nus composite beam i

8/12/2019 NUS Composite Beam I

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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


2/20

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


3/20

Composite beams with profiled

steel deckings

Composite beams with profiledsteel deckings

Steel sections are fire-protected.


4/20

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


5/20

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.


7/20

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


9/20

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


P.N.A


10/20

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


11/20

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.


12/20

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


13/20

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


14/20

Partial and Full Composite

STUDS

Welding of Studs


15/20

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


16/20

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


P.N.

ARs

0.45 fcu

p

y

P.N.A

(a) yp in slab

Rc


17/20

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


18/20

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

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