There are several methods by which two-way slabs can be designed. All methods are viable provided that the safety and serviceability of the elements are within the acceptable limits. The coefficient method may be the simplest, easiest and the quickest approach for the design of two-way slab supported by edge beam on all slab sides.
This method was provided in the American Concrete Institute (ACI) in 1963 to design two-way slabs carried by steel beams, deep beam, or walls. Nonetheless, the coefficient method is not included in the current edition of the ACI code. This is because it is considered to be too conservative and more precise approaches can be employed. However, it should be known that the coefficient method is still applied for two-way slabs.
The coefficient method employs tables of moment coefficients for different slab edge conditions. The conditions are based on elastic analysis but inelastic redistribution is accounted for as well.
As a result, the design moment on both directions is smaller by a specific amount than the ultimate elastic moment in that exclusive direction.
According to the coefficient approach, the slab is divided into the middle strip and column strip in each direction. The width of the latter is equal to the one-quarter of the panel width whereas the width of the former is one-half the panel width, as illustrated in Fig.1.
The following equations can be used to estimate negative and positive moments in the two directions :
As it can be observed from Fig.2, moments in the center area of the slab is the greatest compared with moments imposed on the area adjacent to the slab edge.
That is why the middle strip needs to be designed for the greatest tabulated moment whereas the edge strips are specified to be designed for one-quarter of the maximum value of the calculatedmoment. Such distribution shown in Fig.2 is for (Ma), and similar variations are applied for (Mb).
Moreover, it should be known that the above discussion is related to simply supported two-way slabs, whereas there are several spans in the real conditions as shown in Fig. 3.
The panel A has two discontinuous edges while the other two edges are continuous and adjacent to another slab as it may be observed in Figure 5.
The panel B is continuous at three edges and the other edge is discontinuous. And the panel C is continuous at all its edges.
Etch this into your mind that moments at edges of the slab is negative and the magnitude of positive moment is based on the condition of continuity at the entire edges of the panel.
Various possible support conditions which are considered in the moment coefficient tables are shown in Fig 4.
As far as ACI coefficient tables are concerned, Table 1 provides coefficients for negative moments at continuous edges, and the ultimate moment at slab edge is achieved when both adjacent slabs support full dead and live load. Table 2 provides the coefficient to compute positive moments of slabs that carry dead load only.
Regarding Table 3 coefficients, they are applied to calculate positive moments of slabs on which live loads are acted on. Lastly, coefficients used to estimate shears on slabs and loads on supporting beams.
The following consideration provided by ACI Code shall be taken into account during reinforcement detailing :
1. Placement Sequence
Reinforcement bars for short spans are recommended to be placed closer to the top and bottom of the slab than long span reinforcement. In this way, reinforcements in short spans will have greater effective depth.
This placement configuration should be maintained, and if special reinforcement placement is considered it needs to be clearly noted and shown in the drawing.
2. Concrete Cover
ACI Code section 7.7.1 specifies the minimum clear cover to the surface of reinforcement in slabs as 20mm apart from the condition where the slab is in direct contact with earth to weather.
3. Spacing Requirements
The maximum spacing of reinforcement at critical design sections for positive and negative moments in both the middle and column strips shall not exceed two times the slab thickness (ACI Code Section 13.3.2),
The bar spacing shall not exceed 450 mm at any location (ACI Code Section 184.108.40.206).
Determine the thickness of the slab, according to procedures provided here
Calculate the factored loads.
Determine moment coefficients using Tables.
Compute positive and negative moments in each direction.
Finally, calculate reinforcement area, then number of bars and their spacing.
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