Keywords: building codes, T-beams, effective flange width, finite element analysis, regression analysis.

Most of the reinforced concrete systems are monolithic. During construction, concrete from the bottom of the deepest beam to the top of slab is placed at once. Therefore the slab serves as the top flange of the beams. Such a beam is referred to as T-beam. In a floor system made of T-beams, the maximum axial compressive stress occurs over the web, dropping between the webs. The distribution of compressive stress on the flange depends on the relative dimensions of the cross section, span length, support and loading conditions. For simplification the varying distribution of compressive stress can be replaced by an equivalent uniform distribution. This gives an effective flange width, which is smaller than the real flange width (see, for example, [1]). In various codes there are recommendations for effective flange width formulas. But these code recommendations may be considered as approximate, since they are expressed only in terms of span length or flange and web thickness and ignore the other important variables.

The aim of the present study is to investigate the effective flange width formulas for T-beams. In this study, a three-dimensional finite element analysis is carried out on continuous T-beams. The beam spacing, span, overall depth, web and flange thickness are considered as independent variables in the analysis.

The elastic stress distributions on 243 T-beams are calculated under uniformly distributed load, concentrated load at midspan and concentrated loads at third points. The concrete slab and the beam are modelled by means of solid elements. The element chosen is an eight-node solid element [2].

By using the distribution of the extreme top fiber compressive stresses from the finite element analysis, effective flange widths are calculated for 81 combinations of the independent variables corresponding to each of the three loading conditions.

Linear multiple regression analyses are carried out on this available data using the software SPSS [3]. Following multiple regression analysis, three empirical design formulas for effective flange width are derived. These proposed formulas incorporate the beam span, spacing, depth, and flange and web thickness as independent variables.

Comparisons are made between the proposed formulas and the ACI Building Code [4], Eurocode [5] and TS-500 Turkish Building Code [6] recommendations. The proposed formulas show the effects of loading conditions on effective flange width clearly. The comparison of the results also demonstrates that the building codes considered here give safer values for the effective flange width for the uniformly distributed load case. However, it is found that for the concentrated load cases, the code recommendations seem to be unsafe when the beam spacing is small.

1

Nilson, A.H., Winter, G., "Design of Concrete Structures", 11th ed., McGraw- Hill, New York, 1991.

2

Cook, R.D., Malkus, D.S., Plesha, M.E., "Concepts and Applications of Finite Element Analysis", 3rd ed., John Wiley and Sons, New York, 1989.

3

"Statistical Package for The Social Sciences for Windows", Release 7.5.1, 1996.

4

"Building Code Requirements for Reinforced Concrete Buildings", ACI-318-95, American Concrete Institute, Michigan, 1995.

5

"Design of Concrete Structures-Part 1: General Rules for Buildings", Eurocode 2, 1991.

6

"Building Code Requirements for Reinforced Concrete Structures", TS-500-2000, Turkish Standards Inst., 2000.

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