PJulA07 1

PERFORMANCE-BASED

DESIGN AND ANALYSIS OF COMPOSITE BEAMS

IN BUILDING STRUCTURES

K F Chung1 and A J Wang

2

1

Department of Civil and Structural Engineering, The Hong Kong Polytechnic University,

Hong Kong SAR, China

2 Hyder Consulting Limited, Hong Kong SAR, China

ABSTRACT

In order to enable effective design and construction of composite beams in building structures,

advanced three dimensional non-linear finite element models are established to assist

designers to examine and understand the deformation characteristics of composite beams

during the entire loading history. These models are provided to facilitate the performance-

based design and analysis of long span composite beams with practical constructional features.

Details of the advanced three dimensional finite element models of a composite beam as well

as a composite joint are presented together with careful calibration against test data.

Moreover, the effects of the deformation characteristics of both shear connectors and tensile

reinforcement are also examined and presented.

The proposed numerical analysis and design models are demonstrated to be effective for

detailed analyses and design of composite beams and joints with practical geometrical

dimensions and arrangements. Designers are strongly encouraged to employ these models in

their practical work to exploit the full advantages offered by composite construction.

KEYWORDS

Composite beams, finite element models, integrated analysis and design.

COMPOSITE BEAMS IN BUILDING STRUCTURES

Composite beams are strong and stiff flexural members with long spanning capacities. The

structural form of a composite beam is essentially a thin wide concrete flange connected with

a steel section where the concrete flange is in compression while the steel section is largely in

tension. Shear connectors, usually headed studs, are welded to the top flange of the steel

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section and embedded in the concrete flange. Depending on the number of shear connectors

provided along the interface between the steel section and the concrete flange which is either

a solid concrete slab or a composite slab, the composite beam may operate in either full shear

connection or partial shear connection, and hence, exhibit a wide range of deformation

characteristics according to the flexibility of the shear connectors.

Prescriptive Design of Composite Beams

In many structural design codes, plastic design principles are adopted in designing composite

beams, and their moment resistances under sagging and hogging moments are determined

according to plastic stress blocks. In general, flexibility of shear connectors is often ignored

in strength assessment while stringent requirements on the slippage ductility of shear

connectors are imposed in order to justify uniform distribution of shear resistances along

shear spans at ultimate limit state.

In continuous composite beams, the amount of moment re-distribution is specified in a

prescriptive manner according to the geometrical dimensions of the composite cross-sections

as well as the provision of tensile reinforcement. Moreover, while both full and partial shear

connection may be adopted in composite beams under sagging moments, full shear

connection is usually required in composite beams under hogging moments. In general, this

is readily achieved through the provision of few shear connectors in transferring the tensile

resistances of steel reinforcement over the hogging moment regions.

At present, design methods for composite beams using plastic stress blocks with full or partial

shear connection are given in various design codes such as BS5950 (1), AS2327 (2),

Eurocode 4 (3), and the Hong Kong Steel Code, CoPSteel (4). Design handbooks for

composite beams with either solid concrete slabs or composite slabs with profiled steel

decking may also be found in the literature (5-9).

Practical Issues in Composite Beam Design

In general, it is often necessary for designers to refer to specialist design guides in designing

composite beams and floor systems with practical constructional features:

composite beams with asymmetric rolled or fabricated I sections,

composite beams with fabricated I sections with tapered webs,

composite beams with web openings for full integration with building services,

composite beams with partial continuity offered by the connections with columns, and

long span composite beams against floor vibration in service.

Although there are many design methods available in the literature, their use in practice are

fairly limited. Many methods require extensive design efforts together with a deep learning

curve to achieve high structural efficiency. Some of them are product specific, and hence,

their applicability is rather limited. Moreover, little information on associated failure criteria

is provided.

In general, it is highly desirable to develop performance-based analysis and design tools for

practical design of composite beams. This allows designers to understand the structural

behaviour of the composite beams as well as to monitor their stress and strain condition during the entire loading history. Moreover, different failure criteria in designing composite

PJulA07 3

beams and joints with specific mechanical properties, geometrical dimensions, and member

configurations as well as constructional features may be adopted as required in various

projects.

OBJECTIVES AND SCOPE OF WORK

In this paper, a research and development project is reported which aims to develop advanced

numerical analysis and design models for practical design of long span composite beams in

building structures. Details of advanced finite element models of composite beams and joints

are presented and established to assist designers to examine and understand the deformation

characteristics of composite beams and joints during the entire loading history. Moreover,

the effects of the deformation characteristics of both shear connectors and tensile

reinforcement are also examined and presented. The project aims to develop these models to

facilitate the performance-based design and analysis of long span composite beams with

practical constructional features.

FINITE ELEMENT MODELLING

In order to simulate numerically the structural behaviour of composite beams and joints with

practical member configurations and loading conditions, three dimensional finite element

models are established using the general purpose finite element package ABAQUS (Version

6.4, 2004) (10). In general, the steel sections are modelled with shell element S8, and the

concrete flange and the profiled steel decking are modelled with solid element C3D8.

Material Models

It is important to have a suitable material model for each material in the composite beams and

joints. For steel under uni-axial loading condition, a bi-linear stress-strain curve, as shown in

Figure 1a), is adopted as the material model. Moreover, failure of the steel is assumed to

follow the von Mises failure criteria which failure surface is also shown in Figure 1a).

For concrete under uni-axial loading condition, a non-linear stress-strain curve as shown in

Figure 1b) is adopted in the material model. The compressive strength of concrete is taken to

be equal to its cylinder strength while its tensile strength is taken as only 10 % of its

compressive value. The limiting compressive strain of concrete against crushing is taken to

be 0.35 %. As shown in Figure 1b), failure of the concrete is assumed to follow the Drucker-

Prager failure criteria (10,11) when subjected to tri-axial loading.

In order to simulate controlled concrete cracking in the presence of longitudinal

reinforcement and profiled steel decking, the concept of smeared layers is introduced in which smeared reinforced concrete layers and smeared composite decking layers are adopted.

The mechanical properties of the smeared layers, namely, the equivalent compressive

strength, the equivalent tensile strength and the equivalent Youngs modulus, are evaluated (10,11) according to the respective areas and the respective material curves of concrete, steel

reinforcement and profiled steel decking as shown in Figure 2. It should be noted that the

adoption of smeared layers and the corresponding modified material curves is very effective

in suppressing numerical divergence during solution iterations in the finite element analyses.

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For simplicity, transverse reinforcement and profiled steel decking in the transverse direction

are ignored in the material models.

Material and Geometrical Non-linearities

With both material and geometrical non-linearities incorporated into the finite element

models, large deformation in any severely yielded regions of the steel sections can be

modelled accurately. In addition, the first eigen-mode of the finite element model is adopted

as the initial geometrical imperfection, and the magnitude of the maximum initial

imperfection is taken as 25% of the web thicknesses of the steel beams. The presence of the

Figure 1: Material models

b) Concrete

1

cuf5.5E

0.3 pc

c

c

c p)'/(1

)'/(

pc

cu4'

c f104.2

'

c

0.0035

55.14.32

p3

c

pc = 0.8 fcu

0.025

Uni-axial loading

0.001

Tri-axial loading

2

3

1

Esh = 0.005Eo

a) Steel

2

3

1

Tri-axial loading

1

Eo

1 py

-py

Uni-axial loading

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Equivalent compressive strength of the smeared layer:

cs

cicsisic,eq

AA

A)(A)()(

Equivalent Youngs modulus of the smeared layer:

cs

cicsisieq

AA

A)(EA)(E)(E

Equivalent tensile strength of the smeared layer:

cs

citsisit,eq

AA

A)(A)()(

s(i) is the strength of steel reinforcement or profiled steel decking at

a strain of i; c(i) and t(i) are the compressive and the tensile strengths of concrete at a

strain of i; As is the area of steel reinforcement or profiled steel

decking in the smeared layer;

Ac is the area of concrete in the smeared layer;

Es(i) is the Youngs modulus of steel reinforcement or profiled

steel decking at a strain of i; and

Ec(i) is the Youngs modulus of concrete at a strain of i .

Figure 2: Smeared layers of reinforced concrete and composite decking

Layers of concrete Smeared reinforced concrete layer

for concrete and reinforcement

Layers of steel

ii. Cross-section at troughs

Layers of concrete

Layers of steel

Smeared reinforced concrete layer

for concrete and reinforcement

i. Cross-section between troughs

a) Composite beams under sagging moments

Layers of steel

Smeared composite decking layer for

concrete and profiled steel decking

Smeared reinforced concrete layer for

concrete and reinforcement

Layers of concrete

C

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initial geometrical imperfection in the finite element model will facilitate solution iterations

during non-linear analyses.

Furthermore, it should be noted that in order to avoid local inclusion between the finite

elements of the concrete flanges and the steel sections during non-linear analyses, axial

spring elements with extremely high compressive stiffness but zero tensile stiffness are

provided along the interfaces between the concrete flanges and the steel sections.

Shear Connectors

Every shear connector is modelled with one horizontal spring, one transverse spring and one

vertical spring in order to simulate both the longitudinal and the transverse shear forces as

well as the pull-out force of the shear connector. The load-slippage curves of the horizontal

and the transverse springs are obtained from the normalized load-slippage curve proposed by

Ollgaard et al (12) as follows:

Fh = Ps (1 e -S

) (1)

where

Fh is the longitudinal shear force developed in the shear connector at a slippage of S

(mm);

Ps is the shear resistance of the shear connectors;

is a non-dimensional parameter with its value between 0.5 and 1.5; and

is a parameter with a unit of mm-1; its value is typically between 0.5 and 2.5.

In general, the typical load-slippage curve of headed shear connectors reported by Lawson

(13) may be represented by Equation (1) with = 1.2 and = 2.0.

NUMERICAL INVESTIGATION ON COMPOSITE BEAMS AND JOINTS

In the present study, the structural behaviour of a continuous composite beam and a semi-

rigid composite joint are examined, and effects of the deformation characteristics of flexible

shear connectors and tensile reinforcement are thoroughly studied.

Among dozens of continuous composite beams and semi-rigid composite joints tested and

reported in the literature, the following are adopted in the present study:

Beam CTB4 reported by Ansourian (14), a continuous composite beam exhibiting

significant moment re-distribution.

Joint B5 reported by Brown & Anderson (15), a symmetrically load semi-rigid composite

joint with beam end-plate connections.

Finite Element Study on Composite Beam

Figure 3 illustrates the overall test arrangement of the continuous composite beam, Beam

CTB4, together with the three dimensional finite element model. The predicted load-

deflection curve of Beam CTB4 is plotted in Figure 4 together with the measured data for

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P/2 P/2

3 28 @ 320 c/c

Figure 3: Beam CTB4

Finite element mesh

200 10

At = 804 mm2

19

0

10

0

800

6.5

Beam CTB4

Ab = 767 mm2

Section C-C

three shear connectors three shear connectors

Contact spring elements not shown for clarity

Shear connector: 19 mm headed shear connector

with as-welded height equal to 75 mm. Initial imperfection

Shell elements: S8

Shell elements: C3D8

Details of test specimen

3 5 7

HE

A

200

2250

3 5 7

HE

A

200

P/2 P/2 2250

IPB200

2250 2250

3 28 @ 320 c/c

C

Beam CTB4. py = 236.0 N/mm2, pc = 27.2 N/mm

2.

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direct comparison. It is shown that there is good agreement between the predicted and the

measured data. As shown in Figure 5, it is found that failure of a continuous composite beam

often involves a two-stage mechanism as follows:

Stage 1 Failure at internal support under hogging moment; and

Stage 2 Failure at mid-span under sagging moment.

0

100

200

300

400

500

600

0 10 20 30 40

Deflection at mid-span (mm)

Ap

llie

d l

oad

, P

(k

N)

Figure 4: Load deflection curves of Beam CTB4

To

tal

loa

d, P

(k

N)

0

100

200

300

400

500

0 5 10 15 20

Vertical deflection at mid-span, (mm)

Tota

l lo

ad

, P

(k

N)

E-R P-R-72 N-72

E-100 P-100-72

Test P-50-720

100

200

300

400

500

0 5 10 15 20

Vertical deflection at mid-span, (mm)

Tota

l lo

ad

, P

(k

N)

E-R P-R-72 N-72

E-100 P-100-72

Test P-50-72

Test

405.6

Stage 1

Stage 2

431.2

455.0

430.0

450.8

495.3 (s)max = 0.24 mm

(s)max = 0.45 mm

(s)max = 0 mm

Figure 5: Failure mode of Beam CTB4

von Mises stress

(N/mm2)

0

0.2 py

0.4 py

0.6 py

0.8 py

1.0 py

Stage 1

Failure at internal support under hogging moment

Stage 2

Failure at mid-span under sagging moment.

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Hence, the continuous composite beam is considered to be failed when plastic hinges are

formed at both the internal support and near the mid-span, i.e. when both the hogging and the

sagging hogging moment capacities of the composite beam are fully mobilized. A plastic

hinge is regarded to be fully developed at a critical cross-section when its maximum strain

reaches the limiting value, max , which is defined as follows:

max = s

y

E

f6 (2)

where

fy is the yield strength of the steel; and

Es is the Youngs modulus of the steel.

Hence, it is shown that the proposed three-dimensional finite element model is able to

provide accurate prediction to the structural behaviour of continuous composite beams in

both linear and nonlinear deformation stages.

Moment re-distribution in a continuous composite beam

It is interesting to examine the moment re-distribution behaviour in continuous composite

beams, and the development of moment re-distribution in Beam CTB4 is illustrated in Figure

6. It should be noted that the first plastic hinge is formed at the internal support under a total

load of 455.0 kN while the hogging and the sagging moments at the critical cross-sections are

159.7 and 165.3 kNm respectively. Upon further increase of the applied load, the second

plastic hinge is formed near the mid-span under a total load of 495.3 kN while the hogging

and the sagging moments at the critical cross-sections are 159.7 and 195.5 kNm respectively.

Owing to moment re-distribution in the continuous composite beam, the total load carrying

capacity is increased from 455.0 kN at Stage 1 failure to 495.3 kN at Stage 2 failure, i.e. an

increase of 8.9%. The degree of moment re-distribution at the internal support is found to be

19%. Refer to Chung & Wang (16) for further details on the numerical analysis and design

models of continuous composite beams.

It should be noted that plastic local buckling is also successfully captured in the compressive

flange of the steel sections near internal supports well after plastic hinges have been fully

developed. In general, the occurrence of such plastic local buckling is only important to

composite beams with wide flanges in steel sections in which the hogging moment capacities

of the composite beams may decrease significantly after the onset of plastic local buckling.

Flexibility of shear connectors

In order to examine the effects of flexible shear connectors to the structural behaviour of

continuous composite beams, shear connectors with different load-slippage characteristics as

shown in Figure 3 are incorporated into the finite element model. The corresponding

predicted load-deflection curves are also plotted in the same graph in Figure 4 for direct

comparison.

It is shown that there is a significant variation in the load carrying capacities among all these

beams, and the maximum difference among the load carrying capacities is found to be 15%.

Hence, it is demonstrated that the load-slippage characteristics of shear connectors are

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The degree of hogging moment redistributed from internal support, mr, is

given by:

mr = (Mhog, e - Mhog2) / Mhog,e

where

Mhog, e is the applied moment at the internal support at failure

according to elastic analysis, and

Mhog2 is the applied moment at the internal support at failure

according to nonlinear analysis.

mr = (197.2 159.7) / 197.2

= 19 %

Figure 6: Moment redistribution in Beam CTB4

b) Applied moment at failure

197.2 kNm

159.7 kNm

195.5 kNm

37.5 kNm P/2

176.8 kNm

Elastic analysis

Nonlinear analysis

0

50

100

150

200

250

300

0 200 400 600 800

455.0 495.3

Mhog1 = 159.7 Mhog2 = 159.7

Mhog,e = 197.2

Total load, P (kN)

Mo

men

t, M

(k

Nm

)

Stage 1

Stage 2

FEM: Hogging moment

FEM: Sagging moment

Hogging moment

from elastic analysis

Stage 1 Stage 2

Msag2 = 195.5 Msag1 = 165.3

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important in assessing the load carrying capacities of continuous composite beams as the

internal force distribution depends not only on the flexural rigidities of the composite beams

but also on the flexibility of shear connectors. On the contrary, the flexibility of shear

connectors is considered not important in predicting the load carrying capacities of simply

supported composite beams, although it will affect their deflections.

Finite Element Study on Composite Joint

Figure 7 illustrates the overall test arrangement of a semi-rigid composite joint, Joint BA5.

The corresponding three dimensional finite element model is presented in Figure 8 together

with the details of the beam end-plate connections (17). Figure 9 presents the deformed mesh

of the finite element model, Joint BA5, at failure. It should be noted that in physical tests,

composite connections often fail owing to the rupture of tensile reinforcement. This is

readily predicted in the finite element models. In addition, severe yielding and stress

concentration are found in the following locations:

the upper portion of the end-plate of the steel beam under the pull-out action of the bolt

forces; and

part of the flange to web junction of the steel column under direct bearing of the lower

portion of the end-plate of the steel beam.

The predicted load-deflection curve of the composite joint is plotted in Figure 10 together

with the measured data for direct comparison. It is shown that there is good agreement

between the predicted and the measured data.

Hence, it is shown that the proposed three-dimensional finite element model is able to

provide accurate prediction to the structural behaviour of semi-rigid composite joints with

beam end-plate connections in both linear and nonlinear deformation stages.

Moment capacities of composite joints

According to experimental investigations reported in the literature, most of the tests on

composite joints are terminated due to excessive deformation in the connections or rupture of

tensile reinforcement. Hence, in order to establish the moment capacities of composite joints,

the moment capacities are defined to be the applied moments at which the strain in the tensile

reinforcement reaches a limiting value, t , at 5%. Rupture of the tensile reinforcement, and hence, failure of the composite joint is likely to happen beyond that value.

Development of internal forces

It is interesting to examine the tensile forces in the bolts and the tensile reinforcement as well

as the compressive (bearing) forces near the bottom flanges of the steel beams during the

entire loading history; the development of various internal forces in the composite joint is

presented in Figure 11.

It is found that the forces in the tensile reinforcement are mobilized in the early loading stage,

as shown in Figure 11, because of the relatively large deformation in the tensile

reinforcement, when compared with the deformation in the bolts. This leads to early yielding

of the tensile reinforcement, and the tensile forces in the bolts are subsequently developed at

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Figure 7: Joint BA5

208.7 13.2

At = 804 mm2

52

8.3

1

20

1100

9.6

45 45

57

8

32

8

80

80

25

250

End plate:

578 250 15

Bolts M20

Grade 8.8

90

Connections details

0

20

40

60

80

100

0 1 2 3

h (mm)

Ph (

kN

)

Load-slippage curve of shear

connector

Test

FEM

Fs = F(1 - e-2 S)

0.8

Slippage, s (mm)

Sh

ear

forc

e, F

s (k

N)

Connection BA5py = 355 N/mm2, pc = 38 N/mm

2.

P P

1410 1410

UB 533 210 82

UC

25

4

25

4

73

235 typ

Measured yield strength (N/mm2) Measured cylinder

strength of concrete

(N/mm2)

Steel beam Steel column End- plate Reinforcement

Flange Web Flange Web

351 385 285 331 305 504 38.4

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Figure 8: Finite element model of Joint BA5

Note:

Spring contact elements are not shown for clearity.

Web of column Steel beam End-plate Flange of

column

Steel decking

(Shell elements: S8)

Concrete flange

(Solid elements: C3D8)

Smeared layer for reinforced concrete

(Solid elements: C3D8)

Steel beam

(Shell elements: S8)

Steel column

(Shell elements: S8)

P

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von Mises stress

(N/mm2)

0

0.2 py

0.4 py

0.6 py

0.8 py

1.0 py

a) Perspective view

von Mises stress

(N/mm2)

0

0.2 py

0.4 py

0.6 py

0.8 py

1.0 py

b) Side view

Figure 9: Typical failure mode of Joint BA5

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Figure 10: Moment-rotation curves

of Joint BA5

0

100

200

300

400

500

600

0 10 20 30 40

Mo

men

t, M

(k

Nm

)

Rotation, (10-3 rad)

Figure 11: Development of internal forces in Joint BA5

0

200

400

600

800

1000

0 100 200 300 400 500 600

M3D = 440.1 kNm

Ft = 406.6 kN

Fr = 410.5 kN

Fc = 817.1 kN

Inte

rn

al

force

, F

(k

N)

Moment, M (kNm)

Tensile force in bolts, Ft

Compressive contact force, Fc

Tensile force in reinforcement, Fr Compressive contact force, Fc

Tensile force in reinforcement, Fr Tensile force in bolts, Ft

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large deformation stage of the composite joint. Thus, tensile reinforcement with sufficient

ductility should be provided in order to fully mobilize the moment capacities of the

composite joints.

PARAMETRIC STUDIES

After careful verification of the finite element models for both composite beams and joints, it

is possible to examine the effects of deformation characteristics of both shear connectors and

tensile reinforcement on the structural behaviour of composite beams and joints through

systematic parametric studies. A total of 120 non-linear finite element analyses on composite

joints, continuous composite beams and semi-continuous composite beams with shear

connectors and tensile reinforcement having different deformation characteristic were

conducted (17). Owing to the limited space in this paper, only some of the key findings of

the parametric studies are presented.

In general, three different shear connectors, namely, Shear connectors A, B and C, with

different slippage limits are considered in the parametric studies, and their deformation

characteristics are plotted in Figure 12a). Moreover, two different tensile reinforcement,

namely, tensile reinforcement N and H, with different deformation limits are considered, and

their deformation characteristics are plotted in Figure 12b). Both the slippage limits of the

shear connectors and the deformation limits of the tensile reinforcement are considered to

range within the corresponding limits in practice.

Composite Joints with Different Shear Connectors and Tensile Reinforcement

Figure 13a) illustrates the overall arrangement of a composite joint with beam end-plate

connections; details of the connections are also presented. It should be noted that in the

composite joints, tensile reinforcement H is adopted while three different shear connectors

are used for comparison. The moment-rotation curves of the composite joints with different

shear connectors and tensile reinforcement are plotted in Figure 13b) for comparison. It is

shown that:

The composite joint with Shear connector A exhibits very ductile deformation along

the entire loading history owing to the ductile slippage characteristics of Shear

connector A as well as the ductile deformation characteristics of tensile

reinforcement H.

In the composite joint with Shear connector B, reduction in the moment capacity of

the composite joint at large deformation is found. This may well be explained by the

reduced shear resistance of Shear connector B at any slippage larger than 5 mm.

Despite the ductile deformation characteristics of tensile reinforcement H, the

composite joint with Shear connector C is shown to have severe reduction in its

moment capacity at large deformation owing to the rupture of shear connectors at a

slippage larger than 7 mm. As no composite action is possible, only the moment

capacity of the steel beam is readily mobilized.

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Similarly, the structural behaviour of the composite joints with different tensile reinforcement

is also studied; Shear connector A is used in both cases. The moment-rotation curves of the

composite joints are also plotted in Figure 13b), and it is shown that:

Figure 12: Material models of shear connectors and tensile reinforcement

0

100

200

300

400

500

0 10 20 30 40 50 60

Str

ess,

(

N/m

m2)

Strain, ( 10-2)

Tensile reinforcement N

50 110

Tensile reinforcement H

20 40 60 80 100 120 0

0

100

200

300

400

500

b) Assumed stress-strain curves of tensile reinforcement

450

205 kN/mm2

1

2 4 6 8 10 12

0

20

40

60

80

100

0 2 4 6 8 10 12

h (mm)

Ph (

kN

)

a) Assumed load-slippage curves of shear connectors

5

Shear connector A

7

Shear connector B

Shear connector C

72

36

Lawson (13)

Ollgaard (12)

Fh (

kN

)

S (mm)

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The composite joint with tensile reinforcement H exhibits very ductile deformation

along the entire loading history owing to the ductile deformation characteristics of

tensile reinforcement H as well as the ductile slippage characteristics of Shear

connector A.

In the composite joint with tensile reinforcement N, despite the ductile slippage

characteristics of Shear connector A, the composite joint is shown to have severe

reduction in the moment capacity of the composite joint at large deformation owing to

a) Details of composite joint

92 92

64

1.5

36

5.1

6

2

62

12

368.4

307.0 23.6

18Y6@175, At = 508 mm2

61

7.5

1

30

2500

14.1

70

Notes:

Concrete cylinder strength, pc = 24 N/mm2.

Yield strength of steel, py = 355 N/mm2 .

P

1500 1500

UB 610 305 179

UC

35

6

36

8

15

3

210 typ P

15 15

b) Moment-rotation curves

Figure 13: Parametric study on a composite joint

0

200

400

600

800

1000

0 20 40 60

Mo

men

t, M

(k

Nm

)

Rotation, (10-3 rad)

575.4

Tensile reinforcement H Tensile reinforcement N

Shear connector A

0

200

400

600

800

1000

0 20 40 60

Mo

men

t, M

(k

Nm

)

Rotation, (10-3 rad)

575.4

502.4

452.4

Shear connector A Shear connector B Shear connector C

Tensile reinforcement H Failure, t = 5%

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the rupture of tensile reinforcement. Hence, only the moment capacity of the steel

beam is readily mobilized.

Consequently, it is shown that the proposed models are able to predict the detailed structural

behaviour of composite joints based on the deformation characteristics of both the shear

connectors and the tensile reinforcement.

Composite Beams with Different Shear Connectors and Tensile Reinforcement

The overall arrangement of the internal span of a semi-continuous composite with beam end-

plate connections is illustrated in Figure 14; details of the connections are also presented. It

should be noted that in the composite beam, tensile reinforcement H is adopted while three

different shear connectors are used for comparison. The predicted moment-rotation curves of

the composite beams with different shear connectors and tensile reinforcement are plotted in

Figure 14 for comparison.

In general, the structural behaviour of the composite beams is found to be very similar to

those of the composite joints, i.e. both the slippage characteristics of shear connectors and the

deformation characteristics of tensile reinforcement have significant effects on the structural

behaviour of composite beams. Moreover, the maximum values of slippage in the shear

connectors in various cases are summarized in Figure 14 for easy comparison. It is shown

that

For composite beams with tensile reinforcement H, the maximum values of slippage

on Shear connectors A, B and C are found to be 12.6, 15.2 and 19.1 mm respectively.

Hence, in the presence of non-ductile shear connectors, larger slippage is often needed

to develop the full failure mechanism in the composite beams while lower load

carrying capacities of composite beams is normally obtained.

In the composite beam with Shear connector A and tensile reinforcement N, the

composite beam is shown to have small reduction in its load carrying capacity at large

deformation owing to partial yielding of the tensile reinforcement. It should be noted

that there is a steady load transfer from the tensile reinforcement to the shear

connectors at large deformation. Moreover, partial composite action is developed in

the composite beam at failure.

As demonstrated in the parametric studies, the proposed models are able to predict the

detailed structural behaviour of composite beams based on the deformation characteristics of

both the shear connectors and the tensile reinforcement.

CONCLUSIONS

This paper presents the development of three dimensional finite element models which are

advanced numerical analysis and design models for composite beams under practical member

configurations and loading conditions. These models are provided to facilitate the

performance-based design and analysis of long span composite beams with practical

constructional features.

PJulA07 20

a) Details of composite beam

307.0 23.6

61

7.5

1

30

2500

14.1

70

18Y6@175, At = 508 mm2

Notes:

Concrete cylinder strength, pc = 24 N/mm2.

Yield strength of steel, py = 355 N/mm2.

HEA 200 UB 610 305 179

47 @ 210 c/c

W

10000

UC

35

6

36

8

15

3

UC

35

6

36

8

15

3

b) Load-deflection curves

Beam

Maximum slippage of shear

connectors at failure,

Smax (mm)

Stage 1 Stage 2

Shear connector A 4.9 12.6

Shear connector B 4.9 15.2

Shear connector C 4.9 19.1

Figure 14: Parametric study on a semi-continuous composite beam

Beam

Maximum slippage of shear

connectors at failure,

Smax (mm)

Stage 1 Stage 2

Tensile

reinforcement H 4.9 12.6

Tensile

reinforcement N 4.9 12.2

3489.2

4742.2

1765.4

0

1000

2000

3000

4000

5000

6000

0 50 100 150 200 250 300

Stage 1

Stage 2

First crack

4104.1

3765.1

Ap

pli

ed

loa

d, W

(k

N)

Deflection at mid-span, (mm)

Shear connector A Shear connector B Shear connector C

Tensile reinforcement H

3489.2

4742.2

1765.4

0

1000

2000

3000

4000

5000

6000

0 50 100 150 200 250 300

4504.2

Ap

pli

ed

loa

d, W

(k

N)

Deflection at mid-span, (mm)

Tensile reinforcement H Tensile reinforcement N

Shear connector A

Internal span

PJulA07 21

It is shown that:

1. Prescriptive design methods are often presented in a simplistic formulation as they operate with certain implicit assumptions on both material and structural behaviour.

Hence, they are conservative, but easy to use. The proposed performance-based

analysis and design models allow design to operate beyond what are currently

permitted by those prescriptive design methods. While the analysis and design

models are more rigorous in their prediction capabilities, their effective use certainly

requires a thorough understanding on the material models as well as the structural

behaviour of the structures.

2. Through extensive calibration against a wide range of test data, the proposed models are able to provide detailed information on the structural behaviour of composite

joints, continuous composite beams and semi-continuous composite beams. Based on

the material models of the steel and the concrete as well as the deformation

characteristics of the shear connectors and the tensile reinforcement, the load-

deflection curves of the structures can be obtained along the entire loading history.

Designers are strongly encouraged to employ the models in their practical work to exploit the

full advantages offered by composite construction.

ACKNOWLEDGEMENTS

The project leading to the publication of this paper is supported by the Research Committee

of the Hong Kong Polytechnic University (Project No. G-W039).

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PJulA07 22

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