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©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

1

COMPOSITE BEAMS
-
II


©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

2

CONTENTS


INTRODUCTION


PROVISION FOR SERVICE OPENING IN
COMPOSITE BEAMS


BASIC DESIGN CONSIDERATIONS


DESIGN OF COMPOSITE BEAMS


EFFECT OF CONTINUITY


SERVICEABILITY


CONCLUSION


©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

3

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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IIT Madras, SERC Madras, Anna Univ., INSDAG

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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



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




2


D/t




2


D/t




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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32


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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35

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: 456-1978
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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39

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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42

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
.