This resource material is exclusively for the purpose of knowledge dissemination for the use of Civil engineering Fraternity, professionals & students.
This file contains state of art techniques adopted & practiced as per IS456 code provisions for analysis design & detailing of flat slab structural systems.
The presentation aims to provide clear,concise, technical details of flat slabs design.
The presentation deals with structural actions & behavior of flat slabs with visual representations obtained through finite element analysis.
The knowledge gained can be used for designing building structures frequently encountered in construction.
The presentation covers an important feature of slab systems supported on rigid & flexible support & clearly demarcates the minimum beam dimensions required to consider the supports to be either rigid or flexible.
The presentation alsoincludes clear technical drawings to highlight the importance of detailing w.r.t. rebar lay out - positioning & curtailment. Typical section drawing through middle & column strips are also included for visualizing rebar patterns in 3 -d views.
This presentation is an outcome of series of lectures for undergrad & grad students studying in civil engineering.
My next presentation would be on Analysis & design of deep beams.
Kindly mail me ( vvietcivil@gmail.com) your questions & valuable feedback.
3. Flat Slab with
drop panels
Flat slab with
column head
Flat slab with
drop panel and
column head
Flat Slab resting
directly on
columns
1. What is a flat slab?
31.1 General
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 solid slab
or may have recesses
formed on the soffit so that
the soffit comprises a series
of ribs in two directions.
The recesses may be formed
by removable or permanent
filler blocks.
4. 2. Types of flat slab
• Flat Slab with drop panels
• Flat slab with column head • Flat slab with drop panel
and column head
• Flat Slab resting
directly on columns
Drop
is
a
local
thickening
of
the
slab
in
the
region
of
column
Structural
Advantages
• increase
shear
strength
of
slab
• increase
nega5ve
moment
capacity
of
slab
• s5ffen
the
slab
and
hence
reduce
deflec5on
Column
head
is
a
local
enlargement
of
the
column
at
the
junc5on
with
the
slab
Structural
Advantages
• increase shear strength of slab
(punching shear)
• reduce the moment in the slab by
reducing the clear or effective span
5. A
flat
slab
may
have
recesses
formed
on
the
soffit
so
that
the
soffit
comprises
a
series
of
ribs
in
two
direc5ons
(
waffle
Slabs).
6. Flat
slabs
with
capitals,
drop
panels,
or
both.
These
slabs
are
very
sa4sfactory
for
heavy
loads
and
long
spans.
Although
the
formwork
is
more
expensive
than
for
flat
plates,
flat
slabs
will
require
less
concrete
and
reinforcing
than
would
be
required
for
flat
plates
with
the
same
loads
and
spans.
They
are
par4cularly
economical
for
warehouses,
parking
and
industrial
buildings,
and
similar
structures,
where
exposed
drop
panels
or
capitals
are
acceptable.
7. v Flexibility in room layout
• Introduce partition walls anywhere required
• Change the size of room layout
• Omit false ceiling
v Saving in building height
• Lower storey height will reduce building weight
• approx. saves 10% in vertical members
• reduce foundation load
v Shorter construction time
• flat plate design will facilitate the use of
big table formwork to increase productivity
v Ease of installation of M&E services
• all M & E services can be mounted directly on
the underside of the slab instead of bending
them to avoid the beams
• avoids hacking through beams
3. Benefits of flat slab
8. The
main
disadvantage
is
their
lack
of
resistance
to
lateral
loads
due
to
wind
and
earthquakes.
Lateral
load
resis4ng
systems
such
as
shear
walls
are
oDen
necessary
When
the
loads
or
spans
or
both
become
quite
large,
the
slab
thickness
and
column
sizes
required
for
flat
plates
or
flat
slabs
are
of
such
magnitude
that
it
is
more
economical
to
use
two-‐way
slabs
with
beams,
despite
the
higher
formwork
costs.
9. 4. Behaviour of Slab supported on Stiff , Flexible and no beams
Case
Study:
• Panel
Size
=
4
m
x
4m
• Slab
Thickness
=
125
mm
• Load
=
5
kN/m2
• S5ff
Supports
(
Bearing
wall)
• Flexible
Supports
(Beam)
:
300
x
300
,
300
x
450
,
300
x
600
,
300
x
1000
mm
• Column
supports
at
corners
10. A.
Two
way
Slab
on
Rigid
Supports
(bearing
Walls)
Mx
=
3.616
kNm/m
My
=
3.616
kNm/m
IS
456
Values
(Table
27):
0.062
x
5
x
16
=
4.96
Slab
Deflec6on
=
1.4
mm
11. B.
Two
way
Slab
on
Flexible
Supports
(Beams
on
all
sides)
1.
Beam
Size
:
300
x300
mm
Mx
=
4.45
kNm/m
My
=
4.45
kNm/m
IS
456
Values
(Type
9):
0.056
x
5
x
16
=
4.48
Mxy
=
0.37
kNm/m
Beam
Moment
=
12.2
kNm
Beam
Deflec6on
=
1.33
mm
Slab
deflec6on=
2.9
mm
12. 2.
Beam
Size
:
300
x450
mm
Mx
=
3
kNm/m
My
=
3
kNm/m
IS
456
Values
(Type
9):
0.056
x
5
x
16
=
4.48
Mxy
=
0.73
kNm/m
Beam
Moment
=
15.6
kNm
Beam
Deflec6on
=
0.5
mm
Slab
deflec6on=
1.5
mm
13. 3.
Beam
Size
:
300
x
600
mm
Mx
=
2.43
kNm/m
My
=
2.43
kNm/m
IS
456
Values
(Type
9):
0.056
x
5
x
16
=
4.48
Mxy
=
0.8
kNm/m
Beam
Moment
=
17
kNm
Beam
Deflec5on
=
0.24
mm
Slab
Deflec5on
=
0.98
mm
14. 4.
Beam
Size
:
300
x
1000
mm
Mx
=
2
kNm/m
My
=
2
kNm/m
IS
456
Values
(Type
9):
0.056
x
5
x
16
=
4.48
Mxy
=
0.8
kNm/m
Beam
Moment
=
18
kNm
15. 5.
Beam
Size
:
300
x
125
mm
(Concealed
Beams)
Mx
=
9.8
kNm/m
My
=
9.8
kNm/m
IS
456
Values
(Type
9):
0.056
x
5
x
16
=
4.48
Mxy
=
3
kNm/m
Beam
Moment
=
2.9
kNm
Slab
Deflec6on
=
7.0
mm
16. B.
Two
way
Slab
on
Point
Supports
at
corners
(Flat
Slab)
Mx
=
9.075
kNm/m
(Middle)
=12.4
kNm/m
(Edge
Strip)
Mxy
=
7.76
kNm/m
My
=
9.075
kNm/m
(Middle)
=12.4
kNm/m
(Edge
Strip)
Slab
Deflec6on
=
8.67
mm
18. • Two way Rectangular Slab supported on stiff beams, the shorter spans (stiffer portion
of the slab) carry larger load and subjected to larger moments. The longer spans
carry less load and subjected to less moment.
• Results indicate that decrease in supporting beams stiffness leads to an increase in
bending moments of slabs and decrease in bending moment of the beams (behavior that
is not captured using code recommendations).
• If the slab is supported on bearing walls, slab moments are distributed in similar way.
• If the slab is supported only by the columns, the slab behaves like a two way slab with
an essential difference that all the load is carried in both directions to accumulate it
at the columns.
• With Concealed beams it is reveled that the behaviour is close to Flat slabs rather than any useful
beam action.
Observa4ons
20. A
Zone
of
–ve
BM
(Hogging)
in
both
direc7ons
B
Zone
of
+ve
BM(Sagging)
and
–ve
BM
C
Zone
of
-‐ve
BM
and
+ve
BM
D
Zone
of
+ve
BM
in
both
direc7ons
-‐m4
-‐m2
-‐m4
m3
m1
m3
m5
m7
-‐m8
-‐m4
-‐m2
-‐m4
m7
A
A
A
A
C
C
B
B
D
Column
Strip
Middle
Strip
Column
Strip
Column
Strip
Middle
Strip
Column
Strip
-‐m6
-‐m6
-‐m8
-‐m8
-‐m8
5. Distribution of Total Panel Moment in different zones
21. A
Zone
of
–ve
BM
(Hogging)
in
both
direc7ons
B
Zone
of
+ve
BM(Sagging)
and
–ve
BM
C
Zone
of
-‐ve
BM
and
+ve
BM
D
Zone
of
+ve
BM
in
both
direc7ons
-‐m4
-‐m2
-‐m4
m3
m1
m3
m5
m7
-‐m8
-‐m4
-‐m2
-‐m4
m7
A
A
A
A
C
C
B
B
D
Column
Strip
Middle
Strip
Column
Strip
Column
Strip
Middle
Strip
Column
Strip
-‐m6
-‐m6
-‐m8
-‐m8
-‐m8
m1
-‐m2
-‐m2
D
C
C
m3
-‐m4
-‐m4
B
A
A
m5
-‐m6
-‐m6
D
B
B
m7
-‐m8
-‐m8
C
A
A
22. 6. Definitions
L2
L1
Moment
Direc5on
MIDDLE
STRIP
COLUMN
STRIP
0.25L2
≤
0.25L1
COLUMN
STRIP
0.25L1
≤
0.25L2
MIDDLE
STRIP
COLUMN
STRIP
0.25L1
≤
0.25L2
Moment
Direc5on
SPAN
Region
SPAN
Region:
Bounded
on
all
the
four
sides
by
middle
strips
23.
7. General Design Considerations
CL 31.2 Proportioning
31.2.1 Thickness of Flat Slab
• The thickness of the flat slab shall be
generally controlled by considerations of
span to effective depth ratios given in 23.2.
• For slabs with drops conforming to 31.2.2,
span to effective depth ratios given in 23.2
shall be applied directly; otherwise the span
to effective depth ratios obtained in
accordance with provisions in 23.2 shall be
multiplied by 0.9. For this purpose, the
longer span shall be considered.
• The minimum thickness of slab shall be 125
mm.
31.2.2 Drop
• 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.
• Minimum thickness of Drop
> ¼ of Slab thickness and
> 100 mm
24.
25. 31.2.3 Column Heads
Where column heads are provided, that portion of a column head which lies within the
largest right circular cone or pyramid that has a vertex angle of 900and can be included
entirely within the outlines of the column and the column head, shall be considered for
design purposes.
26. 8. Determination of Bending Moment CL 31.3
31.3.1. Methods of Analysis and Design
It shall be permissible to design the slab system by one of the following
methods:
a) The direct design method as specified in 31.4, and
b) The equivalent frame method as specified in 31.5.
In each case the applicable limitations given in 31.4 and 31.5 shall be met.
27. 9. Direct Design Method CL 31.4
A. Limitations : 31.4.1
Slab system designed by the direct design method shall fulfil the following conditions:
a) There shall be minimum of three continuous spans in each direction,
b) The panels shall be rectangular, and the ratio of the longer span to the shorter span within
a panel shall not be greater than 2.0
c) It shall be permissible to offset columns to a maximum of 10percent of the span in the
direction of the offset notwithstanding the provision in (b)
d) The successive span lengths in each direction shall not differ by more than one-third of
the longer span. The end spans may be shorter but not longer than the interior spans, and
e) The design live load shall not exceed three times the design dead load.
Note:
Applicable to gravity loading condition alone (and not to the lateral loading condition)
29. B. Total Design Moment for a Span: CL31.4.2
CL
of
Panel
1
CL
of
Panel
2
1
2
DESIGN
STRIP
31.4.2.1 In the direct design
method, the total design moment
for a span shall be determined
for a strip bounded laterally by
the centre-line of the panel on
each side of the centre-line of
the supports.
31.4.2.2 The absolute sum of the
positive and average negative
bending moments in each
direction shall be taken as:
1
2
M0x
M0y
lnx
30. wu
kN/m
L1
L2
Ln
Ln
(L1)
(L2)
Note:
1. It
is
the
same
as
the
total
moment
that
occurs
in
a
simply
supported
slab
2. The
moment
that
actually
occurs
in
such
a
slab
has
been
shown
by
experience
and
tests
to
be
somewhat
less
than
the
value
determined
by
the
Mo
expression.
For
this
reason,
l1
is
replaced
with
ln
31. • It
is
next
necessary
to
know
what
propor4ons
of
these
total
moments
are
posi4ve
and
what
propor4ons
are
nega4ve.
10. Distribution of Total Panel Moment M0
• If
a
slab
was
completely
fixed
at
the
end
of
each
panel,
the
division
would
be
as
it
is
in
a
fixed-‐end
beam,
two-‐thirds
nega4ve
and
one-‐third
posi4ve,
as
shown
in
Figure.
• This
division
is
reasonably
accurate
for
interior
panels
where
the
slab
is
con4nuous
for
several
spans
in
each
direc4on
with
equal
span
lengths
and
loads.
Interior
Panel
32. • The
rela4ve
s4ffnesses
of
the
columns
and
slabs
of
exterior
panels
are
of
far
greater
significance
in
their
effect
on
the
moments
than
is
the
case
for
interior
panels.
• The
magnitudes
of
the
moments
are
very
sensi4ve
to
the
amount
of
torsional
restraint
supplied
at
the
discon4nuous
edges.
• This
restraint
is
provided
both
by
the
flexural
s4ffness
of
the
slab
and
by
the
flexural
s4ffness
of
the
exterior
column.
Exterior
Panel
46. 12. Two way Shear in Flat Slab
• Flat
plates
present
a
possible
problem
in
transferring
the
shear
at
the
perimeter
of
the
columns.
• There
is
a
danger
that
the
columns
may
punch
through
the
slabs.
• As
a
result,
it
is
frequently
necessary
to
increase
column
sizes
or
slab
thicknesses
or
to
use
shear
heads.
Shear
heads
consist
of
steel
I
or
channel
shapes
placed
in
the
slab
over
the
columns
47. Note:
Flat
Slab
with
drop
panel
and
capital,
shear
is
required
to
be
checked
at
two
sec4ons
1. at
a
distance
d/2
from
the
face
of
column
capital
2. at
a
distance
d/2
from
the
face
of
drop
panel
48.
49.
50. Design
Example
#1
Design
by
DDM
flat
plate
supported
on
columns
450
mm
square,
for
a
Live
Load
=
3
kN/m2,
Floor
Finish
=
1
kN/m2
use
M20
and
Fe415.
Assume
clear
cover
=
20
mm.
Effec6ve
Column
Height
=
3.35m.
Bay
spacing
in
X
and
Y
direc6on
=
5m
c/c
• Interior
Panel
P5
• Corner
Panel
P7
3
bays
@
5
m
c/c
51. A.
Interior
Panel
Design
5
m
5
m
2.5m
2.5
m
A A
A A
B
B
C
CD
Zone
A
–
Corner
Strip
Zone
B
–
Middle
Strip
along
X
Zone
C
–
Middle
Strip
along
Y
Zone
D
–
Interior
Region
Step 1: Panel Division into Strips
31.1.1(a)
Moment
direc6on
Along
L1
L2
Width
of
Column
Strip
on
either
side
of
Centre
Line
=
0.25L2
and
≤
0.25
L1
Middle
Strip
X
5
5
1.25
and
≤1.25
m
Adopt
1.25
m
2.5m
Y
5
5
1.25
and
≤1.25
m
Adopt
1.25
m
2.5m
52. Step 2: Trial Depth CL 31.2.1
• L/d
=
26
• Modifica5on
Factor
=
1.33,
Assuming
pt
=
0.4%,
FIG
4
IS
456
• d
=
5000/(26
x
1.33)
=
145
mm
>
125
CL
31.2.1
• DS=
145
+
20
+
18
=
183
mm
(
assume
#12
bars,
and
bars
in
two
layers)
• Provide
Ds=
200
mm
d
=
200-‐20-‐18
=
162
mm
53. Step 3 Design Loads / m width of Slab
• wuD = 1.5(25x 0.2 + 1) = 9kN/m
• wuL = 1.5 x 3 = 4.5kN/m
• wu = 13.5 kN/m
Step 4: Check for Applicability of DDM: CL 31.4.1
• No.
of
Con5nuous
Spans
in
each
direc5on
=
3
;
OK
31.4.1(a)
• Long
Span/Short
Span
=
5/5
=
1
<2
;
OK
31.4.1(b)
• Successive
spans
in
each
direc5on
=
Equal;
OK
31.4.1(d)
• wuL/wuD
=
4.5/9
=
0.5
<
3
;
OK
31.4.1(e)
54. Step 5: Check for punching shear around Column
Assumed
d
=
162
mm
Sec4on
1:
• Cri5cal
Sec5on
at
d/2
around
the
column
• Perimeter
of
Cri5cal
Sec5on
=
4
x
0.612=
2.448
m
• Design
Shear
at
cri5cal
sec5on
Vu
• Vu
=
13.5
(
52
–
0.6122)
=
333kN
• τc
=
0.25√fck
=
1.12
MPa
• ks
=
0.5
+1
=
1.5
<=1
;
ks=1
;
ks
τc
=
1.12
• Shear
Resistance
of
Concrete
=
1.12
x
2448
x
162
=
444kN
>
333
kN
OK
Cri4cal
Sec4on
0.612m
0.612m
5m
5m
Contributory
Area
55. Step 6:Design Moments CL 31.4.2.2
Parameters
Along
X
Along
Y
L1
(Span
in
direc4on
of
Mo)
5
5
m
0.65L1
3.25
3.25
m
Ln
(clear
span
extending
from
face
to
face
of
columns,
capitals)
(5-‐0.45)
=
4.55
4.55
m
Ln
>
0.65L1
4.55
4.55
m
L2
(Span
transverse
to
L1)
5
5
m
W
=
wu
L2Ln
307.2
307.2
kN
M0
=
W
Ln
/
8
174.72
174.72
kNm
wu = 13.5 kN /m
56. Step 7 : Distribution of Bending Moment across panel width ;
CL: 31.4.3.2, 31.5.5
Moment
Direc5on
along
X
Y
Nega4ve
Design
Moment
MN
=
-‐
0.65*M0
113.6
113.6
kNm
31.4.3.2
• Column
Strip
M1
=
0.75MN
85.2
85.2
kNm
31.5.5.1
Width
of
Column
Strip
resis4ng
M1
(Csw)
2x1.25
=2.5
2x1.25
=2.5
m
• -‐m1
=
M1/
Csw
(Zone
A)
34.1
34.1
kNm/m
• Middle
Strip
M2
=
0.25MN
28.4
28.4
kNm
31.5.5.4(a)
Width
of
Middle
Strip
resis4ng
M2
(Msw)
2.5
2.5
m
• -‐m2
=
M2/Msw
(Zone
B
&
C)
11.4
11.4
kNm/m
57. Posi5ve
Design
Moment
MP
=
0.35*M0
61.2
61.2
kNm
31.4.3.2
• Column
Strip
M1
=
0.6MP
36.7
36.7
kNm
31.5.5.3
• +m1
=
M1/
Csw
(Zone
B
&C)
14.7
14.7
kNm/m
• Mid
Span
M2
=
0.4MP
24.5
24.5
kNm
31.5.5.4(a)
• +m2
=
M2/Msw
(Zone
D)
9.8
9.8
kNm/m
-‐ve
sign
:
Hogging
Moment
(tension
at
top)
+ve
sign
:
Sagging
Moment
(tension
at
borom)
-‐34.1
-‐11.4
-‐34.1
14.7
9.8
14.7
-‐34.1
-‐11.4
-‐34.1
9.8
14.7
-‐11.4
-‐34.1
-‐34.1
-‐34.1
-‐11.4
-‐34.1
14.7
A B A
D
C C
A
AB
Step 8 : Check for adequacy of Depth
• Max
Design
Bending
moment
=
34.1
kNm/m
• Mu,lim
=
72.41
kNm/m
>
34.1,
•
Depth
is
adequate
G-‐1.1(c)
58. Loca6on
Moment
(kNm/m)
Ast
(mm2
/m)
Ast
(prov)
Bar
dia
Spacing
mm
Along
X
Zone
A
(-‐)
34.1
635
635
10
120
-‐
T
Zone
B
14.7
260
260
8
190
-‐
B
Zone
C
(-‐)11.4
200
240
8
200
-‐
T
Zone
D
9.8
171
240
8
200
-‐
B
Along
Y
Zone
A
(-‐)34.1
635
635
10
120
-‐
T
Zone
B
(-‐)11.4
200
240
8
200
-‐
T
Zone
C
14.7
260
260
8
190
-‐
B
Zone
D
9.8
171
240
8
200
-‐
B
• 7.5
Ast2
–
58490Ast
+
Mu
=
0
G-‐1.1(b)
Step 9 :Rebar Details
• Ast,min
=
0.12
x
200
x
1000
/100
=
240
mm2/m
26.5.2.1
• Minimum
Effec5ve
Depth
of
Slab
=
162
mm
59. #8@190
#8@200
#8@190
#8@200
#8@190
#8@190
0.15Ln
0.15Ln
0.125Ln
0.125Ln
Borom
Rebar
Details
in
Interior
Panel
A
B
A
A
B
A
C
D
C
60. TOP
Rebar
Details
in
Interior
Panel
#10@120
#10@120
#8@200
#8@200
#8@200
0.3Ln
0.2Ln
0.3Ln
0.2Ln
Note:
Distances
for
curtailment
of
rebars
are
measured
from
column
face
A
B
A
C
D
C
61. B.
Corner
Panel
Design
Step 5: Check for punching shear around Column
Assumed
d
=
162
mm
Sec4on
1:
• Cri5cal
Sec5on
at
d/2
around
the
column
• Perimeter
of
Cri5cal
Sec5on
=
2
x
0.531=
1.062
m
• Design
Shear
at
cri5cal
sec5on
Vu
• Vu
=
13.5
(
2.52
–
0.5312)
=
81kN
• τc
=
0.25√fck
=
1.12
MPa
• ks
=
0.5
+1
=
1.5
<=1
;
ks=1
;
ks
τc
=
1.12
• Shear
Resistance
of
Concrete
=
1.12
x
1062
x
162
=
192kN
>
81
kN
OK
450
162/2
=
81
mm
62. Step 7 : Distribution of Bending Moment across panel width ; CL 31.4.3.3 , 31.5.5
𝛼↓𝑐 =∑↑▒ 𝑘↓𝑐 / 𝑘↓𝑠
Assume
Columns
and
Slab
panels
are
with
same
modulus
of
elas5city
5
m
5
m
1.25m
1.25m
A A
A A
B
B
C
CD
Step 6:Design Moments CL 31.4.2.2
M0 = 174.72 kNm
63. Parameters
Along
X
Along
Y
Sum
of
column
s4ffness
above
and
below
the
slab
2
(4EcIc)/Lc
(2
x
4
x
Ec
x
450
x
4503/12)
/3350
=
8.16
Ec
x
106
Slab
s4ffness
ks
=
4EsIs/Ls
(4
Es
x
5000
x
2003/12)/5000
=
2.67Es
x
106
2.67Es
x
106
αc
=
∑kc
/ks
3.06
3.06
β
=
1+
(1/αc)
1.33
1.33
64. Moment
Direc5on
along
X
Y
Nega4ve
Design
Moment
MN
=
-‐
0.65*M0/β
85.4
85.4
kNm
31.4.3.3
• Column
Strip
M1
=
MN
85.4
85.4
kNm
31.55.2(a)
Width
of
Column
Strip
Csw
resis4ng
M1
2x1.25
=
2.5
2.5
m
-‐m1
=
M1/Csw
34.2
34.2
kNm/m
• Middle
Strip
M2=0
0
0
kNm
31.5.5.4(a)
-‐m2
=
0
0
0
kNm/m
A.
Exterior
nega4ve
design
moment:
-‐m1
-‐m1
-‐m1
-‐m1
Exterior
Exterior
Interior
Interior
1.25
1.25
-‐m2
-‐m2
X
Y
65. Moment
Direc5on
along
X
Y
Nega4ve
Design
Moment
MN
=
-‐
(0.75
–
0.1/β)Mo
118
118
kNm
31.4.3.3
• Column
Strip
M1
=
0.75
MN
88.5
88.5
kNm
31.5.5.1
Width
of
Column
Strip
Csw
resis4ng
M1
2x1.25
=2.5
2.5
m
• -‐m1
=
M1/
Csw
-‐35.4
-‐35.4
kNm/m
• Middle
Strip
M2
=
0.25
MN
22.12
22.12
kNm
31.5.5.4(a)
Width
of
Middle
Strip
Msw
resis4ng
M2
2.5
2.5
m
• -‐m2
=
M2/Msw
-‐8.85
-‐8.85
kNm/m
B.
Interior
nega4ve
design
moment:
-‐
m1
-‐
m1
-‐
m2
m1
-‐m1
-‐m1
-‐m2
X
Y
Exterior
Exterior
Interior
Interior
66. Moment
Direc5on
along
X
Y
Design
Moment
MP
=
(0.63
–
0.28/β)Mo
73.29
73.29
kNm
31.4.3.3
• Column
Strip
M1
=
0.6
MP
43.98
43.98
kNm
31.5.5.3
Width
of
Column
Strip
Csw
resis4ng
M1
2x1.25
=2.5
2.5
m
• m1
=
M1/
Csw
17.6
17.6
kNm/m
• Middle
Strip
M2
=
0.4
MP
29.32
29.32
kNm
31.5.5.4(a)
Width
of
Middle
Strip
Msw
resis4ng
M2
2.5
2.5
m
• m2
=
M2/Msw
11.73
11.73
kNm/m
C.
Posi4ve
Moment
in
Mid
Span:
m1
m1
m1
m1
m1
m1
m2
X
Y
Exterior
Exterior
Interior
Interior
m2
67. -‐ve
sign
:
Hogging
Moment
(tension
at
top)
+ve
sign
:
Sagging
Moment
(tension
at
borom)
17.6
11.73
17.6
-‐8.85
-‐35.4
11.73
17.6
17.6
A B A
D
C C
A
AB
-‐35.4
-‐35.4
-‐8.85
-‐35.4
-‐34.2
-‐34.2
0
-‐34.2
-‐34.2
-‐0
Exterior
Exterior
Interior
Interior
Step 7 : Check for adequacy of Depth
• Max
Design
Bending
moment
=
35.4
kNm/m
• Mu,lim
=
72.41
kNm/m
>
35.4,
Depth
is
adequate
G-‐1.1(c)
68. Strip
Loca6on
Moment
(kNm/m)
Ast
(mm2
/m)
Ast
(prov)
Bar
dia
Spacing
mm
Along
X
Zone
A(Exterior)
(-‐)34.2
637
637
10
120(T)
Zone
A(Interior)
(-‐)35.4
662
662
10
115(T)
Zone
B
17.6
314
314
8
160(B)
Zone
C(Interior)
(-‐)8.85
155
240
8
200(T)
Zone
D
11.73
206
240
8
200(B)
Along
Y
Zone
A
(Exterior)
(-‐)34.2
637
637
10
120(T)
Zone
A(Interior)
(-‐)35.4
662
662
10
115(T)
Zone
B
(Interior)
(-‐)8.85
155
240
8
200(T)
Zone
C
17.6
314
314
8
160(B)
Zone
D
11.73
206
240
8
200(B)
Step 8 :Rebar Details
• Ast,min
=
0.12
x
200
x
1000
/100
=
240
mm2/m
26.5.2.1
7.5
Ast2
–
58490Ast
+
Mu
=
0
69. 17.6
11.73
17.6
11.73
17.6
17.6
A
B
A
D
C
C
A
A
B
Exterior
Exterior
Interior
Interior
70. -‐8.85
-‐35.4
A B A
D
C C
A
AB
-‐35.4
-‐35.4
-‐8.85
-‐35.4
-‐34.2
-‐34.2
0
-‐34.2
-‐34.2
-‐0
Exterior
Exterior
Interior
Interior
#8@200
#10@120
#10@115
#10@120
#10@120
#8@200
#8@200
#10@115
#10@115
#8@200
TOP
Rebar
details
in
Corner
Panel
71. Design
Example
#2
Design
by
DDM
flat
plate
supported
on
columns
500
mm
square,
for
a
Live
Load
=
4
kN/m2,
Floor
Finish
=
1
kN/m2
use
M25
and
Fe415.
Floor
slab
is
exposed
to
moderate
environment.
Column
Height
=
3.5m
(c/c).
Bay
spacing
in
X
and
Y
direc6on
=
5.5m
c/c.
Assume
that
building
is
not
restrained
against
sway
• Interior
Panel
P5
• Corner
Panel
P7
3
bays
@
5.5
m
c/c
72. A.
Interior
Panel
Design
5.5
m
5.5
m
2.75m
2.75
m
A A
A A
B
B
C
CD
Zone
A
–
Corner
Strip
Zone
B
–
Middle
Strip
along
X
Zone
C
–
Middle
Strip
along
Y
Zone
D
–
Interior
Region
Step 1: Panel Division into Strips
31.1.1(a)
Moment
direc6on
Along
L1
L2
Width
of
Column
Strip
on
either
side
of
Centre
Line
=
0.25L2
and
≤
0.25
L1
Middle
Strip
X
5
5
1.375
and
≤1.375
m
Adopt
1.375
m
2.75m
Y
5
5
1.375
and
≤1.375
m
Adopt
1.375
m
2.75m
73. Step 2: Trial Depth CL 31.2.1
• L/d
=
26
• Modifica5on
Factor
=
1.33,
Assuming
pt
=
0.4%,
FIG
4
IS
456
• d
=
5500/(26
x
1.33)
=
160
mm
>
125
CL
31.2.1
• DS=
160
+
30
+
18
=
208
mm
(
assume
#12
bars,
and
bars
in
two
layers)
• Provide
Ds=
225
mm
d
=
225-‐30-‐18
=
177
mm
74. Step 3 Design Loads / m width of Slab
• wuD = 1.5(25x 0.225 + 1) = 9.94kN/m
• wuL = 1.5 x 4 = 6kN/m
• wu = 15.94 ≈ 16 kN/m
Step 4: Check for Applicability of DDM: CL 31.4.1
• No.
of
Con5nuous
Spans
in
each
direc5on
=
3
;
OK
31.4.1(a)
• Long
Span/Short
Span
=
5.5/5.5
=
1
<2
;
OK
31.4.1(b)
• Successive
spans
in
each
direc5on
=
Equal;
OK
31.4.1(d)
• wuL/wuD
=
6/9.94
=
0.6
<
3
;
OK
31.4.1(e)
75. Step 5: Check for punching shear around Column
Assumed
d
=
177
mm
Sec4on
1:
• Cri5cal
Sec5on
at
d/2
around
the
column
• Perimeter
of
Cri5cal
Sec5on
=
4
x
0.677=
2.708
m
• Vu
=
16
(
5.52
–
0.6772)
=
477kN
• τc
=
0.25√fck
=
1.25
MPa
• ks
=
0.5
+1
=
1.5
<=1
;
ks=1
;
ks
τc
=
1.25
• Shear
Resistance
of
Concrete
=
1.25
x
2708
x
177
=
599kN
>
477
kN
OK
Cri4cal
Sec4on
0.677m
0.677m
5.5m
5.5m
Contributory
Area
76. Step 6:Design Moments CL 31.4.2.2
Parameters
Along
X
Along
Y
L1
(Span
in
direc4on
of
Mo)
5.5
5.5
m
0.65L1
3.575
3.575
m
Ln
(clear
span
extending
from
face
to
face
of
columns,
capitals)
(5.5-‐0.5)
=
5
5
m
Ln
>
0.65L1
5
5
m
L2
(Span
transverse
to
L1)
5.5
5.5
m
W
=
wu
L2Ln
440
440
kN
M0
=
W
Ln
/
8
275
275
kNm
wu = 16 kN /m
77. Step 7 : Distribution of Bending Moment across panel width ;
CL: 31.4.3.2, 31.5.5
Moment
Direc5on
along
X
Y
Nega4ve
Design
Moment
MN
=
-‐
0.65*M0
179
179
kNm
31.4.3.2
• Column
Strip
M1
=
0.75MN
134.3
134.3
kNm
31.5.5.1
Width
of
Column
Strip
resis4ng
M1
(Csw)
2.75
2.75
m
• -‐m1
=
M1/
Csw
(Zone
A)
48.8
48.8
kNm/m
• Middle
Strip
M2
=
0.25MN
44.8
44.8
kNm
31.5.5.4(a)
Width
of
Middle
Strip
resis4ng
M2
(Msw)
2.75
2.75
m
• -‐m2
=
M2/Msw
(Zone
B
&
C)
16.3
16.3
kNm/m
78. Posi5ve
Design
Moment
MP
=
0.35*M0
96.3
96.3
kNm
31.4.3.2
• Column
Strip
M1
=
0.6MP
57.8
57.8
kNm
31.5.5.3
• +m1
=
M1/
Csw
(Zone
B
&C)
21
21
kNm/m
• Mid
Span
M2
=
0.4MP
38.5
38.5
kNm
31.5.5.4(a)
• +m2
=
M2/Msw
(Zone
D)
14
14
kNm/m
-‐ve
sign
:
Hogging
Moment
(tension
at
top)
+ve
sign
:
Sagging
Moment
(tension
at
borom)
-‐48.8
-‐16.3
-‐48.8
21
14
21
-‐48.8
-‐16.3
-‐48.8
14
21
-‐16.3
-‐48.8
-‐48.8
-‐48.8
-‐16.3
-‐48.8
21
A B A
D
C C
A
AB
Step 8 : Check for adequacy of Depth
• Max
Design
Bending
moment
=
48.8
kNm/m
• Mu,lim
=
108
kNm/m
>
48.8
•
Depth
is
adequate
G-‐1.1(c)
79. Loca6on
Moment
(kNm/m)
Ast
(mm2
/m)
Ast
(prov)
Bar
dia
Spacing
mm
Along
X
Zone
A
(-‐)
48.8
828
828
10
90
-‐
T
Zone
B
21
340
340
8
145
-‐
B
Zone
C
(-‐)16.3
262
270
8
180
-‐
T
Zone
D
14
224
270
8
180
-‐
B
Along
Y
Zone
A
(-‐)
48.8
828
828
10
90
-‐
T
Zone
B
-‐16.3
262
270
8
180
-‐
T
Zone
C
21
340
340
8
145
-‐
B
Zone
D
14
224
270
8
180
-‐
B
• 6
Ast2
–
63906Ast
+
Mu
=
0
G-‐1.1(b)
Step 9 :Rebar Details
• Ast,min
=
0.12
x
225
x
1000
/100
=
270
mm2/m
26.5.2.1
• Minimum
Effec5ve
Depth
of
Slab
=
177
mm
80. #8@145
#8@180
#8@145
#8@180
#8@145
#8@145
0.15Ln
0.15Ln
0.125Ln
0.125Ln
Borom
Rebar
Details
in
Interior
Panel
A
B
A
A
B
A
C
D
C
81. TOP
Rebar
Details
in
Interior
Panel
#10@90
#10@90
#8@180
#8@200
#8@180
0.3Ln
0.2Ln
0.3Ln
0.2Ln
Note:
Distances
for
curtailment
of
rebars
are
measured
from
column
face
A
B
A
C
D
C
82. B.
Corner
Panel
Design
Step 5: Check for punching shear around Column
Assumed
d
=
177
mm
Sec4on
1:
• Cri5cal
Sec5on
at
d/2
around
the
column
• Perimeter
of
Cri5cal
Sec5on
=
2
x
0.5885=
1.177
m
• Vu
=
16
(
2.752
–
0.58852)
=
115.5kN
• τc
=
0.25√fck
=
1.25
MPa
• ks
=
0.5
+1
=
1.5
<=1
;
ks=1
;
ks
τc
=
1.25
• Shear
Resistance
of
Concrete
=
1.25
x
1177
x
177
=
260kN
>
115.5
kN
OK
500
177/2
=
88.5
mm
2.75m
2.75m
83. Step 7 : Distribution of Bending Moment across panel width ; CL 31.4.3.3 , 31.5.5
𝛼↓𝑐 =∑↑▒ 𝑘↓𝑐 / 𝑘↓𝑠
Assume
Columns
and
Slab
panels
are
with
same
modulus
of
elas5city
5
m
5
m
1.25m
1.25m
A A
A A
B
B
C
CD
Step 6:Design Moments CL 31.4.2.2
M0 = 275 kNm
84. Parameters
Along
X
Along
Y
Sum
of
column
s4ffness
above
and
below
the
slab
2
(4EcIc)/Lc
Leff
=
1.2
Lc
(CL
E1)
Lc
=
3.5-‐0.225
=
3.275
(2
x
4
x
Ec
x
500
x
5003/12)
/1.2*3275
=
10.6
Ec
x
106
Slab
s4ffness
ks
=
4EsIs/Ls
(4
Es
x
5500
x
2253/12)/5500
=
2.67Es
x
106
3.8Es
x
106
αc
=
∑kc
/ks
2.8
2.8
αc
min
(Table
17)
(0.7/0.5)*0.1
=0.14
<
αc.
Adopt
αc
=
2.8
β
=
1+
(1/αc)
1.36
1.36
85. Moment
Direc5on
along
X
Y
Nega4ve
Design
Moment
MN
=
-‐
0.65*M0/β
131.4
131.4
kNm
31.4.3.3
• Column
Strip
M1
=
MN
131.4
131.4
kNm
31.55.2(a)
Width
of
Column
Strip
Csw
resis4ng
M1
2.75
2.75
m
-‐m1
=
M1/Csw
47.8
47.8
kNm/m
• Middle
Strip
M2=0
0
0
kNm
31.5.5.4(a)
-‐m2
=
0
0
0
kNm/m
A.
Exterior
nega4ve
design
moment:
-‐m1
-‐m1
-‐m1
-‐m1
Exterior
Exterior
Interior
Interior
1.25
1.25
-‐m2
-‐m2
X
Y
M0 = 275 kNm
86. Moment
Direc5on
along
X
Y
Nega4ve
Design
Moment
MN
=
-‐
(0.75
–
0.1/β)Mo
186
186
kNm
31.4.3.3
• Column
Strip
M1
=
0.75
MN
139.5
139.5
kNm
31.5.5.1
Width
of
Column
Strip
Csw
resis4ng
M1
2.75
2.75
m
• -‐m1
=
M1/
Csw
50.73
50.73
kNm/m
• Middle
Strip
M2
=
0.25
MN
46.5
46.5
kNm
31.5.5.4(a)
Width
of
Middle
Strip
Msw
resis4ng
M2
2.75
2.75
m
• -‐m2
=
M2/Msw
17
17
kNm/m
B.
Interior
nega4ve
design
moment:
-‐
m1
-‐
m1
-‐
m2
m1
-‐m1
-‐m1
-‐m2
X
Y
Exterior
Exterior
Interior
Interior
87. Moment
Direc5on
along
X
Y
Design
Moment
MP
=
(0.63
–
0.28/β)Mo
116.6
116.6
kNm
31.4.3.3
• Column
Strip
M1
=
0.6
MP
70
70
kNm
31.5.5.3
Width
of
Column
Strip
Csw
resis4ng
M1
2.75
2.75
m
• m1
=
M1/
Csw
25.5
25.5
kNm/m
• Middle
Strip
M2
=
0.4
MP
46.7
46.7
kNm
31.5.5.4(a)
Width
of
Middle
Strip
Msw
resis4ng
M2
2.75
2.75
m
• m2
=
M2/Msw
17
17
kNm/m
C.
Posi4ve
Moment
in
Mid
Span:
m1
m1
m1
m1
m1
m1
m2
X
Y
Exterior
Exterior
Interior
Interior
m2
88. -‐ve
sign
:
Hogging
Moment
(tension
at
top)
+ve
sign
:
Sagging
Moment
(tension
at
borom)
25.5
17
25.5
-‐17
-‐50.73
17
25.5
25.5
A B A
D
C C
A
AB
-‐50.73
-‐50.73
-‐17
-‐50.73
-‐47.8
-‐47.8
0
-‐47.8
-‐47.8
-‐0
Exterior
Exterior
Interior
Interior
Step 7 : Check for adequacy of Depth
• Max
Design
Bending
moment
=
50.73
kNm/m
• Mu,lim
=
108
kNm/m
>
50.73,
Depth
is
adequate
G-‐1.1(c)
89. Strip
Loca6on
Moment
(kNm/m)
Ast
(mm2
/m)
Ast
(prov)
Bar
dia
Spacing
mm
Along
X
Zone
A(Exterior)
(-‐)47.8
810
810
10
90(T)
Zone
A(Interior)
(-‐)50.73
864
864
10
90(T)
Zone
B
25.5
415
415
10
180(B)
Zone
C(Interior)
(-‐)17
273
273
8
180(T)
Zone
D
17
273
273
8
180(B)
Along
Y
Zone
A
(Exterior)
(-‐)47.8
810
810
10
90(T)
Zone
A(Interior)
(-‐)50.73
864
864
10
90(T)
Zone
B
(Interior)
(-‐)17
273
273
8
180(T)
Zone
C
25.5
415
415
10
180(B)
Zone
D
17
273
273
8
180(B)
Step 8 :Rebar Details
• Ast,min
=
0.12
x
225
x
1000
/100
=
270
mm2/m
26.5.2.1
6
Ast2
–
63906Ast
+
Mu
=
0
90. 7.2m
7.2m
7.2m
6.4m
6.4m
6.4m
Design
Example
#3
Design
by
DDM
flat
plate
supported
on
columns
of
dia
=
450
mm,
Column
head
=
1.5
m
dia,
Drop
panel
size
=
3.2
x
3.2
m,
for
a
Live
Load
=
4
kN/m2,
Floor
Finish
=
1
kN/m2
use
M20
and
Fe415.
Assume
clear
cover
=
20
mm.
Column
Height
=
3.35m
• Interior
Panel
P5
• Exterior
Panel
P2/P4
• Corner
Panel
P1
91. Step 1: Panel Division into Strips 31.1.1(a)
Moment
direc6on
Along
L1
L2
Width
of
Column
Strip
on
either
side
of
Centre
Line
=
0.25L2
and
≤
0.25
L1
Middle
Strip
X
7.2
6.4
1.6
<
1.8
m;
1.6
m
4m
Y
6.4
7.2
1.8
>
1.6
m;
1.6
m
3.2m
Lx
=
7.2
Ly
=
6.4
1.6
1.6
1.6
1.6
CSx
CSx
MSx
CSy
MSy
CSy
A. Interior
Panel
Design
Zone
A
–
Corner
Strip
Zone
B
–
Middle
Strip
along
X
Zone
C
–
Middle
Strip
along
Y
Zone
D
–
Interior
Region
92. Step 2: Trial Depth CL 31.2.1
• L/d
=
26
• Modifica5on
Factor
=
1.4,
Assuming
pt
≈0.4%,
FIG
4
IS
456
• d
=
7200/(26
x
1.4)
=
198
mm
>
125
CL
31.2.1
• DS=
198+20+18=
236
mm
(
assume
#12
bars)
• Provide
Ds=
240
mm
,
d
=
198mm
93. Step 3: Design Loads / m width of Slab
• wuD = 1.5(25 x 0.24 + 1) = 10.5kN
• wuL = 1.5 x 4 = 6.0kN
• wu = 16.5 kN
Step 4: Check for Applicability of DDM: CL 31.4.1
• No.
of
Con5nuous
Spans
in
each
direc5on
=
3
;
OK
31.4.1(a)
• Long
Span/Short
Span
=
7.2/6.4
=
1.125
<2
;
OK
31.4.1(b)
• Successive
spans
in
each
direc5on
=
Equal;
OK
31.4.1(d)
• wuL/wuD
=
6/10.5
=
0.571
<
3
;
OK
31.4.1(e)
94. Step 5: Drop Panel Size : CL
31.2.2
• Length
along
X
≥
Lx/3
=
2.4
m
• Length
along
Y
≥
Ly/3
=
2.13
m
•
Generally
Drop
Panel
Size
is
set
equal
to
Width
of
Column
Strip
• Proposed
size
3.2
x
3.2
meets
all
the
requirements.
• Minimum
thickness
=
¼
DS
=
60
mm
or
100
mm;
Adopt
100
mm
Step 6:Column Head
• 1/4
to
1/5
of
average
span
=
7.2/5
=
1.44
m
• Provided
=
1.5
m
;
Ok
• Equivalent
Square
Capital
=0.89D
=
1.335
m
95. Step 7 : Check for Shear around Column Capital
• Minimum
Effec5ve
Depth
of
Slab
=
198
mm
• Effec5ve
Depth
at
Drop
loca5on
=
298
mm
Sec4on
1:
• Cri5cal
Sec5on
at
d/2
around
the
column
capital
• Perimeter
of
Cri5cal
Sec5on
=
π
(
1.5
+
0.298)
=
5.65
m
• Weight
of
Drop
Projec5on
below
slab
=
0.1x
25
x
1.5
=
3.75
kN/m2
• Design
Shear
at
cri5cal
sec5on
around
capital
Vu
• Vu
=
16.5
(
7.2
x
6.4
-‐
π
x
1.7982/4)
+
3.75(3.2
x
3.2
-‐
π
x
1.7982/4)
•
=
747
kN
• τc
=
0.25√fck
=
1.12
MPa
• ks
=
0.5
+1
=
1.5
<=1
;
ks=1
;
ks
τc
=
1.12
• Shear
Resistance
of
Concrete
=
1.12
x
5650
x
298
=
1885kN
>
747
kN
OK
1.5
Cri4cal
Sec4on
DROP
3.2
m
3.2
m
1.798
Capital
96. Sec4on
2
:
Check
for
Shear
around
drop
1.5
Cri4cal
Sec4on
DROP
3.2
m
3.2
m
Capital
3.2
+
0.198
=
3.4
• Cri5cal
Sec5on
at
d/2
around
the
drop
• d
=
198mm
• Perimeter
of
Cri5cal
Sec5on
=
4
x
3.4
=
13.6m
• Design
Shear
at
cri5cal
sec5on
• Vu
=
16.5
(
7.2
x
6.4
–
3.42)
=
569
kN
• Shear
Resistance
of
Concrete
=
1.12
x
13600
x
198
=
3015kN
>
569
kN
97. Step 8:Design Moments CL 31.4.2.2
Parameters
Along
X
Along
Y
L1
(Span
in
direc4on
of
Mo)
7.2
6.4
m
0.65L1
4.68
4.16
m
Ln
(clear
span
extending
from
face
to
face
of
columns,
capitals)
(7.2-‐1.335)
=
5.865
(6.4-‐1.335)
=
5.065
m
Ln
>
0.65L1
5.865
5.065
m
L2
(Span
transverse
to
L1)
6.4
7.2
m
W
=
wu
L2Ln
619.34
601.72
kN
M0
=
W
Ln
/
8
454
381
kNm
wu = 16.5 kN /m
98. Step 9 : Distribution of Bending Moment across panel width ;
CL: 31.4.3.2, 31.5.5
Moment
Direc5on
along
X
Y
Nega4ve
Design
Moment
MN
=
-‐
0.65*M0
295.1
247.65
kNm
31.4.3.2
• Column
Strip
M1
=
0.75MN
221.33
185.74
kNm
31.5.5.1
Width
of
Column
Strip
Csw
2x1.6
=3.2
2x1.6
=3.2
m
• -‐m1
=
M1/
Csw
69.17
58.04
kNm/m
• Middle
Strip
M2
=
0.25MN
73.78
61.91
kNm
31.5.5.4(a)
Width
of
Middle
Strip
Msw
3.2
4
• -‐m2
=
M2/Msw
23.06
15.48
kNm/m
99. Posi5ve
Design
Moment
MP
=
0.35*M0
158.9
133.35
kNm
31.4.3.2
• Column
Strip
M1
=
0.6MP
95.34
80.01
kNm
31.5.5.3
• +m1
=
M1/
Csw
29.79
25
kNm/m
• Middle
Strip
M2
=
0.4MP
63.56
53.34
kNm
31.5.5.4(a)
• +m2
=
M2/Msw
19.86
13.34
kNm/m
-‐ve
sign
:
Hogging
Moment
(tension
at
top)
+ve
sign
:
Sagging
Moment
(tension
at
borom)
-‐69.17
-‐23.06
-‐69.17
29.79
19.86
29.79
-‐58.04
-‐15.48
-‐58.04
13.34
25
-‐15.48
-‐58.04
-‐58.04
-‐69.17
-‐23.06
-‐69.17
25
A B A
D
C C
A
AB
Step 10 : Check for adequacy of Depth
• Max
Design
Bending
moment
=
69.17
kNm/m
• Mu,lim
=
126.36
kNm/m
>
69.17,
G-‐1.1(c)
• Depth
is
adequate
101. Strip
Loca6on
Moment
(kNm/m)
Ast
(mm2
/m)
Ast
(prov)
Bar
dia
Spacing
mm
Along
X
Zone
A
(-‐)
69.17
1093
1093
10
70
-‐
T
Zone
B
29.79
437
437
8
110
-‐
B
Zone
C
(-‐)23.06
334
334
8
150
-‐T
Zone
D
19.86
286
288
8
170
-‐
B
Along
Y
Zone
A
(-‐)58.04
896
896
10
85
-‐
T
Zone
B
(-‐)15.48
222
288
8
170-‐T
Zone
C
25
364
364
8
135
-‐B
Zone
D
13.34
190
288
8
170
-‐
B
• 7.5
Ast2
–
71488Ast
+
Mu
=
0
G-‐1.1(b)
Step 11 :Rebar Details
• Ast,min
=
0.12
x
240
x
1000
/100
=
288
mm2/m
26.5.2.1
• Minimum
Effec5ve
Depth
of
Slab
=
198
mm
102. #8@170
#8@135
#8@135
#8@170
#8@110
#8@110
7.2
m
6.4
m
0.15Ln
0.15Ln
Borom
Rebar
Details
in
Interior
Panel
LAP
ZONE
A
A
A
A
B
B
C
D
C
0.125Ln
0.125Ln
103. #8@170
#10@85
#8@150
#10@
70
0.22Ln
0.22Ln
0.22Ln
0.22Ln
0.33Ln
0.33Ln
0.2Ln
0.2Ln
0.33Ln
0.2Ln
Top
Rebar
Details
in
Interior
Panel
Note:
Distances
for
curtailment
of
rebars
are
measured
from
column
face
A
B
A
0.33Ln
0.2Ln
104. Sec6on
Through
Middle
Strip
-‐
CDC
#8@170
7.2
m
#8@340
#8@150
#8@135
Sec6on
Through
Column
Strip
-‐
ABA
#10@70
#10@140
#10@85
#8@170
#8@340
#8@170
105.
106. Step 7 : Check for Shear around Column Capital
• Minimum
Effec5ve
Depth
of
Slab
=
198
mm
• Effec5ve
Depth
at
Drop
loca5on
=
298
mm
Sec4on
1:
• Cri5cal
Sec5on
at
d/2
around
the
column
capital
• Perimeter
of
Cri5cal
Sec5on
=
π
(
1.5
+
0.298)/4
=
1.412
m
• Weight
of
Drop
Projec5on
below
slab
=
0.1x
25
x
1.5
=
3.75
kN/m2
• Design
Shear
at
cri5cal
sec5on
around
capital
Vu
• Vu
=
16.5
(
3.6x
3.2
–
(π
x
1.7982/4)/4)
+
3.75(1.6
x
1.6
–
(π
x
1.7982/4)/4))
•
=
187
kN
• τc
=
0.25√fck
=
1.12
MPa
• ks
=
0.5
+1
=
1.5
<=1
;
ks=1
;
ks
τc
=
1.12
• Shear
Resistance
of
Concrete
=
1.12
x
1412
x
298
=
471kN
>
187
kN
OK
2.
Corner
Panel
Design
107. Sec4on
2
:
Check
for
Shear
around
drop
• Cri5cal
Sec5on
at
d/2
around
the
drop
• d
=
198mm
• Perimeter
of
Cri5cal
Sec5on
=
2
(1.7)=3.4m
• Design
Shear
at
cri5cal
sec5on
• Vu
=
16.5
(
3.6
x
3.2
–
1.72)
=
143
kN
• Shear
Resistance
of
Concrete
=
1.12
x
3400
x
198
=
754kN
>
143
kN
CRITICAL
SECTION
drop
free
edge
free
edge
=1.6
+
0.198/2
=
1.7
m
Step 8:Design Moments CL 31.4.2.2
Along
X
Along
Y
M0
=
W
Ln
/
8
454
381
kNm
108. Step 9 : Distribution of Bending Moment across panel width ;
CL 31.4.3.3 , 31.5.5
𝛼↓𝑐 =∑↑▒ 𝑘↓𝑐 / 𝑘↓𝑠
Equivalent
side
of
circular
column
=
0.89D
=
0.89x
450
=
400
mm
Assume
Ec
=
Es
109. Parameters
Along
X
Along
Y
Sum
of
column
s4ffness
above
and
below
the
slab
2
(4EcIc)/Lc
(2
x
4
x
Ec
x
400
x
4003/12)
/3350
=
5.09
Ec
x
106
Slab
s4ffness
ks
=
4EsIs/Ls
(4
Es
x
6400
x
2403/12)/7200
=
4.1Es
x
106
(4
Es
x
7200
x
2403/12)/6400
=
5.184Es
x
106
αc
=
∑kc
/ks
1.24
0.98
αc
min
(Table
17)
l2/l1
=
6.4/7.2
=
0.89,
WuL/WuD
=
0.571
(0.7/0.5)*0.071
=
0.1
<αc
Adopt
αc
7.2/6.4
=
1.125,
WuL/WuD
=
0.571
≈(0.8/0.5)*0.071
=
0.113
<αc
Adopt
αc
β
=
1+
(1/αc)
1.8
2.02
110. Moment
Direc5on
along
X
Y
Nega4ve
Design
Moment
MN
=
-‐
0.65*M0/β
164
122.6
kNm
31.4.3.3
• Column
Strip
M1
=
MN
164
122.6
kNm
31.55.2(a)
Width
of
Column
Strip
Csw
resis4ng
M1
2x1.6
=3.2
2x1.6
=3.2
m
-‐m1
=
M1/
3.2
-‐51.3
-‐38.3
kNm/m
• Middle
Strip
M2=0
0
0
kNm
31.5.5.4(a)
Width
of
Middle
Strip
Msw
resis4ng
M2
3.2
4
-‐m2
=
0
0
0
kNm/m
A.
Exterior
nega4ve
design
moment:
-‐m1
-‐m1
-‐m1
-‐m1
Exterior
Exterior
Interior
Interior
1.6
1.6
-‐m2
-‐m2
X
Y
111. Moment
Direc5on
along
X
Y
Nega4ve
Design
Moment
MN
=
-‐
(0.75
–
0.1/β)Mo
315.3
266.9
kNm
31.4.3.3
• Column
Strip
M1
=
0.75
MN
236.5
200.2
kNm
31.5.5.1
Width
of
Column
Strip
Csw
resis4ng
M1
2x1.6
=3.2
2x1.6
=3.2
m
• -‐m1
=
M1/
Csw
-‐73.9
-‐62.6
kNm/m
• Middle
Strip
M2
=
0.25
MN
78.83
66.7
kNm
31.5.5.4(a)
Width
of
Middle
Strip
Msw
resis4ng
M2
3.2
4
m
• -‐m2
=
M2/Msw
-‐24.7
-‐16.7
kNm/m
B.
Interior
nega4ve
design
moment:
-‐
m1
-‐
m1
-‐
m2
m1
-‐m1
-‐m1
-‐m2
X
Y
Exterior
Exterior
Interior
Interior
112. Moment
Direc5on
along
X
Y
Design
Moment
MP
=
(0.63
–
0.28/β)Mo
215.4
187.2
kNm
31.4.3.3
• Column
Strip
M1
=
0.6
MP
129.3
112.3
kNm
31.5.5.3
Width
of
Column
Strip
Csw
resis4ng
M1
2x1.6
=3.2
2x1.6
=3.2
m
• m1
=
M1/
Csw
40.4
35.1
kNm/m
• Middle
Strip
M2
=
0.4
MP
86.2
74.9
kNm
31.5.5.4(a)
Width
of
Middle
Strip
Msw
resis4ng
M2
3.2
4
m
• m2
=
M2/Msw
26.94
18.7
kNm/m
C.
Posi4ve
Moment
in
Mid
Span:
m1
m1
m1
m1
m1
m1
m2
X
Y
Exterior
Exterior
Interior
Interior
m2
113. -‐ve
sign
:
Hogging
Moment
(tension
at
top)
+ve
sign
:
Sagging
Moment
(tension
at
borom)
40.4
26.94
40.4
-‐16.7
-‐62.6
18.7
35.1
35.1
A B A
D
C C
A
AB
-‐73.9
-‐73.9
-‐24.7
-‐62.6
-‐51.3
-‐51.3
0
-‐38.3
-‐38.3
-‐0
Exterior
Exterior
Interior
Interior
Step 10 : Check for adequacy of Depth
• Max
Design
Bending
moment
=
73.9
kNm/m
• Mu,lim
=
126.36
kNm/m
>
73.9,
Depth
is
adequate
G-‐1.1(c)
114. Strip
Loca6on
Moment
(kNm/m)
Ast
(mm2
/m)
Ast
(prov)
Bar
dia
Spacing
mm
Along
X
Zone
A(Exterior)
(-‐)51.3
782
782
10
100
-‐
T
Zone
A(Interior)
(-‐)73.9
1180
1180
10
65
-‐
T
Zone
B
40.4
604
604
8
80
-‐B
Zone
C(Interior)
(-‐)24.7
359
359
8
140
-‐
T
Zone
D
26.94
393
393
8
125-‐B
Along
Y
Zone
A
(Exterior)
(-‐)38.3
570
570
10
135
Zone
A(Interior)
(-‐)62.6
976
976
10
80
Zone
B
(Interior)
(-‐)16.7
240
288
8
170
Zone
C
35.1
520
520
8
95
Zone
D
18.7
270
288
8
170
• 7.5
Ast2
–
71488Ast
+
Mu
=
0
G-‐1.1(b)
Step 11 :Rebar Details
• Ast,min
=
0.12
x
240
x
1000
/100
=
288
mm2/m
26.5.2.1
• Minimum
Effec5ve
Depth
of
Slab
=
198
mm
115. Strip
Loca6on
Moment
(kNm/m)
Bar
dia
Spacing
mm
Along
X
Zone
B
40.4
8
80
-‐B
Zone
D
26.94
8
125-‐B
Along
Y
Zone
C
35.1
8
95
Zone
D
18.7
8
170
#8@80
#8@125
#8@95
#8@95
#8@170
#8@80
116. 40.4
26.94
40.4
-‐16.7
-‐62.6
18.7
35.1
35.1
A
B
A
D
C
C
A
A
B
-‐73.9
-‐73.9
-‐24.7
-‐62.6
-‐51.3
-‐51.3
0
-‐38.3
-‐38.3
-‐0
Exterior
Exterior
Interior
Interior
#10@100
#10@100
#10@65
#10@65
#8@140
#10@135
#10@80
#8@170(Min)*
#10@135
#8@170
#8@170(Min)*
*
Op4onal
Top
Rebars
#10@80
Strip
Loca6on
Moment
(kNm/m)
Bar
dia
Spacing
mm
Along
X
Zone
A(Exterior)
(-‐)51.3
10
100
-‐
T
Zone
A(Interior)
(-‐)73.9
10
65
-‐
T
Zone
C(Interior)
(-‐)24.7
8
140
-‐
T
Along
Y
Zone
A
(Exterior)
(-‐)38.3
10
135
Zone
A(Interior)
(-‐)62.6
10
80
Zone
B
(Interior)
(-‐)16.7
8
170
117.
118. Transfer
of
Moments
and
Shears
between
Slabs
and
Columns
• The
maximum
load
that
a
flat
slab
can
support
is
dependent
upon
the
strength
of
the
joint
between
the
column
and
the
slab.
• Load
is
transferred
by
shear
from
the
slab
to
the
column
along
an
area
around
the
column
• In
addi7on
moments
are
also
transferred.
• The
moment
situa7on
is
usually
most
cri7cal
at
the
exterior
columns.
• Shear
forces
resul7ng
from
moment
transfer
must
be
considered
in
the
design
of
the
lateral
column
reinforcement
(i.e.,
7es
and
spirals).
119.
120. EXAMPLE
Compute
moment
transferred
to
Interior
and
corner
Column
in
example
2
Interior
Column
• As
spans
are
same
in
both
direc5ons
• M
=
0.08
(0.5
wL
L2
Ln
2
/(1+1/αc)
=
0.08
x
0.5
x
6
x
5.5
x
52
/
1.36
=
24.3
kNm
• this
moment
is
distributed
to
top
and
borom
column
at
junc5on
in
propor5on
to
their
s5ffness.
• M
=
24.3/2
=
12.2
kNm
Corner
Column
M
=
131.4
kNm
121. Equivalent
Frame
Method
(EFM)
CL
31.5
• More
Comprehensive
and
Logical
method
• Used
when
limita7ons
of
DDM
are
not
complied
with
• Applicable
when
subjected
to
horizontal
loads
31.5.1
(a)
Idealizing
the
3D
slab
–column
system
to
2D
frames
along
column
Centre
lines
in
both
longitudinal
and
transverse
direc6ons.
Longitudinal
Frame
Transverse
Frame
Edge
Frame
122. For
ver6cal
loads,
each
floor,
together
with
the
columns
above
and
below,
is
analyzed
separately.
For
such
an
analysis,
the
far
ends
of
the
columns
are
considered
fixed.
If
there
are
large
number
of
panels,
the
moment
at
a
par6cular
joint
in
a
slab
beam
can
be
sa6sfactorily
obtained
by
assuming
that
the
member
is
fixed
two
panels
away.
This
simplifica6on
is
permissible
because
ver6cal
loads
in
one
panel
only
appreciably
affect
the
forces
in
that
panel
and
in
the
one
adjacent
to
it
on
each
side.
31.5.1(b)
123. En6re
Frame
Analysis
Gravity
+
Lateral
Loads
For
lateral
loads,
it
is
necessary
to
consider
an
equivalent
frame
that
extends
for
the
en4re
height
of
the
building,
because
the
forces
in
a
par4cular
member
are
affected
by
the
lateral
forces
on
all
the
stories
above
the
floor
being
considered.
124. 31.5.1(C
and
d)
I2
=
moment
of
iner4a
at
the
face
of
the
column
/
column
capital
c2
=
dimension
of
column
capital
in
the
transverse
direc4on
l2
=
width
of
equivalent
frame.
varia6on
of
the
flexural
moment
of
iner6a
• Varia4ons
of
moment
of
iner4a
along
the
axis
0f
the
slab
on
account
of
provision
of
drops
shall
be
taken
into
account
• The
s4ffening
effect
of
flared
column
heads
may
be
ignored
126. Cri5cal
Sec5on
Interior
Column
Centre
Line
Column
/Capital
face
C
<
=
C/2
Results
in
Significant
reduc4on
of
design
moments
Design
Posi5ve
Moment
(Span
region)
M3
=
M0
–
(M1+M2)/2
128. Example
3
:
Compute
moments
in
exterior/interior
Panel
along
Longitudinal
Span
Longitudinal
Span
=
7.2m,
Transverse
Span
=
6.4
m,
Interior
Column
=
450mm
dia,
Column
Capital
=
1500mm
dia,
Exterior
Column
=
400x400mm,
Column
Capital
=
870mm(square),
Floor
to
Floor
=
3.35
m,
Slab
Thickness
=
240
mm,
number
of
Panels
=
4
in
each
direc6on
7.2
m
6.4m
6.4m
7.2
m
7.2
m
7.2
m
6.4m
129. Step
1:
S5ffness
Computa5ons
Exterior
Column
(Kce)
=
4E
x
(4004
/12)
/3350
=
2.55E106
=
1
Interior
Column
(KcI)
=
4E
x
π(4504
/64)
/3350
=
2.4E106
=
0.957
Slab(Ks)
=4E
x
(6400
x
2403/12)
/7200
=
4.1E106
=
1.608
Step
2:
Simplified
frame
for
analysis
31.5.1
(b)
7200
7200
3350
3350
1
2
3
A
B
C
D
Joint
Member
Rela5ve
S5ffness
Sum
Distribu5on
Factors
1
1-‐A
1
3.608
0.277
1-‐2
1.608
0.446
1-‐C
1
0.277
2
2-‐B
0.957
5.13
0.187
2-‐1
1.608
0.314
2-‐3
1.608
0.314
2-‐D
0.957
0.187
Fixed
End
Moments
=
(16.5
x
6.4)
x
7.22/12
=
456.2
kNm
130. Joint
1
2
3
Members
FIXED
1A+1C
1-‐2
2-‐1
FIXED
2B+2D
2-‐3
FIXED
3-‐2
DF
0.554
0.446
0.314
0.374
0.314
-‐
FEM
456.2
-‐456.2
456.2
-‐456.2
Bal
-‐252.74
-‐203.46
-‐
-‐
-‐
-‐
CO
-‐
-‐
-‐101.73
-‐
-‐
-‐
Bal
-‐
-‐
31.94
38.04
31.94
-‐
CO
-‐
15.97
-‐
-‐
-‐
15.97
Bal
-‐8.85
-‐7.12
-‐
-‐
-‐
-‐
CO
-‐
-‐
-‐3.56
-‐
-‐
-‐
Bal
1.12
1.33
1.12
Final
end
Moments
-‐261.6
261.6
-‐528.43
39.37
489.26
-‐440.23
1
2
3
261.6
528.43
489.26
440.23
Counter
Clockwise
end
moments
are
posi4ve
131. Step
3:
Design
Moments
in
Exterior
Panel
A.
Design
Nega6ve
Moments
at
Cri6cal
Sec6on
At
Exterior
Support
:
CL
31.5.3.2
870
400
470
235
Cri6cal
Sec6on
from
Column
Centre
line
=
435
mm
261.6
528.43
16.5
x
6.4
=
105.6
kN/m
105.6
x
7.2/2
-‐
(528.43-‐261.6)/7.2
=
343
kN
0.435
Design
Moment
=
343
x
0.435
-‐261.6
-‐105.6x0.4352/2
=
-‐122.4
kNm
(Hogging)
132. At
Interior
Support
:
CL
31.5.3.1
Width
of
equivalent
square
=
0.89D
=
1335
mm
667.5
mm
Cri4cal
Sec4on
loca4on
is
at
capital
face
≤
0.175x7200
=
1260mm
261.6
528.43
16.5
x
6.4
=
105.6
kN/m
343
kN
0.6675
Design
Moment
=
417.32
x
0.6675
-‐528.3
-‐105.6x0.66752/2
=
-‐273.26
kNm
(Hogging)
417.32
133. B.
Design
Posi4ve
Moment
M(+)
=
(16.5
x
6.4x7.2)7.2/8
–
(
528.43
+
261.6)/2
=
289.3
kNm
Moments
DDM
EFM
Posi4ve
Moment
(Span)
215.4
289.3
Nega4ve
Moment(Exterior
Support)
164
122.4
Nega4ve
Moment
(Interior
Support)
315.3
273.3
134. Step
4:
Design
Moments
in
Interior
Panel
A.
Design
Nega6ve
Moments
at
Cri6cal
Sec6on
At
Interior
Support
:
CL
31.5.3.1
16.5
x
6.4
=
105.6
kN/m
387
kN
0.6675
Design
Moment
at
A=
387
x
0.6675
-‐
489.26
-‐105.6x0.66752/2
=
-‐254.5
kNm
(Hogging)
373.32
489.26
440.23
Design
Moment
at
B
=
373.32
x
0.6675
-‐
440.23
-‐105.6x0.66752/2
=
-‐214.6
kNm
(Hogging)
0.6675
A B
135. B.
Design
Posi4ve
Moment
M(+)
=
(16.5
x
6.4x7.2)7.2/8
–
(
489.26
+
440.23)/2
=
219.5
kNm
Moments
DDM
EFM
Posi4ve
Moment
(Span)
158.9
219.5
Nega4ve
Moment
(Interior
Support)
295.1
254.5/214.6
136. Need
for
Computer
Analysis
The
equivalent
frame
method
is
not
sa6sfactory
for
hand
calcula6ons.
It
is
possible,
however,
to
use
computers
and
plane
frame
analysis
programs
if
the
structure
is
modeled
such
that
various
nodal
points
in
the
structure
can
account
for
the
changing
moments
of
iner6a
along
the
member
axis.
SLAB
Drop
Panel
Column
Head
Column
Column
137. FE
Analysis
of
Slab
At
any
point
in
the
plate
bending,
there
will
generally
be
two
bending
moments
Mx
,
My
in
two
mutually
perpendicular
direc5ons
coupled
with
a
complimentary
twis5ng
moment
Mxy
Design
for
flexure
involves
providing
reinforcing
steels
in
two
orthogonal
direc5ons
to
resist
the
moment
field.
Mx,
My
and
Mxy.
Slab
is
idealized
as
an
assembly
of
discrete
plate
bending
elements
joined
at
nodes
Wood
–Armer
equa4ons
are
used
for
this
purpose.
138. Wood
–Armer
equa5ons
(1968)
• This
method
was
developed
by
considering
the
normal
moment
yield
criterion
(Johansen’s
yield
criterion)
aiming
to
prevent
yielding
in
all
direc4ons.
• At
any
point
in
the
slab,
the
moment
normal
to
a
direc4on,
resul4ng
due
to
design
moments
Mx
,
My
,
and
Mxy
must
not
exceed
the
ul4mate
normal
resis4ng
moment
in
that
direc4on.
• Mx
*
cos2θ
+
My
*
sin2θ
-‐
flexural
strength
of
plate
in
the
direc4on
of
θ
with
X
axis.
• Mx
cos2θ
+
Mysin2θ
+
2
Mxy
cosθ
sinθ
-‐
normal
bending
moment
in
the
direc4on
of
θ
139. A.
For
bomom
steel
(
Sagging
Moment
+ve,
Hogging
Moment
–ve)
Compute
:
Mx
*
=
Mx
+|Mxy|
and
My
*
=
My
+|Mxy|
Case
1:
If
Mx
*
≥
0
and
MY
*
≥
0
then
no
change
in
computed
values
of
Mx
*
and
My
*
Case
2:
If
Mx
*
<
0
then
Mx
*
=
0
and
MY
*
=
MY
+
|
Mxy
2/Mx|
Case
3:
If
My
*
<
0
then
My
*
=
0
and
Mx
*
=
Mx
+
|
Mxy
2/My|
B.
For
Top
steel
(
Sagging
Moment
+ve,
Hogging
Moment
–ve)
Compute
:
Mx
*
=
Mx
-‐|Mxy|
and
My
*
=
My
-‐|Mxy|
Case
1:
If
Mx
*
≤
0
and
MY
*
≤
0
then
no
change
in
computed
values
of
Mx
*
and
My
*
Case
2:
If
Mx
*
>
0
then
Mx
*
=
0
and
MY
*
=
MY
-‐|
Mxy
2/Mx|
Case
3:
If
My
*
>
0
then
My
*
=
0
and
Mx
*
=
Mx
-‐|
Mxy
2/My|
140. Example
1
FE
results
at
centre
of
a
plate
element
are:
Mx
=
7
kNm,
My
=
23
kNm,
Mxy
=
9
kNm.
Compute
design
moments
using
Wood
-‐
Armer
equa4ons.
A. Borom
rebars
(Sagging
Moments)
Mx*
=
Mx+|Mxy|
=
16
>
0
,
Mx*
=
16
kNm
My*
=
My+|Mxy|
=
32
>
0
,
My*
=
32
kNm
B.
Top
rebars
(Hogging
Moments)
Mx*
=
Mx-‐|Mxy|
=
-‐2
<
0
,
Mx*
=
2
kNm
My*
=
My-‐|Mxy|
=
14
>
0
Set
My*
=
0
and
compute
Mx
*
=
Mx
-‐|
Mxy
2/My|
=
7
–
|81/23|
=
3.478
kNm
141. Example
2
FE
results
at
centre
of
a
plate
element
are:
Mx
=
7
kNm,
My
=
-‐23
kNm,
Mxy
=
9
kNm.
Compute
design
moments
using
Wood
-‐
Armer
equa4ons.
A. Borom
rebars
(Sagging
Moments)
Mx*
=
Mx+|Mxy|
=
16
>
0
,
Mx*
=
16
kNm
My*
=
My+|Mxy|
=
-‐14
<
0
,
Set
My*
=
0
and
compute
Mx
*
=
Mx
+
|
Mxy
2/My|
=
7
+
|81/23|
=
10.52
kNm
B.
Top
rebars
(Hogging
Moments)
Mx*
=
Mx-‐|Mxy|
=
-‐2
<
0
,
Mx
*
=
2
kNm
My*
=
My-‐|Mxy|
=
-‐32
<
0
,
MY
*
=
32
kNm