ANALYSIS AND DESIGN OF FLAT SLABS USING VARIOUS CODES

BY
HYDERABAD
2
CERTIFICATE
This is to certify that the project entitled “ANALYSIS AND DESIGN OF FLAT SLABS USING
VARIOUS CODES” submitted as partial fulfillment for the award of Masters of Technology
in Computer Aided Structural Engineering, IIIT -Hyderabad is a bonafied work done by
M.Anitha, B.Q.Rahman, JJ.VIJAY
Supervisor
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ACKNOWLEDGEMENT
We sincerely acknowledge and express my deep sense of gratitude to Mr. Ramancharla
Pradeep Kumar (Assistant Professor) the guide of this project. As a guide he gave a
maximum help and coordination in finishi ng the project work. With his past years of
experience and teaching steered me to come out with success through the most difficult
problems faced by me. We would like to place on record our deep sense of gratitude to our
guides for their cooperation and un failing courtesy to me at every stage.
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Chapter II: Design of flat slabs by IS: 456 ……………………………... 07
Chapter III: Design of flat slabs as per NZS: 3101 ….………………………. 21
Chapter IV: Design of flat slabs as per EURO CODE….…………………... 30
Chapter V: Design of flat slabs using ACI-318……………………………. 40
Chapter VI: Results………………………………………………………... 51
Chapter VII: conclusion ………………………………………………………… … 52
Chapter VII: References………………………………………………………… 53
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ABSTRACT
Flat slabs system of construction is one in which the beams used in t he conventional methods of constructions are done away with. The slab directly rests on the column and load from the slab is directly transferred to the columns and then to the foundation. To support heavy loads the thickness of slab near the support with the column is increased and these are called drops, or columns are generally provided with enlarged heads called column heads or capitals.
Absence of beam gives a plain ceiling, thus giving better architectural appearance and also less vulnerability in case of fire than in usual cases where beams are used.
Plain ceiling diffuses light better, easier to construct and requires cheaper form work.
As per local conditions and availability of materials different countries have adopted different me thods for design of flat slabs and given their guidelines in their respective codes.
The aim of this project is to try and illustrate the methods used for flat slab design using ACI-318, NZ- 3101, and Eurocode2 and IS: 456 design codes.
For carrying out this project an interior panel of a flat slab with dimensions 6.6 x 5.6 m and super imposed load 7.75 2/KN m was designed using the codes given above.
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Introduction
Basic definition of flat slab: In general normal frame construction utilizes columns, slabs &
Beams. However it may be possible to undertake construction with out providing beams, in
Such a case the frame system would consist of slab and column without beams. These types of
Slabs are called flat slab, since their behavior resembles the bending of flat plates.
Components of flat slabs:
Drops: To resist the punching shear which is predominant at the contact of slab and column
Support, the drop dimension should not be less than one -third of panel length in that
Direction.
Column heads:
Certain amount of negative moment is transferred from the slab to the column at he support. To resist this negative moment the area at the support needs to be increased .this is facilitated by providing column capital/heads
Flat slab with drop panel & column head
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Design of flat slabs by IS: 456
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 (see Fig. 12). A flat slab may be solid slab or may have recesses formed on the soffit so that the sof fit comprises a series of ribs in two directions. The recesses may be formed by removable or permanent filler blocks.
Components of flat slab design:
a) Column strip : Column strip means a design strip having a width of 0.25 I,, but not greater than 0.25 1, on each side of the column centre-line, where I, is the span in the direction moments are being determined, measured centre to centre of supports and 1, is the -span transverse to 1,, measured centre to centre of supports.
b) Middle strip : Middle strip means a design strip bounded on each of its opposite sides by the column strip.
c) Panel: Panel means that part of a slab bounde d on-each of its four sides by the centre -line of a Column or centre-lines of adjacent-spans.
Division into column and middle strip along:
Longer span Shorter span
( i ) column strip = 0.25 2L = 1.4 m
But not greater than 0.25 1L = 1.65 m
(ii) Middle strip = 5.6 – (1.4+1.4) = 2.8 m
1L =5.6 m , 2L =6.6 m
( i ) column strip = 0.25 2L = 1.65 m
But not greater than 0.25 1L = 1.4 m
(ii) Middle strip = 6.6 – (1.4+1.4) = 3.8 m
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d) Drops :
The drops when provided shall be rectangular in plan, and have a length in each direction not less than one- third of the panel length in that direction. For exterior panels, the width of drops at right angles to the non- continuous edge and measured from the centre -line of the columns shall be equal to one -half the width of drop for interior panels.
Since the span is large it is desirable to provide drop.
Drop dimensions along:
Not less than 1L /3 = 2.2 m
1L =5.6 m , 2L =6.6 m
Not less than 1L /3 = 1.866 m
Hence provide a drop of size 2.2 x 2.2 m i.e. in column strip width.
e) column head :
Where column heads are provided, that portion of a column head which lies with in the largest right circular cone or pyramid that has a vertex angle of 90”and can be included entirely within the outlines of the column and the column head, shall be considered for design purposes (see Fig. 2).
5.6 m
Not greater than 1L /4 = 1.65 m
1L =5.6 m , 2L =6.6 m
Not greater than 1L /4 = 1.4 m
Adopting the diameter of column head = 1.30 m =1300 mm
f) Depth of flat slab:
The thickness of the flat slab up to spans of 10 m shall be generally controlled by considerations of span ( L ) to effective depth ( d ) ratios given as below:
Cantilever 7; simply supported 20; Continuous 26
For slabs with drops, span to effective depth ratios gi ven above shall be applied directly; otherwise the span to effective depth ratios in accordance with above shall be multiplied by 0.9. For this purpose, the longer span of the panel shall be considered. The minimum thickness of slab shall be 125 mm.
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Depth of flat slab:
Considering the flat slab as a continuous slab over a span not exceeding 10 m
L
6600
5600
Say 220 mm
Taking effective depth of 25mm Overall depth D = 260 +25 = 285 mm 125 mm (minimum slab thickness as per IS: 456)
It is safe to provide depth of 285 mm.
g) Estimation of load acting on the slab:
Dead load acting on the slab = 0.285 x 25 = 6.25 2/KN m = 1dw
Floor finishes etc. load on slab = 1.45 2/KN m = 2dw
Live load on slab = 7.75 2/KN m = lw
Total dead load = 1dw + 2dw =7.7 2/KN m = dw
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The design live load shall not exceed three times the design dead load.
Check: 7 .7 5
l
d
h) Total Design Moment for a Span
The absolute sum of the positive and average and is given by negative bending moments in each direction shall be taken as:
0 8 nW l
W = design load on an area 1 2l l
nl = clear span extending from face to face of columns, capitals, brackets or walls, but not less than
0.65 1l
2l = length of span transverse to 1l .
Circular supports shall be treated as square supports havi ng the same area. Equivalent side of the column head having the same area:
2 2(1.3) 1.152 4 4
a d m
6.6 (1.152) (1.152) 5.448 4.29 2 2
m
5.6 (1.152) (1.152) 4.44 3.64 2 2
m m
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2 nW w l l
15 .45 5 .6 5 .448 471 .36W K N
nl =4.44 m , 2l =6.6 m
2 nW w l l
1 5 . 4 5 6 . 6 4 . 4 4 4 5 2 . 7 4W K N
The absolute sum of –ve and +ve moment in a panel along:
Longer span Shorter span
0
8 8 nW l
nl =4.44 m , 2l =6.6 m
0
8 8 nW l
(i) Negative and Positive Design Moments :
The negative design moment shall be at the fac e of rectangular supports, circular supports being treated as square supports having the same 31.4.5.1 Columns built integrally with the slab system area. Shall be designed to-resist moments arising from loads .
In an interior span, the total design moment 0M shall be distributed in the following proportions: Negative design moment 0.65 Positive design moment 0.35
In an end span, the total design moment 0M shall be distributed in the fol lowing proportions:
Interior negative design moment: 1
0.10 0.75
1 c
0.65

c Is the ratio of flexural stiffness of the exterior columns to the flexural stiffness of the slab at a joint taken in the direction moments are being determined and is given by:
c c

cK =sum of the flexural stiffness of the columns meeting at the joint.
sK =flexural stiffness of the slab, expres sed as moment per unit rotation
It shall be permissible to modify these design moments by up to 10 percent, so lon g as the total design moment 0M for the panel in the direction considered is not less than that required by:
0 8 nW l
M
The negative moment section shall be designed to resist the larger of the two interior negative design moments determined for the spans framing into a common support unless an analysis is made to distribute the unbalanced moment in accordance with the stiffness of the adjoining parts.
Column strip : Negative moment at an interior support: At an interior support, the column strip shall be designed to resist 75 percent of the total negative moment in the panel at that support.
Negative moment at an exterior support: a) At an exterior support, the column strip shall be designed to resist the t otal negative moment in the panel at that support.
b) Where the exterior support consists of a column or a wall extending for a distance equal to or
greater than three-quarters of the value of 2l . The length of span transverse t o the direction moments are being determined, the exterior negative moment shall be considered to be uniformly
distributed across the length 2l .
Positive moment for each span : For each span, the column strip shall be designed to r esist 60 percent of the total positive moment in the panel.
Moments in the middle strip : a) That portion of-the design moment not resisted by the column strip shall be assigned to the adjacent middle strips.
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b) Each middle strip shall be proportione d to resist the sum of the moments assigned to its two half middle strips. cl The middle strip adjacent and parallel to an edge supported by a wall shall be proportioned, to resist twice the moment assigned to half the middle strip corresponding to the fir st row of interior columns.
Stiffness calculation:
let the height of the floor = 4.0 m
clear height of the column = height of floor –depth of drop – thickness of slab –thickness of head.
= 4000 – 140 – 285 – 300 = 3275 mm
Effective height of column = 0.8 x 3275 = 2620 mm
(Assuming one end hinged and other end fixed)
stiffness coefficient
su m o f flex u ra l s tiffn ess o f co lu m n ac ti n g a t th e jo in t
flex u ra l s tiffn ess o f th e s lab c
c s
Longer span
34 2 4 520 104 4 4 4 50 2 2
12 327.5c BOTTOM TOP
L L L L
12 560 4 2273.5 c
S C s
2 L
1 D
W





Hence correction for pattern of loading in the direction of longer span is not required.
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2 L
1 D
, m in
, m in
W




Hence the correction for pattern loading in the direction of short span is not required.
From table 17 of IS 456-2000
Imposed load/dead load Ratio 2
1
l
l Value of ,minc
(1) (2) (3) 0.5 1.0 1.0 1.0 1.0 1.0 2.0 2.0 2.0 2.0 2.0 3.0 3.0 3.0 3.0 3.0
0.5 to 2.0 0.5 0.8 1.0 1.25 2.0 0.5 0.8 1.0 1.25 2.0 0.5 0:8 1.0 1.25 2.0
0 0.6 0.7 0.7 0.8 1.2 1.3 1.5 1.6 1.9 4.9 1.8 2.0 2.3 2.8 13.0
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It is an exterior panel.
Longer span
column strip
-ve B.M at exterior support = 00 .6 5 0 .6 5 3 2 0 .9 9 1 .0 1 .0 1 2 1 .3 4 K N m
1 1 1 1
+ve span BM = 0
0 .2 8 0 .2 8 0 .6 3 0 .6 0 0 .6 3 3 2 0 .9 9 0 .6 0 9 0
1 1 1 1
0
0 .1 0 0 .1 0 0 .7 5 0 .7 5 0 .7 5 3 2 0 .9 9 0 .7 5 1 6 6 .5 0 K N m
1 1 1 1
Middle strip
-ve BM at exterior support = 00 .6 5 0 .0 0 .0 K N m
1 1
+ve span BM = 0
0 .2 8 0 .2 8 0 .6 3 0 .4 0 0 .6 3 3 2 0 .9 9 0 .4 0 5 9 .9 6
1 1 1 1
0
0 .1 0 0 .1 0 0 .7 5 0 .7 5 0 .7 5 3 2 0 .9 9 0 .2 5 5 5 .5 0 K N m
1 1 1 1
Short span
column strip
-ve moment at exterior support = 00 .6 5 0 .6 5 2 5 1 .2 1 .0 1 .0 1 2 0 .1 9 K N m
1 1 1 1
1 2.79
0
0 .1 0 0 .1 0 0 .7 5 0 .7 5 0 .7 5 2 5 1 .2 0 .7 5 1 2 7 .4 3 K N m
1 1 1 1
Middle strip
-ve moment at exterior support = 00 .6 5 0 .0 0 .0 K N m
1 1
+ve mid-span moment = 0
0 .2 8 0 .2 8 0 .6 3 0 .4 0 0 .6 3 2 5 1 .2 0 .4 0 4 2 .5 9
1 1 1 1
0
0 .1 0 0 .1 0 0 .7 5 0 .7 5 0 .7 5 2 5 1 .2 0 .2 5 4 2 .4 4 K N m
1 1 1 1
j) Effective depth of the slab
Thickness of the slab, from consideration of maximum positive moment any where in the slab.
Maximum +ve BM occurs in the column strip (long span) = 90.91 KNm
factored moment = 1.50 x 90.91 = 136.36 KNm
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0.138 20 2800 d=132.83 mm 140 mm
ckM f bd b
Overall thickness of slab = 12
140 15 161 mm 170 mm 2


k) Thickness of drop from maximum –ve moment consideration
Thickness of drop from consideration of maximum –ve moment any where in the panel.
Max –ve BM occurs in the column strip = 166.6 KNm 2
6 2
254.3 mm
260 15 281 mm 2
D
l) Shear in Flat Slab
The critical section for shear shall be at a distance d/2 from the periphery of the column/capital/ drop panel, perpendicular to the plane of the slab where d is the effective depth of the section (Fig. 2). The shape in plan is geometrically similar to the support immediately below the slab.
check for shear stress developed in slab
The critical section for shear for the slab will be at a distance d/2 from the face of drop.
Perimeter of critical section = 4 x 2340 = 9340 mm
Total factored shear force: 0 1 21.5 15.45 [ (2.34)(2.34)]
= 1.5 15.45 [6.6 5.6-(5.47)]
shear strength of concrete = 20.25 =0.25 20=1.11 N/mmc ckf
Permissible shear stress = v s ck
2
v
s c c
0 0
V 812.27 KN
b D d
6
2
4209 mm
A
A
38 No.s 113
38
113 3.8 1000
st
st
A
A
3768.9 mm
A
A
3768.9 33 No.s
33
1182 mm
A
A
1182 10 No.s
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DEFINITIONS:
A flat slab is reinforced concrete slab directly supporting on column (without any support of beams).
Flat slabs is divided into column strips & middle strips.
Column strips is a design strip with a width on each side of a column centre line equal to 0.25L1 or 0.25L2,whichever is less.
A middle strip is a design strip bounded by 2 column strips.
A panel is bounded by column, beams, or wall centre lines on all sides .
DESIGN METHOD:
There must a minimum 3 continuous spans in each directions.
Panels shall be rectangular with a ratio of longer to shorter spans ,centre to centre of supports ,not greater than 2.
Successive span lengths, centre -to-centre of supports, in each direction shall not differ by more than 1/3 of the longer spans.
Columns may be offsets a maximum of 10% of the span (in direction o offset) from either axis between centre lines of successive columns.
All loads shall be due to gravity only and uniformly distributed over entire panels. the live loads shall not exceeds 2 times the dead load.
DESIGN PROCEDURE:
First analysis the column strips & middle strips using 0.25L1/0.25l2.
Drop panel is used to reduce the amount of negative moment reinforcement over the column of the flat slab, the size of drop panel shall be 1/6 of the span length measured from centre–to-centre of support in that direction.
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Estimate the depth of flat slabs from clauses 14.2.5 & 3.3.2.2.(b) Assume fy=300MPA.
Fy(MPA) Exteriors panels Interior panels
300 Ln/36 Ln/40
400 Ln/32 Ln/35
The absolute sum for the span shall be determined in a strip bounded laterally by the center line of the panel on each side of centre of the supports.
The absolute sum of positive and average negative moments in each direction at the ultimate limit state shall be not less than:
Mo=WuL2Ln²/8;
In end spans
Exterior edge unrestrained
Exterior edge fully restrained
Positive moments
Exterior – ve moments
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SHEAR STRENGTH
Design of cross section of member subjected to shear shall be based on
v´<=¢Vn.
Where v´=shear force at that sec tion . Vn=nominal shear strength of the section. ¢ =strength reduction factor.
The nominal shear stress Vn shall not exceed 0.2fc,1.1 √fc or 9MPA.
Spacing limits for shear reinforcements shall be:
0.5d in non-prestressed member
600mm.
Design of slab for two way action shall be based on
Vn=Vn/bod
Vc=0.17(1+2βc)√fc
βc=shorter side/long side of the concentrated load
Design the interior panel of flat slabs 6.6 x 5.6 m in size for a super imposed l…