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: 456-2000 1. As a series of concrete ribs with topping. topp ing. 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

Design of Reinforced Concrete & Post-Tensioned flat slab u sing software 1

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 twoway 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 f or f lexure

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

Design of Reinforced Concrete & Post-Tensioned flat slab using software. 2

Chapter 4


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 l ength, defl ection and cracki ng

The rules to check development length, deflection and cracking shall be as per solid slab or flanged beam design as the case may be.


Chapter 4


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


Chapter 4


- to provide flanges to the supporting beams and thus to Increase the moment carrying capacity of supporting b eams. 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 do wnstand 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.


Chapter 4


4.3.4 SPAN: DEPTH CHART FOR WAFFLE SLAB

Fig. 4.3 Span: Depth chart


Chapter 4


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 Concrete grade :M30 Steel grade :Fe415 Conseder live load :-

4

Solution : a) Proposed arrangement :total thickness of slab :Thichness of topping :-

300 mm 75 mm 1000 mm 125 mm 225 mm 500 mm

Spacing of ribs :width of waffle :depth of waffle :slab is made solid for b) Loading :Topping :self wt. 0.075 x floor finish live load Total

8

m

2

kN/m

(Two-way ribbed slab)

width at edges in all panels. 25 :::-

1.875 2 4

kN/m2 kN/m2 kN/m2

:-

7.875

kN/m2

3.9375 0.703125 4.641 6.96

kN/m kN/m kN/m kN/m

Rib :From topping :0.5 x 7.875 :0.125 x self wt. :0.225 x 25 :Total :Factored load :1.5 x 4.641 :c) Shear and moments :shear at support (thickned slab) :- (w x l)/2 :shear 1000 at mm from supp. (ribs) :0.5 x :27.844 6.96 :-

27.84

kN

24.36

kN

For two-way slab :l/b

:-

1.000


Chapter 4


α x (+) :- αy (+) :-

0.024

α x (-) :- αy (-) :-

0.032

2

Mu(+) :- α x w l x

:-

10.69

kNm

:-

14.26

kNm

d x :-

269 mm

d x :-

257 mm

bf :-

1000

mm

bw :-

125

mm

Df :d :-

75 257

mm mm

Df / d :-

0.292

2

Mu(-) :- αy w ly d) Flexure reinforcement :-

Assume

12 mm

diameter bars

Positive moment reinforcement :-

section is designed as a tee beam

(second layer is considered for symmetry)

Mu(+) :-

11 kNm ,

bf / bw :-

2

Mu,lim. T / (f ck bw d ) :Mu,lim. T :Ast :-

8.00 0.845

(Table 58, SP : 16)

209.2928 kNm

134.91

2

>

10.7 kNm

(Mu / (0.87 f y d))

mm

2

mm provide 2 10 # :- 157 Negative moment reinforcement :14.3 1000 Mu(-) :kNm b :mm 2

Mu/bd pt provide

:-

3 :150.72

0.055 Ast 8 #

:-

d :-

269 mm

0.20

pt = 50

{ [1-(1-√(4.6Mu/f ckbd2))] / (f y/f ck) } 2

:147.9833 mm between ribs + 2 -

+ 100.48

:-

251.2

8 #

2

mm

(top bars of rib)

e) Shear :-

500 mm

Shear in ribs at Vu :-

24.36 kN τv

:-

100 As/(b d) :-

b :-

from support 125 mm 2

0.758 N/mm

d :- 257 mm Vu /(b d)

0.49


Chapter 4


τc

2

:-

0.5 N/mm τv

use

6 mm

>

τc

( Page :- 73, IS : 456,2000) Shear design necessary.

vuc :- τc b d :-

16.06 kN

vus :- vu - vuc :-

8.301 kN

dia two-legged stirrups with Asv :sv :- (0.87 f y Asv d) / vus :-

57

2

mm

380.6 mm

spacing required for minimum shear reiforcement. sv :- (0.87 f y Asv) / 0.4b :-

245.9 mm

193 maximum spacing permitted, sv,max :- 0.75 d :mm provide 6 mm dia @ 193 mm two-legged stirrups throught. f) Development lenfth :177.2 Ld for negative moment bars :mm ….ok :anchorage available 1000 mm for positive moment bars :Mu1 :- 0.87 Fy Ast d 13.123 kN

1.3 Mu1/vu + L0 > Ld

Vu

:-

L0

:0.7002 + 8#

24.3633 kN 8 #

> 22.0684 8 # < # g) Check for moment design at junction of solid slab and ribbed slab ::-

negative moment reinforcement is designed considering the section

from support Mu(-) 1 m :h) Deflection :basic span / d ratio

pt :- 100 As / (bf d) modification factor permissible span / d actual span / d

10.11 :-

::::-

kNm

<

1000 mm

177 mm ….ok

x 300 mm

Mu(-)

….ok

26 0.05 2.0 52 31

(page no. 38; IS 456-2000) <

52

….ok


Chapter 4


i) Topping reinforcement :2

mm /m. 90 d :56 assume Maximum spacing :- 5 d :# wrapping mesh @ 200 mm As :-

use

6 mm

6.00 280

dia bar.

c/c :-

141

mm.

2

mm /m at the centre of topping. steel quantity along long span (+ve)steel :L :No. of bars :weight of steel :along short span (+ve) steel :L :No. of bars :weight of steel :along long span (-ve)steel :L :No. of bars :weight of steel :along short span (-ve) steel :L :No. of bars :weight of steel :along long span (-ve)steel :L :No. of bars :weight of steel :along short span (-ve)steel :L :No. of bars :weight of steel :-

2 8 16 79 2 8 16 79 2 8 16 51 2 8 16 51 3 4 24 38 3 4 24 38

topping reinforcement along long span steel :6 # L :1

10 # m nos. kg. 10 # m nos. kg. 8 # m nos. kg. 8 # m nos. kg. 8 # m nos. kg. 8 # m nos. kg.

200

(bottom steel of rib beam)

(bottom steel of rib beam)

(top steel of rib beam)

(top steel of rib beam)

(between ribs)

(between ribs)

mm c/c

m


Chapter 4


No. of bars weight of steel along short span steel :L No. of bars weight of steel

:::::-

shear reinforcement : along long span steel :L :No. of bars :weight of steel :along short span steel :L :No. of bars :weight of steel :-

384 85 6 1 384 85

nos. kg. 200 m nos. kg.

6 # 0.85 332 63 6 # 0.85 332 63

193

mm c/c

m nos. kg. 193 m nos. kg.

mm c/c

total steel required for 3 span. total steel required :Total cost of steel :-

mm c/c

12915 419724.3

kg. Rs. 3

quantity of conc.in topping slab :-

43.20

m

quantity of solid slab near mainbeam :-

86.40

m

quantity of ribbed beams :-

28.35

m

quantity of main beams :-

46.08

m

total quantity of concrete :3

quantity of steel in m :% of steel :Total cost of slab :interior panel bottom fibre stress :-M y / I :-

3 3 3

3

204.03

m

1.65 0.81

m %

1431773

Rs.

3

2

7.60E+00 N/mm


Chapter 4 Ribbed Slabs and Waffle Slabs

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