composite beam i

Chiew SingChiew Sing--PingPing

School of Civil and Environmental EngineeringNanyang Technological University, Singapore

Design of Composite Beams Simply-supported beams

Sagging moments:Basic behaviour, concepts and codified design

2

Composite construction

4

Composite construction

Greater stiffness and higher load carrying capacities.

Fast erection of structural members.

Reduce height of a structure and offer further savings in associated features through integration with building services.

Good inherent fire resistance in slabs and columns.

Steel deckings as permanent formwork provide additional safety features during construction.

5

Prescriptive Codified Design Approach

Typical use and practical cross-section configurations

Modern design standards

Composite action in beams

Full and partial shear connection

Basic resistances

Design of a composite beam

Practical design procedures

Effective width / sagging moment resistance / shear resistance /moment resistance under high shear / transverse reinforcement / deflection / serviceability stress

Comparison between different design approaches

Scope

6

Composite beams with profiled steel deckings

7Composite beam with composite slab using profiled steel deckings

Composite beam with solid concrete slab

Beam span parallel to slab spanB

D

Transverse reinforcement

Ds

Profiled deckling

Beam span perpendicular to slab span

DpDsDp

D

B

Be

Profiled deckling



Be

B

D

8

The 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 mobilization in both the concrete slab and the steel section is limited by the shear resistance along the concrete interface.

Composite beams

Rc

Rq

Rs

9

Modern design codes

British Standards Institution.BS5950: Structural use of steelwork in building. Part 3 Section 3.1: Code of practice for design of composite beams.

British Standards Institution.BS EN1994-1-1 Eurocode 4: Design of Composite Steel and Concrete Structures.Part 1.1: General Rules and Rules for Buildings.

Standards Australia.Composite Structures. Part 1: Simply Supported Beams. Australian Standard AS2327.1 – 1996.

10

Buildings Department, Government of Hong Kong SARCode of Practice for the Structural Use of Steel 2005Chapter 10: Composite construction.

Composite slabsComposite beamsComposite columnsShear connection

Harmonized designBS 5400: Part 5, BS 5950: Parts 1 to 8, and EC3 & 4: Parts 1.1 & 1.2.

Modern design codes

11

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.

Moment capacities / lateral buckling / shear capacity / deflection

At the composite stage, the steel section and the concrete slab together will resist the loads resulting from the usage of the structure, i.e. Composite Beam Design.

Sagging & hogging moment capacities / degree of shear connection / shear resistance / transverse reinforcement / deflection / serviceability stress

Practical design of a composite beam

12

Composite action in beams ε σ

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 composite action at the interface.

13

Free slippage at the concrete-steel interface.

Strain

Concrete slab and 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 of the combined section.

Composite action in beams

14

Prescriptive design approach

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 of shear connection.

Current design methodology

15

Forces:

Rc = Compressive resistance in the concrete slab

Rs = Tensile resistance in the steel section

Rq = Shear resistance in the shear connectors

Basic resistances against sagging moment

Rc

Rq

Rs

16

Prescriptive design approach- Plastic section analysis

Various degree of shear connection

Assume a rigid plastic load-slippage curve of shear connectors.

(b) yp in steel flange

P.N.A

(c) yp in steel web

P.N.A

(a) yp in slab

Rs

P.N.A

0.45 fcu

py

Rc

17

Development of moment resistance along beam span

Rigid shear connectors

Compressive force

Tensile force

Sufficient shear connectors provided for full strength mobilization

Various degree of shear connection(c) yp in steel web

P.N.A

(a) yp in slab

P.N.A

(b) yp in steel flange

P.N.A

18

Full shear connection- Large concrete slab with small steel section

Full resistance mobilized in the steel section

Rc

Rs

Rq ≥ RS

Force equilibrium

Rc’ ≦ Rc

= Rs

Rs

Z

P.N.A

19

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

Force equilibrium (Rc + Rft + Rwt = Rwb + Rfb)

Rc

Rwb

Rft

Rfb

RwtP.N.A

20

Partial shear connection

When insufficient shear connectors are provided, the full resistance of neither the steel section nor the concrete slab is mobilized, i.e.

Partial shear connection is achieved when

Rq < Smaller of Rs and Rc

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Example: Design of a composite beam

Grade 30 concrete with UB457x152 x 52 kg/m Grade S355

DimensionsL = 12 mB = 2.8 mDcs= 125 mm solid slab

Design data:

Shear connectors19 mm diameter headed shear studs95 mm as welded heightQk = 76.3kN (Characteristic value from design code)

B

Dcs Solid slab

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Example: Design of a composite beamComposite stage designConsider the composite section at mid-span

As Rs ≦ Rc, the full tensile resistance of the steel section will be mobilized while only part of the concrete slab will be mobilized in compression.

Resistance of the steel sectionRs = A x py = 66.6 x 102 x 355 x 10-3 = 2364 kN

Resistance of the concrete slabRc = 0.45 x Be x fcu x Dcs = 0.45 x 2800 x 30 x 125 x 10-3 = 4725 kN

Resistance of a shear connector (headed shear stud)Qp = 0.8 x 76.3 = 61.0 kN (The coefficient 0.8 is adopted for shear connectors in sagging moment region.)

Effective width of the concrete slabBe = 12000 / 4

= 3000 mm > B=2800 mm∴Be=2800 mm

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The depth of the compression zone, dc, in the concrete slab is

dc = Rs / (0.45 x fcu x Be)= 2364 x 103 / (0.45 x 30 x 2800)= 62.5 mm

Sagging moment resistance

Force equilibrium

or dc = Ds x c

s

R

R

As the depth of the compression zone in the concrete slab is smaller than the slab thickness of the concrete slab, the plastic neutral axis of the composite beam is located within the concrete slab.

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The lever arm, z between the tensile resistance, Rs and the compressive resistance, Rc’ is given by:


mmcd

sD

Dz 7318

2

562125

2

8449

22.=)

.(+

.=)(+= --

=> M = Rs x z = 2364 x 318.7 x 10-3 = 753.4 kNm

Assume full shear connection.

Moment equilibrium

449.8

125

Rc’

Rs

dc = 62.5

Z

P.N.A

25

In order to fully mobilize the tensile resistance of the steel section,

Rq ≧ Rs = 2364 kN for full shear connection

n x Qp ≧ 2364 => n = 38.8 or 39 (min.)

Use 40 no. shear connectors at a spacing of 150mm over half span, i.e. 6000 mm, i.e. a total of 80 headed shear studs along the beam length.

Provision of shear connectors

Rc’ = Rs= 2364kN

Rs = 2364kN

Rq RS≧Z = 318.7

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Steel beam: Ms = 389.0 kNm

Composite beam: Mcs = 754.3 kNm

=> Mcs : Mc = 754.3 : 389.0 = 1.94 : 1

An increase of 94% in the moment resistance in the beam is achieved with proper provision of shear connectors.

Moment resistances

Similar increase in the flexural rigidity, (EI)cp of the beam is found. However, in some cases, design of composite beam for partial shear connection is more economical, depending on the applied moment.

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Prescriptive design approach- Simplified load slippage curve

Sh

ear

forc

e, F

s

Slippage, S

0.5QK

0.5 mm 5 mm 7 mm

Typical

Fs

s

QK

Not more than 20% decrease

R-72

Assume a rigid plastic load-slippage curve of shear connectors.

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Section classification of composite cross-sectionMoment resistance with full shear connectionShear resistanceShear connectionMoment resistance with partial shear connectionTransverse reinforcement

Design procedures

For structural adequacy, the following checks should be satisfied:

Ultimate Limit State

Serviceability Limit StateDeflection

Serviceability stresses

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For those composite beam with Rq ≥ the lesser of Rc and Rs

Sagging moment resistanceFull shear connection

Partial shear connection

For those composite beams with Rq < both Rc and Rs

Applicable only to symmetric I or H section with equal flanges

– [Case 1a] Plastic neutral axis in steel web

– [Case 2a] Plastic neutral axis in steel flange

– [Case 2b] Plastic neutral axis in concrete flange

– [Case 3a] Plastic neutral axis in steel web

– [Case 4] Plastic neutral axis in steel flange

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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 Beam:

Resistance of Shear Connection:

Resistance of Steel Flange:

Resistance of Overall Web Depth:

Plastic moment resistance of steel beam:

Plastic moment resistance of composite beam:

Rc = 0.45 fcu Be (Ds – Dp)

Rs = A py

Rq = Na Q

Rf = B T py

Rw = Rs – 2 Rf

Ms = py Sx or 1.2py Zx

Mc


Dp

Ds

Be

B

td

T

T

D

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Full Shear Connection : Rc < Rw

[Case 1a] Plastic neutral axis in steel web


Full Shear Connection : Rc ≥ Rw

( )42

)(

2

2 T

R

RRDDR

DRM

f

cspscsc

−−

++=

( )⎭⎬⎫

⎩⎨⎧ −

−+=22

ps

c

sssc

DD

R

RD

DRM

[Case 2b] Plastic neutral axis in concrete slab (Rs ≤ Rc)

[Case 2a] Plastic neutral axis in steel flange (Rs > Rc)

Typicaldesign

( )42

2 d

R

RDDDRMM

v

cpscsc −

+++=

P.N.A

P.N.A

3232

Section classification in composite cross-sections

In general, the moment capacities of composite cross-sections are limited by local buckling in the steel web or in the steel compression flange.

For composite cross-sections of either class 1 plastic or class 2 compact, the moment capacities of composite beams are determined with rigid plastic theory, i.e. rectangular stress blocks.

The section classification of a composite cross-section is oftensimilar to that of the steel beam.

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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 bending stress in concrete slab

Idealized stress

Actual stress

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Beam span is perpendicular to slab spanbe = Lz /8 but not greater than b

Beam span is parallel to slab spanbe = Lz /8 but not greater than 0.8b

Beam at edgebe = Lz /8 + projection of slab beyond

centreline of beam

Effective width of the concrete slab

Effective width, Be ,is calculated as follows:

Be = Σ bei

Lz = distance between points of zero moments

b = actual width

be1 be2

b

35

Effective breadth of the concrete slab in continuous beams

0.8L1 0.7L2 0.8L3 - 0.3L4

but ≥ 0.7L3

L2L1 L3 L4

0.25(L1 + L2) 0.25(L1+ L2) 1.5L4

but ≤ L4 + 0.5L3

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It is assumed that the vertical shear due to factored loading isresisted by the steel section only.

The calculation of the shear resistance (Pv) should be with reference to BS5950: Part 1.

Shear resistance

Pv = 0.6py x Av where Av = shear area of the steel section

= D x t for rolled sections

= d x t for fabricated sections

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Where the shear force Fv exceeds 0.5Pv, the moment capacity should be reduced to allow for the influence of shear. The reduced moment capacity Mcv should be determined from the following equation:

( )2

12

⎟⎟⎠

⎞⎜⎜⎝

⎛−−−=

v

vfcccv P

FMMMM

Mc = Plastic moment capacity of composite beam

Mf = Plastic moment capacity of the remaining composite section after deducting the shear area (Av) of the steel section 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 under high shear

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Moment resistance under high shear

Sh

ear,

Fv

Moment, M

Mf0

0.5 Pv

Pv

Mc

Moment - shear interaction curve for a composite beam

The interaction between moment and shear is considered not to be significant.

Linear interaction

Non-linear interaction

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Partial shear connection : Rq < Rw

[Case 3a] Plastic neutral axis in steel web

( )422

2d

R

RDD

R

RD

DRMM

v

qps

c

qsqsc −

⎭⎬⎫

⎩⎨⎧ −

−++=


Partial shear connection : Rq ≥ Rw

[Case 4] Plastic neutral axis in steel flange

( ) ( )422

2T

R

RRDD

R

RDR

DRM

f

qsps

c

qsqsc

−−

⎭⎬⎫

⎩⎨⎧ −

−+=

Rq = NaQp

P.N.A

P.N.A

40

Global transfer of force in slab

Transverse distribution of forces along the A-A

Support

Transverse tension

Transverse compression

Uniform compression in slab

Beam

AA

12345

3 4

Line of principle compression

Very large shear forces acting at the shear connectors

41

Transverse reinforcement refers to the reinforcement in the concrete slab running transversely to the span of the beam.

Sufficient transverse reinforcement should be used to enable theconcrete slab to resist the longitudinal shear transmitted by the shear connectors, both immediately adjacent to the shear connectors and elsewhere within its effective breadth, Be.

When profiled steel sheets are used, they may also act as transverse reinforcement.


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The total longitudinal shear force per unit length (v) to be resisted at any point in the span of the beam should be determined from the spacing of the shear connectors by the following equation:

v = N Q / s

v ≤ vr

Longitudinal shear force

For structural adequacy, the longitudinal shear force, v, shouldnot be larger than the local shear resistance in the concrete slab, vr :

N = Number of shear connectors in a group

s = Longitudinal spacing of shear connectors

Q = Smaller of Qp and Qn

Qp = Resistance of shear connectors in sagging moment (positive)

Qn = Resistance of shear connectors in hogging moment (negative)

43


Section A-A

S


Q

Q

A A


v = N Q / s

44

The local shear resistance of the concrete slab is given by

fcu = characteristic cube strength of concrete in N/mm2 but ≤ 40 N/mm2

η = 1.0 for normal weight concrete and 0.8 for lightweight concrete

Acv = mean cross-sectional area, per unit length of the beam, of theconcrete shear surface under consideration = (Ds + Dp )/2

Asv = mean cross-sectional area, per unit length of the beam, of

both the top and bottom reinforcement crossing the shear surface

vp = contribution of the profiled steel sheeting, if any.

vr = 0.7 Asv fy + 0.03 η Acv fcu + vp

but vr ≤ 0.8 η Acv √ fcu + vp

Local shear resistance

45

d) Composite slab. Profiled decking spanning perpendicular to the beam

e) Composite slab. Profiled decking spanning parallel to the beam

Transverse area crossing the shear surfaces, Asv

Shear surface Asv1-1 (Ab+At)2-2 2Ab

3-3 At

a) Solid slabsAt

Ab2

1

1 2

3 Lap joint in profiled decking

3

At3

3

At3

3

Profiled decking

46

Profiled decking may be assumed to contribute to the transverse reinforcement provided that it is either continuous across the top flange of the steel beam or that it is welded to the steel beam by stud shear connectors.

d = nominal shank diameter of the stud

n = 4

pyp = design yield strength of profiled decking

tp = thickness of profiled decking

vp = tp pyp

a) Continuous profiled decking with ribs perpendicular to the beam span

vp = (N/s)(n d tp pyp) but vp ≤ tp pyp

b) Discontinuous profiled decking with studs welded to the steel beam

Contribution of profiled decking

47

Deflection needs to be checked under the serviceability limit state in both the construction and the composite stages. The deflections for both stages (δcon & δ ) are then added up to determine if any precamber is necessary.

Construction stage (δcon)

Dead loads (Steel beam and slab weight)

Deflection calculations based on steel beam

Composite stage (δ )Imposed loads only

Deflection calculations based on composite beam

Depends on the degree of shear connection

Deflection

48

An effective modular ratio, αe, is used to express the elastic section properties of the composite section in terms of an equivalent steel section. It is determined from the proportions of the both short and long term loadings.

αe = αs + ρl (αl – αs)

ρl = (Dead load + 1/3 Imposed load) / Total load

Short termαs

Long termαl

Normal weight concrete 6 18

Lightweight concrete 10 25

Deflection for composite stage

49

Deflection calculation is based on the gross uncracked composite section. Reference for the calculation of the second moment of area, Ig, can be made to Appendix B.3.1 for steel beam with equal flanges and any concrete within the depth of the ribs of the profiled decking is neglected.

( ) ( )( )( ){ }psee

pspse

e

psexg DDBA

DDDDDABDDBII

−+

++−+

−+=

αα 412

23


50

The increased deflection under serviceability loads arising frompartial shear connection should be determined from the following equations:

δs = Deflection of steel beam under dead loads = δcon

δc = Deflection under imposed loads of composite beam with full shear connection

δ = δc + 0.5(1 – Na / Np)(δs – δc)

Propped construction

Unpropped construction

δ = δc + 0.3(1 – Na / Np)(δs – δc)


51

Serviceability stresses need to be checked for the construction and composite stage. It is to be checked under the serviceability limit state with the allowable stresses.

Construction stage

Dead loads (Md)

Elastic properties based on the steel section

Composite stage

Imposed loads (Mi)

Elastic properties based on the composite section

Either cracked or uncracked sections should be considered, depending on the position of the neutral axis.

Serviceability stress

52

Construction stage

Dead loads – Self weights of steel section, concrete slab and profiled deckingElastic properties based on steel sectionCalculate bending stresses in the steel section only

x

d

Z

MstressBending =

Zx = Elastic section modulus of steel section


53

Composite stage

( )( ) ep

eps

DD

BDDA

α2

2

+

−≥

Need to check whether the concrete slab is cracked (Case 1) or uncracked (Case 2) – Appendix B.4.1

Case 1: Elastic neutral axis in the concrete slab

( )( ) ep

eps

DD

BDDA

α2

2

+

−<

Case 2: Elastic neutral axis in the steel section


A = cross-sectional area of steel section

54

Composite stage

Case 1: Elastic neutral axis in concrete slab

23

23⎟⎠⎞

⎜⎝⎛ −+++= es

e

eexp yD

DA

yBII

α

The concrete on the tension side of the elastic neutral axis is taken as cracked and the properties of the cracked section is used.

( )

( )5.0

211

2

⎭⎬⎫

⎩⎨⎧

+++

+=

se

e

se

DDAB

DDy

α

Concrete slab: Zp = Ipαe / ye

Bottom flange of steel section: Zs = Ip / (D + Ds – ye)


55

Elastic analysis of a composite beamBe / αe

Transformed section

Ds

D

Dp

Propped construction

Stress ≤ 0.5fcu

Composite stage

E.N.A

Unpropped construction

Ds

D

Stress ≤ 0.5fcu

Composite stage

E.N.ADp

Construction stage

56

Composite stage

Case 2: Elastic neutral axis in steel section

The concrete is uncracked and the gross section properties apply.

( ) ( )( ){ }psee

pseseg DDBA

DDBDDAy

−+

−++=

αα

2

2 2

Concrete slab: Zg = Igαe / yg

Bottom flange of steel section: Zs = Ig / (D + Ds – yg)


57

Bending stress at extreme fibre of member

Applied stressAllowable stress

Cl 2.4.3

Concrete slab (Compression)

Mi / Zp (Case 1)

Mi / Zg (Case 2)0.5 fcu

Steel section (Tension)

Md / Zx + Mi / Zs py

Assume composite beam is simply supported.


58

Comparison between different approaches

Prescriptive design approach in design codesSimplified design assuming rigid and ductile shear

connectors in strength calculation.Empirical formulae to allow for partial shear connection in

deflection calculation.

Performance-based design approachAllow non-linear deformation characteristic of shear connectors.Allow non-uniform distribution of forces and deformations

of shear connectors along beam length.Allow various failure criteria.Accurate prediction in deflection, allowing for actual deformationsof shear connectors.

Important in continuous composite beams with both hogging and sagging moment regions.

59

Conclusions (1)

1. Composite beam design is well established to achieve effective use of materials, i.e. the concrete slab in compression and the steel section largely in tension.

2. Composite action is achieved with proper provision of shear connectors.

3. Design rules for composite beams under sagging moment are provided.

4. Dimensional detailing on the installation of shear connectors should be carefully considered.

5. Transverse reinforcement should be provided to avoid longitudinal splitting in the concrete slab.

60

Conclusions (2)

6. Deflection calculation is very similar to that of reinforced concrete beam.

7. Serviceability stresses in both steel sections and concrete flanges may be readily evaluated.

composite beam i

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