Civil structural engineering - Flat slab design

Resources
used
for
compiling
this
presenta4on

are
acknowledged

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.

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

A
flat
slab
may
have
recesses
formed
on
the
soffit
so
that
the
soffit
comprises
a
series
of
ribs

in
two
direc5ons
(
waffle
Slabs).

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.

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

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.

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

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

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

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

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

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

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

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

Type
of

Support

Mx
My
Mxy

Beam

Moment

Deﬂec4on

Slab
Beam

Rigid
3.616
3.616
2.6
-‐
1.4
-‐

300
x125

(Concealed

Beams)

9.84
9.85
3.0
2.88
7.0
4.3

300
x300
4.45
4.45
0.37
12.2
2.9
1.33

300
x450
3
3
0.73
15.6
1.5
0.50

300
x600
2.43
2.43
0.8
17.0
0.98
0.24

300x1000
2
2
0.8
18.0
0.60
0.05

Flat
Slab
9.0
9.0
7.76
-‐
8.676
-‐

Results
Summary

•  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

4.  Structural Behaviour of Flat Slab
Deﬂected
Shape

Column
Strip

Column
Strip

Middle
Strip

Column
Strip
Middle

Strip

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

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

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

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

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.

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.

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)

1
2
3

2

3

Lx1

Lx2

Lx3

Ly1

Ly2

Ly3

≤
0.1Ly2

≤
0.1Lx1

Lx1
≤
Lx2

Lx3
≤
Lx2

Ly1
≤
Ly2

Ly3
≤
Ly2

Lx1
≥
2Lx2/3

Lx3
≥
2Lx2/3

Ly1
≥
2Ly2/3

Ly3
≥
2Ly2/3

wuL/wuD
≤
3

For
any
Panel

Longer
Span/Shorter
Span≤
2

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

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

•  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

•  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

Distribution of Bending Moments across panel width Code Recommendations

11. Rebar Detailing - Code Recommendations

Bent
bars
are

also
used.

There
seems
to
be
a
trend

among
designers
to
use

straight
bars
more
than

bent
bars.

ELEVATION

Rebar Detailing - Code Recommendations
e
e
e
e
e

b
b
b
b
b

Ln
greater
of
adjacent
clear
spans
CL
31.7.3
(b)

Sec6on
through
Middle
Strip

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

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

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

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

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

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)

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

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

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

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)

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

#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

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

B.
Corner
Panel
Design

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

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
M0 = 174.72 kNm

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

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

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

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

-‐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

•  Max
Design
Bending
moment
=
35.4
kNm/m

•  Mu,lim

=
72.41
kNm/m
>
35.4,
Depth
is
adequate

G-‐1.1(c)

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)

•  Ast,min

=
0.12
x
200
x
1000
/100
=
240
mm2/m

26.5.2.1

7.5
Ast2
–
58490Ast
+
Mu
=
0

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

-‐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

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

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


•  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

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
•  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)

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

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

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

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
•  Max
Design
Bending
moment
=
48.8
kNm/m

•  Mu,lim

=
108

kNm/m
>
48.8

• 
Depth
is
adequate

G-‐1.1(c)

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)

•  Ast,min

=
0.12
x
225
x
1000
/100
=
270
mm2/m

26.5.2.1

•  Minimum
Eﬀec5ve
Depth

of
Slab
=
177
mm

#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

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

B.
Corner
Panel
Design

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

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
M0 = 275 kNm

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

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

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

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

-‐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

•  Max
Design
Bending
moment
=
50.73
kNm/m

•  Mu,lim

=
108
kNm/m
>
50.73,
Depth
is
adequate

G-‐1.1(c)

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)

•  Ast,min

=
0.12
x
225
x
1000
/100
=
270
mm2/m

26.5.2.1

6
Ast2
–
63906Ast
+
Mu
=
0

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

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


•  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

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
•  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)

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

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

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

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

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

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
•  Max
Design
Bending
moment
=
69.17
kNm/m

•  Mu,lim

=
126.36

kNm/m
>
69.17,
G-‐1.1(c)

•  Depth
is
adequate

Moment

Direc4on

Moment

Direc4on

CS

MS

CS

FE
Results
from

ETAB

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)

•  Ast,min

=
0.12
x
240
x
1000
/100
=
288
mm2/m

26.5.2.1

•  Minimum
Eﬀec5ve
Depth

of
Slab
=
198
mm

#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

#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

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

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

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

Along
X
Along
Y

M0

=
W
Ln
/
8

454
381
kNm

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

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

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

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

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

-‐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

•  Max
Design
Bending
moment
=
73.9
kNm/m

•  Mu,lim

=
126.36

kNm/m
>
73.9,
Depth
is
adequate

G-‐1.1(c)

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)

•  Ast,min

=
0.12
x
240
x
1000
/100
=
288
mm2/m

26.5.2.1

•  Minimum
Eﬀec5ve
Depth

of
Slab
=
198
mm

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

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

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).

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

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

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)

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.

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

31.5.2
Loading
Paiern

wu
LL

>
¾
wu,DL

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

Distribu5on
of
Moment

Similar
to
DDM

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

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

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

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)

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

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

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

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

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

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.

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

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

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

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Civil structural engineering - Flat slab design

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