chapter 4 ribbed slabs and waffle slabs
DESCRIPTION
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 constructionsTRANSCRIPT
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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Chapter 4 Ribbed Slabs And Waffle Slabs
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.
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Chapter 4 Ribbed Slabs And Waffle Slabs
(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,
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Chapter 4 Ribbed Slabs And Waffle Slabs
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.
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Chapter 4 Ribbed Slabs And Waffle Slabs
4.3.4 SPAN: DEPTH CHART FOR WAFFLE SLAB
Fig. 4.3 Span: Depth chart
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Chapter 4 Ribbed Slabs And Waffle Slabs
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 :-
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Chapter 4 Ribbed Slabs And Waffle Slabs
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 :-
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Chapter 4 Ribbed Slabs And Waffle Slabs
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
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Chapter 4 Ribbed Slabs And Waffle Slabs
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
No. of bars :- 16 nos.weight of steel :- 79 kg.
along long span (-ve)steel :- 2 8 # (top steel of rib beam)
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Chapter 4 Ribbed Slabs And Waffle Slabs
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
No. of bars :- 16 nos.weight of steel :- 51 kg.
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
No. of bars :- 24 nos. weight of steel :- 38 kg.
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
No. of bars :- 384 nos.weight of steel :- 85 kg.
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
No. of bars :- 332 nos. weight of steel :- 63 kg.
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Chapter 4 Ribbed Slabs And Waffle Slabs
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
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