Chapter 4 Ribbed Slabs and Waffle Slabs

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Ribbed slabs are used for long spans with relatively light loads. They are constructed in one of the following ways as described in clause 30 of IS: 456-20001. As a series of concrete ribs with topping.2. As a series of concrete ribs or solid blocks, between precast hollow as a solid blocks.3. With continuous top and bottom but containing voids of rectangular, oval or other shapes.These three types of constructions

Text of Chapter 4 Ribbed Slabs and Waffle Slabs

Chapter 2

Chapter 4 Ribbed Slabs and Waffle Slabs

Chapter 4 Ribbed Slabs And Waffle Slabs

Ribbed slabs are used for long spans with relatively light loads. They are constructed in one of the following ways as described in clause 30 of IS: 456-20001. As a series of concrete ribs with topping.2. As a series of concrete ribs or solid blocks, between precast hollow as a solid blocks.3. With continuous top and bottom but containing voids of rectangular, oval or other shapes.These three types of constructions are shown in fig. 14.1.

(a) Series of concrete ribs with topping

(b) Concrete ribs or solid blocks, between precast hollow as a solid blocks

(c) Continuous top and bottom but containing voidsFig. 4.1 Ribbed slab construction4.1 PROPORTIONING THE DIMENSIONS OF RIB The ribs may have rectangular, trapezoidal or any other appropriate shape. If trapezoidal (or other shaped) rib is provided, the width of rib is calculated as an average width excluding topping. The minimum width of the rib shall be determined in accordance with minimum cover required to the reinforcement. The minimum width of the rib shall not be less than 65 mm. The depth of the rib excluding topping shall not be more than four times the width of rib. Maximum spacing of the ribs shall be 1.5 m.

4.2 ANALYSIS AND DESIGN PROCEDURE OF RIBBED SLABRibbed slab can be idealized as a solid slab replaced by a series of beams which are spaced at smaller distances. Loading from the topping shall be transferred to the ribs simply by two-way reinforced jail, usually formed by minimum reinforcement.The ribs can be analyzed by the usual procedure applicable to the solid slabs. If the ribs are continuous, they can be analyzed by one of the following ways.(1) As continuous ribs, which may be analyzed by using coefficients applicable to continuous beams or slabs if it has three or more than three uniformly loaded and approximately equal spans; if not, these can be analyzed by moment distribution considering various live load arrangement.(2) If the ribs are not exposed to the weather or corrosive conditions, and if the support cracks can be permitted, then continuous ribs are designed as a series of simply supported ribs. In addition, few reinforcement at the support shall be provided to reduce the cracks at the support.The ribs are now designed as follows:

(a) Design for flexureThe ribs are designed as tee or ell beams. The width of the flange is usually the actual width of the flange owing to the smaller spacing of the ribs. For example, a central tee beam has a flange width equal to the spacing of the ribs. For continuous ribs, support section is designed as a rectangular section.Moment reinforcement consists of one bar or more than one bar at the bottom or at the top as the case may be.If the continuous ribs are designed as simply supported ribs, support reinforcement equal to 25 per cent of span reinforcement shall be provided. These reinforcement shall extend at least one-tenth of clear span into adjoining spans.Clear cover to the main reinforcement shall be as per the solid slabs. However, If the ribbed slab Is provided with permanent hollow concrete blocks, the side cover may be 10 mm.The topping shall be usually provided with minimum reinforcement i.e. 0.12% with HYSD bars and 0.15% with mild steel bars. The spacing of topping reinforcement shall not be more than one-half the spacing of the ribs. If the ribs are widely spaced. the reinforcement shall be designed.

(b) Design for shearRibs are designed for shear as follows:(1) If v < c/2, shear reinforcement Is not required.(2) If c > v > c/2, minimum shear reinforcement as per beam design should be provided, if the rib contains two or more bars. Top bars of diameter at least equal to the diameter of stirrups, two in number, should be used to hold the shear reinforcement. If the rib contains only one bar, shear reinforcement is not necessary.(3) If v > c, shear reinforcement shall be designed as per beam design for shear.(4) According to IS: 456, art. 30.3, where hollow blocks are used, for the purpose of calculating shear stress, the rib width may be increased to take account of the wall thickness of the block on one side of the rib; with narrow precast units, the width of the joining mortar or concrete may be included.

(c) Development length, deflection and crackingThe rules to check development length, deflection and cracking shall be as per solid slab or flanged beam design as the case may be.4.3 WAFFLE SLABS

Fig. 4.2 Waffle slab

4.3.1 TWO-WAY SPANNING RIBBED SLABS: WAFFLE SLABSRibbed slabs discussed in the previous articles are one-way spanning. We shall now discuss two-way spanning ribbed slabs. Such slabs are also termed as waffle slabs. The analysis and design set out for one-way spanning ribbed slabs in previous articles are applicable to waffle slabs also. The moments in the ribs may be determined by using the coefficients for two-way, solid slabs. Load transfer from waffle slabs to the supporting beams shall be assumed as per two-way solid slabs. Waffle slabs are usually made solid in some portion around the supporting beams- to resist negative bending moment- to resist torsion at the edges In the end spans- to provide flanges to the supporting beams and thus toIncrease the moment carrying capacity of supporting beams.Introducing voids to the soffit reduces dead weight and these deeper, stiffer floors permit longer spans which are economic for spans between 9 and 14 m. The saving of materials tends to be offset by complication in site operations.Standard moulds are 225, 325 and 425 mm deep and are used to make ribs 125 mm wide on a 1000 mm grid. Toppings are between 50 and 150 mm thick. The chart and data assume surrounding and supporting downstand beams, which should be subject to separate consideration, and solid margins. Both waffles and downstand beams complicate formwork.

4.3.2 ADVANTAGES Medium to long spans Lightweight Profiles may be expressed architecturally, or used for heat transfer.

4.3.3 DISADVANTAGES Higher formwork costs than for other slab systems Slightly deeper members result in greater floor heights Construction work is slow, difficult to prefabricate reinforcement.

4.3.4 SPAN: DEPTH CHART FOR WAFFLE SLAB

Fig. 4.3 Span: Depth chart

4.4 SAMPLE CALCULATION OF DESIGN OF REINFORCED CONCRETE WAFFLE SLABDesign of interior panel of a WAFFLE slab (Two-way slab)

Size of slab :-8m x8m

Concrete grade :-M30

Steel grade :-Fe415

Conseder live load :-4kN/m2

Solution :

a) Proposed arrangement :-

total thickness of slab :-300 mm

Thichness of topping :-75 mm(Two-way ribbed slab)

Spacing of ribs :-1000 mm

width of waffle :-125 mm

depth of waffle :-225 mm

slab is made solid for 500 mmwidth at edges in all panels.

b) Loading :-

Topping :-self wt.0.075 x25 :-1.875kN/m2

floor finish :-2kN/m2

live load :-4kN/m2

Total :-7.875kN/m2

Rib :-

From topping :-0.5 x7.875 :-3.9375kN/m

self wt.:-0.125 x0.225 x25 :-0.703125kN/m

Total:-4.641kN/m

Factored load :-1.5 x4.641 :-6.96kN/m

c) Shear and moments :-

shear at support (thickned slab) :- (w x l)/2 :-27.84kN

shear at 1000 mmfrom supp. (ribs) :-

:-27.844 -0.5 x 6.96:-24.36kN

For two-way slab :-

l / b:-1.000

x(+) :- y(+) :- 0.024

x(-) :- y(-) :- 0.032

Mu(+) :- x w lx2 :-10.69kNm

Mu(-) :- y w ly2 :-14.26kNm

d) Flexure reinforcement :-

Assume 12 mmdiameter barsdx :-269 mm

dx :-257 mm

Positive moment reinforcement :-

section is designed as a tee beambf :-1000mm

bw :-125mm

Df :-75mm

(second layer is considered for symmetry)d :-257mm

Mu(+) :-11 kNm ,bf / bw :-8.00Df / d :-0.292

Mu,lim. T / (fck bw d2) :-0.845(Table 58, SP : 16)

Mu,lim. T :-209.2928kNm>10.7 kNm

Ast :-134.91mm2(Mu / (0.87 fy d))

provide 2 -10 #:- 157mm2

Negative moment reinforcement :-

Mu(-) :-14.3 kNmb :-1000 mmd :-269 mm

Mu/bd2:-0.20

pt :-0.055pt = 50 { [1-(1-(4.6Mu/fckbd2))] / (fy/fck) }

Ast :-147.9833mm2

provide 3 -8 #between ribs + 2 -8 #

:- 150.72+ 100.48:-251.2mm2(top bars of rib)

e) Shear :-

Shear in ribs at 500 mmfrom support

Vu :-24.36 kNb :-125 mmd :-257 mm

v :-0.758N/mm2Vu /(b d)

100 As/(b d) :-0.49

c :-0.5N/mm2( Page :- 73, IS : 456,2000)

v >c Shear design necessary.

vuc :- c b d :- 16.06 kN

vus :- vu - vuc :- 8.301 kN

use 6 mmdia two-legged stirrups with Asv :-57mm2

sv :- (0.87 fy Asv d) / vus :-380.6 mm

spacing required for minimum shear reiforcement.

sv :- (0.87 fy Asv) / 0.4b :-245.9 mm

maximum spacing permitted, sv,max :- 0.75 d :-193 mm

provide 6 mmdia @193 mmtwo-legged stirrups throught.

f) Development lenfth :-

Ld for negative moment bars :-177.2 mm

anchorage available :-1000 mm.ok

for positive moment bars

Mu1 :- 0.87 Fy Ast d :-13.123 kN

Vu :-24.3633 kN

L0:-8 #

1.3 Mu1/vu + L0 > Ld:-0.7002 + 8#>177 mm

8 #