BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Chapter 1
INTRODUCTION
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
1.1 OVERVIEW
Reinforced concrete slabs are relatively thin, flat, structural elements, whose main
function is to transmit loading acting normal to their plane. Slabs are used as floors and
roofs of buildings, as walls in tanks and buildings, and as bridges to transmit relatively
heavy concentrated loading.
Reinforced concrete slabs are among the most common structural elements, but despite
the large number of slabs design and built, the details of the elastic and plastic behavior of
slabs are not always appreciated or properly taken into account. This occurs at least
partially because of the mathematical complexities of dealing with elastic equations,
especially for support conditions which realistically approximate those in building floor
slabs.
Regardless of which design method is used, the resulting slab must be serviceable at the
working load level, with deflections and cracking remaining within acceptable limits .slab
design methods are concerned largely with flexure, but the shear forces may also be a
limiting factor .The particular problem of shear is in beamless slabs, especially when
acting in combination with transfer of unbalanced moments from slabs to columns.
The bi-axially voided bubble deck technology is based upon the patented integration
technique - the direct way of linking air and steel. The bubble deck technology comprises
of a bi axial carrying hollow slab in which plastic balls serves the purpose of eliminating
concrete that has no carrying effect. In other words, it removes the non working dead
load, while maintaining bi axial strength.
This project report contains the details of innovative design, detailing and estimation of bi
axially voided bubble deck slab and a comparative study with conventional slab systems,
namely, beam slab and conventional flat slab.
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
1.2 OBJECTIVES
The main objective of this project is to design and compare structural, economic, and environmental panorama of the following floor slab systems –
Conventional beam slab system
Conventional flat slab system
Bi-axially voided bubble deck system
In order to accomplish the advantages of the new bi-axially voided bubble deck floor slab systems over other conventional floor slab systems.
1.3 Project Outlines
There are eight chapters in this project report. Chapter one gives introduction and
objectives of this project. Chapter 2 provides literature review for this project. This chapter
gives the theory behind this project. Chapter 3 gives the information related to design and
detailing of flat slab system. Chapter 4 gives the information about design and detailing of
conventional beam slab system. Chapter 5 gives the information about design and
detailing of bi-axially voided bubble deck floor slab system. Chapter 6 contains material
and economic estimation of all above mentioned floor slab systems. Chapter 7 contains
results and discussions. Chapter 8 gives conclusions on the experimental outcome and
the scope for future work.
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
CHAPTER 2
LITERATURE REVIEW
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
2.1 CLASSIFICATION OF SLABS
Different types of load patterns and support conditions require different types of floor slab
systems. To accomplish this, the different types of floor slab systems used can be broadly
grouped into the following four classes –
a ) Conventional beam slab system
b) Flat slab system
c) Hollow core floor slab system
d) Bi-axially voided bubble deck floor slab system
Slabs can be classified as follows:
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
2.2 BEAM SLAB
Slabs supported on beams on all sides or selected sides of each poannel are generally
termed as beam slabs. In a beam slab system, it is quite easy to visualize the path from
load point to columns as being from slab to beam to column and them to compute realistic
moments and shears for the design of all members. A conventional beam slab system can
be classified as :
One way slab
Two way slab
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SLAB
BEAM SLAB BEAM LESS SLAB
CONVENTIONAL FLAT SLAB
HOLLOW CORE SLAB
BIAXIALLY VOIDED BUBBLE
DECK SLAB
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
A typical beam slab is shown in figure 2.1
2.2 FLAT SLABS
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
The term flat slab means a reinforced concrete slab with or without drops, supported
generally without beams, by columns with or without flared column heads. A flat slab may
be a solid slab or may have recesses formed on the soffit so that the soffit comprises a
series of ribs in two direction.
The following two methods are recommended by the code for determining the bending moments in the slab panel:
1) Direct design method (DDM)
2) Equivalent frame method (EFM)
These methods are applicable only for two way rectangular slabs.
2.2.1 DIRECT DESIGN METHOD
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Direct design method is a simplified procedure of determining the negative and positive
design moment at critical section in the slab. The code specifies that the following
conditions must be satisfied by the two way slab system for the application of direct
design method:
1) There must be at least three continuous spans in each direction.
2) Each panel must be rectangular, with the long to short span ratio not exceeding 2.0
3) The columns must not be offset by more than ten percent of span from either axis
between centre lines of successive columns. As shown in figure 2.3.
4) The successive span length in each direction must not differ by more than 1/3rd of longer span.
5) The factored live load must not exceed three times the factored dead load.
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
2.2.2. EQUIVALENT FRAME METHOD
The equivalent frame method (EFM) of design of two way beam supported slabs, flat
slabs, flat plates and waffle slab is a more general and more rigorous method than DDM,
and is not subjected to the limitations of DDM.
The equivalent frame concept simplifies the analysis of three dimensional reinforcement
concrete building by sub dividing it into a series of two dimensional frames centered on
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
column lines in longitudinal as well as transverse direction. The EFM differs from DDM in
the determination of total `negative` and `positive` design moments in the slab panel for
the condition of gravity loading. However, the apportioning of the moments to column strip
and middle strip is common for both methods.
2.3 HOLLOW CORE SLAB
Hollow core slabs are pre fabricated, one way spanning, concrete elements with hollow
cylinders.
FIG 2.5
Due to the pre fabrication, these are inexpensive and reduce building time, but can be
used only in one way spanning construction and must be supported by beams and/or
walls.
2.3.1 LIMITATIONS OF HOLLOW CORE SLAB
Manufactured
It requires higher capacity cranes
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Prevalence of post construction inflexibility
It has one way action
It is suitable only for certain applications
2.4 BI-AXIALLY VOIDED BUBBLE DECK SLAB SYSTEM
The bi-axially voided bubble deck technology is based upon the patented integration
technique - the direct way of linking air and steel.
The bubble deck technology comprises of a bi axial carrying hollow slab in which plastic
balls serves the purpose of eliminating concrete that has no carrying effect. In other
words, it removes the non working dead load, while maintaining bi axial strength.
By adopting the geometry of the ball in the mesh, an optimized concrete construction is
obtained, with simultaneous maximum utility of both moment and shear zones.
The construction literally creates itself as a result of the geometry of two well known
components:
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
a) Reinforcement b) Hollow plastic balls
When the top and bottom reinforcement are linked in the usual way, a geometrical and
statically stable bubble deck bubble-unit evolves.
The reinforcement catches, distributes and locks the balls in exact position, while the balls
shape the air volume, control the level of reinforcement and at the same time stabilize the
spatial lattice. When the steel lattice unit is concreted, a monolithic bi-axial hollow slab is
obtained.
2.4.1 GENERAL THEORY
A bubble deck behaves like a solid slab, with true bi axial behavior, uniform in arbitrary
direction.
Tension and compression zone is not influenced by the voids.
Forces can be distributed freely, with no singularities, in the three dimensional structure,
hence, making all concrete effective.
Fig: 2.6
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
When cutting out holes, the difference between the two deck types becomes obvious.
With one way span it is necessary to place beams around the hole to transport the forces
to principle beams.
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Two way spans can be completely without beams.
FIG 2.7
2.4.2 TESTS AND STUDIES
The bubble deck technology has been tested thoroughly. Results confirm that a bubble
deck slab behaves like a solid slab in every way.
2.4.2.1 SHEAR STRENGTH
Tests confirm that all concrete in the slab can be taken into account when calculating any
type of forces. For safety reasons, it is recommended to use a factor of 0.6 compared to
values of a solid slab of same height.
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
2.4.2.2 BENDING STRENGTH AND DEFLECTION BEHAVIOUR
A bubble deck slab has the same bending strength as a solid slab of same height. The
bending stiffness is 0.9, compared to a solid slab. But since the weight of the slab is only
0.65 of a solid slab, the deflection will be considerably less.
2.4.2.3 ANCHORING
Tests confirm that the balls have no influence on the anchoring values. The values are
exactly the same s for a solid slab.
2.4.2.4 FIRE
A bubble deck slab can be tailored to meet any requirements by optimizing the actual
concrete cover.
The bubbles only slightly influence the patterns of heat transfer through the cover after a
certain time and distance from the bottom,. Again, a bubble deck behaves like a solid
slab.
TABLE 2.1
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
2.4.2.5 SOUND
Values for air borne, impact sound (vertical or horizontal) exists. Below are the
representative values.
TABLE 2.2
2.4.3 Bubble deck slab versions
The appropriate bubble deck slab version is engineered to suit building configuration,
span length between supports, applied loadings and vertical alignment of supports.
TABLE 2.3
2.4.4 ELEMENT TYPES
Bubble deck can be manufactured in three types of manufactured elements:
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
TYPE A – FILIGREE ELEMNTS
When the bottom of the bubble reinforcement sandwich includes a 70mm thick pre cast
concrete layer acting as formwork within part of the finished slab depth replacing the need
for soffit shuttering. The elements are placed on temporary propping, loose joint, the shear
and edge reinforcement added, perimeter and tolerance shuttered and then the remaining
slab depth concreted.
Most commonly specified being suitable for the majority of new-build projects. Requires
fixed or mobile crane to lift into position due to weight of manufactured elements as
delivered to site.
TYPE B-REINFORCEMENT MODULES
Comprising pre-fabricated ‘bubble reinforcement’ sandwiched elements. The modules are
placed on traditional site formwork, loose joint, shear and edge reinforcement added and
then concrete in two stage to the full slab depth. Suitable for suspended ground floor slabs
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
and alteration/refurbishment projects, particularly where site access is extremely
restricted. Can be manually lifted into position.
TYPE C-FINISHED PLANKS
Delivered to the building site as complete pre-cast factory made slab elements with full
concrete thickness . These span in one direction only and require the inclusion of
supporting beams or walls within the structure.
2.4.5 POST-TENSION
When mega spans are required (above 15 meter) we can provide a post tension (PT)
bubble deck solution. The above deflection limits can be increased by up-to 30 percent
with post-tension bubble deck slab.
2.4.6 GREEN CREDENTIALS
By virtually eliminating concrete in the middle of a slab bubble deck makes a significant
contribution to reducing environmental impact. Guidance from the ODPM requires the
direct environmental effects of building to be considered, including usage of natural
resources and emission resulting from construction. Not only is concrete usage reduced
up-to 50 percent within a building structure but knock-on benefits can be realized through
reduced foundation side. Bubble deck can make a a big contribution towards achieving
BREEAN targets.
Every 5000 m2 of bubble deck floor slab can save:
1000 m2 site concrete
166 ready mix lorry trips
1798 tonnes of foundation loads –or 19 less piles
1745 GJ energy used in concrete production and haulage
278 tonnes of CO2- green house gases-emission
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
CHAPTER 3
DESIGN OF FLAT SLABS
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
ANALYTICAL PLAN
FIG 3.1
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
3. DESIGN OF FLAT SLAB (USING EQUIVALENT FRAME METHOD)
3.1 Slab thickness
For deflection control d ≥ l
n / 26 [IS-456, Clause 23.2.1] Since drop is not provided d ≥ l
n/(26*0.9) [IS-456, Clause 23.2.1] d ≥ 6500/(26*0.9)
d ≥ 277.77 mm Approx. d ≈ 275 mm Therefore D = d + 25 (clear cover)
D = 275 + 25
D = 300 mm
3.2 Load Calculation
Self weight of slab = 25 * 0.3 = 7.5 KN / m2
Floor finish = 1 KN / m2
Live load = 2.4 KN / m2
Total = 10.9 KN / m2
Factored load = 1.5 * 10.9 = 16.35 KN / m2
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3.3 Equivalent Frame Analysis
Along N-S direction
Middle strip
Fig 3.2
Fixed end moment Mf-ab = w * l2 / 12
= - 98.1 * 6.52 / 12
= - 345.39 KN-m
[Due to symmetry fixed end moments are same for all spans]
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Distribution factor (DF Table)
Span K ∑K DF = K / ∑KA2B2 I / 6.5 0.15 I 1B2A2
B2C2
I / 6.5
I / 6.5
0.3 I 0.5
0.5D2C2
D2E2
I / 6.5
I / 6.5
0.3 I 0.5
0.5E2F2
E2D2
I / 6.5
I / 6.50.3 I
0.5
0.5F2E2
F2G2
I / 6.5
I / 6.5
0.3 I 0.5
0.5G2F2 I / 6.5 0.15 I 1 TABLE 3.1
Moment Distribution Table
Joint A2 B2 C2 D2 E2 F2 G2
Span A2B2 B2A2 B2C2 C2B2 C2D2 D2C2 D2E2 E2D2 E2F2 F2E2 F2G2 G2F2
DF 1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1FEM -345 345 -345 345 -345 345 -345 345 -345 345 -345 345FinalMoment
-345 345 -345 345 -345 345 -345 345 -345 345 -345 345
TABLE 3.2
Since A and G are fixed ends and also due to symmetry, all moments are balanced, hence fixed end moments are equal to final moments
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
For edge strip
Fig 3.3 Fixed end moment
Mf-ab = w * l2 / 12
= - 49.05 * 6.52 / 12
= - 172.70 KN - m
[Due to symmetry fixed end moments are same for all spans]
Distribution factor (DF Table)
Span K ∑K DF = K / ∑KAB I / 6.5 0.15 I 1BA
BC
I / 6.5
I / 6.5
0.3I 0.5
0.5DC
DE
I / 6.5
I / 6.5
0.3 I 0.5
0.5EF
ED
I / 6.5
I / 6.50.3 I
0.5
0.5FE
FG
I / 6.5
I / 6.5
0.3 I 0.5
0.5GF I / 6.5 0.15 I 1 Table 3.3
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Moment Distribution Table
Joint A B C D E F GSpan AB BA BC CB CD DC DE ED EF FE FG GFDF 1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1FEM -172 172 -172 172 -172 172 -172 172 -172 172 -172 172FinalMoment
-172 172 -172 172 -172 172 -172 172 -172 172 -172 172
TABLE 3.4
Since A and G are fixed ends and also due to symmetry, all moments are balanced, hence fixed end moments are equal to final moments
Along E-W direction
EDGE STRIP
Fig 3.5
Fixed End Moment
Mf-a1a2 = w * l2 / 12
= - 53.13 * 62 / 12
= -153.39 KN - m
[Due to symmetry fixed end moments are same for all spans]
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Distribution factor (DF Table)
Joint Span K ∑K DF = K / ∑KA1 A1A2 I / 6 0.166I 1
A2
A2A1
A3A2
I / 6
I / 60.33I
0.5
0.5A3 A3A2 I / 6 0.166I 1
Table 3.5
Joint A1 A2 A3
Span A1A2 A2A1 A2A3 A3A2
DF 1 0.5 0.5 1FEM -159.39 159.39 -159.39 159.39Final Moment -159.39 159.39 -159.39 159.39
Moment Distribution Table
Since A1 and A3 are fixed ends and also due to symmetry, all moments are balanced, hence fixed end moments are equal to final moments
Table 3.6
MID STRIP
Fig 3.6
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Fixed End Moment
MF-B1B2 = W * l2 / 12
= -106.27 * 62 / 12
= -318.825 KN – m
[Due to symmetry fixed end moments are same for all spans]
Distribution factor (DF Table)
Joint Span K ∑K DF = K / ∑KB1 B1B2 I / 6 0.166I 1
B2
B2B1
B3B2
I / 6
I / 60.33I
0.5
0.5B3 B3B2 I / 6 0.166I 1
Table 3.7
Moment Distribution TableJoint B1 B2 B3
Span B1B2 B2B1 B2B3 B3B2
DF 1 0.5 0.5 1FEM -318.25 318.25 - 318.25 318.25Final Moment -318.25 318.25 -318.25 318.25
Table 3.8
Due to symmetry of span and supports, maximum positive moment will occur at centre
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Fig 3.7
M+ive = w * l2 / 8
= 98.1 * 6.52 / 8
= 518.09 KN – m
3.4 Moment Calculation
N-S direction
Negative moment calculation (for mid strip along N-S dir)
From left support , M-ive = Ml – (98.1 * 0.352 / 2)
= -345.39 - 6.008
= -351.39 KN – m
(Since all the spans are symmetrical, moment from right support will be equal to moment from left support)
Total design moment, for span (face to face) , Mo = w * ln / 8
= 98.1 * 5.8 / 8
= 71.125 KN - m
Calculation of Ast (N-S direction)
Adopting M+ive for calculation of Ast, since its value is highest and reducing it by 10% in accordance with clause 31.4.3.4 of IS – 456.
Mu = 0.90 * 518.09
= 466.28 KN – m
Mu / bd2 = 466.28 * 10 ^ 6 / (6000 * 275 2)
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
= 1.05
(Using Fck = 30, from table 4 of SP – 6)
pt = 0.304
Considering 1m strip
Ast = pt * b * d / 100
= 0.304 * 1000 * 275 / 100
= 836 mm2
Using 16mm ᴓ bars
Spacing = (π * 162 / 4) * 1000 / 836
= 240 mm
E-W Direction
Due to symmetry, maximum positive moment will occur at centre
M+ive = w * l2 / 8
= 106.27 * 62 / 8
= 478.21 KN – m
Maximum negative moment,
From left support , M-ive = Ml – w * l2 /2
= -318.82 – (106.27 * 0.352 / 2)
= -325.33 KN – m
Total design moment, Mo = w * ln / 8
= 106.275 * 5.3 / 8
= 70.41 KN – m
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Calculation of Ast (E-W direction)
Adopting M+ive for calculation of Ast, since its value is highest and reducing it by 10% in accordance with clause 31.4.3.4 of IS – 456. MU = .90*478.21
= 430.39 KN-m
MU/b*d2 = 430.39*10^6/(6500*275) = 0.90 (Using Fck = 30, from table 4 of SP – 6)
pt = 0.259
Considering 1m strip
Ast = pt * b * d / 100
= 0.259*1000*275/100
= 712.25 mm2
Using 16mm ᴓ bars
Spacing = (π * 162 / 4) * 1000 / 712.25
= 280mm
3.4.1 Shear check
Ԏv = VU /b*d
=( 318.82 * 2 * 103 )/( 6000* 275)
= 0.38 N/mm2
For 100Ast/bd = 0.304
Referring to table 19 of IS-456
ԎC = 0.40
Hence ԎC > Ԏv
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Therefore SAFE
Detailing of flat slab
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Fig 3.8
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
CHAPTER 4
DESIGN OF CONVENTIONALBEAM SLAB
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
4. Design of Conventional Beam Slab (Using limit state method)
4.1 Design of slab
4.1.2 Check For one way / two way type of slab
Ratio of longer span to shorter span = ly / lx = 6.5/6 = 1.08 > 2
Therefore slab is designed as two way slab. Lx = 6m Ly = 6.5m Consider 1m stripAssume slab thickness =150mmUsing 15mm clear cover with 10mm ᴓ bar d = 150-15-10/2 = 130mm
4.1.3 load calculation
Dead load = 0.15*25 = 3.75 KN/m2
Live load = 2.4 KN/m2
Floor finish = 1 KN/m2
Total load = 7.15 KN/m2
Ultimate load = 1.5 * 7.15 = 10.725 KN/m2
4.1.4 Calculation of moment co-efficient
1.0 1.08 1.1α x 0.062 0.0716 0.074α y 0.062 0.0612 0.061
Table 4.1
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
4.1.5 Calculation of moments
MX = 0.0716 * 10.725 * 62
= 27.64 KN-m
My = 0.0612 * 10.725 * 62
= 23.63 KN-m
M max = 27.64 KN-m
4.1.6 Check for depth
MU = (0.36 * Xu-max ( 1-0.42(Xu-max /d))b*d2fck )/ d
27.64 *106 = 0.36*0.48( 1-0.42*0.48)*1000*d2 * 20
d = 81.72mm < 150mm
Hence safe
Provide D =150mm; d =130mm
From IS-456 ; Pg 76
M = 29.66 KN-m
Spacing = 110mm
Provide 10mm ᴓ bar @ 110mm c/c along long direction and short direction
4.2 DESIGN OF BEAMS
AREA OF 1 + 2 = 2*((6.5 + 0.5)/2*3)
= 21 m3
Volume = 21 * 0.15
= 3.15 m3
Weight = 25 * 3.15
= 78.75 KN
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Uniformly distributed load = 78.65 / 6.5
= 12.12 KN / m
4.2.1 Depth Calculation
For simply supported beam (clause 23.2.2 of IS - 456)
L / d = 20
d = 6500 / 20
Approx. d ≈ 325 mm
Therefore D = d + 50 (clear cover)
D = 325 + 50
D = 375 mm
Assuming width, b = 230mm
4.2.2 Load Calculation
Self weight of slab = 25 * 0.375 * 0.23 = 2.16 KN / m2
Dead load due to slab = 12.12 KN / m2
Floor finish = 1 KN / m2
Live load = 2.4 KN / m2
Total = 17.68 KN / m2
Factored load = 1.5 * 17.68 = 26.52 KN / m2
Moment Mu = w * l2 / 8 = 26.52 * 6.52 / 8
= 140.06 KN –m Shear force at support, Vu = w * l / 2
= 26.52 * 6.5 / 2
= 86.19 KN
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Limiting value of moment,
Mulim = 0.36 * Xumax *(1- 0.42Xumax/d)bd2 fck /d
Referring to clause 38.1 of IS – 456
For Fe 415, Xumax/d = 0.48
Mulim = 0.36 * 0.48 (1-0.42*0.48)*230*3252*20
= 67.033 KN – m
Mu > Mulim, hence design as doubly reinforced section Xumax = 0.48 * 325
= 156 mm
4.2.3 Calculation of area
Compression steel
Strain = 0.0035 (Xumax – d`)/Xumax
= 0.0035 (156 – 50)/156
=2.37 * 10-3
From SP 16, figure 3
Stress, Fsc = 380 N/mm2
Mu - Mulim = Fsc * Asc (d-d`)
10^6(140.06 – 67.03) = 380 * Asc (325 - 50)
Asc= 698.85 mm2
Using 20mm ᴓ bars Number of bars = 698.85 / (π * 202 / 4) = 2.23 ≈ 3 bars
Hence provide 3 bars of ᴓ 20mm as compression steel
Tension steel
Xu / d = Xumax / d =( 0.87 fyAst1) /(0.36 fck bd)
0.48 = (0.87 * 415 * Ast1) / (0.36 * 20 * 230 * 325 )
Ast1=715.51mm2
Department of Civil Engineering, M.S.R.I.T.Page 38
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Ast2 = Asc * fsc /(0.87 fy)
= 698.85 * 380 / (0.87 * 415)
= 735.53 mm2
Total area of tension steel , Asc = Asc1 + Ast2
= 715.51 + 735.53
= 1451.04 mm2
Using ᴓ 22mm bars No of bars = 1451.04 / (π * 222 / 4)
= 3.81 ≈ 4 bars
Provide 4 bars of ᴓ 22mm as tension steel
4.2.4 Design for shear
\Vu = 86.19 KN
b = 230 mm
d = 325 mm
Actual steel = 4 * π *222 / 4
= 1520.53 mm2
Ԏv = Vu / bd
= 86.19 * 10 ^3 /( 230 * 325)
= 1.17 N / mm2
100 Ast / bd = 100 * 1520.53 / (230 * 320)
= 2.03
Referring to table 19 of IS 456, for M20,
Ԏc = 0.79
Ԏc < Ԏv
Hence provide shear reinforcement
Department of Civil Engineering, M.S.R.I.T.Page 39
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Using Vus = 0.87 * fy * Asv * d / Sv
Using 2 legged , ᴓ 8 mm stirrups,
Asv = 2 * π * 82 / 4
= 100.53 mm2
Vus = Vu - Ԏc bd
= 86.19 * 10^3 –(0.79 * 230 * 325)
= 27.13 * 10 ^3 N
27.13 * 10 ^3 = 0.87 * 415 * 100.53 * 325 / SV
Sv = 434.68 mm
But, As per IS 456, maximum spacing = 0.75 * d
= 0.75 * 325
= 243.75 mm
OR 300 mm
Hence provide 2 L ᴓ 8mm @ 300mm c/c stirrups
Department of Civil Engineering, M.S.R.I.T.Page 40
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Detailing of conventional beam slab
Fig 4.1
Department of Civil Engineering, M.S.R.I.T.Page 41
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Fig 4.2
Department of Civil Engineering, M.S.R.I.T.Page 42
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
CHAPTER 5
DESIGN OF BUBBLE DECK SLAB
Department of Civil Engineering, M.S.R.I.T.Page 43
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
5. Design Of Bubble Deck Slab
5.1Slab thickness
For deflection control
Modifying l / d ratio by 0.5 [BS8110, product introduction]
d ≥ ln / (26*0.9*1.5) [IS-456, Clause 23.2.1]
d ≥ 6500 / (35.1)
d ≥ 185.19 mm
Approx. d ≈ 190 mm
Therefore D = d + 20 (clear cover) considering
D = 190 + 20
D = 210 mm Provide D = 230 mm (considering slab version BD 230)
Hence , d = 230 – 25 = 205 mm
(25mm cover provides 60 min of fire resistance)
5.2 Load Calculation
Self weight of slab = 25 * 0.23 *2/ 3 = 3.83 KN / m2
Floor finish = 1 KN / m2
Live load = 2.4 KN / m2
Total = 7.23 KN / m2
Factored load = 1.5 * 7.23 = 10.845 KN / m2
Department of Civil Engineering, M.S.R.I.T.Page 44
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
5.3 Equivalent Frame Analysis
Along N-S direction
For middle strip
Fig 5.1
Fixed end moment
Mf-ab = w * l2 / 12 = - 65.07 * 6.52 / 12
= - 229.1 KN-m
[Due to symmetry fixed end moments are same for all spans]
Distribution factor (DF Table)Span K ∑K DF = K / ∑KA2B2 I / 6.5 0.15 I 1B2A2
B2C2
I / 6.5
I / 6.5
0.3 I 0.5
0.5D2C2
D2E2
I / 6.5
I / 6.5
0.3 I 0.5
0.5E2F2
E2D2
I / 6.5
I / 6.50.3 I
0.5
0.5F2E2
F2G2
I / 6.5
I / 6.5
0.3 I 0.5
0.5G2F2 I / 6.5 0.1 I 1
Table 5.1
Department of Civil Engineering, M.S.R.I.T.Page 45
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Moment Distribution Table
Joint A2 B2 C2 D2 E2 F2 G2
Span A2B2 B2A2 B2C2 C2B2 C2D2 D2C2 D2E2 E2D2 E2F2 F2E2 F2G2 G2F2
DF 1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1FEM -229 229 -229 229 -229 229 -229 229 -229 229 -229 229FinalMoment
-229 229 -229 229 -229 229 -229 229 -229 229 -229 229
Table 5.2
Since A and G are fixed ends and also due to symmetry, all moments are balanced, hence fixed end moments are equal to final moments
For edge strip
Fig 5.2
Fixed end moment
Mf-ab = w * l2 / 12
= - 32.535 * 6.52 / 12
= - 114.55 KN - m
[Due to symmetry fixed end moments are same for all spans]
Department of Civil Engineering, M.S.R.I.T.Page 46
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Distribution factor (DF Table)
Span K ∑K DF = K / ∑KAB I / 6.5 0.15 I 1BA
BC
I / 6.5
I / 6.5
0.3 I 0.5
0.5DC
DE
I / 6.5
I / 6.5
0.3 I 0.5
0.5EF
ED
I / 6.5
I / 6.50.3 I
0.5
0.5FE
FG
I / 6.5
I / 6.5
0.3 I 0.5
0.5GF I / 6.5 0.15 I 1
Table 5.3
Moment Distribution Table
Joint A B C D E F GSpan AB BA BC CB CD DC DE ED EF FE FG GFDF 1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1FEM -114.5 114.5-114.5 114.5-114.5 114.5-114.5 114.5-114.5 114.5-114.5 114.5FinalMoment
-114.5 114.5-114.5 114.5-114.5 114.5-114.5 114.5-114.5 114.5-114.5 114.5
Table 5.4
Since A and G are fixed ends and also due to symmetry, all moments are balanced, hence fixed end moments are equal to final moments
Along E-W direction
EDGE STRIP
Department of Civil Engineering, M.S.R.I.T.Page 47
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Fig 5.3Fixed End Moment
Mf-a1a2 = w * l2 / 12
= - 35.24 * 62 / 12
= -105.72 KN - m
[Due to symmetry fixed end moments are same for all spans]
Distribution factor (DF Table)
Joint Span k ∑K DF = K / ∑KA1 A1A2 I / 6 0.166I 1
A2
A2A1
A3A2
I / 6
I / 60.33I
0.5
0.5A3 A3A2 I / 6 0.166I 1
Table 5.5 Moment Distribution Table
Joint A1 A2 A3
Span A1A2 A2A1 A2A3 A3A2
DF 1 0.5 0.5 1FEM -105.72 105.72 -105.72 105.72Final Moment -105.72 105.72 -105.72 105.72
Table 5.6
Since A1 and A3 are fixed ends and also due to symmetry, all moments are balanced, hence fixed end moments are equal to final moments
Department of Civil Engineering, M.S.R.I.T.Page 48
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
MID STRIP
Fig 5.4
Fixed End Moment
MF-B1B2 = W * l2 / 12
= -70.49* 62 / 12
= -211.47 KN – m
[Due to symmetry fixed end moments are same for all spans]
Distribution factor (DF Table)
Joint Span K ∑K DF = K / ∑KB1 B1B2 I / 6 0.166I 1
B2
B2B1
B3B2
I / 6
I / 60.33I
0.5
0.5B3 B3B2 I / 6 0.166I 1
Table 5.5
Department of Civil Engineering, M.S.R.I.T.Page 49
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Moment Distribution Table
Joint B1 B2 B3
Span B1B2 B2B1 B2B3 B3B2
DF 1 0.5 0.5 1FEM -211.47 211.47 - 211.47 211.47Final Moment -211.47 211.47 - 211.47 211.47
Table 5.6
Due to symmetry of span and supports, maximum positive moment will occur at centre
Fig 5.5Va = 65.04*6.5/2
=211.47 KN
M+ive = w * l2 / 8
= 98.1 * 6.52 / 8
= 518.09 KN – m
5.4 Moment Calculation
N-S direction
Negative moment calculation (for mid strip along N-S dir)
From left support , M-ive = Ml – (65.07 * 0.352 / 2)
= -229.1- 3.98
= -233.08 KN – m
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
(Since all the spans are symmetrical, moment from right support will be equal to moment from left support)
Total design moment, for span (face to face) , Mo = w * ln / 8
= 65.07 * 5.8 / 8
= 47.17 KN - m
Calculation of Ast (N-S direction)
Adopting M+ive for calculation of Ast, since its value is highest and reducing it by 10% in accordance with clause 31.4.3.4 of IS – 456.
Mu = 0.90 * 343.08
= 308.772 KN – m
Mu / bd2 = 308.772 * 10 ^ 6 / (6000 * 205 2)
= 1.25
(Using Fck = 30, from table 4 of SP – 6)
pt = 0.365
Considering 1m stripAst = pt * b * d / 100
= 0.365 * 1000 * 205 / 100
= 748.25 mm2
Using 16mm ᴓ bars
Spacing = (π * 162 / 4) * 1000 / 748.25
= 270 mm
E-W Direction
Due to symmetry, maximum positive moment will occur at centre
M+ive = w * l2 / 8
= 70.49 * 62 / 8
= 317.20 KN – m
Department of Civil Engineering, M.S.R.I.T.Page 51
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Maximum negative moment,
From left support , M-ive = Ml – w * l2 /2
= -211.47 – (70.49* 0.352 / 2)
= -215.78 KN – m
Total design moment, Mo = w * ln / 8
= 70.49* 5.3 / 8
= 46.69 KN – m
Calculation of Ast (E-W direction)
Adopting M+ive for calculation of Ast, since its value is highest and reducing it by 10% in accordance with clause 31.4.3.4 of IS – 456. MU = .90*317.2
= 285.48 KN-m
MU/b*d2 = 285.48*10^6/(6500*205) = 1.05 (Using Fck = 30, from table 4 of SP – 6)
pt = 0.304
Considering 1m strip
Ast = pt * b * d / 100
= 0.304*1000*205/100
= 623.2 mm2
Using 16mm ᴓ bars
Spacing = (π * 162 / 4) * 1000 / 623.2
= 325 mm
Department of Civil Engineering, M.S.R.I.T.Page 52
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Detailing of bubble deck
Department of Civil Engineering, M.S.R.I.T.Page 53
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Fig 5.6
Department of Civil Engineering, M.S.R.I.T.Page 54
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
CHAPTER 6
COSTING AND ESTIMATION
6.1 FLAT SLAB
Department of Civil Engineering, M.S.R.I.T.Page 55
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
6.1.1 Reinforcement
Along N-S Direction
Length of main reinforcement
L= l + 2 * 0.5*d- 2c
= 39700+ 2*0.5*1.5 – 2*25
= 39666 mm
Length of crank bar L = l-2c +2 *0.5d +2 *9d1 (d1 = D -2c-d = 300-50-16 =234 mm)
= 39700- 2*25 +2*0.5*16+2*9*234
= 43878mm Number of main reinforcement = ((span/spacing)+1)/2
= ((12.7/0.24/2)+1)/2
= 27 bars
Number of cranked bars = 54-27
= 27 bars Along E-W direction
Length of main reinforcement,
L = l + 2*0.5d-2c
=12700 + 2*0.5*16 -2*25
=12666 mm
Length of cranked bar,
L = l – 2c + 2*0.5*d +2*9*d1
= 12700 -50 +2*0.5*16 +2*9*234
Department of Civil Engineering, M.S.R.I.T.Page 56
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
= 16878mm
Number of main reinforcement = ((span/spacing)+1)/2
= ((39.7/0.24)+1)/2
= 84 bars
Number of cranked bars = 167-84
= 83 bars
Table 6.1
Reinforcement Number Length(m)
Weight/meter0.616d2
=0.616*1.62
Total weight(kilogram, kg)
N-S direction Main
Cranked
27
27
39.7
44
1.57
1.57
1683
1865
E-W direction Main
Cranked
84
83
12.7
16.9
1.57
1.57
1675
2202
TOTAL = 7425
6.1.2 CONCRETE
Volume =12700 *39700 *300
= 151.3 m3
Table 6.2Particular Quantity Rate (Rs) Amount (Rs)Steel 7.425 M Ton 42000 3,11,950Concrete 151.3 m3 3500 5,29,550
Department of Civil Engineering, M.S.R.I.T.Page 57
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
TOTAL = 8,41,500
6.2 BUBBLE DECK SLAB
6.2.1 Bottom Reinforcement
Along N-S Direction
Length of main reinforcement
L= l + 2 * 0.5*d- 2c
= 39700+ 2*0.5*1.5 – 2*25
= 39666 mm
Length of crank bar L = l-2c +2 *0.5d +2 *9d1 (d1 = D -2c-d = 230-50-16 =164 mm)
= 39700- 2*25 +2*0.5*16+2*9*164
= 42618mm
Along E-W direction
Length of cranked bar,
L = l – 2c + 2*0.5*d +2*9*d1
= 12700 -50 +2*0.5*16 +2*9*164
= 15618mm
6.2.2 Top Reinforcement
Along N-S direction
Length of main reinforcement,
L = l + 2 * 0.5*d- 2c
= 39700+ 2*0.5*6 – 2*25
= 39656 mm
Department of Civil Engineering, M.S.R.I.T.Page 58
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Length of crank bar L = l-2c +2 *0.5d +2 *9d1 (d1 = D -2c-d = 230-50-6=174 mm)
= 39700- 2*25 +2*0.5*6+2*9*174 = 42788mm
Along E-W direction
Length of main reinforcement, L = l + 2 * 0.5*d- 2c
= 12700+ 2*0.5*6 – 2*25
= 12656 mm
Length of crank bar L = l-2c +2 *0.5d +2 *9d1 (d1 = D -2c-d = 230-50-6=174 mm)
= 12700- 2*25 +2*0.5*6+2*9*174
= 15788mm
Number of bars
Along N-S direction (bottom reinforcement)
Number of main reinforcement = ((span/spacing) + 1)/2
= ((12.7/0.27)+1)/2
= 24 bars
Number of Cranked bar = 48-24 =24 bars
Along E-W direction (bottom reinforcement)
Number of main reinforcement = ((span/spacing)+1)/2
Department of Civil Engineering, M.S.R.I.T.Page 59
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
= ((39.7/0.27)+1)/2
= 74 bars
Number of cranked bar = 148-74 =74 bars
Along N-S direction (top reinforcement)
Number of main reinforcement =((span/spacing)+1)/2
= ((39.7/0.2)+1)/2
= 199 bars
Along E-W direction (top reinforcement)
Number of main reinforcement = ((span/spacing)+1)/2
= ((12.7/0.2)+1)/2
= 64 bars
Details of bottom reinforcement ( using fe415 steel)
Table 6.3Reinforcement Number Length
(m)Weight/meter
0.616d2
=0.616*1.62
Total weight(kilogram, kg)
N-S direction Main 48 39.7 1.57 2992
E-W direction Main 148 12.7 1.57 2950
TOTAL = 5942
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Details of top reinforcement (using fe250steel)
Table 6.4Reinforcement Number Length
(m)Weight/meter
0.616d2
=0.616*0.62
Total weight(kilogram, kg)
N-S direction Main 64 39.6 0.22 558
E-W direction Main 199 12.6 0.22 552
TOTAL = 1110
6.2.3 Concrete
Total volume = 12700 *39700*230
= 115.96 m3
Number of balls
Along N-S direction = (span / spacing)-1
= (39.7/0.2)-1
= 197.5 ≈ 198 balls
Along E-W direction = (span/spacing)-1 = (12.7/0.2)-1 = 62.5 ≈ 63 balls Total = 197*62 = 12,214 balls
Reduction at column
Department of Civil Engineering, M.S.R.I.T.Page 61
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Solid slab is to be provided for areas of high shear that is 1/6th of the distance from centre to centre of column.
Therefore, area of 1 column = 2000 *2166.
Number of balls = (2000*2166.6)/(2000 *2000)
= 20.83 ≈ 21 balls
Number of equivalent columns units = 1*5+0.5*12 +0.25*4 = 5+6+1 = 12
Number of balls to be reduced =12* 21
= 252 balls
Therefore, total number of balls actually provided
= 12,214 –252
= 11,962
Volume of one ball = (4 *π *r 3)/3
= (4* π *0.0903)/3
= 3.05 * 10 -3 m3
Hence, volume of concrete = 115.96 -36.53
= 79.43 m3
Abstract
Table 6.5Particular Quantity Rate (Rs) Amount (Rs)Steel (fe415) 5.942 M Ton 42000 2,49,564Steel (fe250) 1.11 M Ton 42000 46,620Concrete 79.43 m3 3500 2,78,005Balls 11,962 Lump-sump 30,000
TOTAL = 6,04,189
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
6.3 BEAM SLAB
6.3.1 SLAB
ConcreteVolume of concrete = 6.25* 5.75 *0.15
= 5.39 m3
Total = 12 * 5.39 = 64.68 m3
Reinforcement
Along N-S direction
Number of main bars = ((span/spacing)+1)/2
= ((5.75/0.11)+1)/2
= 27 bars
Cranked = 54-27
= 27 bars
Length of main reinforcement
L = l + 2 * 0.5*d- 2c
= 6250+ 2*0.5*1 – 2*25
= 6210 mm
Length of crank bar L = l-2c +2 *0.5d +2 *9d1
(d1 = D -2c-d = 150-50-10= 90 mm)
= 6250- 2*25 +2*0.5*10+2*9*90
= 7830mm
Department of Civil Engineering, M.S.R.I.T.Page 63
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Along E-W direction
Number of main bars = ((span/spacing)+1)/2
= ((6.85/0.11)+1)/2
= 29 bars
Cranked = 59-29
= 30 bars
Length of main reinforcement
L = l + 2 * 0.5*d- 2c
= 5750+ 2*0.5*10 – 2*25
= 5710 mm Length of crank bar L = l-2c +2 *0.5d +2 *9d1
(d1 = D -2c-d = 150-50-10= 90 mm)
= 5750- 2*25 +2*0.5*10+2*9*90
= 7330mm
6.3.2 Beam
Along N-S direction
Length of main reinforcement
L = l + 2 * 0.5*d- 2c
= 6500+ 2*0.5*10 – 2*25
= 6460 mm Length of the stirrups
Department of Civil Engineering, M.S.R.I.T.Page 64
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
L = 2 ( l1 + l2 ) + 2 * 9*d
= 2(180+275) +2*9*8
= 1054 mm
Number of stirrups = (6.5/0.3)+1
= 23
Along E-W direction
Length of main reinforcement
L = l + 2 * 0.5*d- 2c
= 6000+ 2*0.5*10 – 2*25
= 5960 mm
Number of stirrups = (6/0.3) + 1
= 21
Volume of concrete for beam = 18(6.5*0.23*0.375)
= 14(6*0.23*0.375)
= 17.43 m3
Department of Civil Engineering, M.S.R.I.T.Page 65
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Details of reinforcementTable 6.6
Reinforcement Number Length(m)
Weight/meter Total weight(kilogram, kg)
SlabN-S direction
Main
Cranked
E-W directionMain
Cranked
12*27=324
12*27=324
12*29=348
12*30=360
6.2
7.8
5.7
7.3
0.616
0.616
0.616
0.616
1236
1560
1222
1619
BeamN-S direction
Top
Bottom
E-W direction
Top
Bottom
Stirrup
18*3=54
18*4=72
14*3=42
14*4=56
708
6.5
6.5
6
6
1.05
2.46
2.98
2.46
2.98
0.39
865
1395
621
1001
290
TOTAL = 9809
Total quantity of concrete =17.34 +64.68
= 82.02 m3
Abstract
Table 6.7Particular Quantity Rate (Rs) Amount (Rs)Steel 9.8 M Ton 42000 4,11,600Concrete 82.02 m3 3500 2,87,070
TOTAL = 6,98,670
Department of Civil Engineering, M.S.R.I.T.Page 66
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
6.4 ABSTRACT
TYPE VOLUME RATE AMOUNT( RS)
FLAT SLAB
Steel
Concrete
7.425 M-Ton
151.3 m3
42000
3500
3,11,850
5,29,550
BEAM SLAB
Steel
Concrete
9.8 M-Ton
82.02 m3
42000
3500
4,11,600
2,87,070
BUBBLE DECKSLAB
Steel (fe415 )
Concrete
Recycled plastic
Steel (fe250)
5.94 M-Ton
79.43 m3
11,962
1.11 M-Ton
42000
3500
Lump-sump
42000
2,49,480
2,78,005
30,000
46,620
Table 6.8
Department of Civil Engineering, M.S.R.I.T.Page 67
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
CHAPTER 7
RESULTS AND DISCUSSION
Department of Civil Engineering, M.S.R.I.T.Page 68
BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
7.1 IINTRODUCTION
Design and analysis of three types of slabs was done using their respective design
considerations. Costing and estimation was carried out to compute and compare the
structural, economic and environmental results. The outcome of the comparison is
presented in this chapter.
7.2 THICKNESS OF SLAB
Based on the design outcome (given in chapter 3,4,5) comparison of thickness of slab for
the different type of floor slab systems is plotted in the figure 7.1.
Beam sla
b
Flat s
lab
BUBBLEDECK
0
100
200
300
Thickness of slab in mm
Thickness of slab in mm
Fig 7.1
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Graph shows that bubble deck slab has considerably less thickness as compared to
conventional flat slab. Tough the conventional beam slab has least thickness; the addition
of beam nullifies the advantage.
7.3 QUANTITY OF CONCRETE
Based on the design outcome (given in chapter 6) comparison of quantity of concrete
used in slab for the different type of floor slab systems is plotted in the figure 7.2.
Beam sla
b
Flat s
lab
BUBBLEDECK
020406080
100120140160
Quantity of concrete in cubic metre
Quantity of concrete in cubic metre
Fig 7. 2
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Graph shows, the conventional flat slab system uses highest amount of concrete and
conventional beam slab system and bubble deck slab uses equal amount of concrete. But
addition of beams in conventional beam slab system nullifies this advantage.
7.4 QUANTITY OF STEEL
Based on the design outcome (given in chapter 6) comparison of quantity of steel used in
slab for the different type of floor slab systems is plotted in the figure 7.3
Beam sla
b
Flat s
lab
BUBBLEDECK
0
2
4
6
8
10
12
Quantity of steel in Mton(Fe415)Quantity of steel in Mton(Fe250)
Fi g7.3
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
From the graph we conclude that the bubble deck slab used least amount of steel and
usage of steel in conventional beam slab is maximum.
7.5 TOTAL QUANTITY AND ECONOMICS OF MATERIALS
Figure 7.4 shows the diagrammatic comparison of quantity of steel as well as quantity of
concrete used in different type of slab systems
concrete
steel
050
100150200250300350
Flat slabBeam slabBUBBLEDECK
Fig 7.4
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Cost of concreteCost of steel
0
100000
200000
300000
400000
500000
600000
BUBBLEDECKBeam Slab
BUBBLEDECKFlat slabBeam Slab
Fig 7.5
Figure 7.5 shows the comparison of cost of concrete and cost of steel in slabs for different
types of floor slab systems. It can be seen that the bubble deck slab has least cost of both
steel and concrete as compared to conventional flat slab and conventional beam slab
7.6 ENVIRONMENTAL COMPARISON
Table 7.1 shows the CO2 emissions for different types of slabs at given slab thickness
The table gives relevant data with reference to designed slabs as the thickness of slabs in
table are identical to the slabs designed
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Table 7.1
From table 7.1 we conclude that CO2 emission for bubble deck slab is least and that for
conventional flat slab is most. Figure 7.4 shows the diagrammatic comparison of quantity
of steel as well as quantity of concrete used in different type of slab systems
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
CHAPTER 8
CONCLUSIONS AND SCOPE FOR FUTURE WORK
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
8.1 CONCLUSIONS
A floor slab was designed using three different floor slab systems, namely conventional
beam slab system, conventional flat slab system, new bubble deck floor slab system.
Design and estimation was carried out for all the three types of slab systems. On the basis
of this work the following conclusions are drawn.
46.3 % of Concrete was saved by using bubble deck slab instead of conventional
flat slab system
38.7 % of steel was saved in bubble deck slab system as compared to
conventional beam slab system.
Almost 20 M.tones of CO2 emission was reduced by use of bubble deck
technology
Intangibles – other intangible benefits derived from the use of bubble deck
technology are –
1) Increase in number of floors due to less slab thickness
2) Reduction in foundation depth and size, which alsoi reduces the earthwork
excavation.
3) Reduction in number of columns used and larger spans are possible
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
8.2 SCOPE FOR FUTURE WORK
The present study on bi-axially voided bubble deck slab system has the following scope
for further improvement
Design can be improved so as to provide bubbles at the areas of high punching
shear
The technology can be extended to design of rigid pavements and design of
foundation slabs.
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
APPENDIX A
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Fig A.1 Ball diameter
Fig A.2 Bending strength design
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Fig A.3 Bending stiffness
Fig A.4 Shear capacity
Fig A.5 Shear capacity
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Fig A.6 Nominal cover to meet specified period of fire resistance
Fig A.7 Minimum permissible values of αc
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Fig A.8 Design shear strength of concrete
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Fig A.9 Maximum shear stress
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
Fig A.10 Bending moment coefficient for slab spanning in two directions at right angles,
simply supported on four sides
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
BIBLOGRAPHY
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BIAXIALLY VOIDED BUBBLE DECK SLAB SYSTEM AND OTHER CONVENTIONAL FLOOR SLAB SYSTEMS
REFERENCES
[1] S UNNIKRISHNA PILLAI, DEVDAS MENON (1999) Reinforced concrete design, Tata
Mcgraw Hill.
[2] P.C. Varghese (2009) Design of Reinforced Concret Foundations, P H India.
[3] S.S. Bhavikatti (2009) Advanced RCC Design (RCC Volume-ii), New Age International
Publishers.
[4] Indian Standard Plain and Reinforced Concrete – Code of Practice (FOURTH
REVISION) IS 456:2000.
[5] ACI code 318-02,2002.
[6] Nederlands BV-QR code.
[7] Bubbledeck Voided Flat slab solutions Technical Manual and Documents (June, 2008)
[8] British Standard code 8110.
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