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Simply Supported Composite Beams
J Y Richard Liew
Associate ProfessorDepartment of Civil EngineeringNational University of SingaporeBLK E1A, 05-13, 1 Engineering Drive 2Singapore 117576
Email:[email protected]
Composite construction
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Buildability
Precast Concrete SlabComposite Slab
Composite beam with composite slab using profiled steel deckings
Composite beam with solid concrete slab
D
B
Beam span perpendicular to slab span
D
B
DpDs
Beam span parallel to slab span
DsDp
D
B
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Composite beams with profiled
steel deckings
Composite beams with profiledsteel deckings
Steel sections are fire-protected.
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Composite beams with profiled steel deckings
Deck
perpendicular to
secondary beam
Deck
parallel to
primary beam
Why Composite?
Minimum floor weight
Self-supporting during
construction
Buildability
Integration of mechanical
and electrical services Fire resistance
Long span and large floor
plate
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Long span composite floor system
Full integration with building services.
The design of a composite beam is a two-stage process:
At the construction stage, the steel section alone will resist the
dead weight of the slab and the construction load, i.e. Steel
Beam Design.
Check: Moment capacities / lateral buckling / shear capacity / deflection
At the composite stage, the steel section and the concrete slab
acting together will resist the loads resulting from the usage ofthe structure, i.e. Composite Beam Design.
Check: Sagging & hogging moment capacities / degree of shear connection/ shear resistance / transverse reinforcement / deflection / serviceabilitystress
Practical design of a composite beam
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At Construction StageCheck steel section alone for
Self Weight + Construction Loads
(Not less than 0.5kN/m2 or 4kN point
load)
Beam flange is effective restrained by
metal decking and design steel beams
for ultimate strength limit states
Check unfactored load deflection toavoid ponding of web concrete.
Composite action in beams
No composite action at the interface.
Composite action developed at specified locations
at the interface.
a
a b
b
a-a
b-b
Fully developed compos ite action at the interface.
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Free slippage at the concrete-steel interface.
Strain
Concrete slaband steel
section each
bends about
its own neutral
axis.
Controlled slippage at the concrete-steel interface.
Strain
Concrete slab
and steel
section bends
about the
neutral axis ofthe combined
section.
Composite action in beams
Concrete slab works best in compression while the steel
section works best in tension, hence, a large moment
resistance is generated as a force couple.
Resistance in the concrete slab and the steel section is
limited by the shear resistance along the concrete
interface.
Composite Beam Action
Rc
Rq
Rs
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Forces:
Rc = Compressive resistance in the concrete slab
Rs = Tensile resistance in the steel section
Rq
= Shear resistance in the shear connectors
Basic resistances
Rc
Rq
Rs
Moment capacities according plastic stress blocks.
Sagging moment capacities with full or partial shear connection.
Hogging moment capacities with full shear connection.
Full shear connection, partial shear connection, minimum degree ofshear connection.
Current design methodology
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Plastic section analysis
P.N.A
(b) yp in steel flange (c) yp in steel web
P.N.A
Rs
0.45 fcu
py
P.N.A
(a) yp in slab
Rc
Compressive
force
Tensile
force
Sufficient shear connectors provided for full strength mobilization
Development of moment resistance alongbeam span
(a) yp in slab
P.N.AP.N.A
(b) yp in steel flange (c) yp in steel web
P.N.A
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Full shear connection
- Large concrete slab with small steel section
Full resistance mobilized in the steel section
Rc
Rs
Rq RS
Full shear connection
- Small concrete slab with large steel section
Full shear connection is achieved when
Rq Smaller of Rs and Rc
Full resistance mobilized in the concrete slab
Rc
Rs
Rq Rc
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Optimum Span/Depth Ratio of
Composite Beam
Simply Supported Beam: L/D = 18 to 22
Continuous Beam: L/D = 25 to 28
L = Span Length
D= Overall depth, including the
concrete or composite slab
Effect of Shear Lag
T-beam:
be = L/4, but not greater
than the actual width.
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Contribution of the concrete slab
Allowance is made for the in-plane shear flexibility (shear lag)
of a concrete slab by using the concept of effective width
Actual width
Effective width
Mean bendingstress in
concrete slab
Idealized stress
Actual stress
Effective WidthL/8 or bo /2
Be Be = smaller of L/4 or bo
bo
smaller of
Secondary beam Primary beam
Edge beam
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Effective Width
Secondary beams (The slab is perpendicular tothe beam span)
Be = L/4 < bo
Primary beams (The slab & the beam span in the
same direction):
Be = L/4, but < 0.8bo
Edge beams:
L/8 + any projection of the slab beyond the centre-line of the beam.
Failure modes for simply-supported
composite beams
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Partial and Full Composite
STUDS
Welding of Studs
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The plastic moment capacity is expressed in terms of the resistance of
the various elements of the beams as follows:
Resistance of Concrete Flange:
Resistance of Steel Flange:
Resistance of Slender Steel:
Resistance of Slender Web:
Resistance of Shear Connection:Resistance of Reinforcement:
Resistance of Steel Beam:
Resistance of Clear Web Depth:
Resistance of Overall Web Depth:
Rc = 0.45 fcuBe (Ds Dp)
Rf= B T py
Rn = Rs Rv + Ro
Ro = 38 t2py
Rq = Na QRr= 0.87 fyAr
Rs = A py
Rv = d t py
Rw = Rs 2 Rf
Appendix B.2.1
Sagging moment resistance
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0.45fc
Ds - Dp
D
Rs
Rc
ys AR =
R f B D Dc cu e s p= 0 45. ( )
DpDs
Parellel DeckingPerpendicular Decking
DpDs
Concrete SlabSteel deck
Be
Concrete SlabSteel deck
Be
Moment Resistance in Positive (Sagging) bending
P.N.A
(b) yp in steel flange (c) yp in steel web
P.N.
ARs
0.45 fcu
p
y
P.N.A
(a) yp in slab
Rc
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Plastic Moment Capacity of a Full Composite Beam
Case 2b: cs RR (PNA in concrete flange)
xD - D
s p
Rs
D
Ds D p
Be
Rs
Tension =
Compression =
Find Neutral axis depth, x
Tension = CompressionA f B xy cu e = 0 45.
xA
f By
cu e=
0 45.
xR
RD Ds
c
s p= ( )
R f B D Dc cu e s p= 0 45. ( )
Taking moment about the top of
the slab, and substituting for x
M R DD
Rx
c s s s= + ( )2 2
M R DD R
RD Dc s s
s
cs p= +
2 2
( )
Case 2a: (PNA lies in steel beam flange)
fsw R2RR =wcs RRR >
yf BTpR =
From equilibrium:2y c sBx R R + = 2y s cBx R R =
xR R
B
R R
R Ts c
y
s c
f
=
=
2 2 /
Moment about top flange of steel beam
M RD
R DD D
R Rx
c s c p
s p
s c= + +
2 2 2( )
M RD
RD D R R
RT
c s c
s p s c
f= +
+
2 2 4
2( )
x
Ds- Dp
D
DsDp
Be
Rc
y(Ds-Dp)/2+Dp
PNA
T
X
Rc
y
y
PNA
2
(R - R )s c
Rs
B
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Case 1a: R Rc w< (PNA lies in steel beam web)
x
Ds- Dp
D
DsDp
Be
PNA
T
Rc
y
y
Rc
y
Rc
2y
y
x
Ms
2y=
Neutral axis from the centroidal axis of the beam, x2y ctx R=
xR
t
R
R d
dR
R
c
y
c
v
c
v
= = =2 2 2 /
resistance of the clear web depthwhere R dtv y= =
Moment about the centroid of the beam
M M RD
DD D
Rx
c s c p
s p
c= + + +
2 2 2
( )
M M RD D D D
RdR
Rc s cp s p
cc
v
= + + +
2
2 212
)
M M RD D D d R
Rc s cs p c
v
= + + +
)
2 4
2
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+= )DD(
R2
R
2
DDRM ps
c
sssc
M RD
RD D R R
RT
c s c
s p s c
f= +
+
2 2 4
2( )
M M R D D D d RRc s c
s p c
v
= + + +
)
2 4
2
R Rc w
R Rs c
Summary
Positive Moment Capacity for Full Composite Action
PNA in concrete flange
PNA in s teel flange
PNA in steel web
Rw = dtpy
Rv = Rs 2RfRc = 0.45fcuBe(Ds-Dp)
Rs = AgpyRf= BTpy
It is assumed that the vertical shear due to
factored loading is resisted by the steel section
only.
The calculation of the shear resistance (Pv) should
be with reference to BS5950: Part 1.
Shear resistance
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Cl 5.3.4 Moment capacity with high shear
Where the shear force Fv exceeds 0.5Pv:
( )2
21v
cv c c f
v
FM M M M
P
=
Mc = Plastic moment capacity of composite beam
Mf= Plastic moment capacity of the remaining section
after deducting the
shear area (Av) defined in BS5950: Part 1
Pv = Lesser of shear capacity and the shear buckling
resistance, both determined from BS5950: Part 1
The above equation is only applicable for a web that is plastic and compact.
Moment resistance with high shear
D
t