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Two-way slab systems
Types
Flat lateDr. Ahmed Shuraim
DDM limitations
Flat SlabFlexure Design: Direct Design method (DDM)CE 472- 2007
SWB
a eFloor Frames and strips
Statical Moment concept
Minimum ThicknessDDM- flat plate-example
M0
DDM- SWB-example
Column Moment
all
M+ve & M-ve
Mcs & Mms
M+ve & M-ve
Mcs & Mms
Beamless slabs
SWB
an ax a oa
RebarsRebarsPunching shear
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Types of two-way slabs-Flat PlateFor relatively light loads
spans : 4.5-6 m
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2007
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Types of two-way slabs- Waffle slab
For relatively light loads
- .
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2007
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Shuraim
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Types of two-way slabs-flat slabFor heavy industrial loads
spans : 6-9 m
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2007
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Shuraim
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Types of two-way slabs- slabs with beamsFor heavy industrial loads
spans : 6-9 m
CE 472
2007
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Shuraim
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Floor types
SWB
plate
Flat
Slab
Waffle
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2007
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Shuraim
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Floor Frames
Frame 1 F1
e
C
e
B
m e A
e
DM
o
r
e
Frame 3 F r a
F r a F
r F r a
F3
rame F4
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2007
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Shuraim
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Defining
design
strips
CE 472
2007
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Shuraim
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SECTION 13.6
DDM Limitations
DIRECT DESIGN METHOD
13.6.1 Limitations
es gn o s a sys ems w n e m a ons o . . . roug . . . y e
direct design method shall be permitted.
13.6.1.1 There shall be a minimum of three continuous spans in each direction.
13.6.1.2 Panels shall be rectan ular with a ratio of lon er to shorter s an center-to-centerof
supports within a panel not greater than2.
13.6.1.3 Successive span lengths center-to-center of supports in each direction shall not
differ by more than one-third the longer span.
13.6.1.4 Offset of columns by a maximum of 10 percent of the span (in direction of offset)rom e t er ax s etween center nes o success ve co umns s a e perm tte .
13.6.1.5 All loads shall be due to gravity only and uniformly distributed over an entire panel.
Live load shall not exceed two times dead load.
13.6.1.6 For a panel with beams between supports on all sides, the relative stiffness of beams
2
12
2
21
ll
α α (13-2)
shall not be less than 0.2 nor greater than 5.0.. . . .
designed by the Direct Design Method. See 13.6.7.
13.6.1.8 Variations from the limitations of 13.6.1 shall be permitted if demonstrated by
analysis that requirements of 13.5.1 are satisfied.CE 4722007
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Shuraim
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Statical Moment
For any continuous mem er eam
or slab), the static moment is given
by
M 0=wl2 /8=M pos+average(M neg)
0
8
2
2
0
nu llw
M =
M
o
r
e
M 0 ln
l2
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2007
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Shuraim
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Assignment of M0 to positive and negative
M
o
r
e
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2007
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Shuraim
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Assignment of M0 to positive and negative in the end span
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2007
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Shuraim
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( ) ( )12121 /1/3075 llll −⋅⋅+ α
−
M
o
r
e .
0.1/ 121 ≤llα UseCE 472
2007
Dr. Ahmed
Shuraimα
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13.6.4.2 Column stri s shall be ro ortioned to resist the followin ortions in ercent of exterior negative factored moments:
/ ll 0.5 1.0 2.0
( ) 0/ 121 =llα 0=t β 100 100 1005.2≥t β 75 75 75
( ) 0.1/ 121 ≥llα t
5.2≥t β 90 75 45Linear interpolations shall be made between values shown.
12121 −⋅+− α t t
Use .t .
CE 472
2007
Dr. Ahmed
Shuraim
βt
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Span Statical Moments-FP examples=7.0 m =8 m =7.0 m
Example data:
Live load = 3 kN/m2
dead load = 2 kN/m2
= M 0= 298.31
=6.5 m
Span C-1-2:l n
=6.5-2*.2 = 6.1
m
Span A-1-2:
l n
=6.5-(0.2+.25)
= 6.05 m
mm
Wu=1.4(2+0.25*24)+1
.7*3= 16.3 kN/m2 M 0= 568.62kN-m
kN-m
e C
m
e A
Span C-2-3:*
Span A-2-3:
l n =7.0-2*.25 = 6.5
m M 0= 665.65 C-1-2
F r a F
r= . m n. - . .
m-
0= .
kN-m C-2-3
=6.5 m Frame C:l 2 =8/2+7/2 = 7.5 m
Frame A:
l 2
=7/2+ext = 4.0 m
- -
A-2-3
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2007
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Shuraim
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Span negative- positive-FP examples=7.0 m =8 m =7.0 m
Live load = 3 kN/m2
dead load = 2 kN/m2
Slab thickness =250
mm
Wu=1.4 2+0.25*24 +147.8477.56
=6.5 m
1.7*3= 16.3 kN/m2
M 0= 568.62 kN-m295.68155.12 M 0= 298.31 kN-m
.
M 0= 665.65 kN-m
432.67
232.98
.
223.82
120.52 M = 344.34 kN-m= . m
C-1-2432.67223.82
=6.5 m Frame C:l 2 =8/2+7/2 = 7.5 m
Frame A:
l 2
=7/2+ext = 4.0 m
C-2-3
A-1-2
A-2-3
CodeCE 472
2007
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Shuraim
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FP- Reinforcement=7.0 m =8 m =7.0 m
6.5/46.5/48/2-6.5/4 7/2-6.5/47/2-6.5/46.5/4
2 5 0
2 5 0
=6.5 m
0 φ 1 4 @ 2 0
0
φ 1 4
@
0 1 2 @ 2 5 0 φ 1
2
φ 2 0 @ 2
4 @
2 8 0
φ 1 2 @ 2
@ 2 5 0
= . m
r i p
r i p
r ps-7/47/48/2-7/4 7/4
7/47/4 φ 1
φ 1
CS bot
=6.5 m Frame C:l 2 =8/2+7/2 = 7.5 m
Frame A:
l 2
=7/2+ext = 4.0 m l u m n
s t
l u m n
s
Strips-A
CS top
MS top
A-1-2 A-2-3
C C MS bot
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2007
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Shuraim
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FP-Reinforcement detailing in frame C
φ20@240φ20@240 φ14@250φ14@250
φ14@280 φ14@200φ14@200
φ12@250φ12@250 φ12@250φ12@250
Column strip
φ12@250 φ12@250φ12@250
middle strip
Calculation sheets
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2007
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Shuraim
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Span C-1-2 flexure
CE 472
2007
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Shuraim
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- -
CE 472
2007
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Shuraim
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Span A-2-3 flexure
CE 472
2007
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Shuraim
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- -
CE 472
2007
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Shuraim
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Span A-1-2 flexure
CE 472
2007
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Shuraim
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- -
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2007
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Shuraim
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Span Static Moments-SWB examples=7.0 m =8 m =7.0 m
Example data:
Live load = 3 kN/m2
dead load = 3.682 M 0= 298.31
=6.5 m
Span C-1-2:
l n
=6.5-2*.2 = 6.1
m
Span A-1-2:
l n
=6.5-(0.2+.25)
= 6.05 m
Slab thickness =180
mm
Wu=1.4(3.68+0.18*24
)+1.7*3= 16.3 kN/m2
M 0= 568.62kN-m
kN-m
e C
m
e A
Span C-2-3:*
Span A-2-3:
l n =7.0-2*.25 = 6.5
m M 0= 665.65 C-1-2
F r a F
r= . m n. - . .
m-
0= .
kN-m C-2-3
=6.5 mFrame C:
l 2 =8/2+7/2 = 7.5 m
Frame A:
l 2
=7/2+ext = 4.0 m
- -
A-2-3
CE 472
2007
Dr. Ahmed
Shuraim
Code
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SWB-Reinforcement
=7.0 m =8 m =7.0 m
6.5/46.5/48/2-6.5/4 7/2-6.5/47/2-6.5/46.5/4
3 0 0
3 0 0
=6.5 m
0 φ 1 2 @ 3 0 0
φ 1 2 @
0 1 4 @ 3 0 0 φ 1
2
Strips-C φ 1 2 @ 3
2 @
3 0 0
φ 1 4 @ 2
@
3 0 0
= . m
CS top
CS bot
r i p
r i p
7/47/48/2-7/4 7/47/47/4
φ 1
φ 1
=6.5 mFrame C:
l 2 =8/2+7/2 = 7.5 m
Frame A:
l 2
=7/2+ext = 4.0 m l u m n
s t
l u m n
s
MS topMS bot
A-1-2 A-2-3
C C
Strips-A beamsCE 472
2007
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Shuraim
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SWB-Reinforcement detailing in frame C
φ12@300φ12@300 φ12@300φ12@300
φ12@300 φ12@300φ12@300
Column strip
φ14@250φ14@250 φ12@300φ12@300
φ12@300 φ14@300φ14@300
middle stripCE 472
2007
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Shuraim
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Minimum thickness- flat plate & slabs9.5.3.2 For slabs without interior beams spanning between the supports and having a ratio of long to short
span not greater than 2, the minimum thickness shall be in accordance with the provisions of Table 9.5(c) and
shall not be less than the following values:
(a) Slabs without drop panels as defined
in Section 13.3.7.1 and 13.3.7.2 120 mm
(b) Slabs with drop panels as defined inSection 13.3.7.1 and 13.3.7.2 100 mm
Without drop panels With drop panels
Exterior panels Interior Exterior panels Interior
Yield
strength,
f MPa
. c -
Without
edge beams
With edge
beams
Without
edge beams
With edge
beams
300nl nl nl nl nl nl
33
36 36 36
40 40
42030
nl 33
nl 33
nl 33
nl 36
nl 36
nl
28
n 31
n 31
n 31
n 34
n 34
n
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Shuraim
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Minimum thickness- flat plate & slabs-
Example=7.0 m =8 m =7.0 m
=6.5 mmm Ln 218
306550
30==mm
Ln 25030
7500
30 ==mm Ln 218
306550
30 ==
Ln 7500 == mm L
n 2186550
==mm L
n 2186550
=== . m
3333
=6.5 m mm Ln 21830
655030
==mm Ln 218
306550
30== mm Ln 250
307500
30==
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2007
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Shuraim
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9.5.3.3 For slabs with beams spanning between the supports on all sides, the minimum
Minimum thickness- Slab with beams
thickness shall be as follows:
(a) For mα equal to or less than 0.2, the provisions of Section 9.5.3.2 shall apply;
(b) For mα greater than 0.2 but not greater than 2.0, the thickness shall not be less than
( )2.053615008.0
−+
⎟⎟ ⎠
⎞
⎜⎜⎝
⎛
+=
m
y
n
f
hα β
l (9-12)
an no ess an mm;
(c) For mα greater than 2.0, the thickness shall not be less than
8.0 ⎟
⎞
⎜⎜
⎛
+ y
n
f
l
β 936+=h (9-13)
and not less than 90 mm;
(d) At discontinuous edges, an edge beam shall be provided with a stiffness ratio α not
less than 0.80 or the minimum thickness required by Eq. (9-12) or (9-13) shall be
increased by at least 10 percent in the panel with a discontinuous edge.α = ratio of flexural stiffness of beam section to flexural stiffness of a width of
slab bounded laterally by centerlines of adjacent panels (if any) on each side
of beam. See Chapter 13
mα = average value of a for all beams on edges of a panel
β = ratio of clear spans in long to short direction of two-way slabsCE 472
2007
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Shuraim
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Minimum thickness- SWB
=7.0 m =8 m =7.0 m
=6.5 m15008.0 ⎟⎟
⎞⎜⎜⎛
+ y
n
f l
08.12.67.6
3.05.63.07 ==
−−= β
h=158.3 mm
24.12.670.7
3.05.63.08 ==−
−= β
= β 936+
= .
15.170.73.08 ==−
= β
=7.0 m
... −
h=179.4 mm
=6.5 m
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2007
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Shuraim
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CE 472
2007
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Shuraim
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CE 472
2007
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Shuraim
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CE 472
2007
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Shuraim
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Two-way shear- around C2
[ ] kN V u 1.81871.0*61.0)75.6*5.7(3.16 =−=y1=d_avg+yc = 0.21+0.4= 0.61 m
x1=d_avg+yc = 0.21+0.5= 0.71 m
mmmb
c
264064.2)71.061.0(2
25.14.0
.
0 ==+=
== β
kN V c 12011000*6
210*2640*25)1(
25.12 =+= k V c 0.924
1000*3
210*2640*25==
kN V c 11971000*12
210*2640*25)2(
2640210*40 =+=
OK Not
Vu
c .185.0
1.818
..
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Two-way shear- around A1
**
y1=d_avg/2+yc/2 +ext= 0.21/2+0.4/2+0.5= 0.805 m
x1=d_avg/2+xc/2 +ext= 0.21/2+0.4/2+0.5= 0.805 m
u ..... −
c 0.14.0== β
mmmb
210*1610*25
161061.1)805.0805.0(
.
0 ==+= kN V c 5.563
1000*3
210*1610*25==
c1000*6
0.1 =+=
210*1610*25*
c1000*12
1610 ==
V c 5.563*75.0 ==φ
Vu..
9.233
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2007
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Shuraim
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bw=300 mm
hw=420 mm
hf =180 mm
Span C-1-2
b I =α s
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2007
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Shuraim
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Torsional member-Slab with beams- βt
bw=300 mm
hw=420 mm
=
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2007
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Shuraim
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2007
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Shuraim
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Distribution of Moments in flat lates
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2007
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Shuraim
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Effect of edge beams on moments in slabs
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2007
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Dr. Ahmed Shuraim
CE 472- 2003
CE 472 2007 Dr. Ahmed Shuraim
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CE 472
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Shuraim
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Shuraim
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