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CivilComp Proceedings
ISSN 17593433 CCP: 77
PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 57
Size Effect of Compressed Concrete in the Ultimate Limit States of RC Elements A.P. Fantilli+, I. Iori* and P. Vallini+
+Department of Structural and Geotechnical Engineering, Politecnico di Torino, Italy
A.P. Fantilli, I. Iori, P. Vallini, "Size Effect of Compressed Concrete in the Ultimate Limit States of RC Elements", in B.H.V. Topping, (Editor), "Proceedings of the Ninth International Conference on Civil and Structural Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 57, 2003. doi:10.4203/ccp.77.57
Keywords: reinforced concrete, interaction curves, size effect, limit states, concrete in compression, ductility, stressstrain relationship.
Summary
In order to evaluate the progressive damage produced by crushing of compressed
concrete, a numerical model has been proposed in [1]. With this model, it was possible
to reproduce the postpeak branch in the moment curvature relationship of
RC beams in bending. The diagrams obtained, also applied to elements in bending
and compression, seem to be close to the curves obtained by testing RC beams
with and without stirrups [2]. Moreover, the stress of compressed concrete is a
function of the strain
and of the extension of the compressed zone, according
to the size effect theory proposed by Hillerborg [3]. However, in the case of
beams in bending, the stress obtained with the proposed model seems to depend
also on the crosssectional curvature .
All this aspects cannot be computed by means of Eurocode 2 [4], where the size effect on the structural response of compressed concrete is not taken into account. In the Eurocode 2 the concrete in compression is modelled by the parabolarectangle diagram. Thus in a generic crosssection the maximum moment is reached only when one of the materials attains its limit strain. The aim of this paper is to highlight how Eurocode 2 is not able to reproduce the structural effects produced by the post peak branch of . The influence of the mechanical behaviour of compressed concrete on the interaction curves of RC crosssections is investigated by adopting different approaches. For a given value of the normal force , the maximum bending moments obtained by the proposed model are compared to the ones of Eurocode 2 [4]. Both the approaches are applied to similar crosssections, whose dimensions are obtained by scaling the size factor . In each case, there is a deterministic evaluation of the maximum bending moment, so the partial factors for materials are not applied. The nondimensional bending moment , normal force and mechanical reinforcement ratio are introduced in order to compare the numerical results. Varying the dimensions of the crosssection, the proposed model provides different stress distributions in the compressed concrete and, consequently, more than one interaction curves. These curves, obtained for symmetrically reinforced crosssections and for asymmetrically reinforced ones (no reinforcement in the compressed zone), with size factors and , are compared with the curves computed by assuming the parabola rectangle stressstrain diagram for concrete in compression [4]. For a given value of , a reduction of the bending moment with the increase of is obtained. This phenomenon is particularly evident for , in the section symmetrically reinforced and in the case of high mechanical reinforcement ratio. From a practical point of view, it is also interesting to evaluate the rotation of a beam portion having a length equal to the height of its crosssection. If the value of the curvature at maximum bending moment is considered in the evaluation of , the effect of the inelastic behaviour of the beam are also included in the rotation. The curves obtained in case of asymmetrically reinforced concrete sections and for different size factors , show an increase of when decreases. Similarly, for a given value of , there is an increase of with the decrease of . When and , the rotation can be times lower than . This difference considerably decreases with the increase of and , and is particularly evident in beams with lower and . This scaling behaviour cannot be reproduced with the classical approach proposed in the Eurocode 2 [4]. In conclusion, with the proposed model for compressed concrete, the softening branch of the stress strain relationship, and its effects on moment curvature diagrams, can be defined. The postpeak branch of the diagram clearly shows a size effect, which remarkably affects the crosssectional strength of a RC beam and its corresponding rotation . The decrease of , observed when increases, can be explained as a reduced capability of larger structures to bear plastic deformations. Since sizeeffect is not currently considered into Eurocode 2, it is desirable that future code requirements will be take into account these phenomena. References
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