Abstract—The flexural behavior of reinforced concrete beams is a well-known problem. In the classical studies about this subject, shear strength is neglected or taken into account by simple formula from the linear theory of elasticity, neglecting flexure and shear interaction. For this reason, these classical methods allow to predict only the flexural fracture modes, not the shearing fracture modes.
We present in this paper an analytical model able to analyze reinforced concrete structures loaded in combined bending, axial load and shear in the frame of non linear elasticity. In this model, the expression adopted for the section’s stiffness matrix does not take into account a constant shearing modulus G=f(E) as in linear elasticity, but a variable shearing modulus which is a function of the shear variation using simply formula.
In this part, we present a calculus model of reinforced concrete beams on the three dimensions (3D). This model of computation is then expanded to spatial structures in the second part. A computing method is then developed and applied to the calculus of some reinforced concrete beams. The comparison of the results predicted by the model with several experimental results show that, on the one hand, the model predictions give a good agreement with the experimental behavior in any field of the behavior (after cracking, post cracking, post steel yielding and fracture of the beam).
Index Terms—Beams, concrete, modeling, non linear elasticity, shear modulus.
The authors are with University “Mouloud Mammeri” of Tizi-Ouzou, 15000, Algeria (e-mail: adjradarezki@yahoo.fr)
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Cite: Arezki Adjrad, Youcef Bouafia, Mohand Said Kachi, and Hélène Dumontet, "Non-Linear Modelling of Three Dimensional Structures Taking Into Account Shear Deformation," International Journal of Engineering and Technology vol. 6, no. 4, pp. 290-298, 2014.
