The ACI Codes adopted two methods for evaluating deflection of reinforced concrete beams. The First method uses the basic deflection formula, in which an effective moment of inertia is introduced to calculate the deflection of partially pre- stressed members. The second method is based on existing load-deflection curves to calculate the deflection of such types of members. Other techniques include Burns' [1] Moment-Curvature (stress-strain) relationship for pre-stressed concrete beams, by which deflections were obtained using the principles of moment inertia; Maher and Ghali's [2] procedure for predicting deflections of cracked and non-cracked pre- stressed concrete members under live load and Maher's [3] tables and computer program for determining the effective moment of inertia and deflection for cracked and non-cracked sections. Chang [4] also developed a computer program for pre- stressed composite and non-composite concrete beams by using a series of layered strips approximating section dimensions.

The purpose of this paper is to present a numerical study for the deflection of double tee concrete slabs. A combined finite element and finite strip method is used to calculate deflections of double tee slabs. Beam elements are used for webs and finite strips are used for roof slabs. The interactions between the roof slabs and the double-tee supports are considered by imposing the conditions of displacement continuity along the beam-slab interfaces. This is achieved through the application of a flexibility approach, in which flexibility matrices are established for relevant elements. For the purpose of comparisons, two other types of analyses are also used in the calculations. First a solution is obtained by expressing displacements as Fourier series expansions in the longitudinal direction for both slabs and beams, where the support beams are modelled by plates subjected to both bending and in- plane stresses. Secondly, the traditional finite element solutions are obtained, where the slabs and beams are modelled by plate and beam elements, respectively. Computer programs are developed and numerical results are obtained to validate the techniques.

From the comparisons, it is found that the predicted deflections from the finite element method and the combined spline strip method agree well and are smaller than those obtained from the finite strip method based on series expansions. Hence, it can be concluded that a design based on the series expansion type analysis may be more conservative that the one where beam supports are treated as beam elements.

1

Burns, Ned H., "Moment Curvature Relationships for Partially Pre-stressed Concrete Beams" PCI Journal, Vol. 9, No. 1, February, 52-63, 1964.

2

Tadros, M. K., Ghali, A., and Meyer, A. W., "Pre-stressed Loss and Deflection of Pre-cast Concrete Members" PCI Journal, January-February, pp. 114-141, 1985

3

Tadros, M. K., "Expedient Service Load Analysis of Cracked Pre-stressed Concrete Beams" PCI Journal, Vol. 27, No. 6, Nov.-Dec., 86-111, 1982.

4

Chang, Donald Chief, "A Numerical Method of Analyzing Composite Pre-stressed Concrete Members" MS thesis, The University of Texas at Austin, 1969.

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