Keywords: reinforced concrete, non-linear modelling, joist floors, cracking.

Reinforced concrete floors composed of joists connected to wide shallow beams having the same depth as the joists and supported on elongated rectangular columns are probably the most widely used systems throughout the Middle East and particularly in Saudi Arabia. Despite the wide use, there are genuine concerns whether the design approach followed is consistent with the actual behaviour, due to the lack of sufficient experimental and nonlinear numerical studies.

Reinforced concrete floors have been classified into a number of regular systems where each system has a code simplified procedure for the distribution of its internal forces and moments in order to ensure strength and serviceability criteria. Among these procedures are the ACI-318 [1] direct design method and equivalent frame method for two-way rectangular floor systems.

This paper briefly describes the modelling of a full-scale reinforced concrete building composed of joist-shallow beam floor system supported on columns. In this model, the concrete and rebars were modelled by three-dimensional and one-dimensional elements, respectively, to represent the actual non-prismatic geometry of the floor and account for eccentricity of the columns. In developing the complex model, a pre-processor program was written to allow precise and practical creation of the model. Similarly, a post-processor program was written to convert nodal forces to normal, shear and bending moment diagrams for any selected portion of the model.

The constitutive behaviour of concrete is in accordance with the plastic-damage model in ABAQUS, which is based on models proposed in the literature [2,3,4]. It is widely accepted that a plasticity model must involve three basic assumptions [2,3,4,5,6,7]: (1) An initial yield surface in stress space that defines the stress level at which plastic deformation begins; for concrete, different yield strengths in tension and compression, with the initial yield stress in compression being a factor of 10 or higher than the initial yield stress in tension; (2) A hardening rule defines the change of the loading surface as well as the change of the hardening properties of the material during the course of plastic flow; and (3) A flow rule, which is related to a plastic potential function, gives an incremental plastic stress-strain relation. In ABAQUS, the flow potential chosen for this model is the Drucker-Prager hyperbolic function. The model uses a non-associated flow rule, therefore requires the solution of non-symmetric equations. In plasticity modelling of concrete, the ultimate strength condition, i.e., the failure condition which sets the upper bound of the attainable states of stress, has to be provided, in addition to the above three assumptions.

The model and the experiment agree on the behaviour at macroscopic level in terms of deflections and cracking patterns all over the building members, which confirms the model validity. Both the model and the experimental findings indicate that the behaviour of one-way joist systems on wide shallow beams differs significantly from their intended behaviour, for which they have been designed. The flexibility of the shallow beams permitted the development of double curvature behaviour when single curvature was assumed.

Finally, cracks can provide valuable information on the behaviour because they are free to occur at any location and orientations as required by the stress-distribution mechanism and there is no need to predetermine their locations as should be done for strain measurements. When the numerical model reproduces these cracks, one can be certain that these cracks are load-induced since the numerical model does not take into consideration non-loading cracks. Agreement with test results in cracking prediction as well as deflection prediction gives the current finite element model solid ground for use in predicting the performance of reinforced concrete floors in future studies where the design parameters are varied.

1

ACI Committee 318, "Building Code Requirements for Reinforced Concrete and Commentary (ACI 318-95/ACI 318R-95)", American Concrete Institute, Farmington Hills, 369 pp, 1995.

2

HKS, "ABAQUS - Users Manuals and Theory Manual Version 6.5", Pawtucket, RI, USA, 2004.

3

J. Lubliner, J. Oliver, S. Oller, and E. Oñate, "A Plastic-Damage Model for Concrete", International Journal of Solids and Structures, 25(3), 229-326, 1989. doi:10.1016/0020-7683(89)90050-4

4

J. Lee, and G.L. Fenves, "Plastic-Damage Model for Cyclic Loading of Concrete Structures", Journal of Engineering Mechanics,124(8), 892-900, 1998. doi:10.1061/(ASCE)0733-9399(1998)124:8(892)

5

ASCE Task Committee on Finite Element Analysis of Reinforced Concrete, STATE OF THE ART Report on "Finite Element Analysis of Reinforced", ASCE Special Publications, ASCE, New York, 545 pp., 1982.

6

W.F. Chen, "Plasticity in Reinforced Concrete", McGraw-Hill Book Co., New York, 474 pp., 1982.

7

W.F. Chen, D.J. Han, "Plasticity for Structural Engineers", Springer-Verlag, New York, 606 pp., 1988.

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