# chapter 3 rc flat slab

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Chapter 2

Chapter 3 RC Flat Slab

Chapter 3 RC Flat Slab

GENERALIn reinforced concrete flat slab buildings, floors are directly supported by columns as shown in Fig. 3.1 without the use of intermediary beams. Flat slab systems are popular for use in office and residential buildings, hospitals, schools and hotels. Omission of the beams yields larger thickness of slabs.

SlabSupporting columns

Fig. 3.1 Simple flat slabFor covering a large area, three methods are usually adopted. These are(1) Conventional Tee beam - slab construction.(2) Flat slabs where the beams are omitted except the edge beams which may or may not be provided.(3) Grid slabs where deeper beams are used with closer spacing and columns are omitted.

3.1 ADVANTAGES OF FLAT SLAB(1) The formwork is simpler than the tee beam-slab construction which gives economy and simplicity in formwork.(2) Construction of flat slab is simple and speedy.(3) The architectural finish can be directly applied to the underside of the slab. (4) Absence of beams allows lower storey heights and, as a result, cost saving in vertical cladding, partition walls, mechanical systems, plumbing and a large number of other items of construction especially for medium and high rise buildings. (5) They provide flexibility for partition location and allow passing and fixing services easily. (6) Windows can be extended up to the underside of the ceiling. (7) The absence of sharp corners gives better fire resistance and less danger of concrete sapling and exposing the reinforcement. (8) Flat slab can result in more storey being accommodated within a restricted height of the building.

3.2 TYPE OF FLAT SLAB CONSTRUCTION(1) Simply the slab is supported on columns having no drop and no column head.(2) The slab is strengthened by thickening the slab around the column, known as the drop.(3) The slab is additionally strengthened by providing flared column head also known as capital.Fig. 3.2 Types of flat slab construction

The flat slab is a two-way slab bending in both the directions and hence the reinforcement in both the directions is necessary. The exact theoretical analysis is quite complex and can be made by numerical techniques like finite element method or finite difference method. In fact such exact analysis is not must all the times because of the moment redistribution phenomenon. The code gives two methods for designing such slabs.(1) Direct design method {D.D.M.}: In this method. Empirical coefficients are used to find out the design moments at various points. (2) Equivalent frame method {E.F.M.}: In this' method. The structure is divided into plane continuous frames and the analysis is carried out.

3.3 COLUMN AND MIDDLE STRIPS The flat slab panels are divided as set out in clause 31.1 IS:456-2000, into column strips and middle strips as shown in fig. 3.3.

Fig. 3.3 Elements of flat slab

Column strip is a design strip with a width 0.25 lx or 0.25 ly whichever is smaller, on each side of the column. When the drop is present, the width of the column strip shall be taken as the width of the drop provided that the width of drop is not less than one-third of the panel length in that direction.Middle strip is the part of the slab bounded on each of its opposite sides by a column strip.Panel is the part of a slab bounded on each four sides by the centre-line of a column or centre-lines of adjacent spans.

3.4 PROPORTIONING OF FLAT SLAB ELEMENTSThe elements of flat slab are proportioned as set out in clause 30.2, IS: 456 and described as follows: (1) Thickness of flat slab: The thickness of slab shall be generally controlled by deflection requirements same as that for solid slabs. The minimum thickness should be 125 mm. If the flat slab contains drops and if the width of the drops in both directions is at least equal to one-third of the respective spans, the deflection rules as applied to solid slabs are directly applied to such slabs, otherwise the permissible span to effective depth ratios should be multiplied by 0.9. For this purpose, the longer span should be considered (unlike the two-way slab where the short span is considered), Also for finding out the modification factor for tension reinforcement, the average percentage of steel across the whole width of panel at mid-span should be used.(2) Drops: The drops are provided to reduce the shear stresses around the column supports and also to reduce the negative moment reinforcement. When the drops are provided in flat slabs, they should satisfy the following requirements:(a) They should be rectangular in plan and have a length in each direction not less than one-third of the panel length in that direction.(b) For exterior panels, the width of drops at right angles to the non-continuous edge and measured from the centre-line of the columns shall be equal to one-half the width of drop for interior panels.(c) The minimum projection of drop below the slab may be taken as one-fourth the thickness of slab (not specified by code but referred in SP:24). The maximum thickness of drop for the purpose of calculating negative moment reinforcement shall be the thickness of slab plus one quarter the distance between the edge of drop and the edge of capital (column head). (3) Column head: Where column heads are provided, that portion of a column head which lies within the largest right circular cone or pyramid that has a vertex angle of 90 and can be included entirely within the outlines of the column and the column head shall be considered for design purpose.

3.5 METHODS OF ANALYSIS AND DESIGNIt shall be permissible to design the slab system by one of the following methods:a) The direct design method as specified in clause 31.4 of IS 456-2000 andb) The equivalent frame method as specified in clause 31.5 of IS 456-2000.

3.6 LIMITATIONS OF DIRECT DESIGN METHODSlab system designed by the direct design method shall fulfill the following conditions:a) There shall be minimum of three continuous spans in each direction,b) The panels shall be rectangular, and the ratio of the longer span to the shorter span within a panel shall not be greater than 2.0,c) It shall be permissible to offset columns to a maximum of 10 percent of the span in the direction of the offset not withstanding the provision in (b),d) The successive span lengths in each direction shall not differ by more than one-third of the longer span. The end spans may be shorter but not longer than the interior spans, ande) The design live load shall not exceed three times the design dead load.

3.7 DISTRIBUTION OF MOMENTS IN SLABS This is dealt with in clause 31.4.2, IS: 456 and described below.In the direct design method, the total design moment for a span shall be determined for a strip bounded laterally by the centre-line of the panel on each side of the centre-line of the supports. The total moment Mo to be resisted by the slab equals the sum of positive and average negative bending moments in the span. It is the same as that for a simply supported span. For a uniform load it is given byMo = (w ly ) lx2 / 8where lx and ly are as defined in fig. 3.3. In the interior span, the total design moment Mo shall be distributed in the following proportions:Negative design moment 0.65 Mo. Positive design moment 0.35 Mo

Fig. 3.4 Distribution of total momentsNote that the negative design moment sha1l be located at the face of rectangular supports, circular supports being treated as square supports having the same area. Refer to fig. 3.4. For external span, the slab is not completely fixed at discontinuous edge. Fixity at the edge depends on torsional restraint supplied at the discontinuous edge which is provided by flexural stiffness of the exterior panel and exterior column. If the stiffness of edge support were infinite, the slab at the edge can be considered as fixed, e.g. the discontinuous edge is supported by a large beam having a large value of torsional stiffness or by an R.C.C. wall. When the discontinuous edge is supported only at the column, fixity may be created only in the region around the column. In such a case, rotation of the slab at the column will be zero and maximum at the centre of discontinuous edge. Thus, distribution of total moment in the exterior panel depends on relative stiffness of columns and slab meeting at a joint.To take into account, the above facts, code defines the ratio.Where c = the ratio of flexural stiffness of the exterior columns to the flexural stiffness of the slab at a joint taken in the direction moments are being determined.Kc = sum of the flexural stiffness of the columns meeting at the joint (upper and lower columns) Ks = flexural stiffness of the slab, expressed as moment per unit rotation.The total design moment Mo shall be now distributed as follows in the end span. Refer to fig.3.4.Interior negative design moment:= -------------------------------(1)Positive design moment:= -------------------------------(2)Exterior negative design moment:= -------------------------------(3)It shall be permissible to modify these design moments by up to 10 per cent so long ,as the total design moment Mo for the panel in the direction considered is not less than that calculated by equation (1). This relaxation given by the code is due to the moment redistribution phenomenon. The negative moment section shall be designed to resist the larger of the two interior negative design moments determined for the spans framing in to a common support unless an analysis is made to distribute the unbalanced moment in accordance with the stiffness of the adjoining parts. The total moment distribution in to negative and positive moments for internal and external spans is shown in fig.3.4. We have no