Composite beams design and composite column-1.ppt

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

2
CONTENTS
• INTODUCTION
• ELASTIC BEHAVIOUR OF COMPOSITE BEAMS
• SHEAR CONNECTORS
• ULTIMATE LOAD BEHAVIOUR OF COMPOSITE
BEAM
• SERVICEABILITY LIMIT STATES
• CONCLUSION

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.

4
ELASTIC BEHAVIOUR OF COMPOSITE BEAMS
• No interaction case
Effect of shear connection on
bending and shear stresses
 

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 





6
• 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





 

7
/2
-/2
Typical Deflections, slip strain and slip.

8
• 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

9
Uplift Forces
Shear stress variation over
span length




  

10
SHEAR CONNECTORS
• Types of shear connectors
• Rigid type
• Flexible type
• Bond or anchorage type

11
SHEAR CONNECTORS -1
rigid connectors

12
SHEAR CONNECTORS -2
Flexible connectors

13
SHEAR CONNECTORS - 4
(ii). Helical connector
Typical bond or anchorage
connectors

14
Characteristics of shear connectors
Load/Slip characteristics
Typical load-slip curve for 19mm stud
connectors

15
k=
Idealised load-slip characteristics

16
“push- out” tests for
determining load-slip curve
Standard push test
[Eurocode – 4]

17
Standard test for shear
connectors
(As per IS: 11384-1985)
SHEAR CONNECTORS -8

18
• Load bearing mechanism of shear connectors
Transfer of force at a shear
connector

19
Dowel mechanism of shear studs
dowel
Bearing stress on the shank of a stud connector

20
• Strength of connectors
• dowel strength (D) is a function of the following
parameters: -
D = f [Ad, fu,( fck)cy, Ec/Es]
• design resistance of shear studs with h/d  4.
v
2
u
Rd
4
d
f
8
0
P

 )
/
(
.

v
2
1
cm
cy
ck
2
Rd
E
f
d
29
0
P

/
)
)
((
.


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 (fck)cy /c (where (fck)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 fy/a where fy is the yield strength of
steel and a is the material safety factor for steel.

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(fck)cy / c 0.85(fck)cy / c 0.85(fck)cy / c
D
T
t
B

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











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 (Fc < Fcf)
between points of zero and maximum
moment.
• Partial shear connection

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







26
0.85(fck)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









27
Design methods of partial shear connection
MRd / Mp
Map / Mp
Fc / Fcf
0.7

28
– Moment of resistance reduces due to partial shear
connection.
– The curve ABC is not valid for very low value of
shear connection.
– At Fc/Fcf = 0.7, the required bending resistance is
slightly below Mp.
– 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




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.

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 = (Es/Ec).
– 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.

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





32
– The increase in deflection can be disregarded
 either np /nf > 0.5 or when force on connector
does not exceed 0.7 PRK where PRK is the
characteristic resistance of the shear
connector; and
 when the transverse rib depth is less than 80
mm.

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.

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”.

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.

36
Curves of constant human response to
vibration, and Fourier component factor

37
– Natural frequency of beam and slab
– Response factor
Cross-section of vibrating floor structure
showing typical fundamental mode

38
CONCLUSIONS
– Theory of composite beam and the underlying
philosophy behind its evolution were
discussed.
– Design procedures of simply supported as well
as continuous beams have been elaborately
discussed.

Composite beams design and composite column-1.ppt

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