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1Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Lecture-11Analysis and Design of Two-way Slab Systems
(Two-way Slab with Beams & Two Way joist Slabs)
B P f D Q i Ali
Prof. Dr. Qaisar Ali CE 5115 Advance Design of Reinforced
Concrete Structures 1
By: Prof Dr. Qaisar Ali
Civil Engineering Department
NWFP UET [email protected]
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Topics Addressedy Moment Coefficient Method for Two way slab
with
bbeams
y Introduction
y Cases
y Moment Coefficient Tables
R i f t R i t
Prof. Dr. Qaisar Ali
y Reinforcement Requirements
y Steps
y Example
2
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2Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Topics Addressedy Two-way Joist Slaby Introduction
y Behavior
y Characteristics
y Basic Steps for Structural Design
Prof. Dr. Qaisar Ali
y Example
3
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Moment Coefficient Method (Introduction)
Two Way Slabs
z The Moment Coefficient Method included for the first time
in1963 ACI Code is applicable to two-way slabs supported onfour
sides of each slab panel by walls, steel beams relativelydeep,
stiff, edge beams (h = 3hf).
z Although, not included in 1977 and later versions of ACI
code,
Prof. Dr. Qaisar Ali
its continued use is permissible under the ACI 318-08
codeprovision (13.5.1). Visit ACI 13.5.1.
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3Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Moment Coefficient Method laMa,neg
Ma,pos
Two Way Slabs
y Moments:Ma, neg = Ca, negwula2
Mb, neg = Cb, negwulb2
Ma, pos, (dl + ll) = M a, pos, dl + M a, pos, ll = Ca, pos, dl
wu, dl la2 + Ca, pos, ll wu, ll la2
Mb, pos, (dl + ll) = Mb, pos, dl + Mb, pos, ll = Cb, pos, dl wu,
dl lb2 + Cb, pos, ll wu, ll lb2
y Where C C = Tabulated moment coefficients
Ma,neglb
Mb,neg Mb,negMb,pos
Prof. Dr. Qaisar Ali
y Where Ca, Cb = Tabulated moment coefficientswu = Ultimate
uniform load, psf
la, lb = length of clear spans in short and long directions
respectively.
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Moment Coefficient Method: Cases
Two Way Slabs
y Moment Coefficient Method: Casesy Depending on the support
conditions, several cases are possible:
Prof. Dr. Qaisar Ali 6
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4Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Moment Coefficient Method: Cases
Two Way Slabs
y Moment Coefficient Method: Casesy Depending on the support
conditions, several cases are possible:
Prof. Dr. Qaisar Ali 7
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Moment Coefficient Method: Cases
Two Way Slabs
y Moment Coefficient Method: Casesy Depending on the support
conditions, several cases are possible:
Prof. Dr. Qaisar Ali 8
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5Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Moment Coefficient Method: Cases
Two Way Slabs
y Moment Coefficient Method: Casesy Depending on the support
conditions, several cases are possible:
Prof. Dr. Qaisar Ali 9
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Slabs
y Moment Coefficient Tables:y Moment Coefficient Tables:
Prof. Dr. Qaisar Ali 10
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6Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Slabs
y Moment Coefficient Tables:y Moment Coefficient Tables:
Prof. Dr. Qaisar Ali 11
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Slabs
y Moment Coefficient Tables:y Moment Coefficient Tables:
Prof. Dr. Qaisar Ali 12
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7Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Slabs
y Moment Coefficient Tables:y Moment Coefficient Tables:
Prof. Dr. Qaisar Ali 13
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Slabs
y Moment Coefficient Tables:y Moment Coefficient Tables:
Prof. Dr. Qaisar Ali 14
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8Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Slabs
y Moment Coefficient Tables:y Moment Coefficient Tables:
Prof. Dr. Qaisar Ali 15
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Slabs
y Load Coefficient Table:y Load Coefficient Table:
Prof. Dr. Qaisar Ali 16
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9Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Maximum spacing and minimum reinforcement
Two Way Slabs
requirement:
z Maximum spacing (ACI 13.3.2):
smax = 2 hf in each direction.
z Minimum Reinforcement (ACI 7.12.2.1):
Asmin = 0.0018 b hf for grade 60.
Prof. Dr. Qaisar Ali 17
Asmin 0.0018 b hf for grade 60.
Asmin = 0.002 b hf for grade 40 and 50.
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Special Reinforcement at exterior corner of Slabz The
reinforcement at exterior ends of the slab shall be provided as per
ACI
Two Way Slabs
z The reinforcement at exterior ends of the slab shall be
provided as per ACI13.3.6 in top and bottom layers as shown.
z The positive and negative reinforcement in any case, should be
of a size andspacing equivalent to that required for the maximum
positive moment (per footof width) in the panel.
Prof. Dr. Qaisar Ali 18
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Moment Coefficient Method
Two Way Slabs
y Stepsy Find hmin = perimeter/ 180 = 2(la + lb)/180
y Calculate loads on slab (force / area)
y Calculate m = la/ lby Decide about case of slab,
Prof. Dr. Qaisar Ali
Decide about case of slab,
y Use table to pick moment coefficients,
y Calculate moments and then design.
y Apply reinforcement requirements (smax = 2hf, ACI 13.3.2)
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Moment Coefficient Method: Example
Two Way Slabs
o e t Coe c e t et od a p e
y A 100 60, 3-storey commercial building is to be designed.The
grids of column plan are fixed by the architect.
Prof. Dr. Qaisar Ali 20
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Department of Civil Engineering, N-W.F.P. University of
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y Moment Coefficient Method: Example
Two Way Slabs
o e t Coe c e t et od a p e
y Complete analysis of the slab is done by analyzing four
panels
Panel I Panel IPanel III Panel III
Prof. Dr. Qaisar Ali 21
Panel I Panel I
Panel II Panel II
Panel III Panel III
Panel IV Panel IV
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y Moment Coefficient Method: Example
Two Way Slabs
p
y A 100 60, 3-storey commercial building: Sizes and Loads.y
Sizes:
y Minimum slab thickness = perimeter/180 = 2 (20+25)/180 = 6
However, for the purpose of comparison, take hf = 7
y Columns = 14 14 (assumed)
Prof. Dr. Qaisar Ali
y Beams = 14 20 (assumed)y Loads:
y S.D.L = Nil ; Self Weight = 0.15 x (7/12) = 0.0875 ksfy L.L =
144 psf ; wu = 0.336 ksf
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Moment Coefficient Method: Example
Two Way Slabs
y Panels are analyzed using Moment Coefficient MethodCase = 4m =
la/lb = 0.8
Mb,neg Mb,negMb,pos
Ma,neg
Ma,pos
Ma,neg
Prof. Dr. Qaisar Ali 23
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Moment Coefficient Method: Example
Two Way Slabs
y Panels are analyzed using Moment Coefficient MethodCase = 4m =
la/lb = 0.8
Ca,neg = 0.071Cb,neg = 0.029Ca,posLL = 0.048Cb,posLL = 0.020C 0
039
Prof. Dr. Qaisar Ali 24
Ca,posDL = 0.039Cb,posDL = 0.016
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Moment Coefficient Method: Example
Two Way Slabs
y Panels are analyzed using Moment Coefficient MethodCase = 4m =
la/lb = 0.8
Ca,neg = 0.071Cb,neg = 0.029Ca,posLL = 0.048Cb,posLL = 0.020C 0
039
Prof. Dr. Qaisar Ali 25
Ca,posDL = 0.039Cb,posDL = 0.016
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Moment Coefficient Method: Example
Two Way Slabs
y Panels are analyzed using Moment Coefficient MethodCase = 4m =
la/lb = 0.8
Ca,neg = 0.071Cb,neg = 0.029Ca,posLL = 0.048Cb,posLL = 0.020C 0
039
Prof. Dr. Qaisar Ali 26
Ca,posDL = 0.039Cb,posDL = 0.016
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Moment Coefficient Method: Example
Two Way Slabs
y Panels are analyzed using Moment Coefficient MethodCase = 4m =
la/lb = 0.8
Ca,neg = 0.071Cb,neg = 0.029Ca,posLL = 0.048Cb,posLL = 0.020C 0
039
Prof. Dr. Qaisar Ali 27
Ca,posDL = 0.039Cb,posDL = 0.016
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Moment Coefficient Method: Example
Two Way Slabs
y Panels are analyzed using Moment Coefficient MethodCase = 4m =
la/lb = 0.8
Ca,neg = 0.071Cb,neg = 0.029Ca,posLL = 0.048Cb,posLL = 0.020C 0
039
Prof. Dr. Qaisar Ali 28
Ca,posDL = 0.039Cb,posDL = 0.016
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Moment Coefficient Method: Example
Two Way Slabs
y Panels are analyzed using Moment Coefficient MethodCase = 4m =
la/lb = 0.8
Ca,neg = 0.071Cb,neg = 0.029Ca,posLL = 0.048Cb,posLL = 0.020C 0
039
Prof. Dr. Qaisar Ali 29
Ca,posDL = 0.039Cb,posDL = 0.016
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Moment Coefficient Method: Example
Two Way Slabs
y Panels are analyzed using Moment Coefficient Method
Panel I
Case = 4m = la/lb = 0.8
Ca,neg = 0.071Cb,neg = 0.029Ca,posLL = 0.048Cb,posLL = 0.020C 0
039
Mb,neg Mb,negMb,pos
Ma,neg
Ma,pos
Ma,neg
Prof. Dr. Qaisar Ali 30
Ca,posDL = 0.039Cb,posDL = 0.016
Ma,neg = 9.5 k-ftMa,pos = 6.1 k-ftMb,neg = 6.1 k-ftMb,pos = 3.9
k-ft For slab supported on Spandrals, Mneg,ext = 1/3Mpos
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Department of Civil Engineering, N-W.F.P. University of
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Two Way Slabsy Moment Coefficient Method: Example
Panel II
Case = 9m = la/lb = 0.8
Ca,neg = 0.075Cb,neg = 0.017Ca,posLL = 0.042Cb,posLL = 0.017C 0
029 M MM
Ma,neg
y Panels are analyzed using Moment Coefficient Method
Prof. Dr. Qaisar Ali 31
Ca,posDL = 0.029Cb,posDL = 0.010
Ma,neg = 10.1 k-ftMa,pos = 5.1 k-ftMb,neg = 3.6 k-ftMb,pos = 3.1
k-ft
Mb,neg Mb,negMb,pos
Ma,pos
Ma,neg
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Slabsy Moment Coefficient Method: Example
Panel III
Case = 8m = la/lb = 0.8
Ca,neg = 0.055Cb,neg = 0.041Ca,posLL = 0.044Cb,posLL = 0.019C 0
032
Mb,neg Mb,negMb,pos
Ma,neg
Ma,pos
Ma,neg
y Panels are analyzed using Moment Coefficient Method
Prof. Dr. Qaisar Ali 32
Ca,posDL = 0.032Cb,posDL = 0.015
Ma,neg = 7.4 k-ftMa,pos = 5.4 k-ftMb,neg = 8.6 k-ftMb,pos = 3.7
k-ft
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Slabsy Moment Coefficient Method: Example
Panel IV
Case = 2m = la/lb = 0.8
Ca,neg = 0.065Cb,neg = 0.027Ca,posLL = 0.041Cb,posLL = 0.017C 0
026 M MM
Ma,neg
y Panels are analyzed using Moment Coefficient Method
Prof. Dr. Qaisar Ali 33
Ca,posDL = 0.026Cb,posDL = 0.011
Ma,neg = 8.7 k-ftMa,pos = 4.9 k-ftMb,neg = 5.7 k-ftMb,pos = 3.2
k-ft
Mb,neg Mb,negMb,pos
Ma,pos
Ma,neg
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Slabsy Moment Coefficient Method: Exampley Slab analysis
summary
8.77.4
7.4
8.6 8.65.43.7
10.19.5
9.5
6.1 6.13.9
6.1
Prof. Dr. Qaisar Ali 34
3.2
4.95.75.7
8.7
3.25.13.6
10.1
3.6
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Slabsy Moment Coefficient Method: Exampley Slab
Reinforcement Details
A
C
C
C CBA
A
C
C
B BA
A= #4 @ 12
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A
BBB
C
A
BA
C
@B = #4 @ 6C = #4 @ 4
Two-Way Joist Slab
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y Introduction
Two-Way Joist
z A two-way joist system, or waffle slab, comprises evenlyspaced
concrete joists spanning in both directions and areinforced
concrete slab cast integrally with the joists.
37
Joist
y Introduction
Two-Way Joist
z Like one-way joist system, a two way system will be
qualifiedto be said as two-way joist system if clear spacing
betweenribs (dome width) does not exceed 30 in.
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y Introduction
Two-Way Joist
39
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Engineering and Technology Peshawar
y Introduction
Two-Way Joist
z The joists are commonly formed by using Standard Squaredome
forms and the domes are omitted around the columnsto form the solid
heads.
Prof. Dr. Qaisar Ali 40
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y IntroductionStandard Dome Data
Two-Way Joist
z Standard Dome Data
z Generally the dome for waffle slab can be of any size. However
thecommonly used standard domes are discussed as follows:
z 30-in 30-in square domes with 3-inch flanges; from which
6-inchwide joist ribs at 36-inch centers are formed: these are
available instandard depths of 8, 10, 12, 14, 16 and 20 inches.
19 i h 19 i h d ith 2 i h fl f hi h
Prof. Dr. Qaisar Ali
z 19-inch 19-inch square domes with 2 -inch flanges, from
which5-inch wide joist ribs at 24-inch centers are formed. These
areavailable in standard depths of 8, 10, 12, 14 and 16 inches.
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y IntroductionStandard Dome Data
Two-Way Joist
z Standard Dome Data
Prof. Dr. Qaisar Ali 42
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Behavior
Two-Way Joist
z The behavior of two-way joist slab is similar to a two way
flatSlab system.
Prof. Dr. Qaisar Ali
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Characteristics
Two-Way Joist
z Dome voids reduce dead load
z Attractive ceiling (waffle like appearance)
z Electrical fixtures can be placed in the voids
z Particularly advantageous where the use of longer spans
Prof. Dr. Qaisar Ali
and/or heavier loads are desired without the use ofdeepened drop
panels or supported beams.
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Basic Steps for Structural Designz Step No 01 (Sizes): Sizes
of all structural and non
Two-Way Joist
z Step No. 01 (Sizes): Sizes of all structural and nonstructural
elements are decided.
z Step No. 02 (Loads): Loads on structure are determinedbased on
occupational characteristics and functionality (referAppendix C of
class notes).
z Step No 03 (Analysis): Effect of loads are calculated on
all
Prof. Dr. Qaisar Ali
z Step No. 03 (Analysis): Effect of loads are calculated on
allstructural elements.
z Step No. 04 (Design): Structural elements are designed for
the respective load effects following code provisions.
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Department of Civil Engineering, N-W.F.P. University of
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y Sizesz Minimum Joist Depth
Two-Way Joist
z Minimum Joist Depth
z For Joist depth determination, waffle slabs are considered as
flat slab(ACI 13.1.3, 13.1.4 & 9.5.3).
z The thickness of equivalent flat slab is taken from table 9.5
(c).
z The thickness of slab and depth of rib of waffle slab can be
thencomputed by equalizing the moment of inertia of equivalent flat
slab tothat of waffle slab
Prof. Dr. Qaisar Ali
that of waffle slab.
z However since this practice is time consuming, tables have
beendeveloped to determine the size of waffle slab from equivalent
flat slabthickness.
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Sizesz Minimum Joist Depth
Two-Way Joist
z Minimum Joist Depth
z Equivalent Flat Slab Thickness
z ACI 318-05 Sect. 9.5.3
z Minimum thickness = ln/33
Prof. Dr. Qaisar Ali 47
y Sizesy Minimum Joist Depth
Two-Way Joist
y Minimum Joist Depthy Slab and rib depth from equivalent flat
slab thickness
Table 01: Waffle flat slabs (19" 19" voids at 2'-0")-Equivalent
thicknessRib + Slab Depths (in.) Equivalent Thickness te (in.)
8 + 3 8.898 + 4 10.1110 + 3 10.51
48
10 + 4 11.7512 + 3 12.12
12 + 4 13.3814 + 3 13.72
14 + 4 15.0216 + 3 15.31
16 + 4 16.64Reference: Table 11-2 of CRSI Design Handbook
2002.
Note: Only first two columns of the table are reproduced
here.
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y Sizesy Minimum Joist Depth
Two-Way Joist
y Minimum Joist Depthy Slab and rib depth from equivalent flat
slab thickness
Table 02: Waffle flat slabs (30" 30" voids at 3'-0")-Equivalent
thicknessRib + Slab Depths (in.) Equivalent Thickness te (in.)
8 + 3 8.618 + 4 9.7910 + 3 10.18
10 + 4 11.37
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12 + 3 11.7412 + 4 12.9514 + 3 13.3
14 + 4 14.5416 + 3 14.85
16 + 4 16.1220 + 3 17.92
20 + 4 19.26Reference: Table 11-2 of CRSI Design Handbook
2002.
Note: Only first two columns of the table are reproduced
here.
y Sizesy Minimum Width of Rib
Two-Way Joist
y Minimum Width of Riby ACI 8.11.2 states that ribs shall be not
less than 4 inch in width.
y Maximum Depth of Riby A rib shall have a depth of not more
than 3 times the minimum
width of rib.
y Minimum Slab Thickness
50
y Minimum Slab Thicknessy ACI 8.11.6.1 states that slab
thickness shall be not less than one-
twelfth the clear distance between ribs, nor less than 2 in.
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y Loadsy Floor dead load for two-way joist with certain dome
size, dome depth can
Two-Way Joist
y j , pbe calculated from the table shown for two options of
slab thicknesses (3inches and 4 inches).
Table 03: Standard Dome Dimensions and other Data
Dome Size Dome Depth (in.) Volume of Void (ft3)
Floor Dead Load (psf) per slab thickness
3 inches 4 inches
8 3.98 71 9010 4 92 80 99
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30-in
10 4.92 80 9912 5.84 90 10914 6.74 100 11916 7.61 111 12920 9.3
132 151
19-in
8 1.56 79 9810 1.91 91 11012 2.25 103 12214 2.58 116 13416 2.9
129 148
Reference: Table 11-1, CRSI Design Handbook 2002
y Loadsy Floor dead load (w ) for two way joist can also be
Two-Way Joist
y Floor dead load (wdj) for two-way joist can also becalculated
as follows:
36
8
3
30
Volume of solid:Vsolid = (36 36 11)/1728 = 8.24 ft3Volume of
void:Vvoid = (30 30 8)/1728 = 4.166 ft3Total Load of joists per
dome:
52
Total Load of joists per dome:wdj = (Vsolid Vvoid) conc
= ( 8.24 4.166) 0.15 = 0.61 kipTotal Load of joists per sq.
ft:wdj/ (dome area) = 0.61/ (3 3) = 0.0679 ksf
= 68 psf 71 psf (from table 03)The difference is because sloped
ribs are not considered.
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y Loadsy At locations where solid head is present the floor dead
load
Two-Way Joist
y At locations where solid head is present, the floor dead
loadcan be calculated as follows:
y If, wdj = dead load in joist area
y Wsh = dead load in solid head area
= hsolid concy Wdj+sh = {wshb + wdj(l2-b)}/l2
wdjWdj+sh
ln
a a
Wdj+sh
53
dj+sh { sh dj( 2 )} 2
bl2a a
y Loadsy Factored loads can be calculated as:
Two-Way Joist
y Factored loads can be calculated as:
y If wL = live load (load/area), theny Load out of solid head
region
wosh = 1.2 wdj + 1.6wL
y Load in solid head region
1 2 1 6
wish wish
woshWish
ln
a a
Wish
54
wish = 1.2wdj+sh+1.6wL bl2a a
wosh
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Department of Civil Engineering, N-W.F.P. University of
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y AnalysisACI code allows use of DDM for analysis of waffle
slabs (ACI
Two-Way Joist
z ACI code allows use of DDM for analysis of waffle slabs
(ACIR13.1). In such a case, waffle slabs are considered as
flatslabs, with the solid head acting as drop panels (ACI
13.1.3).
Prof. Dr. Qaisar Ali 55
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y AnalysisStatic moment calculation for DDM analysis:
Two-Way Joist
z Static moment calculation for DDM analysis:
wosh
ln
woshWish
lna a
Wish
Mosh Mish
ln
Prof. Dr. Qaisar Ali 56
Mosh = woshl2ln2/8 Mish = (wish-wosh)ba2/2
Mish
Mo = Mosh + Mish
b
l2a a
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Department of Civil Engineering, N-W.F.P. University of
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y DesignDesign of slab for punching shear
Two-Way Joist
z Design of slab for punching shear
z The solid head shall be checked against punching shear.
z The critical section for punching shear is taken at a section
d/2 from faceof the column, where d is the effective depth at solid
head.
Prof. Dr. Qaisar Ali 57
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y DesignDesign of slab for
Two-Way Joist
z Design of slab forpunching shear
z Load on tributary area willcause punch out shear.
z Within tributary area, twotypes of loads are acting:
l1
Prof. Dr. Qaisar Ali
z Solid head load
z Joist load
z Both types shall beconsidered while calculatingpunching shear
demand
58
l2 d/2
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Department of Civil Engineering, N-W.F.P. University of
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y DesignDesign of slab for punching
Two-Way Joist
z Design of slab for punchingshear
z Total area = l1 l2z Solid area = Asolid
z Joist part area (Aj) = (l1l2) -Asolidz Critical perimeter area
= Acp
l1
Prof. Dr. Qaisar Ali
z Critical perimeter area Acp
z Vu =Ajwosh+ (Asolid Acp) wishz Where,
wosh = joist part load
wish = load inside solid head
59
l2 d/2
Department of Civil Engineering, N-W.F.P. University of
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y Designz Shear Strength of Slab in punching shear:
Two-Way Joist
Shear Strength of Slab in punching shear:
z Vn = Vc + Vs
z Vc is least of:
z 4 (fc)bod
z (2 + 4/c) (fc)bod
z {(sd/bo +2} (fc)bod
Prof. Dr. Qaisar Ali 60
c = longer side of column/shorter side of column
s = 40 for interior column, 30 for edge column, 20 for corner
columns
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Department of Civil Engineering, N-W.F.P. University of
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y Designz Design of Joist for Beam Shear:
Two-Way Joist
Design of Joist for Beam Shear:
z Beam shear Demand
z Beam shear is not usually a problem in slabs including waffle
slabs.However for completion of design beam shear may also
bechecked. Beam shear can cause problem in case where largerspans
and heavier loads with relatively shallow waffle slabs areused.
Prof. Dr. Qaisar Ali 61
z The critical section for beam shear is taken at a section d
from faceof the column, where d is the effective depth at solid
head.
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Designz Design of Joist for Beam Shear:
Two-Way Joist
g
z Beam shear capacity of concrete joist
z Vn = Vc + Vs
z Vc is least of:
z 2 (fc)bribd
z Vs = Avfy/bribs
Stirrup
Prof. Dr. Qaisar Ali 62
z If required, one or two single legged stirrups are provided in
the rib to increase the shear capacity of waffle slab.
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y DesignDesign for Flexure
Two-Way Joist
z Design for Flexure
z The design of waffle slab is done by usual procedures.
z However, certain reinforcement requirements apply discussed
next.
Prof. Dr. Qaisar Ali 63
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y ACI recommendations on reinforcement requirement of waffle
slab:
Two-Way Joist
requirement of waffle slab:
z ACI 10.6.7 states that if the effective depth d of a beam
orjoist exceeds 36 in., longitudinal skin reinforcement shall
beprovided as per ACI section 10.6.7.
z According to ACI 13.3.2, for cellular or ribbed
constructionreinforcement shall not be less than the requirements
of ACI
Prof. Dr. Qaisar Ali
reinforcement shall not be less than the requirements of
ACI7.12.
z As per ACI 7.12, Spacing of top bars cannot exceed 5h or18
inches.
64
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y ACI recommendations on reinforcement requirement of waffle
slab:
Two-Way Joist
requirement of waffle slab:
Prof. Dr. Qaisar Ali 65
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Other important points:The amount of reinforcement and if
necessary the top slab
Two-Way Joist
z The amount of reinforcement and, if necessary, the top
slabthickness can be changed to vary the load capacities
fordifferent spans, areas, or floors of a structure.
z Each joist rib contains two bottom bars. Straight bars
aresupplied over the column centerlines for negative
factoredmoment.
Prof. Dr. Qaisar Ali 66
Bottom bar
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34
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Other important points:For layouts that do not meet the
standard 2 feet and 3 feet
Two-Way Joist
z For layouts that do not meet the standard 2-feet and
3-feetmodules, it is preferable that the required additional width
beobtained by increasing the width of the ribs framing into
thesolid column head.
z The designer should sketch out the spacing for a typical
paneland correlate with the column spacing as a part of the
early
Prof. Dr. Qaisar Ali
p g p yplanning.
67
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Example: Design the slab system of hall shown in figure as
waffleslab, according to ACI 318. Use Direct Design Method for
slab
Two-Way Joist
analysis.z fc = 4 ksi
z fy = 60 ksi
z Live load = 100 psf
Prof. Dr. Qaisar Ali 68
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Solution:z A 108 144 building divided into twelve (12) panels
supported at
Two-Way Joist
z A 108 144 building, divided into twelve (12) panels, supported
attheir ends on columns. Each panel is 36 36.
z The given slab system satisfies all the necessary limitations
for DirectDesign Method to be applicable.
Prof. Dr. Qaisar Ali 69
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Step No 01: SizesColumns
Two-Way Joist
z Columns
z Let all columns be 18 18.
z Slab
z Adopt 30 30 standard dome.
z Minimum equivalent flat slab thickness (hf) can be found using
ACI Table9 5 (c):
Prof. Dr. Qaisar Ali
9.5 (c):
z Exterior panel governs. Therefore,
hf = ln/33
= [{36 (2 18/2)/12}/33] 12 = 12.45
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Step No 01: SizesSlab
Two-Way Joist
z Slab
z The closest depth of doom that will fulfill the requirement of
equivalentthickness of flat slab equal to 12.45 is 12 in. with a
slab thickness of 4 in. for a dome size of 30-in.
Table: Waffle flat slabs (30" 30" voids at 3'-0")-Equivalent
thickness
Rib + Slab Depths (in.) Equivalent Thickness te (in.)
8 + 3 8.618 + 4 9.79
Prof. Dr. Qaisar Ali 71
10 + 3 10.1810 + 4 11.3712 + 3 11.74
12 + 4 12.9514 + 3 13.3
14 + 4 14.5416 + 3 14.85
16 + 4 16.1220 + 3 17.92
20 + 4 19.26Reference: Table 11-2 of CRSI Design Handbook
2002.
Note: Only first two columns of the table are reproduced
here.
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Step No 01: SizesPlanning of Joist layout
Two-Way Joistl = 36-0 = 432Standard module = 36 36
z Planning of Joist layout No. of modules in 36-0:n = 432/36 =
12
Planning:First module is placed on interiorcolumn centerline and
providedtowards exterior ends of panel.In this way, width of
exterior joistcomes out to be 15.
Prof. Dr. Qaisar Ali 72
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Step No 01: SizesSolid Head
Two-Way Joist
z Solid Head
z Solid head dimension from column centerline = l/6 = 36/6 =
6
z Total length of solid head= 2 6 = 12z As 3 3 module is
selected, therefore 4 voids will make an interior solid
head of 12.5 12.5.z Depth of the solid head = Depth of standard
module = 12 + 4.5 = 16.5
Prof. Dr. Qaisar Ali 73
Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
y Step No 02: Loadsz Floor (joist) dead load (wdj) = 109 psf = 0
109 ksf
Two-Way Joist
z Floor (joist) dead load (wdj) 109 psf 0.109 ksf
Table: Standard Dome Dimensions and other Data
Dome Size Dome Depth (in.) Volume of Void (ft3)
Floor Dead Load (psf) per slab thickness
3 inches 4 inches
30-in
8 3.98 71 9010 4.92 80 9912 5.84 90 10914 6.74 100 11916 61 111
129
Prof. Dr. Qaisar Ali 74
16 7.61 111 12920 9.3 132 151
19-in
8 1.56 79 9810 1.91 91 11012 2.25 103 12214 2.58 116 13416 2.9
129 148
Reference: Table 11-1, CRSI Design Handbook 2002
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y Step No 02: Loadsy Floor (joist) dead load (wdj) = 109 psf = 0
109 ksf
Two-Way Joist
y Floor (joist) dead load (wdj) 109 psf 0.109 ksf
y Solid Head dead load (wsh) = {(12 + 4.5)/12} 0.15 = 0.206
ksf
y Wdj+sh = {wshb + wdj(l2-b)}/l2= {0.20612.5 + 0.109 (36
12.5)}/36= 0.143 ksf
wdjWdj+sh
l
a a
Wdj+sh
75
ln
b = 12.5l2a = 5.25 a
y Step No 02: Loadsy w = 100 psf = 0 100 ksf
Two-Way Joist
y wL = 100 psf = 0.100 ksf
y Load out of solid head region
wosh = 1.2 wdj + 1.6wL
= 1.20.109 + 1.60.100= 0.291 ksf
wish wish
76
y Load in solid head region
wish = 1.2wdj+sh+1.6wL
= 1.2 0.143 + 1.6 0.100 = 0.33 ksf
bl2a a
wosh
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 03: Frame Analysis (E-W Interior
Frame)
Two-Way Joist
z Step 1: Marking E-W Interior Frame:
l 36 0
l2 = 36-0
l1 = 36-0ln = 34-6
Prof. Dr. Qaisar Ali 77
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 03: Frame Analysis (E-W Interior
Frame)
Two-Way Joist
z Step 01: Marking E-W Interior Frame
z Design Span of frame (c/c) = l1 = 36
Design Length of frame = ln = 36 (2 18/2)/12 = 34.5
Width of frame = l2 = 36
Half column strip width = (Shorter span)/ 4 = 36/4 = 9
Prof. Dr. Qaisar Ali 78
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 03: Frame Analysis (E-W Interior
Frame)
Two-Way Joist
z Step 2: Marking Column and Middle Strips
MS/2 = 9-0
a = 5-3 CS/2 = 9-0
CS/2 = 9-0
a 5 -3
b= 12-6
CS/2 = Least of l1/4 or l2/4
l /4 = 36/4 = 9
MS/2 = 9-0
Prof. Dr. Qaisar Ali 79
l2/4 = 36/4 = 9
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 03: Frame Analysis (E-W Interior
Frame)
Two-Way Joist
z Step 03: Static Moment Calculation
z Mosh (outside head) = woshl2ln2/8
= 0.291 36 34.52/8 = 1557.56 ft-k
Mish (solid head) = (wish wosh) ba2/2
= (0.330.291)12.55.252/2 = 6.70 ft-k
Mo (total static moment) = Mosh + Mish = 1557.56 + 6.70 =
1564.26 ft-k
Note: Since normally, Mish is much smaller than Mosh the former
can be conveniently ignored in design calculations
Prof. Dr. Qaisar Ali 80
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 03: Frame Analysis (E-W Interior
Frame)
Two-Way Joist
z Step 04: Longitudinal distribution of Total static moment
(Mo).
Prof. Dr. Qaisar Ali 81
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 03: Frame Analysis (E-W Interior
Frame)
Two-Way Joist
z Step 05: Lateral Distribution of Longitudinal moment
(L.M).
INT36 =0 {no interior beams}
l2/l1 = 36/36 = 1
INT36l2/l1 = 0
Prof. Dr. Qaisar Ali 82
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 03: Frame Analysis (E-W Exterior
Frame)
Two-Way Joist
z Step 01: Marking E-W exterior Frame
l 36 0l1 = 36-0ln = 34-6
l2 = 18-0 + (9/12) = 18.75
Prof. Dr. Qaisar Ali 83
2 ( )
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 03: Frame Analysis (E-W Exterior
Frame)
Two-Way Joist
z Step 01: Marking E-W exterior Frame
z Design Span of frame (c/c) = l1 = 36
Design Length of frame = ln = 36 (2 18/2)/12 = 34.5
Width of frame = l2 = 9 + 9 + (9/12) = 18.75
Half column strip width = (Shorter span)/ 4 = 36/4 = 9
Prof. Dr. Qaisar Ali 84
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 03: Frame Analysis (E-W Exterior
Frame)
Two-Way Joist
z Step 02: Marking Column and Middle Strips
l 36 0l1 = 36-0ln = 34-6
CS/2 = Least of l1/4 or l2/4
l /4 = 36/4 = 9
MS/2 = 9-0a = 5 3
Prof. Dr. Qaisar Ali 85
CS/2 = 9-0l2/4 = 36/4 = 9 a = 5 -3
b= 7-0
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 03: Frame Analysis (E-W Exterior
Frame)
Two-Way Joist
z Step 03: Static Moment Calculation
z Mosh (outside head) = woshl2ln2/8
= 0.291 18.75 34.52/8 = 811.78 ft-k
Mish (solid head) = (wish wosh) ba2/2
= (0.330.291)75.252/2 = 3.76 ft-k
Mo (total static moment) = Mosh + Mish = 811.78 + 3.76 = 815.54
ft-k
Note: Since normally, Mish is much smaller than Mosh the former
can be conveniently ignored in design calculations
Prof. Dr. Qaisar Ali 86
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 03: Analysis
Two-Way Joist
z Step 04: Longitudinal distribution of Total static moment
(Mo).
Prof. Dr. Qaisar Ali 87
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 03: Analysis
Two-Way Joist
z Step 05: Lateral Distribution of Longitudinal moment
(L.M)[Refer to ACI 13.6.4 to ACI 13.6.6].
z EXT36 =0 {no exterior beams}
z l2/l1 = 36/36 = 1
z EXT36l2/l1 = 0
Prof. Dr. Qaisar Ali 88
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 03: Analysis
Two-Way Joist
z Analysis of N-S Interior and Exterior Frame will be same as
E-W respectiveframes due to square panels.
N-S Exterior Frame
N-S Interior Framel2 = 36-0
l2 = 18-9
Prof. Dr. Qaisar Ali 89
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 04: Design
Two-Way Joist
z For E-W Interior slab strip:
z davg = 12 + 4.5 1 (concrete cover) 0.75 (avg. bar dia) =
14.75g
z Asmin = 0.0018bte (Where te = equivalent flat slab
thickness)
Asmin = 0.0018 12 12.95 = 0.279 in2
z Now, Equation used to calculate () in table below is as
follows:
Mu = fybdavg2{1 0.59fy/fc} = 0.9601214.752{1 0.5960/4}
z After solving the above equation for , we get:
= [140980.5 {(140980.5)2 (4 1247677 Mu 12)}]/2(1247677).(A)
Prof. Dr. Qaisar Ali 90
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 04: Design
Two-Way Joist
z For E-W Interior slab strip:
Prof. Dr. Qaisar Ali 91
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 04: Design
Two-Way Joist
z For E-W exterior slab strip:
z davg = 12 + 4.5 1 0.75 = 14.75 g
z Asmin = 0.0018bte (Where te = equivalent flat slab
thickness)
Asmin = 0.0018 12 12.95 = 0.279 in2
z Now, Equation used to calculate () in table below is as
follows:
Mu = fybdavg2{1 0.59fy/fc} = 0.9601214.752{1 0.5960/4}
z After solving the above equation for , we get:
= [140980.5 {(140980.5)2 (4 1247677 Mu 12)}]/2(1247677).(A)
Prof. Dr. Qaisar Ali 92
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 04: Design
Two-Way Joist
z For E-W exterior slab strip:
Prof. Dr. Qaisar Ali 93
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 04: Design
Two-Way Joist
z Design of N-S Interior and Exterior Frame will be same as E-W
respective frames due to square panels and also for thereason that
davg is used in design.
Prof. Dr. Qaisar Ali 94
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 04: Design
Two-Way Joist
z Note: For the completion of design problem, the waffle
slabshould also be checked for beam shear and punching shear.
Prof. Dr. Qaisar Ali 95
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 05: Detailing (E-W Frames)
Two-Way Joist
#6 @ 12 #6 @ 6 #6 @ 6 #6 @ 12
Prof. Dr. Qaisar Ali 96#6 @ 12 #6 @ 6 #6 @ 6 #6 @ 12
#6 @ 18 #6 @ 18 #6 @ 18 #6 @ 18
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 05: Detailing (N-S Frames)
Two-Way Joist
#6 @ 12#6 @ 18#6 @ 12
#6 @ 6#6 @ 18#6 @ 6
#6 @ 6#6 @ 18#6 @ 6
Prof. Dr. Qaisar Ali 97
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 05: Detailing (E-W Interior Frame)
Two-Way Joist
#6 @ 6 c/c
18-0
Column Strip (Interior Frame); section taken over support
#6 @ 12 c/c2 #7 Bars
#6 @ 12 c/c
Prof. Dr. Qaisar Ali 98Column Strip (Exterior Frame); section
taken over support2 #7 Bars
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 05: Detailing (E-W Interior Frame)
Two-Way Joist
#6 @ 18 c/c
18-0
Middle Strip (Interior Frame); Section taken over column
line
#6 @ 18 c/c2 #7 Bars
#6 @ 18 c/c
Prof. Dr. Qaisar Ali 99Middle Strip (Exterior Frame); Section
taken over column line2 #7 Bars
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 05: Detailing (E-W Exterior Frame)
Two-Way Joist
#6 @ 6 c/c
9-0
Column Strip (Interior Frame); section over support2 #7 Bars
#6 @ 12 c/c
Prof. Dr. Qaisar Ali 100
Column Strip (Exterior Frame); section over support2 #7 Bars
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
Two Way Joisty Step No 05: Detailing (E-W Exterior Frame)
Two-Way Joist
#6 @ 18 c/c
9-0
Middle Strip (Interior Frame) ; section over support2 #7
Bars
#6 @ 18 c/c
Prof. Dr. Qaisar Ali 101
Middle Strip (Exterior Frame); section over support2 #7 Bars
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Department of Civil Engineering, N-W.F.P. University of
Engineering and Technology Peshawar
The End
Prof. Dr. Qaisar Ali 102