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©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



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



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






©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

5

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






©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

6

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



IIT Madras, SERC Madras, Anna Univ., INSDAG

7

ELASTIC BEHAVIOUR OF COMPOSITE BEAMS
-
3


/2

-

/2

Typical Deflections, slip strain and slip.


©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

8

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



IIT Madras, SERC Madras, Anna Univ., INSDAG

9

Uplift Forces

Shear stress variation over

span length
















©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

10

SHEAR CONNECTORS


Types

of

shear

connectors



Rigid

type



Flexible

type



Bond

or

anchorage

type




©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

11

SHEAR CONNECTORS
-
1

rigid connectors


©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

12

SHEAR CONNECTORS
-
2


Flexible connectors


©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

13

SHEAR CONNECTORS
-

4

(ii). Helical connector

Typical bond or anchorage
connectors


©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

14

Characteristics of shear connectors

SHEAR CONNECTORS
-

5

Load/Slip characteristics

Typical load
-
slip curve for 19mm stud
connectors


©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

15

SHEAR CONNECTORS
-

6

k=


Idealised load
-
slip characteristics


©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

16



push
-

out”
tests for

determining load
-
slip curve

Standard push test

[Eurocode


4]

SHEAR CONNECTORS
-

7


©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

17

Standard test for shear
connectors

(As per IS: 11384
-
1985)

SHEAR CONNECTORS
-
8


©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

18



Load bearing mechanism of shear connectors



SHEAR CONNECTORS
-

9


Transfer of force at a shear
connector


©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

19

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



IIT Madras, SERC Madras, Anna Univ., INSDAG

20


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



IIT Madras, SERC Madras, Anna Univ., INSDAG

21

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



IIT Madras, SERC Madras, Anna Univ., INSDAG

22



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


©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

23



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



IIT Madras, SERC Madras, Anna Univ., INSDAG

24


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



IIT Madras, SERC Madras, Anna Univ., INSDAG

25


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







©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

26

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









©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

27

Design methods of partial shear connection

M
Rd
/ M
p

M
ap
/ M
p

F
c
/ F
cf

0.7


©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

28


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



IIT Madras, SERC Madras, Anna Univ., INSDAG

29

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



IIT Madras, SERC Madras, Anna Univ., INSDAG

30



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
.



©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

31


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





©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

32


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
.



©Teaching Resource in Design of Steel Structures



IIT Madras, SERC Madras, Anna Univ., INSDAG

33



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



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



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



IIT Madras, SERC Madras, Anna Univ., INSDAG

36

Curves of constant human response to
vibration, and Fourier component factor



©Teaching Resource in Design of Steel Structures



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



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
.