Coefficient of Moment of Inertia for Ribbed RC Slab Beams

Abstract

During the design process of monolithic ribbed slabs, engineers face a common issue how to correctly evaluate stiffness of the beams. When Bar and Plate elements are used for analysis of the slabs, the neutral axis of those members are in the same level, therefore the stiffness of (T) shape cross-section is not considered correctly in the calculations. In this case the internal forces are obtained incorrectly as well as deflections of the beams are overestimated. A simple method is discussed in this paper, which allows engineers to calculate internal forces and deformations of mentioned type slabs more accurately with FEM programs by using Bar and Plate elements. The method is based on Bar elements moment of inertia adjustment.

After the comparative analysis of differences between moment of inertia of (T) and (+) shape cross-sections as well as deflection discrepancies, the adjustment coefficient expression is presented. In order to reflect the actual behaviour of ribbed slabs even more accurately the influence of shear deformations is also considered. In this case not only the member geometry but the material properties, loading scheme and even supports are taken into account in the calculations of the adjustment coefficient. Selection of the most appropriate (effective) flange width of (T) shape cross-section is also analysed in this paper. Comparative calculations were done using different effective flange widths b_eff calculated by EC2 (Eurocode 2), “STR” (Lithuanian Construction Technical Regulations) and ACI (American Concrete Institute) methods. In order to assess the reliability of the proposed calculation method and the calculation results all plates were also analysed using Solid elements.

Application of the presented expressions of moment of inertia coefficient will allow engineers to evaluate stiffness of (Γ) and (T) shape cross section beams simply, fast and accurately enough for most of structural engineering calculations.