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: 456-2000

1. 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 voids

Fig. 4.1 Ribbed slab construction

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Chapter 4 Ribbed Slabs And Waffle Slabs

4.1 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 SLAB

Ribbed 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 flexure

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The 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 shear

Ribs are designed for shear as follows:

(1) If τv < τc/2, shear reinforcement Is not required.

(2) If τc > τv > τc/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 τv > τc, 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 cracking

The 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 SLABS

Ribbed 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 to

Increase 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 SLAB

Design of interior panel of a WAFFLE slab (Two-way slab)Size of slab :- 8 m x 8 mConcrete grade :- M30Steel grade :- Fe415Conseder live load :- 4 kN/m2

Solution :a) Proposed arrangement :-

total thickness of slab :- 300 mmThichness of topping :- 75 mm (Two-way ribbed slab)

Spacing of ribs :-1000 mm

width of waffle :- 125 mmdepth of waffle :- 225 mm

slab is made solid for 500 mm width at edges in all panels.b) Loading :-

Topping :- self wt. 0.075 x 25 :- 1.875 kN/m2floor finish :- 2 kN/m2live load :- 4 kN/m2Total :- 7.875 kN/m2

Rib :-



From topping :- 0.5 x 7.875 :- 3.9375 kN/mself wt. :- 0.125 x 0.225 x 25 :- 0.703125 kN/mTotal :- 4.641 kN/mFactored load :- 1.5 x 4.641 :- 6.96 kN/m

c) Shear and moments :-shear at support (thickned slab) :- (w x l)/2 :- 27.84 kNshear at

1000 mm from supp. (ribs) :-

:- 27.844 -0.5 x 6.96 :- 24.36 kN

For two-way slab :-l / b :- 1.000

αx(+) :- αy(+) :- 0.024

αx(-) :- αy(-) :- 0.032

Mu(+) :- αx w lx2 :- 10.69 kNm

Mu(-) :- αy w ly2 :- 14.26 kNmd) Flexure reinforcement :-

Assume 12 mm diameter bars dx :- 269 mm

dx :- 257 mmPositive moment reinforcement :-

section is designed as a tee beam bf :- 1000 mm

bw :- 125 mm

Df :- 75 mm(second layer is considered for symmetry) d :- 257 mm

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

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

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

Ast :- 134.91 mm2 (Mu / (0.87 fy d))provide 2 - 10 # :- 157 mm2

Negative moment reinforcement :-



Mu(-) :-14.3 kNm b :-

1000 mm d :- 269 mm

Mu/bd2 :- 0.20

pt :- 0.055 pt = 50 { [1-(1-√(4.6Mu/fckbd2))] / (fy/fck) }Ast :- 147.9833 mm2

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

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

e) Shear :-Shear in ribs at 500 mm from support

Vu :- 24.36 kN b :- 125 mm d :- 257 mm

τv :- 0.758 N/mm2 Vu /(b d)

100 As/(b d) :- 0.49

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

τv > τc Shear design necessary.

vuc :- τc b d :- 16.06

kN

vus :- vu - vuc :- 8.301 kN

use 6 mm dia two-legged stirrups with Asv :- 57 mm2

sv :- (0.87 fy Asv d) / vus :- 380.6 mmspacing 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 mm dia @ 193 mm two-legged stirrups throught.f) Development lenfth :-

Ld for negative moment bars :-177.2 mm

anchorage available :- 1000 mm ….okfor positive moment bars

Mu1 :- 0.87 Fy Ast d :- 13.123 kNVu :- 24.3633



kN

L0 :- 8 #

1.3 Mu1/vu + L0 > Ld :-0.7002 +

8# > 177 mm

8 # <22.0684

# ….okg) Check for moment design at junction of solid slab and ribbed slab :-

negative moment reinforcement is designed considering the section 1000 mmx 300 mm

1 mfrom support Mu(-) :- 10.11 kNm < Mu(-) ….ok

h) Deflection :-basic span / d ratio :- 26

pt :- 100 As / (bf d) :- 0.05modification factor :- 2.0 (page no. 38; IS 456-2000)permissible span / d :- 52actual span / d :- 31 < 52 ….ok

i) Topping reinforcement :-

As :- 90 mm2/m.d :- 56 assume 6.00 dia bar.

Maximum spacing :- 5 d :- 280 mm.use 6 mm # wrapping mesh @ 200 mm c/c :- 141

mm2/m at the centre of topping.steel quantity

along long span (+ve)steel :- 2 10 # (bottom steel of rib beam)L :- 8 m

No. of bars :- 16 nos.weight of steel :- 79 kg.

along short span (+ve) steel :- 2 10 # (bottom steel of rib beam)L :- 8 m


along long span (-ve)steel :- 2 8 # (top steel of rib beam)



L :- 8 mNo. of bars :- 16 nos.weight of steel :- 51 kg.

along short span (-ve) steel :- 2 8 # (top steel of rib beam)L :- 8 m


along long span (-ve)steel :- 3 8 # (between ribs)L :- 4 m

No. of bars :- 24 nos. weight of steel :- 38 kg.

along short span (-ve)steel :- 3 8 # (between ribs)L :- 4 m


topping reinforcementalong long span steel :- 6 # 200 mm c/c

L :- 1 mNo. of bars :- 384 nos.weight of steel :- 85 kg.

along short span steel :- 6 200 mm c/c L :- 1 m


shear reinforcement :along long span steel :- 6 # 193 mm c/c

L :- 0.85 m No. of bars :- 332 nos.weight of steel :- 63 kg.

along short span steel :- 6 # 193 mm c/c L :- 0.85 m




total steel required for 3 span.total steel required :- 12915 kg.Total cost of steel :- 419724.3 Rs.

quantity of conc.in topping slab :- 43.20 m3

quantity of solid slab near mainbeam :- 86.40 m3

quantity of ribbed beams :- 28.35 m3

quantity of main beams :- 46.08 m3

total quantity of concrete :- 204.03 m3

quantity of steel in m3 :- 1.65 m3

% of steel :- 0.81 %

Total cost of slab :- 1431773 Rs.

interior panel bottom fibre stress :-M y / I :- 7.60E+00 N/mm2


Chapter 4 Ribbed Slabs and Waffle Slabs

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