©Teaching Resource in Design of Steel Structures
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1
COMPOSITE BEAMS

II
©Teaching Resource in Design of Steel Structures
–
IIT Madras, SERC Madras, Anna Univ., INSDAG
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CONTENTS
•
INTRODUCTION
•
PROVISION FOR SERVICE OPENING IN
COMPOSITE BEAMS
•
BASIC DESIGN CONSIDERATIONS
•
DESIGN OF COMPOSITE BEAMS
•
EFFECT OF CONTINUITY
•
SERVICEABILITY
•
CONCLUSION
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INTRODUCTION
•
Composite
beam
with
profiled
sheeting
with
concrete
topping
.
•
Profiled
sheets
are
of
two
types
•
Trapezoidal
profile
•
Re

entrant
profile
(a) Trapezoidal profile deck
(b) Re

entrant profile
Types of profile deck
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•
The
deck
slab
with
profiled
sheeting
is
of
two
types
•
The
ribs
of
profiled
decks
running
parallel
to
the
beam
.
•
The
ribs
of
profiled
decks
running
perpendicular
to
the
beam
.
Orientation of Profiled deck slab in a composite beam
(b) Ribs perpendicular to
the beam
(a) Ribs parallel to the beam
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PROVISION FOR SERVICE OPENING IN
COMPOSITE BEAMS
•
Simple Construction with Rolled Sections
•
Fabricated Sections
•
Haunched Beams
•
Parallel Beam Approach
•
Castellated Sections
•
Stub Girders
•
Composite Trusses
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Fabricated Sections
Fabricated sections for commercial buildings
(a) Straight Taper
(b) Semi

Taper
(c)Cranked Taper
(d) Stepped Beam
(where automatic welding is not crucial)
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Haunched Beams
(a) sections of different size
(b)
haunches cut from main beam
Haunched beams: Two types of haunches
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Parallel Beam Approach
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Castellated Sections
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Stub Girders
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Composite Trusses
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BASIC DESIGN CONSIDERATIONS
•
Design Method suggested by Eurocode 4
•
ultimate
strength
is
determined
from
plastic
capacity
.
•
serviceability
is
checked
using
elastic
analysis
.
•
full
shear
connection
ensures
that
full
moment
capacity
of
the
section
develops
.
•
in
partial
shear
connection,
the
design
should
be
adequate
to
resist
the
applied
loading
.
•
partial
shear
connection
is
sometimes
preferred
due
to
economy
.
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•
Span to depth ratio
Span to Depth ratio as according to EC4
EC4
Simply supported
15

18 (Primary Beams)
18

20 (Secondary Beams)
Continuous
18

22 (Primary Beams)
22

25 (end bays)
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•
Effective breadth of flange
Use of effective width to allow for shear lag
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•
For
simply
supported
beam,
effective
breadth
of
simply
supported
beam
is
taken
as
o
/
8
on
each
side
of
the
steel
web
•
For
continuous
beam,
B
but
4
b
eff
Value of
0
for continuous beam as per EC4
1
2
3
4
0.25
(
1
+
2
)
0.25
(
2
+
3
)
0.8
1
0.7
2
0.8
3

0.3
4
〮0
3
4
+0.5
3
1.5
4
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•
Modular
ratio
•
Shear
Connection
–
The
elastic
shear
flow
at
the
interface
increases
linearly
from
zero
at
the
centre
to
its
maximum
value
at
the
end
under
uniform
load
.
–
At
the
elastic
limit
of
connectors,
redistribution
of
forces
occurs
.
–
At
collapse
load
level
it
is
assumed
that
all
the
connectors
carry
equal
force
.
–
The
design
capacity
of
shear
connectors
is
taken
as
80
%
of
their
nominal
static
strength
in
EC
4
.
Shear flow at interface
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Load
Partial safety factor,
f
Dead load
1.35
Live load
1
.5
Materials
Partial safety factor,
m
Concrete
1.5
Structural Steel
1.15
Reinforcement
1.15
•
Partial Safety Factor
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Type of Element
Type of
Section
Class of Section
Plastic (
1
)
Compact
(
2
)
Semi

compact (
3
)
Outstand
element
of
compression
flange
Welded
b/t
㜮7
b/t
㠮8
戯b
ㄳ⸶
副汬R
戯b
㠮8
b/t
㤮9
戯b
ㄵ⸰
䥮瑥牮慬
敬e浥湴
潦
捯浰牥獳i潮
晬慮来
W敬摥
戯b
㈴⸲
戯b
㈶⸳
戯b
㈹⸴
副汬R
戯b
㈷⸳
戯b
㌳⸶
戯b
㐱⸰
Web
with
neutral
axis
at
mid
depth
All
d/t
㠳⸰
d/t
㈮1
d/t
ㄲ㘮1
Web
under
uniform
compression
Welded
d/t
㈹⸴
副汬R
搯
㐱⸰
卩湧汥S摯畢汥
慮a汥
T

獴敭s
副汬R
戯b
㠮8
搯
㠮8
戯b
⸰
搯
⸰
戯b
ㄵ⸸
搯
ㄵ⸸
䍩牣畬慲
畢e
w楴i
潵瑥
摩慭整敲
D
D/t
㐴
2
D/t
㘳
2
D/t
㠸
2
y
f
250
•
Section Classifications
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DESIGN OF COMPOSITE BEAMS
•
Moment
Resistance
•
Reinforced
Concrete
Slabs,
supported
on
Steel
beams
Notations as per IS: 11384

1985
b
eff
d
s
D
T
t
x
u
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Position of
Plastic Neutral
Axis
Value of
x
u
Moment Capacity
M
p
Within slab
x
u
= a
A
a
/
b
eff
M
p
=0.87A
a
f
y
(d
c
+ 0.5d
s
– 0.42
x
u
)
Plastic neutral
axis in steel
flange
Ba
d
b
aA
d
x
s
eff
a
s
u
2
M
p
= 0.87f
y
[
A
a
(d
c
+0.08
d
s
) –B(
x
u
–
d
s
)(
x
u
+ 0.16
d
s
) ]
Plastic neutral
axis in web
at
d
b
A
A
a
T
d
x
s
eff
f
a
s
u
2
2
M
p
= 0.87f
y
A
s
(d
c
+0.08
d
s
) – 2A
f
(0.5T+0.58
d
s
)–2t(
x
u
–
d
s
–T)(0.5
x
u
+ 0.08
d
s
+ 0.5 T)
Moment capacity of composite Section with full shear
interaction (according to IS:11384

1985)
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•
Reinforced concrete slabs, with profiled sheeting
supported on steel beams
•
IS: 11384
–
1985,
gives no reference to profiled deck slab
and partial shear connection
Resistance to sagging bending moment in plastic or compact
sections for full interaction.
0.85(f
ck
)
cy
/
c
0.85(f
ck
)
cy
/
c
0.85(f
ck
)
cy /
c
D
T
t
B
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Resistance to hogging Bending Moment
h
c
+ h
p
D
(a)
f
y
/
a
f
y
/
a
f
sk
/
s
f
y
/
a
F
s
F
a1
F
a2
f
y
/
a
(b)
f
sk
/
s
F
s
F
a1
F
a2
a
(c)
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Positive moment capacity of section with full shear
connection(According to EC4)
Position of Plastic Neutral Axis
Condition
Moment Capacity
M
p
Plastic neutral axis in concrete slab
(
Fig.
13b
)
a
y
a
c
eff
c
cy
ck
f
A
h
b
f
85
.
0
)
2
/
(
x
h
h
f
A
M
t
g
a
y
a
p
Plastic neutral axis in steel flange
(
Fig.
13c)
2
/
)
(
)
2
/
(
.
t
c
ac
c
t
g
pl
a
p
h
h
x
N
h
h
h
N
M
P
lastic neutral axis in web
(
Fig.
13d)
a
y
a
a
y
c
cy
ck
c
eff
γ
f
A
/
γ
B*T*f
γ
f
0.85
h
b
2
/
)
(
)
2
/
2
/
(
)
2
/
(
.
.
c
t
w
a
c
t
acf
c
t
g
pl
a
p
h
T
h
x
N
h
T
h
N
h
h
h
N
M
Negative moment capacity of section with full shear connection (according EC4)
Position of Plastic Neutral Axis
Condition
Moment Capacity
M
p
Plastic neutral axis in steel flange
(
Fig.
14b
)
Plastic neutral axis in web
(
Fig.
14c)
a
y
a
c
cy
ck
c
eff
f
A
f
h
b
85
.
0
a
y
aw
s
sk
s
f
A
f
A
a
y
a
s
sk
s
a
y
aw
f
A
f
A
f
A
a
f
A
D
f
A
M
s
sk
s
a
y
a
p
2
a
y
s
sk
s
s
sk
s
ap
p
f
t
f
A
a
D
f
A
M
M
/
*
*
4
2
2
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•
Vertical Shear
The
shear
force
resisted
by
the
structural
steel
section
should
satisfy
:
V
V
p
where
,
V
p
is
the
plastic
shear
resistance
given
by,
•
The
shear
buckling
of
steel
web
can
be
neglected
if
following
condition
is
satisfied
)
(
)
(
sections
I
up
built
for
sections
C
H,
I,
rolled
for
3
f
t
d
f
t
D
0.6
V
a
y
a
y
p
γ
concrete
in
encased
web
for
concrete
in
encased
not
web
for
120
t
d
67
t
d
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•
Effect of shape of deck slab on shear connection
Behaviour of a shear connection fixed
through profile sheeting
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•
Longitudinal Shear Force
•
Full Shear Connection
•
Single span beams
V
= F
cf
=A
a
f
y
/
a
or
V
= 0.85 (f
ck
)
cy
b
eff
h
c
/
c
whichever is smaller.
•
Continuous span beams
V
= F
cf
+ A
s
f
sk
/
s
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Full Shear Connection

I
•
The number of required shear connectors in the zone under
consideration for full composite action is given by:
n
f
= V
/P
•
The shear connectors are usually equally spaced
•
Minimum degree of shear connection
•
Ideal plastic behaviour of the shear connectors may be assumed
if a minimum degree of shear connection is provided.
•
The minimum degree of shear connection is defined by the
following equations:
b
t
f
A
A
where
0.03
0.4
n
n
3
/
b
t
f
A
A
where
0.03
0.25
n
n
/
b
t
f
A
A
where
0.0
n
n
4
/
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•
Interaction between shear and moment
V
M
M
p
V
p
A
o
B
0.5V
p
M
f
Resistance to combined bending and vertical shear
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•
Transverse reinforcement
Surfaces of potential
shear failure
Truss model analysis
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EFFECT OF CONTINUITY
•
Moment
and
Shear
Coefficients
for
continuous
beam
Bending moment coefficients according to
IS: 4561978
TYPE OF LOAD
SPAN MOMENTS
SUPPORT MOMENTS
Near
middle
span
At middle of
interior span
At support next
to the end
support
At other
interior
supports
Dead load + Imposed
load (fixed)
+ 1/12
+1/24
 1/10
 1/12
Imposed load (not
fixed)
+1/10
+1/12
 1/9
 1/9
For obtaining the bending moment, the coefficient shall be multiplied by the total design
load and effective span.
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EFFECT OF CONTINUITY

I
Shear force coefficients
At support next to the end
support
TYPE OF
LOAD
At end
support
Outer side
Inner side
At all other
interior
supports
Dead load +
Imposed
load(fixed)
0.40
0.60
0.55
0.50
Imposed
load(not fixed)
0.45
0.60
0.60
0.60
For obtaining the shear force, the coefficient shall be multiplied by the total design
load
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•
Lateral Torsional Buckling of Continuous Beams
Inverted
–
U frame Action
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SERVICEABILITY
•
Deflection
–
Influence
of
partial
shear
connection
–
Shrinkage induced deflections
–
Crack Control
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CONCLUSIONS
•
Provision
for
service
opening
in
composite
beams
was
discussed
.
•
Basic
design
considerations
of
composite
beams,
connected
to
solid
slab,
as
well
as
profiled
deck
slab
was
discussed
.
•
Effect
of
continuity
on
composite
beam
was
discussed
.
•
Serviceability
Limit
state
for
composite
beam
was
discussed
.
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