©Teaching Resource in Design of Steel Structures
–
IIT Madras, SERC Madras, Anna Univ., INSDAG
1
COMPOSITE BEAMS

I
©Teaching Resource in Design of Steel Structures
–
IIT Madras, SERC Madras, Anna Univ., INSDAG
2
CONTENTS
•
INTODUCTION
•
ELASTIC BEHAVIOUR OF COMPOSITE BEAMS
•
SHEAR CONNECTORS
•
ULTIMATE LOAD BEHAVIOUR OF COMPOSITE
BEAM
•
SERVICEABILITY LIMIT STATES
•
CONCLUSION
©Teaching Resource in Design of Steel Structures
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IIT Madras, SERC Madras, Anna Univ., INSDAG
3
INTRODUCTION
ADVANTAGES
effective
utilisation
of
steel
and
concrete
.
more
economical
steel
section
(in
terms
of
depth
and
weight)
is
adequate
in
composite
construction
when
compared
with
conventional
non

composite
construction
.
enhanced
headroom
due
to
reduction
in
construction
depth
less
deflection
than
steel
beams
.
efficient
arrangement
to
cover
large
column
free
space
.
amenable
to
“fast

track”
construction
.
encased
steel
beam
sections
have
improved
fire
resistance
and
corrosion
.
©Teaching Resource in Design of Steel Structures
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IIT Madras, SERC Madras, Anna Univ., INSDAG
4
ELASTIC BEHAVIOUR OF COMPOSITE BEAMS
•
No interaction case
Effect of shear connection on
bending and shear stresses
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IIT Madras, SERC Madras, Anna Univ., INSDAG
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ELASTIC BEHAVIOUR OF COMPOSITE BEAMS

1
•
Maximum bending stress
•
Maximum shear stress
•
maximum deflection
2
2
max
8
3
bh
w
I
My
f
bh
w
bh
w
q
8
3
1
4
2
3
max
3
4
4
64
5
384
)
2
/
(
5
Ebh
w
EI
w
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IIT Madras, SERC Madras, Anna Univ., INSDAG
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ELASTIC BEHAVIOUR OF COMPOSITE BEAMS

2
•
Tensile
strain at the bottom fibre of the upper beam and the
compression stress at the top fibre of the lower beam is
2
2
2
max
8
)
4
(
3
Ebh
x
w
EI
My
x
©Teaching Resource in Design of Steel Structures
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IIT Madras, SERC Madras, Anna Univ., INSDAG
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ELASTIC BEHAVIOUR OF COMPOSITE BEAMS

3
/2

/2
Typical Deflections, slip strain and slip.
©Teaching Resource in Design of Steel Structures
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IIT Madras, SERC Madras, Anna Univ., INSDAG
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ELASTIC BEHAVIOUR OF COMPOSITE BEAMS

4
•
Maximum bending stress
•
Maximum shear stress
•
maximum deflection
2
2
max
16
3
bh
w
I
My
f
bh
w
h
b
w
q
8
3
)
2
(
1
2
2
3
max
3
4
256
5
Ebh
w
•
100% interaction case
©Teaching Resource in Design of Steel Structures
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IIT Madras, SERC Madras, Anna Univ., INSDAG
9
Uplift Forces
Shear stress variation over
span length
©Teaching Resource in Design of Steel Structures
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IIT Madras, SERC Madras, Anna Univ., INSDAG
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SHEAR CONNECTORS
•
Types
of
shear
connectors
•
Rigid
type
•
Flexible
type
•
Bond
or
anchorage
type
©Teaching Resource in Design of Steel Structures
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IIT Madras, SERC Madras, Anna Univ., INSDAG
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SHEAR CONNECTORS

1
rigid connectors
©Teaching Resource in Design of Steel Structures
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12
SHEAR CONNECTORS

2
Flexible connectors
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SHEAR CONNECTORS

4
(ii). Helical connector
Typical bond or anchorage
connectors
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Characteristics of shear connectors
SHEAR CONNECTORS

5
Load/Slip characteristics
Typical load

slip curve for 19mm stud
connectors
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SHEAR CONNECTORS

6
k=
Idealised load

slip characteristics
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“
push

out”
tests for
determining load

slip curve
Standard push test
[Eurocode
–
4]
SHEAR CONNECTORS

7
©Teaching Resource in Design of Steel Structures
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IIT Madras, SERC Madras, Anna Univ., INSDAG
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Standard test for shear
connectors
(As per IS: 11384

1985)
SHEAR CONNECTORS

8
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•
Load bearing mechanism of shear connectors
SHEAR CONNECTORS

9
Transfer of force at a shear
connector
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SHEAR CONNECTORS

10
Dowel mechanism of shear studs
dowel
Bearing stress on the shank of a stud connector
©Teaching Resource in Design of Steel Structures
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•
Strength
of
connectors
•
dowel
strength
(D
)
is
a
function
of
the
following
parameters
:

D
=
f
[A
d
,
f
u
,(
f
ck
)
cy
,
E
c
/E
s
]
•
design
resistance
of
shear
studs
with
h/d
4
.
SHEAR CONNECTORS

11
v
2
u
Rd
4
d
f
8
0
P
)
/
(
.
v
2
1
cm
cy
ck
2
Rd
E
f
d
29
0
P
/
)
)
((
.
©Teaching Resource in Design of Steel Structures
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ULTIMATE LOAD BEHAVIOUR OF COMPOSITE BEAM
The
tensile
strength
of
concrete
is
ignored
.
Plane
sections
of
both
structural
steel
and
reinforced
concrete
remain
plane
after
bending
.
The
effective
area
of
concrete
resists
a
constant
stress
of
0
.
85
(f
ck
)
cy
/
c
(where
(
f
ck
)
cy
)=cylinder
strength
of
concrete
;
and
c
=partial
safety
factor
for
concrete)
over
the
depth
between
plastic
neutral
axis
and
the
most
compressed
fibre
of
concrete
.
The
effective
area
of
steel
member
is
stressed
to
its
design
yield
strength
f
y
/
a
where
f
y
is
the
yield
strength
of
steel
and
a
is
the
material
safety
factor
for
steel
.
©Teaching Resource in Design of Steel Structures
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IIT Madras, SERC Madras, Anna Univ., INSDAG
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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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IIT Madras, SERC Madras, Anna Univ., INSDAG
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•
Full shear connection
•
Neutral axis within the concrete slab
•
Neutral axis within the steel top flange
•
The neutral axis lies within web
)
2
/
(
x
h
h
f
A
M
t
g
a
y
a
p
2
/
)
(
)
2
/
(
.
t
c
ac
c
t
g
pl
a
p
h
h
x
N
h
h
h
N
M
2
/
)
(
)
2
/
2
/
(
)
2
/
(
.
.
c
f
t
w
a
c
f
t
acf
c
t
g
pl
a
p
h
t
h
x
N
h
t
h
N
h
h
h
N
M
©Teaching Resource in Design of Steel Structures
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IIT Madras, SERC Madras, Anna Univ., INSDAG
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•
partial
shear
connections
are
provided
–
to
achieve
economy
.
–
when
there
is
problem
of
accommodating
shear
connectors
uniformly
.
•
the
force
resisted
by
the
connectors
are
taken
as
their
total
capacity
(F
c
<
F
cf
)
between
points
of
zero
and
maximum
moment
.
•
Partial shear connection
©Teaching Resource in Design of Steel Structures
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IIT Madras, SERC Madras, Anna Univ., INSDAG
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–
Degree of shear connection =
–
the neutral axis is within top flange
cf
c
f
p
F
F
n
n
2
2
c
t
a
c
c
t
g
a.pl
Rd
x
h
x
F
)
x
h
(h
N
M
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0.85(f
ck
)
cy
/
c
Resistance to sagging bending of composite
section in class 1 or 2 for partial interaction
If the neutral axis lies in web
2
)
2
(
2
)
(
.
f
t
a
aw
f
t
cf
c
c
t
g
pl
a
Rd
t
h
x
N
t
h
N
x
F
h
h
N
M
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Design methods of partial shear connection
M
Rd
/ M
p
M
ap
/ M
p
F
c
/ F
cf
0.7
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–
Moment
of
resistance
reduces
due
to
partial
shear
connection
.
–
The
curve
ABC
is
not
valid
for
very
low
value
of
shear
connection
.
–
At
F
c
/F
cf
=
0
.
7
,
the
required
bending
resistance
is
slightly
below
M
p
.
–
saving
in
the
cost
of
shear
connectors
can
be
achieved
without
unduly
sacrificing
the
moment
capacity
.
–
for
design
purpose
the
curve
ABC
is
replaced
by
a
straight

line
AC
given
by
cf
ap
p
ap
c
F
M
M
M
M
S
©Teaching Resource in Design of Steel Structures
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SERVICEABILITY LIMIT STATES
–
For
simply
supported
composite
beams
the
most
critical
serviceability
Limit
State
is
usually
deflection
.
–
the
effect
of
vibration,
cracking
of
concrete,
etc
.
should
also
be
checked
under
serviceability
criteria
.
–
in
exposed
condition,
it
is
preferred
to
design
to
obtain
full
slab
in
compression
to
avoid
cracking
in
the
shear
connector
region
.
©Teaching Resource in Design of Steel Structures
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•
Stresses and deflection in service
–
elastic
analysis
is
employed
to
check
the
serviceability
performance
of
composite
beam
.
–
concrete
area
is
converted
into
equivalent
steel
area
by
applying
modular
ratio
m
=
(
E
s
/E
c
)
.
–
analysis
is
done
in
terms
of
equivalent
steel
section
.
–
It
is
assumed
that
full
interaction
exists
between
steel
beam
and
concrete
slab
.
–
effect
of
reinforcement
in
compression,
the
concrete
in
tension
and
the
concrete
between
rib
of
profiled
sheeting
are
ignored
.
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–
For
distributed
load
w
over
a
simply
supported
composite
beam,
the
deflection
at
mid

span
is
–
For
partial
shear
connections
the
increase
in
deflection
occurs
due
to
longitudinal
slip
.
Total
deflection,
–
with
k
=
0
.
5
for
propped
construction
–
and
k
=
0
.
3
for
un

propped
construction
–
a
=
deflection
of
steel
beam
acting
alone
I
E
wL
a
c
384
5
4
1
1
1
c
a
f
c
N
N
k
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–
The
increase
in
deflection
can
be
disregarded
either
n
p
/n
f
>
0
.
5
or
when
force
on
connector
does
not
exceed
0
.
7
P
RK
where
P
RK
is
the
characteristic
resistance
of
the
shear
connector
;
and
when
the
transverse
rib
depth
is
less
than
80
mm
.
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IIT Madras, SERC Madras, Anna Univ., INSDAG
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•
Effects of shrinkage of concrete and of temperature
–
In
case
of
composite
beam
the
slab
is
restrained
from
shrinking
by
steel
beam
.
–
shear
connectors
resist
the
force
arising
out
of
shrinkage,
by
inducing
a
tensile
force
on
concrete
which
reduces
the
apparent
shrinkage
of
composite
beam
than
the
free
shrinkage
.
–
no
account
of
this
force
is
taken
in
design
as
it
acts
in
the
direction
opposite
to
that
caused
by
load
.
–
the
increase
in
deflection
due
to
shrinkage
may
be
significant
.
©Teaching Resource in Design of Steel Structures
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IIT Madras, SERC Madras, Anna Univ., INSDAG
34
–
In
an
approximate
approach
the
increase
in
deflection
in
a
simply
supported
beam
is
taken
as
the
long

term
deflection
due
to
weight
of
the
concrete
slab
acting
on
the
composite
member
.
–
Generally the span/depth ratios specified by codes take
care of the shrinkage deflection.
–
check
on
shrinkage
deflection
should
be
done
in
case
of
thick
slabs
resting
on
small
steel
beams,
electrically
heated
floors
and
concrete
mixes
with
high
“
free
shrinkage”
.
©Teaching Resource in Design of Steel Structures
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IIT Madras, SERC Madras, Anna Univ., INSDAG
35
•
Vibration
–
To
design
a
floor
structure,
only
the
source
of
vibration
near
or
on
the
floor
need
be
considered
.
–
Other
sources
such
as
machines,
lift
or
cranes
should
be
isolated
from
the
building
.
–
In
most
buildings
following
two
cases
are
considered

•
People
walking
across
a
floor
with
a
pace
frequency
between
1
.
4
Hz
and
2
.
5
Hz
.
•
An
impulse
such
as
the
effect
of
the
fall
of
a
heavy
object
.
©Teaching Resource in Design of Steel Structures
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IIT Madras, SERC Madras, Anna Univ., INSDAG
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Curves of constant human response to
vibration, and Fourier component factor
©Teaching Resource in Design of Steel Structures
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IIT Madras, SERC Madras, Anna Univ., INSDAG
37
–
Natural
frequency
of
beam
and
slab
–
Response factor
Cross

section of vibrating floor structure
showing typical fundamental mode
©Teaching Resource in Design of Steel Structures
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IIT Madras, SERC Madras, Anna Univ., INSDAG
38
CONCLUSION
–
the
theory
of
composite
beam
and
the
underlying
philosophy
behind
its
evolution
were
discussed
.
–
The
design
procedures
of
simply
supported
as
well
as
continuous
beams
have
been
elaborately
discussed
.
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