Keywords: ribbed plates, building slabs, rib to plate eccentricity, finite element method, reinforced concrete.

Although exhaustedly discussed in other fields of engineering, the eccentricity existing between the ribs axes and the average cover plane in beam-stiffened building slabs is always considered as simplified in analysis models or completely mistakenly disregarded when computational tools for simulations using more realistic models are available. Designers of civil structures generally do not know much about the influence of the eccentricity on the behaviour of these systems (displacement and strength responses of these structures).

The technical design codes allow the structural analysis of reinforced concrete ribbed-slabs to be considered as elastic according to two main mechanical models, without mentioning the existence of the eccentricity:

• a plane grid of crossing beams model, where the eccentricity remains implicit and simplified due to inertial consideration of the T-sections composed of ribs and the ribbed-cement cover;
• a stiffened plates model applying the Equivalent Orthotropic Plate Model considering the T-sections to obtain an equivalent constant thickness for the slab with equivalent stiffness to the bending of the components that form the ribbed-slab.

The consideration of T-sections is a resource widely employed in the calculation of slab concrete beams monolithic to the slabs, and the best way to quantify the geometric properties of the sections for the application in the calculation models are discussed in the codes. A more exact result is obtained by the integration of the normal stress over the cover plate next to the cover-rib bonding, once they decrease as they apart from the bonding. Thus, due to the complexity, the standards provide resources for the T-dimensions to be obtained in a simplified way.

The plane grid model in the simulation of reinforced concrete slabs is based on the ACI-435 (1989) [1], which demonstrates the process developed by Ewell at al. [2]. With regard to the application of the same process for the simulation of ribbed-slabs, no comments were made, however, this process is accepted in practice by many researchers as feasible, once ribbed-slabs present a behaviour closer to the grid than the reinforced slab itself. The Brazilian reinforced concrete code NBR6118:2004 [3] indicates it as a suitable model for the analysis. However, some authors such as Sheik & Mukhopadhyay [4], affirm that the modeling of stiffened plates by means of a grid has failed in the evolution of a satisfactory generic solution.

The most realistic models that generally use software applying the Finite Element Model with a diversity of numerical resources such as the concept of master and slave displacements, optimum resource in the eccentricity simulation, are not mentioned in the technical standards. Designers of civil structures have easy access to these computational tools, however, many of them ignore the importance of considering the eccentricity between ribs and the ribbed-cement slab building's pavements, being the publication of comparative results of numeric simulations and physical tests necessary.

In the context of this discussion, this article presents results obtained by the computer modeling of waffle slabs, varying the ratio of the inter-rib gap to the length of the slab (a₁/l), by increasing or decreasing the number of ribs along each side of the slab, employing diverse mechanical models and various types of finite element, and taking into account or ignoring the eccentricity between the parts. The differences found between these cases and models are evaluated and the choices to be made when interpreting the results to work out the correct dimensions for structural elements are enumerated.

1

American Concrete Institute (1989). "ACI-435: Deflection of two-way reinforced concrete floor systems: state-of-the-art report". Detroit.

2

Ewell, W.W., Okubo, S. and Abrams, J.J. "Deflection in gridworks and slabs", Trans. ASCE, vol. 117, 1952, p.869.

3

Associação Brasileira De Normas Ta'ecnicas NBR 6118:2004: Projeto de estruturas de concreto. Rio de Janeiro, 2004.

4

Sheikh, A.H., Mukhopadhyay, M. (1992). "Analysis of stiffened plate with arbitray planform by the general spline finite strip method", Computers and Structures, v. 42, n. 1, p. 53-67. doi:10.1016/0045-7949(92)90536-9

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