RC2 Lecture 3.1 - Design of Two-Way Floor Slab System
RC2 Lecture 3.1 - Design of Two-Way Floor Slab System
RC2 Lecture 3.1 - Design of Two-Way Floor Slab System
A
=
B
EI
Ll w
EI
Ls w
384
5
384
5
4
l
4
s
=
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EI EI 384 384
l s
4
4
l
s
16 2Ls Ll For w w
Ls
Ll
w
w
= = =
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Stati c Equi li br i um for Two Stati c Equi li br i um for Two- -way way
Slabs Slabs
Analogy of two-way slab to plank and
beam floor
Consider Section A-A:
Moment per m width in
planks:
m/m - kN
8
2
1
wl
M =
beam floor
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Total Moment
8
( ) m - kN
8
2
1
2 T
l
wl M =
Stati c Equi li br i um for Two Stati c Equi li br i um for Two- -way way
Slabs Slabs
wl
Uniform load on each beam:
Moment in one beam (Sec: B-B)
Total Moment in both beams:
kN/m
2
1
wl
m - kN
8 2
2
2 1
lb
l wl
M
=
( ) kN
2
2
l
l M
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Total Moment in both beams: ( ) m - kN
8
2
1
wl M =
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Method of Desi gn Method of Desi gn
(1) (1) Direct Design Method (DDM): Direct Design Method (DDM):
Limited to slab systems with uniformly distributed Limited to slab systems with uniformly distributed
loads and supported on equally spaced columns. loads and supported on equally spaced columns.
Method uses a set of coefficients to determine Method uses a set of coefficients to determine
the design moment at critical sections. Two the design moment at critical sections. Two--way way
slab systemthat do not meet the limitations of slab systemthat do not meet the limitations of
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slab system that do not meet the limitations of slab system that do not meet the limitations of
the ACI Code 13.6.1 must be analyzed using the ACI Code 13.6.1 must be analyzed using
more accurate procedures. more accurate procedures.
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Method of Desi gn Method of Desi gn
(2) (2) Equivalent Frame Method (EFM) : Equivalent Frame Method (EFM) :
A three A three--dimensional building is divided into a dimensional building is divided into a
series of two series of two--dimensional equivalent frames by dimensional equivalent frames by
cutting the building along lines midway between cutting the building along lines midway between
columns. The resulting frames are considered columns. The resulting frames are considered
separately in the longitudinal and transverse separately in the longitudinal and transverse
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separately in the longitudinal and transverse separately in the longitudinal and transverse
directions of the building and treated floor by directions of the building and treated floor by
floor. floor.
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Equi valent Fr ame Method (EFM) Equi valent Fr ame Method (EFM)
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Longitudinal
equivalent frame
Transverse
equivalent frame
Equi valent Fr ame Method (EFM) Equi valent Fr ame Method (EFM)
Elevation of
the frame
Perspective
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Perspective
view
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Column and Mi ddle Str i ps Column and Mi ddle Str i ps
The slab is
b k i t broken up into
column and
middle strips for
analysis
L/4
L/4
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L/4
L/4
L/4 L/4 L/4 L/4
Mi ni mum Slab Thi ckness for Mi ni mum Slab Thi ckness for
Two Two- -way Constr ucti on way Constr ucti on
The ACI Code 9.5.3 specifies a minimum slab The ACI Code 9.5.3 specifies a minimum slab
thickness to control deflection There are three thickness to control deflection There are three thickness to control deflection. There are three thickness to control deflection. There are three
empirical limitations for calculating the slab empirical limitations for calculating the slab
thickness (h), which are based on experimental thickness (h), which are based on experimental
research. If these limitations are not met, it will research. If these limitations are not met, it will
be necessary to compute deflection. be necessary to compute deflection.
For slabs without interior beams spanning For slabs without interior beams spanning
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For slabs without interior beams spanning For slabs without interior beams spanning
between supports between supports - - Table 9.5 (c) Table 9.5 (c) and: and:
With drop panels 125 mm With drop panels 125 mm
Without drop panels .. 100 mm Without drop panels .. 100 mm
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Mi ni mum Slab Thi ckness for Mi ni mum Slab Thi ckness for
Two Two- -way Constr ucti on way Constr ucti on
For slabs with beams spanning between the For slabs with beams spanning between the
supports on all sides: supports on all sides: supports on all sides: supports on all sides:
> 0 . 2 ) (
fm
for a
mm 90 >
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< < 0 . 2 0.2 ) (
fm
for b
mm 125 >
Mi ni mum Slab Thi ckness for Mi ni mum Slab Thi ckness for
Two Two- -way Constr ucti on way Constr ucti on
2 . 0 ) (
fm
for c
With drop panels: With drop panels:
h > 125mm h > 125mm
Without drop Without drop
panels: panels:
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h > 100mm h > 100mm
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Mi ni mum Slab Thi ckness for Mi ni mum Slab Thi ckness for
Two Two- -way Constr ucti on way Constr ucti on
Definitions: Definitions:
h = Minimum slab thickness without h = Minimum slab thickness without
interior beams. interior beams.
l l
nn
= Clear span in the long direction = Clear span in the long direction
measured face to face of column measured face to face of column
Th ti f th l t h t l Th ti f th l t h t l
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= The ratio of the long to short clear = The ratio of the long to short clear
span span
mm
= = The average value of a for all The average value of a for all
beams on the sides of the panel. beams on the sides of the panel.
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Beam Beam--to to- -Slab Sti ffness Rati o, Slab Sti ffness Rati o,
Accounts for stiffness effect of beams located Accounts for stiffness effect of beams located
along slab edge reduces deflections of along slab edge reduces deflections of along slab edge reduces deflections of along slab edge reduces deflections of
panel adjacent to beams. panel adjacent to beams.
beam of stiffness flexural
=
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slab of stiffness flexural
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Beam Beam--to to- -Slab Sti ffness Rati o, Slab Sti ffness Rati o,
b cb b cb
E
/
/ 4E I
l
l I
= =
s cs s cs
E / 4E I l I
beam uncracked of inertia of Moment I
slab of elasticity of Modulus E
beam of elasticity of Modulus E
b
sb
cb
=
=
=
Reinforced Concrete II Reinforced Concrete II
With width bounded laterally by centerline of With width bounded laterally by centerline of
adjacent panels on each side of the beam. adjacent panels on each side of the beam.
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slab uncracked of inertia of Moment I
s
=
Beam and Slab Secti ons for Beam and Slab Secti ons for
calculati on of calculati on of
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Beam and Slab Secti ons for Beam and Slab Secti ons for
calculati on of calculati on of
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Beam and Slab Secti ons for Beam and Slab Secti ons for
calculati on of calculati on of
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Spandrel (Edge) Beam
Interior Beam
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PCA Char ts for calculati on of PCA Char ts for calculati on of
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PCA Char ts for calculati on of PCA Char ts for calculati on of
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Example :Flat Slab wi thout Beams Example :Flat Slab wi thout Beams
A flat plate floor system
with panels 7 3 by 6 0 m with panels 7.3 by 6.0 m
is supported on 0.50m
square columns.
Determine the minimum
slab thickness required
for the interior and
corner panels.
Reinforced Concrete II Reinforced Concrete II Dr. HazimDwairi Dr. HazimDwairi The Hashemite University The Hashemite University
p
Use f
c
= 28 MPa and
f
y
= 420 MPa
Exteri or Slab Exteri or Slab
Slab thickness, from table for Slab thickness, from table for f f
yy
=420 =420 MPa MPa and and
no edge beams is no edge beams is no edge beams is no edge beams is
m l
l
h
n
n
8 . 6 5 . 0 3 . 7
30
min
= =
=
Reinforced Concrete II Reinforced Concrete II Dr. HazimDwairi Dr. HazimDwairi The Hashemite University The Hashemite University
mm use mm h
n
230 7 . 226
30
1000 8 . 6
min
=
=
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I nteri or Slab I nteri or Slab
Slab thickness, from table for Slab thickness, from table for f f
yy
=420 =420 MPa MPa and and
no edge beams is no edge beams is no edge beams is no edge beams is
m l
l
h
n
n
8 . 6 5 . 0 3 . 7
33
min
= =
=
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mm use mm h
n
210 1 . 206
33
1000 8 . 6
min
=
=
Example : Flat Slab wi th Beams Example : Flat Slab wi th Beams
A flat plate floor system
with panels 7 3 by 6 0 m is with panels 7.3 by 6.0 m is
supported on beams in two
directions which supported
on 0.40m square columns.
Determine the minimum
slab thickness required for
an interior panel.
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p
Use f
c
= 28 MPa and
f
y
= 414 MPa
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Flat Slab wi th Beams Example Flat Slab wi th Beams Example
Beam cross Beam cross- -sections sections
All Dimensions in millimeters All Dimensions in millimeters
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II
bb
= 1.170 x 10 = 1.170 x 10
10 10
mm mm
44
II
bb
= 7.952 x 10 = 7.952 x 10
99
mm mm
44
I nteri or Slab I nteri or Slab
) 180 )( 6000 (
10 170 . 1
: *
3
4 10
=
beam
mm I
Direction Long
: *
01 . 4
10 916 . 2
12
) 180 )( 6000 (
4 9
3
= =
= =
slab
beam
long
slab
Direction Short
EI
EI
mm I
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30 . 3
10 548 . 3
12
) 180 )( 7300 (
4 9
3
= =
= =
slab
beam
short
slab
EI
EI
mm I
avrg
fm
66 . 3
2
3 . 3 01 . 4
: slab interior for Average The *
=
+
=
l
l
fm
short
long
2 for thickness Compute
232 . 1
4 . 0 0 . 6
4 . 0 3 . 7
: t Coefficien the Compute
2
>
=
= =
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mm
f
l
h
y
n
4 . 160
236 . 1 9 36
1400
414
8 . 0 9 . 6
9 36
1400
8 . 0
=
+
+
=
+
+
=
USE
h = 180mm
Thickness of Edge & Corner Slabs Thickness of Edge & Corner Slabs
10 952 . 7
: direction long in Compute *
4 9
=
beam L
fm
mm I
: direction short in Compute *
11 . 5
10 555 . 1
10 952 . 7
10 555 . 1
12
) 180 )( 3200 (
9
9
4 9
3
=
=
= =
fm
long
slab
mm I
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25 . 4
10 871 . 1
10 952 . 7
10 871 . 1
12
) 180 )( 3850 (
9
9
4 9
3
=
=
= =
short
slab
f
mm I
3.30
3.30
4.01
5.11
93 . 3
4
fm
01 4 30 3 11 5 25 4 + + +
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4.25
3.30
4.01
17 . 4
4
01 . 4 30 . 3 11 . 5 25 . 4
=
+ + +
=
fm
Thickness of Edge & Corner Slabs Thickness of Edge & Corner Slabs
4.01
3 30
89 . 3
4
01 . 4 30 . 3 01 . 4 25 . 4
=
+ + +
=
fm
00 7 10 0 20 0 30 7 l
4.25
3.30
4.01
230 . 1
30 . 0 0 . 6
30 . 0 3 . 7
: t Coefficien the Compute
00 . 7 10 . 0 20 . 0 30 . 7
=
= =
= =
short
long
n
l
l
m l
y
n
fm
0 . 163
230 . 1 9 36
1400
414
8 . 0 00 . 7
9 36
1400
8 . 0
2 for thickness Compute
=
+
+
=
+
+
=
>
USE
h = 180mm