Materials (Volume 749)
• Pages: 379-385
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.749.379
• Online since: April 2015
• Authors: Arezki ADJRAD*, Youcef BOUAFIA, Mohand said KACHI, Hélène Dumontet
• Keywords: External Prestress, Modeling, Non Linear Elasticity, Shear Modulus, Slipping of the Tendon

References

[1] A. Zona, L. Ragni, and Dall'asta, Finite element formulation for geometric and material non linear analysis of beams pretressed with external slipping tendons, Finite Element in Analysis and Design, Volume: 44. Issue: 15, November 2008, pp.910-919.

DOI: 10.1016/j.finel.2008.06.005

[2] M. Virlogeux, External pretressing : from construction history to modern technique and technology, External prestressing in bridges, ACI, SP-120, Éd. Antoine Naamane and John Breen, (1990).

DOI: 10.14359/3223

[3] J.A. Garcia-Vargas, N. Menezes, and J.L. Trinh, Effect of external tendon slipping at deviators on beam behaviour, Workshop, Behaviour of external prestressing in structures, Saint-Rémy-lès-Chevreuse, France, June (1993).

[4] M.S. Kachi, B. Fouré., Y. Bouafia., P. Muller,  L'effort tranchant dans la modélisation du comportement jusqu'à rupture des poutres en béton armé et précontraint, Revue Européenne de Génie Civil, Vol 10 n°10, 2006, pp.1235-1264.

DOI: 10.3166/regc.10.1235-1264

[5] M.S. Kachi, Modélisation du comportement jusqu'à rupture des poutres à précontrainte extérieure,. Doctoral Thesis on Civil Engineering, University of Tizi Ouzou, November (2006).

[6] B. Fouré, P.C. Rezende-Martins, and L.M. Howang, Problèmes de sécurité à rupture et de modélisation du comportement des poutres en béton à précontrainte extérieure". Annales de l,I.T.B.T.P., Paris, Février (1991).

DOI: 10.3166/regc.10.1235-1264

[7] B Fouré., Rezende-Martins P.C., Comportement en flexion jusqu'à rupture des poutres à précontrainte extérieure, A.F.P.C., XI° Congrès de la F.I.P., Hambourg, (1990).