The effects of axial tension on the sagging-moment regions of composite beams

Journal of Constructional Steel Research 72 (2012) 240–253

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Journal of Constructional Steel Research

The effects of axial tension on the sagging-moment regions of composite beams G. Vasdravellis ⁎, B. Uy, E.L. Tan, B. Kirkland Institute for Infrastructure Engineering, University of Western Sydney, Locked Bag 1797, Penrith NSW 2751, Sydney, Australia

a r t i c l e

i n f o

Article history: Received 19 June 2011 Accepted 3 January 2012 Available online 2 February 2012 Keywords: Composite beams Sagging moment Axial tension Finite element analysis

a b s t r a c t This paper studies the effects of axial tension on the sagging moment regions of steel–concrete composite beams. The study comprised an extensive experimental programme and nonlinear finite element analyses. Six composite beams were designed and tested under the combined effects of axial tension and positive bending moment. The beams were loaded to their ultimate capacity and the experimental moment-axial tension interaction diagram was constructed. Following the tests, a finite element model was used to simulate the nonlinear response of the composite beams. The validity of the model was thoroughly assessed against the available experimental data and a parametric study was conducted to study different beam sizes and the effect of partial shear connection on the interaction diagram. It was found that the moment capacity of a composite beam is reduced under the presence of an axial tensile force acting in the steel beam section. In addition, the use of partial shear connection does not affect significantly the shape of the interaction diagram. The tensile capacity of the composite section, however, is limited by the axial capacity of the steel beam alone. Based on the experimental results and the finite element analyses, a simplified equation is proposed for the design of composite beams subjected to positive bending and axial tension. © 2012 Elsevier Ltd. All rights reserved.

1. Introduction Steel-concrete composite systems have seen widespread use in recent decades because of their advantages against conventional construction. The optimal use of the two materials together with their individual properties, e.g. steel strength and ductility in tension and concrete robustness and high stiffness in compression, results in a very efficient and economical structural solution. Furthermore, reinforced concrete is inexpensive and provides good fire resistance, while steel members are lightweight and easy to assemble. The effective collaboration between a concrete slab and a steel beam which is achieved through the shear connection system significantly increases the rigidity and the ultimate moment capacity of a composite beam compared with the properties of a bare-steel or reinforced concrete beam. In this way much larger beam spans can be obtained. There are situations where a composite beam is subjected to axial loads and bending moments [1]. Some characteristic examples include: • Beams located at the leeward side of high-rise buildings. In these buildings the wind suction can assume large values, depending on the height of the building, and imposes axial loads to the steel beams of the structural frame.

⁎ Corresponding author at: Institute for Infrastructure Engineering, University of Western Sydney, Locked Bag 1797, Penrith South NSW 2751, Sydney, Australia. Tel.: +61 2 4736 0119; fax: +61 2 4736 0054. E-mail address: [email protected] (G. Vasdravellis). 0143-974X/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2012.01.002

• The effect of shrinkage in the concrete slab indirectly imposes an axial tensile load to the steel beam. • Inclined car park ramps and grandstands in stadia are usually constructed with a large inclination angle, and thus the beam is subjected to combined bending and axial forces. • Cable stayed bridges, where the cables can introduce tensile forces in the concrete deck. The effects that the simultaneous action of axial load and bending moment produce in the ultimate capacity of a composite beam are not yet covered in a comprehensive way by the current code of practice. In fact, modern steel and composite construction codes, including Eurocode 4 [2], Australian code AS2327 [3] and American AISC [4], give detailed guidance on the design of composite columns under bending and axial loads, but they do not address the effects of combined loading in composite beams, which are asymmetric in nature. There exists a considerable amount of research on the flexural behaviour of composite beams [5–7], although the behaviour under combined actions is not yet thoroughly investigated. Limited research results exist on the behaviour of composite beams under generalised loading conditions. The effect of pre-stressing on composite beams under positive bending was studied by Uy and Bradford [8] and Uy [9]. The performance of composite beams under combined bending and torsion was reported by Nie et al. [10] by studying experimentally and theoretically eleven steel-concrete composite beams. The effects of torsion on straight and curved beams were also studied by Tan and Uy [11,12]. Their research provided experimental data for the

G. Vasdravellis et al. / Journal of Constructional Steel Research 72 (2012) 240–253

effects of torsion on composite beams with both full and partial shear connection. Design equations for ultimate limit analysis of composite beams have also been provided. Baskar and Shanmugan [13] tested a number of steel–concrete composite girders under bending and shear loading. They found that the ultimate load carrying capacity is increased significantly compared to bare steel girders. Elghazouli and Treadway [14] presented results from a series of tests on partiallyencased composite steel–concrete beam–columns. The experimental inelastic behaviour of the specimens under lateral loading and axial gravity loads was examined. The specimens in their study, however, were symmetrical through both their x and y axes and thus more appropriate for use as columns. Uy and Tuem [15] were the first to look at the effect of tension on composite beams. An analytical study on combined axial load and bending was performed through a crosssectional analysis and a rigid plastic analysis. The ultimate strength of composite beams under negative (hogging) bending and axial tension was studied by Vasdravellis et al. [16] both experimentally and numerically. The experiments provided data for the construction of an interaction diagram for composite beams, while finite element analyses extended the results to more general cases, including the effects of partial shear connection. A design equation was finally proposed to assist in the practical design of composite beams. This paper presents an experimental and numerical study on the behaviour of composite beams under the combined effects of positive bending and axial tension. Six composite beams of identical crosssections were tested under different combinations of tension and bending and the ultimate capacities and failure modes were identified. A detailed nonlinear finite element model was constructed based on the use of the ABAQUS software to simulate the experimental response. The three-dimensional model was compared against the available experimental data and found to be capable of simulating the inelastic behaviour of the composite beams with efficiency and to trace the failure modes up to the ultimate deformation levels. The established model was then used to extend the analyses to a number of sections commonly used in engineering practice, including different beam spans and various slab effective widths. It was found that the moment capacity of a composite section is reduced under the presence of an axial tensile force acting in the steel beam section. In

241

addition, the use of partial shear connection does not affect significantly the shape of the interaction diagram. The tensile capacity of the composite section, however, is limited by the axial capacity of the steel beam alone. Based on the experimental results and the finite element analyses, a simplified equation is proposed for the design of composite beams subjected to positive bending and axial tension. 2. Experimental programme 2.1. Details of test specimens Six composite beams of 4500 mm length were designed and tested as part of the experimental programme. The tested beams are denoted throughout this paper as CB1 to CB6. The relevant geometry and details of the reinforcement and shear studs are shown in Fig. 1. All specimens were constructed with a 600 mm wide and 120 mm deep concrete slab connected to a 200UB29.8 steel section. The beam to slab connection was achieved through 19 mm diameter, 100 mm long headed shear studs welded in a single line along the centre of the top flange of the steel beam. The shear stud number was calculated in order to provide partial shear connection between the concrete slab and the steel beam. The degree of shear connection achieved was 0.6. A group of 3 studs was welded at the ends of each of the beams. This was done in order to increase the connection stiffness at the beam ends, where slip is a maximum and delay shear stud failure at this region. Longitudinal and transverse reinforcement was placed in the concrete slab. 2.2. Material tests Both concrete and steel material tests were performed to obtain the actual properties of the materials. Concrete tests consisted of standard cylinder compressive tests and flexural splitting tests. The latter aimed to determine the tensile strength of the concrete. Each cylinder compressive test was carried out on the same day as the corresponding composite beam test. The cylinders were 200 mm high with a diameter of 100 mm, while the flexural tests were performed on 100 × 100 × 400 mm specimens. The results are summarised in 600.0

4 N12

120.0

9.6 188.0

6.4

9.6

" West "

134.0

D=19/H=100 SHEAR STUDS

N12 BARS @ 200MM

4N12 BARS @ 120MM

" East"

600

100

350

400

400

400

400

400

400

400

400

400

4500 Fig. 1. Composite beam cross-section (dimensions in mm) and plan view of slab reinforcement and shear stud layout.

350 100

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Table 1 Material test results for concrete. Specimen

Age at testing (days)

Compressive strength (MPa)

Tensile strength (MPa)

CB1 CB2 CB3 CB4 CB5 CB6

32 45 47 52 53 60

29.5 31.8 30.9 31.9 32.1 34.6

3.6 4.2 4.0 4.0 3.3 3.8

Table 2 Material test results for steel. Coupon

Sample no.

Flange

Web

Reinforcement

1 2 3 Average 1 2 3 Average 1 2 3 Average

Yield stress (MPa)

Tensile stress (MPa)

Modulus of Elasticity (GPa)

332 375 348 352 369 396 395 387 549 542 550 547

498 544 545 529 532 543 535 537 640 637 645 641

197 193 211 200 214 229 240 227 196 199 203 199

Table 1. Tensile tests were also conducted on coupons cut out from the flange and web of the steel beams as well as the reinforcing bars. The values obtained from the tests for the yield stresses, the ultimate stresses at fracture, and the modules of elasticity are reported in Table 2. 2.3. Push-out tests

Fig. 3. Load applicator system used to apply axial load.

2.4. Test setup A combination of load actuators was used in order to produce simultaneous axial tensile loads and bending moments in the composite beam specimens. Two hydraulic actuators were used to provide the required levels of tension. To create the axial load two 800 kN and 160 mm-stroke hydraulic actuators were combined and attached at the east of the beam through a specially designed load applicator system while the west end was fixed to a cross-head. East and west are indicated in Figs. 1 and 4. The cross-head system consisted of two plates connected to the beam through a large greased pin, as shown in Fig. 3. The web of the universal beam section of the composite beams was reinforced by welding two 10 mm thick plates to each side of the web in order to prevent localised web yielding. The vertical load was applied with the use of a 1000 kN capacity hydraulic actuator with a usable stroke of 250 mm. A view of a specimen on the loading rig is shown in Fig. 4. 2.5. Instrumentation

In order to evaluate the load–slip characteristics of the shear studs three push-out specimens were constructed using shear studs and concrete from the same batches as those used to form the steel–concrete composite beams in the main experimental series. Each of the pushout specimens were tested following the testing procedure described in current codes [2]. Results of the three push-out tests, denoted as P1 to P3, are plotted in Fig. 2 in terms of load per stud versus slip. The resulting load–slip curves show that the average load capacity of one shear stud is about 110 kN, while the maximum slip achieved during the tests varies from 8 to 16 mm. According to Eurocode 4 [2], the maximum slip capacity of a shear stud is defined as the slip corresponding to a load equal to 90% of the maximum applied load during the push-out test. Thus, the slip capacities of the tested studs are approximately 8, 10 and 14 mm.

A combination of linear transducers and strain gauges was employed to record the relevant parameters and to obtain the experimental behaviour of the beams. An automatic data acquisition system was employed to automatically record data from all measuring devices including load cells,

Load/stud (kN)

120 100 75 50

P1

P2

West

P3

25 0

East 0

2

4

6

8

10

12

14

16

18

Slip (mm) Fig. 2. Load per stud versus slip curves.

Fig. 4. View of the test setup.

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the location of the load application pin and the plastic neutral axis of the composite beam. In this experimental series, the amount of concrete contributing to the strength of the section, and thus the calculation of the plastic neutral axis, are an estimate based on the strain profile and the crack depth at the ultimate load.

strain gauges and linear potentiometers throughout the test. Strain gauges were used to measure strains of the steel beam and reinforcing bars. A total of 21 strain gauges were used for each beam specimen. Strain gauges were located in sets of seven through each cross-section with one set at midspan and one set at each quarter point, as shown in Fig. 5. At each section there was one strain gauge attached to each longitudinal reinforcing bar, numbered 1 to 4, one each on the top and bottom flanges and one at the centre of the web. Linear potentiometers were used for measuring the deflection of the beam. These were placed at the midspan and at the quarter points. The connector slip and interface slip were also measured by linear potentiometers. The slip was measured at the ends, quarter points and midpoint, as indicated in Fig. 5.

3. Theoretical analysis 3.1. Rigid Plastic Analysis (RPA) In order to check the conservatism of current design recommendations, the theoretical moment and axial force resistances of the experimental composite section were calculated by means of sectional Rigid Plastic Analysis (RPA), as prescribed in the context of current structural codes (e.g. EC 4). In the calculations, the experimental strength of the material was used (Table 1) and no partial safety factors were considered in order to provide a direct comparison with the test results.

2.6. Test procedure The beam CB1 was loaded in pure positive bending; therefore it was only subjected to a vertical load. The vertical load was increased until either material failure occurred or the stroke limit of the vertical load actuator was reached. In the case of specimens CB2 to CB5, vertical loading was carried out in incremental steps in the order of 10% of the theoretical design strength of the composite section. To obtain different levels of axial tension, the increments of applied axial load were varied. Both loads were increased until either material failure occurred or maximum stroke of either load actuators was reached. The final beam, CB6, was tested in pure axial tension and only the axial loading rig was used to apply the load. During the test, a load cell was placed in contact with the bottom flange of the steel section at the midspan of the composite beam in order to prevent second-order bending of the beam due to the eccentricity caused by the location of the axial load applicators relative to the plastic centroid. The resulting moment in each tested beam was calculated taking into account the equilibrium of the external forces acting on it. The following equation was used to calculate the ultimate bending moment: M¼

PV L þ PH e 4

3.2. Finite element model A three-dimensional solid finite element model (FEM) was developed in order to simulate the behaviour of the tested composite beams. The model was established using the commercial finite element software ABAQUS [17]. A detailed description of the model geometry, element types, materials and solution method is outlined within the following sections. 3.3. Geometry and element types The concrete slab was modelled using eight-node linear hexahedral solid elements with reduced integration, namely C3D8R in ABAQUS, while the steel beam was represented by eight-node linear solid elements with incompatible modes (C3D8I). This distinction was made primarily due to hourglass modes detected on the C3D8R elements when large concentrated forces are introduced to the mesh at the locations of the studs. It was found that incompatible modes can solve this problem and predict the behaviour of a composite beam more accurately. The reinforcing rebars were modelled as

ð1Þ

where PV is the vertical force applied at the centre of the beam, PH is the horizontal force applied by the pins, and e is the eccentricity between

1

1000

STRAIN GAUGE LVDT

3

2

1000

1000

SECTIONS 1, 2, 3 C1

243

C2

C3

C4

B3 B2 B1 Fig. 5. Specimen instrumentation.

1000

244

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Embedded rebars (T3D2 elements)

Symmetry plane

C3D8R elements

N

interaction was applied to the beam-slab interface which did not allow separation of the surfaces after contact in order to prevent uplift. The node-to-surface contact with small sliding formulation technique was used while the “hard” normal contact with friction was specified as the contact property. Eurocode 4 [2] recommends the value 0.5 for the friction coefficient between steel and concrete in composite members for steel sections without painting; however, the more conservative value 0.4 was assumed in the present study.

V C3D8I elements slab nodes

Contact interaction + nonlinear springs (SPRING2 elements)

zero beam nodes

Fig. 6. Finite element mesh and elements used for modelling the composite beams.

two-node three-dimensional linear truss elements, T3D2. Due to the symmetrical geometry and loading, only half of the beam was modelled, while appropriate boundary conditions were applied on the plane of symmetry. A finite element view comprising the various modelling assumptions is depicted in Fig. 6. 3.3.1. Interactions The embedded element technique was employed to model the reinforcement in the slab. The embedded element technique in ABAQUS is used to specify an element or a group of elements that lie embedded in a group of host elements whose response will be used to constrain the translational degrees of freedom of the embedded nodes. In the present case, the truss elements representing the reinforcement are the embedded region while the concrete slab is the host region. Using this technique, it is assumed that perfect bond exists between the rebars and the surrounding concrete. In addition, a contact

a) Concrete

3.3.2. Materials The stress-strain relations obtained from material tests were converted into piecewise linear laws and used to model the steel material for the beam and the reinforcing bars, as shown in Fig. 7b and c. The built-in Mises plasticity with associated plastic flow and isotropic hardening was used as the constitutive law for all the steel parts of the model. The concrete material stress-strain relationship was calibrated according to the values obtained from the concrete cylinder compressive and flexural tests. The stress-strain curve for compression follows the formula proposed by Carreira and Chu [18], while the tensile behaviour is assumed to be linear up to the uniaxial tensile stress provided by the material tests. The stress-strain law used is plotted in Fig. 7a. The post-failure behaviour for direct straining across cracks is modelled using the tension-stiffening option and determining a linear relation until stress is zero at a strain value of 0.05. This value is used for avoiding numerical problems in the computational procedure while accuracy is not affected considerably. There are two plastic models available in ABAQUS for modelling the concrete behaviour. In the present analysis the damaged plasticity model was preferred over the smeared cracked model. The damaged plasticity model provides a general capability for the analysis of concrete structures under static or dynamic and monotonic or cyclic loading based on a damaged plasticity algorithm. Compared to the companion model (smeared crack model), it models the concrete behaviour more realistically but it is computationally more expensive. Although, this model was

b) Structural steel 600 500

0

Stress (Mpa)

Stress (MPa)

10

-10 -20

400 300 200 100

-30 -20

-15

-10

-5

0

5

0

10

0

0.05

0.1

0.25

0.3

120

Load per stud (kN)

800

Stress (MPa)

0.2

d) Shear studs and nonlinear spring

c) Reinforcement steel 600 400 200 0

0.15

Strain

Strain (x10e3)

0

0.02

0.04

0.06

Strain

0.08

0.1

0.12

100 80 60 40 SPRING 20 0

PUSH TESTS 0

2

4

6

8

10

12

14

Slip (mm)

Fig. 7. Material stress-strain laws adopted in the finite element model a) concrete, b) structural steel parts, c) reinforcement, and d) shear stud force-slip law.

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245

chosen for monotonic loading due to its numerical efficiency when full inelastic response has to be traced.

convergence problems. To avoid these, the discontinuous analysis option was also used in the general solution control options.

3.3.3. Shear connection model The shear connection modelling in a composite beam is probably the most complicated task due to the complex interactions between the studs and the concrete slab. The most accurate way is to model the studs using solid elements and apply contact interactions with the elements of the slab. However, this technique is cumbersome both in terms of geometry construction and computational time, while convergence problems during the solution are likely to arise due to the severe immediate cracking of concrete in the region surrounding the studs. A nonlinear spring model representation of shear studs is chosen to simulate the interface slip in the present study. The nonlinear spring element SPRING2 was adopted to connect a beam flange node with a slab node at the interface, as schematically shown in Fig. 6. The force slip law for the spring element is derived by the standard push-out tests on 19 mm-diameter shear studs. The experimental curve was converted into a piecewise linear force-slip relationship and defined as the force-slip law for the springs, as shown in Fig. 7d. If only a small number of shear connectors is considered at the interface, then the force which will be distributed to each stud can be very high and this may cause numerical problems due to large tensile forces introduced suddenly in the concrete slab. The nonlinear springs used in the FEM model are distributed in the steel-concrete interface using a spacing of about 175 mm. This, in most of the cases studied in this paper, results in a higher number of springs than the number/of shear studs required for a full shear connection if a nominal diameter of 19 mm is assumed for the shear studs. Although, this method is preferred in the present analysis because it distributes the stud forces at the interface more smoothly and delays numerical problems associated with the introduction of large concentrated forces to the mesh and concrete material modelling in ABAQUS. In the FEM model the degree of shear connection, β, is calculated by the equation:

3.3.5. Failure criteria and calculation of internal forces There are three possible failure modes of a composite beam under sagging, or positive, bending: 1) concrete crushing of the slab, 2) excessive yielding of the steel beam, and 3) shear connection failure. Nevertheless, in a regular composite beam the first and the third modes are usually met in practice. In the present analysis specific criteria were established in order to identify the associated failure loads. A compressive strain limit equal to εc = − 0.0035 was imposed in order to identify a compressive failure mode in the slab, while a yielding tensile strain equal to εs = 0.2 was used for steel fracture due to excessive yielding. Accordingly, shear connection failure was reached when the slip in the most heavily loaded stud (nonlinear spring in the analysis), Sult, was approaching the stud failure slip, defined by the following equation [19]:

β¼

Nss F stud Nsteel

ð2Þ

where Nss is the number of the studs in the shear span, Fstud is the load capacity of an individual stud, and Nsteel is the axial capacity of the steel section. In this equation it is assumed that the concrete slab compressive resistance is greater than the steel axial capacity, Nsteel, and thus the plastic neutral axis is always located in the slab, as it is the case for the most regular composite beams. By setting the number of shear studs (Nss) constant (i.e. the nonlinear springs in the model) the desired degree of shear connection is obtained by changing the strength of each shear stud, Fstud, according to: F stud ¼

βNsteel Nss

ð3Þ

3.3.4. Loading and solution method The vertical load was applied as an imposed displacement on the top of the slab, while the axial load was applied as an edge pressure on the steel beam section. The analysis consisted of two steps. In the first step the contact interactions were established, ensuring that numerical problems due to contact formulation will not be encountered during the next steps, while in the second step the vertical and the axial loads were applied simultaneously, following the experimental procedure. The static nonlinear solution algorithm with adaptive stabilisation as a fraction of dissipated energy was employed to solve for the nonlinear response of the composite beams. Finite element analysis with concrete elements in tension may result in

0
Sult ¼ 0:42−0:0042f c dstud

ð4Þ

where fc′ is the compressive capacity of concrete, dstud is the diameter of the stud and the units are in N and mm. Eq. (4) defines the 5% characteristic slip capacity of an individual stud shear connector that is encased in a solid slab. The characteristic slip is used as a conservative value for the design at ultimate loads, as the stud failure is a brittle failure which propagates fast through all the length of the beam. The value of the failure slip was different in each analysis, depending on the shear studs employed to determine the shear connection. In any case, the force-slip relationship was modified according to the stud force obtained by Eq. (3) and the resulting diagram, shown in Fig. 7d for 19 mm-studs, was used to define the stud failure point. Combined axial and vertical loading, large deformations and associated eccentricities make the interpretation of the results cumbersome in the ABAQUS model. For this purpose, the normal stress through the composite section was monitored and plotted after each analysis and a section integration scheme was employed to define the ultimate axial force and bending moment acting in the composite beam. Afterwards, equilibrium with external loads was checked to ensure accuracy. 4. Results and discussion A detailed description of the experimental outcome regarding the failure modes, the ultimate strength and the slip and strain evolution during the tests is given in the present section. Furthermore, the finite element model presented in the previous section is validated against the experimental data and its accuracy is assessed in terms of loaddeflection curves, slip distribution, and moment-axial load interaction relationships. 4.1. Ultimate strength and failure modes A summary of the maximum vertical and axial loads attained by all specimens is given in Table 3. The resulting sagging bending moment calculated according to Eq. (1) is also reported in the same table. It is observed that specimens CB3 and CB4 were subjected to a low to moderate axial tensile force, which was equal to 35% and 18% of the theoretical plastic axial resistance of the composite section, respectively, while specimens CB2 and CB5 were tested under high tensile loads acting together with the applied sagging moment. For the last one, the final value of the axial force reached the 93% of the plastic resistance of the composite section. From the values of Table 3 it is concluded that the experimental moment capacity has slightly increased under the effects of low and moderate axial forces (specimens CB3 and CB4 in Table 3), while moment strength decreases considerably when axial tensile load takes high values.

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Table 3 Experimental strength and theoretical values for the tested specimens. Specimen

Experimental values Axial load (kN)

Failure modes

Vertical load Bending moment (kN) (kNm)

CB1 CB2 CB3

0 216 − 760.5 (51%)a 337 a − 525 (35%) 306

221 180 227

CB4 CB5 CB6

− 310 (18%)a − 1400 (93%)a − 1503

220 55 0

a b

276 48 0

Compressive failure SCb failure Compressive and SCb failure Compressive failure SCb failure SCb failure

Percentage of experimental axial force to plastic axial capacity of beam. SC denotes shear connection.

Table 3 also outlines the various failure modes observed during the experiments. For the composite beams subject to pure bending moment (CB1) or bending moment and low axial force (CB4) the prominent failure mode was concrete crushing in the midspan region, adjacent to the application point of the vertical load. On the other hand, specimens CB5 and CB6 experienced severe cracking due to stud failure. It has to be noted, however, that shear connection failure was observed in all the experimental beams, and this was expected due to the low degree of shear connection used in the experimental programme. The characteristic failure modes are summarised in Fig. 8.

4.2. Interface slip The readings of the LVDT's measuring the relative slip between the bottom surface of the slab and the top steel flange at the midspan and the two ends of the beams (denoted as east and west) in relation to the midspan deflection are plotted in Fig. 9 for all specimens. For beam CB1, although slip was initially symmetric, it becomes asymmetric as the vertical deflection approaches its maximum value. When the maximum load was reached the slip was measuring

1.5 mm at both ends of the beam, indicating that the studs were loaded at their maximum load capacity according to the pushout tests (Fig. 2), while at the ultimate beam deformation the slip values at the east and west ends were 18 mm and 5 mm, respectively. The large slip values indicate stud failure at the ends of the beam, which is also evidenced by the crack pattern in this region, as can be seen in Fig. 8b. The slip evolution during the tests is slightly asymmetric also for specimens CB2 to CB4. For CB3 and CB4, the slip values are similar, with the value at the west end not exceeding 4.5 mm, and the slip at the east end reaching 8 mm. For specimen CB2, the corresponding slip is about 5 mm (west) and 6 mm (east). For specimens CB5 and CB6, the slip diagrams are plotted up to the value of 5 mm, after which the transducers measuring the slip were detached from the specimen due to severe cracking and excessive slip values.

4.3. Crack and strain profiles In all specimens the most severe cracks were located at the midspan (concrete compressive crushing) and at the ends of the beam due to stud failure, as shown in Fig. 8a through c. At the midspan, apart from the compressive crushing of the slab, a wide flexural crack initiating from the bottom part of the slab was evident at the end of the test, as can be seen in Fig. 8a. In the beams loaded with the highest axial tension, cracks were formed at the edges of the slab at the positions of the studs throughout the length of the beams (Fig. 8c). The strain versus vertical load diagrams regarding the strain gauges placed at the midspan of the beams (Fig. 5) are shown in Fig. 10 for all specimens. Using the average yield stresses and elastic modulus of elasticity from the material tests (Table 2) the average yield strain was found to be 2748 με for the reinforcing bars, 1760 με for the steel beam flanges and 1705 με for the steel web. It can be seen from the strain measurements that the reinforcing bars were yielded under compression during the tests of the specimens which were subjected to bending, except for CB5. For specimens CB1 to CB4, the strain in the beam and in the reinforcement assume

a)

b)

c)

d)

Fig. 8. Observed failure modes during experiments. a) Concrete slab crushing, b) and c) cracking at the locations of studs, d) excessive deformation of stud at the end of specimen CB6.

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a) CB1

247

b) CB2

10

10

Slip (mm)

Slip (mm)

5 0 -5 -10

east midspan west

-15 -20

0

50

5 0 midspan east west

-5

100

150

200

250

-10

0

50

10

5

5

0

-10

midspan east west

50

100

150

-10

200

0

50

Deflection (mm)

10

5

Slip (mm)

Slip (mm)

10

0 midspan east west

0

150

200

f) CB6

20

-20

100

Deflection (mm)

e) CB5

-10

200

0 -5

east west

0

150

d) CB4

10

Slip (mm)

Slip (mm)

c) CB3

-5

100

Deflection (mm)

Deflection (mm)

0

midspan east west

-5

20

40

60

-10

0

Deflection (mm)

20

40

60

80

100

Axial displacement (mm) Fig. 9. Slip evolution during tests.

opposite values, due to the predominant effect of bending. For specimens CB1, CB3 and CB4 strain gauges on the steel section have shown that large inelastic strain were sustained by the bottom flange and the web of the beam (readings B1 and B2), while strain at the top flange (B3) has assumed a small elastic compressive strain. Instead, in beam CB2, all strain readings on the steel beam and the slab assume large inelastic values, clearly indicating yielding. On the other hand, bars in the last two specimens (CB5 and CB6) were not stressed in compression. In fact, the strain readings seem to have the same direction as those measured in the steel beam. This was expected, as these beams were subjected to very high axial tension loading. In both CB5 and CB6 specimens, the reinforcing bars were not yielded, as can be seen in Fig. 10e and f. Thus, the axial tensile load, which was applied to the steel section, was not wholly transferred to the reinforcement bars due to excessive concrete cracking and premature shear connection failure. It has to be noted that some strain gauges were detached at early stages of the tests, mainly due to severe cracking, and the corresponding measurements were interrupted (for example specimen CB5 in Fig. 10e). 4.4. Force-deformation curves The load versus deflection curve for beam CB1 is shown in Fig. 11a. The beam has reached a peak load value of 216 kN at a midspan deflection equal to 48 mm. After that point the curve softens until the ultimate deformation. The load-deformation curve indicates that the

behaviour of the composite beam is characterised by high ductility levels. Also plotted in Fig. 11a are the theoretical values of the plastic moment resistance based on Rigid Plastic Analysis with full shear connection (denoted as RPA FSC) and partial shear connection equal to 0.6 (denoted as PSC 0.6) as well as the ABAQUS analysis. The moment achieved experimentally is less than the moment resistance of the beam calculated by the RPA with full shear connection, and greater than the moment resistance calculated by the RPA with β = 0.6, which is the theoretical value for the experimental degree of shear connection. It is noteworthy that the experimental strength (221 kNm) is about 18% greater than the value given by RPA with β = 0.6 (180 kNm) using the experimental material yield stresses. This is mainly attributed to material strain-hardening effects, which are not taken into account by the sectional analysis. Experimental and theoretical normalised axial load versus axial displacement curves for the beam CB6 are shown in Fig. 11b together with the plastic axial resistance calculated based on the measured material strength. Note that the experimental curve plots the total stroke displacement against the total axial force in the steel beam and, thus, it doesn't capture any local flexibilities, as will be discussed later. The plastic axial resistance is calculated as the axial resistance of the steel beam alone (denoted as Nsteel in the diagram) and as the axial resistance of the steel beam and the reinforcement of the slab (denoted as Ncomposite), while the concrete strength in tension was neglected. The values of Nsteel and Ncomposite are 1315 kN and 1541 kN, respectively, while the experimental axial strength is

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b) CB2

250

400

200

300

Load (kN)

Load (kN)

a) CB1

150 100

B3 B2 B1

50 0 -5000

0

5000

C2 B3 B2 B1

200 100

10000

15000

0 -1

20000

0

300

250

250

200 150 C2 B3 B2 B1

100 50 0 -1

-0.5

0

0.5

1

Strain (x10e6)

1.5 x 10

200 150 C2 B3 B2 B1

100 50 0 -1

2

-0.5

4

0

0.5

1

Strain (x10e6)

1.5

2

x 10

4

f) CB6

e) CB5 40

20 C2 B3 B2 B1

10

0

2000

4000

6000

8000

Axial force (kN)

2000

30

Load (kN)

2 4

x 10

d) CB4

300

Load (kN)

Deflection (kN)

c) CB3

0

1

Strain (x10e6)

Strain (x10e6)

1500 1000 C2 B3 B2 B1

500 0

0

500

1000 1500 2000 2500 3000

Strain (x10e6)

Strain (x10e6) Fig. 10. Total load versus strain for all specimens.

1503 kN. The FEM model predicts an ultimate value of 1487 kN, which is 1% lower than the experimental one. Furthermore, it can be seen from the diagram that the actual yield point of the FEM curve lies on the onset of the steel beam resistance, Nsteel, and continues with a hardening behaviour up to the ultimate failure at 80 mm elongation, where the analysis has stopped due to convergence problems. Due to the high tensile loads acting in the composite beam, an elongation of the load application holes was caused, as shown in Fig. 12. This elongation caused a considerable deterioration of the initial axial stiffness, and partly explains the difference in stiffness between the experimental curve and the FEM prediction. 4.5. Interaction diagram The ultimate values of positive bending moment versus the corresponding axial tension loads achieved by all specimens in the tests are plotted in the interaction diagram of Fig. 13. The theoretical plastic capacities obtained by the ABAQUS model are also plotted on the same graph. From the available experimental data points it is observed that the moment capacity of the tested composite beams is slightly increased under the effects of low axial loads (beams CB3 and CB4 in Fig. 13), while it is considerably decreased when the axial load assumes large values (specimens CB2 and CB5). Although, more experimental data are probably needed in order to evaluate

the shape of the experimental interaction curve with acceptable reliability. The nonlinear finite element model developed herein will be used, after the assessment of its accuracy, to cover this gap and derive more precise and reliable interaction relationships. 4.6. Assessment of the FEM model The values of the experimental vertical load-midspan deflection curve are in good agreement with those obtained by the FEM model, both in terms of initial stiffness and ultimate strength, as shown in Fig. 11a. The FEM model predicts a plastic moment resistance equal to 214 kNm which is 3% lower compared to the experimental strength of 221 kNm. In addition, the model gives accurate estimations on the load level where concrete crushing and shear connection failure occur, as indicated in the same figure, where "conc. fail" and "SC fail" denote concrete crushing failure and shear connection failure, respectively. The discrepancy in initial stiffness of the axial load versus axial displacement curve (Fig. 11b) of specimen CB6 is explained by the undesirable elongation of the web holes that occurred during the testing of this specimen, as described in Section 4.4. However, the predicted ultimate axial resistances are in close agreement. The FEM model is also capable of predicting with acceptable accuracy the ultimate strength of composite beams when simultaneous

G. Vasdravellis et al. / Journal of Constructional Steel Research 72 (2012) 240–253

0

250

RPA FSC

M (kNm)

200

RPA PSC 0.6

150 100

TESTS FEM conc fail SC fail

50 0

0

50

100

150

Axial Force (kN)

a)

249

CB1

FEM CB4

Tests

-500

CB3 CB2

-1000 CB6

CB5

-1500 0

50

200

100

150

200

250

Moment (kNm)

Deflection (mm) Fig. 13. Bending moment-axial force interaction diagram resulting from the tests and the FEM model.

b)

Ncomposite 1500

N (kN)

Nsteel 1000

500

0

TEST FEM 0

20

40

60

80

Displacement (mm) Fig. 11. a) Load versus midspan deflection curve for specimen CB1 and b) axial load versus axial displacement for specimen CB6.

positive bending moment and axial tension act on the section. The experimental values are in good agreement with the FEM predictions except for the cases of specimens CB3 and CB4, where the experimental strength is considerably greater than the predicted value. However, the values pertaining to specimens CB1, CB2, CB5 and CB6 are in very close agreement with the predictions. The discrepancy between the FEM model and the test results for beams CB3 and CB4 can be attributed to the following reasons: a) possible variability in both material and geometrical properties is likely to be present even in nominally identical steel samples, as evidenced by inspection of Table 2 and reported in the work by Byfield and Nethercot [20]; thus a higher value of yield stress in combination with a probable early strain hardening of the material can cause an increase in the ultimate strength of a composite beam; and b) the calculation method of the ultimate experimental strength, which is based on the use of Eq. (1) and experimental observation. As mentioned earlier, this method makes an estimation of the amount of concrete that

contributes in compression, while it neglects the contribution of concrete in tension. The slip evolution at the beam ends and at the midspan is plotted for both the experimental beam and the ABAQUS model in Fig. 14. In general, the model prediction is in good agreement with the experimental values under the assumption that the asymmetric experimental behaviour was partly caused by the various uncertainty factors expected in an experimental procedure. Given the complexity of the loading and the unavoidable uncertainties related to an experimental process, it can be concluded that the FEM model developed herein is a reliable tool for the analysis of composite beams under combined actions. The developed model is used to conduct further parametric studies on steel-concrete composite beams and derive more accurate and reliable interaction relationships, as discussed within the following sections.

4.7. General remarks In general, all composite beams behaved well, exhibiting high ductility levels. In fact, no sudden collapse of any structural component has occurred, and failure was gradual during the tests. The two common failure modes for all specimens were the crushing of the slab and the shear connection failure, as can be seen by the strain and slip measurements, as well as the experimental observation. Due to the weak degree of shear connection, all specimens have experienced shear connection failure initiating from the ends of the beam and causing severe cracking of concrete at the region of the studs. The shear connection failure was more evident in the beams subjected to high axial loads. Specimens CB5 and CB6 had similar behaviour in terms of cracking and failure modes.

15

west midspan east FEM west FEM midspan FEM east

10

Slip (mm)

5 0 -5 -10 -15

0

50

100

150

200

250

Deflection (mm) Fig. 12. Elongation caused in the load application holes in the beam web.

Fig. 14. Comparison of slip evolution between the tests and the FEM model.

250

G. Vasdravellis et al. / Journal of Constructional Steel Research 72 (2012) 240–253

Concrete core

g, q w

g, q

w

[M] +

H

-

L

[N]

L

a) Structure and loading

b) Static system and internal force diagrams

Fig. 15. Schematic representation of the structural system considered as the design example.

Table 4 Parametric beam design details. Span (m)

Md (kNm)

Vd (kN)

beff (mm)

Beam section

Studs/spacing

Mpl (kNm)

Md/Mpl

Vd/Vpl

6 8 10 12 14 16

153 273 427 615 837 1094

102 136 171 205 239 273

1500 2000 2500 3000 3000 3000

IPE240 IPE300 IPE360 IPE400 IPE500 IPE600

24/260 32/258 42/243 58/210 68/208 90/179

204 318 478 690 932 1408

0.75 0.86 0.89 0.89 0.89 0.77

0.32 0.31 0.29 0.31 0.27 0.24

(UB254 × 102 × 28) (UB305 × 165 × 40) (UB356 × 171 × 57) (UB406 × 178 × 67) (UB457 × 191 × 98) (UB610 × 229 × 125)

5. Parametric studies and design models The finite element model is used for studying the interaction of sagging bending and axial tension on composite beams with various span lengths and, consequently, slab effective widths and steel beam sections. A realistic case study is considered in order to choose the composite beam sections. The design example is taken as a floor slab connected on a typical layout of simply-supported steel beams. In this example, positive (or sagging) bending moment is acting simultaneously with axial forces in the beam, when the beams are located at the leeward direction of a high-rise building. Fig. 15 shows a schematic representation of the static system, loading conditions, and internal force diagrams of the beam under study. The span lengths considered in the parametric study range from 6 m to 16 m with a step of 2 m. The distance between the main beams is taken as 3 m. It is assumed that the dead load of the floor (including the self weight of the 120 mm-thick slab) is DL=4.0kN/m2 and the live load is LL=5.0k N/m2. The Ultimate Limit State (ULS) static design load combination is assumed according to Eurocode 1 as qdes =1.35∗DL+1.5∗LL, giving a design load of 38.7 kN/m on each internal beam. Serviceability checks are neglected in the present example. The maximum (positive) moment in the midspan is equal to Mdes =0.125∗qdes ∗L2, while the design shear force is equal to Vdes =0.5∗qdes ∗L, where L is the span length. By varying the span length, the effective width of the slab is also affected, starting from 1.5 m for the 6 m span length and assuming a maximum value of 3 m [2]. A summary of the parametric beam designs is given in Table 4. For comparison reasons, the steel sections are given in both European shapes (IPE) and Universal Beam shapes (UB), although the IPE sections are used in the finite element analyses. Also reported in Table 5 are the ratio of the design shear force to the plastic shear resistance (Vd/Vpl), and the shear stud number and spacing needed to achieve a full shear connection degree employing 19 mm-diameter studs. It has to be noted that the design shear force is lower than the 50% of the plastic shear resistance of the steel section, which means that the shear-moment interaction effects can be neglected

in the design (plastic moment resistance is not reduced due to shear force effects), according to Eurocode 3 [21]. 5.1. Interaction diagram for composite beams with full shear connection The strength of the six parametric beams with full shear connection (FSC) was studied first using the FEM model developed in the present work. The strength of the nonlinear springs was calibrated in order to obtain a high degree of shear connection (β > 1.0) for all parametric beams, according to Eq. (3). The same loading procedure as the one used for the experimental beam was followed to apply simultaneous axial tension and positive bending moment in the composite beams. The failure criteria established in Section 3.3.5 were used to define whether the failure mode of the beam was concrete slab compressive crushing or shear connection failure. The resulting interaction diagrams are plotted in Fig. 16a for beams IPE240, IPE300 and IPE360, while Fig. 16b plots the results for beams IPE400, IPE500 and IPE600. The division into two groups was made for visualization purposes. It is evident that the interaction diagrams for all beams follow a comparable trend. A general conclusion is that the moment capacity is reduced with the increase in Table 5 Axial capacity values obtained by the FEM model and comparison with the steel section axial capacities. Beam

Nst (kN)

FEM β = 0.6

FEM06−Nst % Nst

FEM β = 0.8

FEM08−Nst % Nst

FEM FSC

FEM−Nst % Nst

IPE240 IPE300 IPE360 IPE400 IPE500 IPE600

919 1265 1709 1985 2714 3580

900 1255 1790 1882 2639 3800

98 99 105 96 97 106

975 1308 1851 1940 2772 4012

106 103 108 98 102 111

1020 1345 2000 2143 3012 4168

110 106 115 107 110 114

G. Vasdravellis et al. / Journal of Constructional Steel Research 72 (2012) 240–253

a) Moment-deflection curve

0 -200

600

-700 -1200

IPE240 IPE300 IPE360

-1700 -2200

0

100

200

300

400

500

500

Moment (kNm)

N (kN)

a)

400 300 200

600

0

0

100

200

300

400

Deflection (mm)

0

b) Axial Force-displacement curve 2500

-2000 -3000

IPE400 IPE500 IPE600

-4000 0

500

1000

Axial Force (kN)

-1000

N (kN)

FSC PSC (0.6) conc fail SC fail

100

M (kNm)

b)

251

2000 1500 1000

1500

0

M (kNm)

5.2. Interaction diagrams for composite beams with partial shear connection The parametric beams were analysed again using this time a lower degree of shear connection. Partial shear connection is often used in practice due to economy reasons or to increase ductility of a composite beam with a small compromise in the design resistance. The lowest degree of shear connection allowed to be used in buildings by the Eurocode 4 is 0.4. In the present analyses, the force of the nonlinear springs in the FEM model is calibrated in order to achieve degrees of shear connection β = 0.8 and β = 0.6 (Eq. (3)). The failure modes can be different in a composite beam with a low degree of shear connection. In fact, as can be seen in Fig. 17a, shear connection failure occurs prior to concrete compressive failure when a degree of shear connection equal to 0.6 is employed to connect the two parts. When the beam is subjected to pure axial tension, shear connection failure defines the axial composite capacity in the FEM model, and failure slip at the most severely loaded stud is observed earlier than the FSC case, as shown in Fig. 17b, thus limiting the axial capacity of the composite beam. Usually the most severely loaded stud is the one located at the edge of the beam, near the application point of the axial load. When subjected to combined tension and flexure, the failure mode depends on the percentage of axial force being applied and the degree of shear connection: as the amount of axial load introduced in the steel beam increases, the studs are already loaded to a certain slip level prior to beam bending, thus the failure mode could be the shear connection failure even if a relatively strong shear connection is used. However, to the extent that ultimate response is concerned and provided that ductile shear studs are used, plastic redistribution of the shear forces take place

20

40

60

80

100

Fig. 17. Load vs. deflection curves for full and partial shear connection of parametric beam IPE360.

across the shear span of the beam; this ensures a ductile ultimate response of a partially connected composite beam. This is also verified by the experimental section, which had a degree of shear connection equal to 0.6, although no sudden failures were observed. The shape of the interaction diagram is not affected significantly by the use of partial shear connection. Fig. 18 depicts the resulting interaction diagrams for the PSC cases. Similar to the FSC case, the moment capacity is reduced by increasing the tensile force acting on the steel beam section and a bilinear trend can also be assumed in the most of the cases. However, the reduction in the PSC case seems to

a)

0 -1000

N (kN)

axial tensile force acting in the steel beam section. The reduction in moment capacity seems to follow a bilinear trend. Initially, the moment capacity is reduced to a value equal to about 40 to 50% of the Mu when the applied force approaches the plastic axial capacity. After that point, the moment resistance reduces more abruptly until the pure axial tension resistance.

0

Displacement (mm)

-2000 -3000 -4000 0

500

1000

IPE240 IPE300 IPE360 IPE400 IPE500 IPE600 1500

M (kNm)

b)

0 -1000

N (kN)

Fig. 16. Moment–axial force interaction diagram for the parametric beams with full shear connection.

FSC PSC (0.6) SC fail

500

-2000 -3000 -4000 0

500

1000

IPE240 IPE300 IPE360 IPE400 IPE500 IPE600 1500

M (kNm) Fig. 18. Moment-axial force interaction diagram for the parametric beams with partial shear connection: a) β = 0.8 and b) β = 0.6.

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G. Vasdravellis et al. / Journal of Constructional Steel Research 72 (2012) 240–253

a)

1.2

0

n=N/Nu

N (kN)

1

-500

-1000 0

50

100

150

FSC PSC08 PSC06 200 250

0.8

IPE240 IPE300 IPE360 IPE400 IPE500 IPE600 DESIGN

0.6 0.4 0.2 0 0

0.2

0.4

b)

-1000

N (kN)

0.8

1

1.2

Fig. 21. Parametric beams data points and proposed design equation for composite beams with partial shear connection under sagging moment and axial tension (β = 0.8 case).

0

-2000 FSC PSC08 PSC06

-3000 -4000

0.6

m=M/Mu

M (kNm)

0

200

400

600

800

1000

M (kNm) Fig. 19. Comparison of interaction curves for different degrees of shear connection: a) IPE240 beam, b) IPE500 beam.

be less evident when low to moderate levels of axial tension are applied in the steel beam section. This is more obvious if the individual cases are plotted in the same graph, as in Fig. 19, where the cases of FSC and PSC for beams IPE240 and IPE500 are plotted. It is observed that the interaction diagrams are not parallel in all the cases, as someone could expect. Specifically, for the beam with β = 0.6, some of the interaction strength values are comparable to those of the β = 0.8 and FSC cases, although the pure bending and axial capacities are clearly the lowest of the cases considered. This could be explained if the failure modes are considered. In fact, when a weak shear connection is used, larger slip is permitted to take place and this reduces the compressive stresses in the slab, passing from compression failure mode to shear connection failure mode, which in turn result in different ultimate capacities. 5.3. Tensile plastic resistance of a composite beam In this study, it was assumed that the axial force acts on the steel beam only, which should be the realistic case in most of the cases in an actual structure. A part of the axial force is transferred to the concrete slab and in turn to the reinforcement through the shear connection. Although, severe cracking in the slab and shear connection failure limit the amount of axial load that can be transferred. In the experimental test, the axial capacity of the composite beam was increased by 8%

with respect to the axial capacity of the steel beam alone. This is about the half of the theoretical contribution of rebars to the plastic axial capacity. Furthermore, Table 5 gives a summary of the axial capacities achieved in the FEM analyses, and compares these values with the steel beam plastic axial resistance (Nsteel). The percentage difference between FEM and Nsteel is also outlined. From these values it is concluded that in the case of FSC a maximum increase of 15% is observed for the case of the IPE360 section. For the PSC cases the maximum difference is about −4% for β = 0.6, while all but one of the values are above 100% for the β = 0.8 case. This means that the composite beam reaches, in most of the cases, an axial capacity at least equal to the steel beam plastic axial resistance even for low degrees of shear connection. Thus, the axial capacity of a composite beam can be defined, with reasonable safety, as the axial capacity of the steel section alone. 5.4. Proposed design models for composite beams under combined positive bending and axial tension Based on the experimental results and the FEM parametric study, a simple design model for steel-concrete composite beams under combined sagging bending and axial tension is proposed in this section. For this purpose, the interaction data points resulting from the parametric study are plotted in non-dimensional form in Figs. 20, 21 and 22 for the FSC case and the β=0.8 and β=0.6 case, respectively. This is done by dividing the acting moments and axial forces by the corresponding plastic resistances of the sections. In the same graphs, the design equation is superimposed and denoted as “DESIGN”. In order to provide for a conservative design method, the slight change in the slope of the moment reduction is not taken into account and the design formula is common for composite beams with full and partial shear connection. The following equation is proposed for the interaction of positive bending moment and axial tension in a composite beam: M N þ 0:6 ¼ 1:0 MU NU

ð5Þ

where Mu is the plastic resistance of a composite beam to bending, according to structural code provisions (including the associated safety

1.2 1 IPE240 IPE300 IPE360 IPE400 IPE500 IPE600 DESIGN

0.6 0.4 0.2 0

n=N/Nu

n=N/Nu

1 0.8

0

0.2

0.8 IPE240 IPE300 IPE360 IPE400 IPE500 IPE600 DESIGN

0.6 0.4 0.2

0.4

0.6

0.8

1

1.2

m=M/Mu Fig. 20. Parametric beams data points and proposed design equation for composite beams with full shear connection under sagging moment and axial tension.

0

0

0.2

0.4

0.6

0.8

1

1.2

m=M/Mu Fig. 22. Parametric beams data points and proposed design equation for composite beams with partial shear connection under sagging moment and axial tension (β = 0.6 case).

G. Vasdravellis et al. / Journal of Constructional Steel Research 72 (2012) 240–253

factors for materials), and Nu is the plastic resistance of the steel section to axial tensile loading, e.g. the steel reinforcement in the slab is neglected under an axial force acting in the steel section. According to this equation, the moment capacity of a composite section is reduced linearly until the 40% of the Mu by increasing the axial tensile force acting on the steel section. It has to be pointed out, however, that in practice it is very rare for a beam to be subjected to tensile axial forces greater than the 30 to 40% of its axial capacity, although it was judged as necessary to study the whole range of axial force percentages in order to complete the interaction diagram and have a full picture on the behaviour of composite beams under combined actions. 6. Conclusions and further research This paper presented the results of an extensive experimental and numerical investigation that was carried out to study the effects of axial tension on the sagging moment regions of steel-concrete composite beams. The experiments permitted the construction of an interaction diagram located in the fourth quadrant of the complete moment-axial load interaction plot. The three-dimensional finite element model presented herein was proved to be capable of predicting the nonlinear response of the composite section up to the ultimate load and to capture well the failure modes and the slip distribution in the steel-concrete interface. The model was used to extend the experimental results to a number of beam sections used in engineering practice and the resulting interaction diagrams verified the shape of the curve obtained by the experiments. The main conclusion is that the moment capacity of a composite beam is reduced under the presence of an axial tensile force acting in the steel beam section. In addition, the analyses demonstrated that the axial tensile force that the composite section can sustain is limited by concrete cracking and premature shear connection failure and for this reason the design axial tensile resistance should be taken equal to the plastic axial capacity of the steel beam alone. Partial shear connection, which is often used in practice, does not change the shape of the interaction diagram considerably. Based on the experimental results and the finite element analyses, a simplified equation is proposed for the design of composite beams subjected to positive bending and axial tension. It should be emphasised, however, that more experimental data is needed in order to fully understand the behaviour of composite beams under generalised loading and to establish safe and reliable design equations and analytical solutions.

253

Acknowledgements The experimental research presented in this paper was funded by the Australian Research Council (ARC) Discovery Project DP0879734. The authors would also like to thank Dr. Mithra Fernando and all the technical staff of the Structures Laboratory at University of Western Sydney for their valuable assistance with the experimental work. References [1] Banfi M. Composite beams with web openings subject to axial load. EUROSTEEL 2008, 3-5 September, Graz, Austria; 2008 p. 339–44. [2] Eurocode 4. Design of composite steel and concrete structures. London (UK): British Standards Institution; 2004. [3] Standards Australia. Composite structures Part 1: simply supported beams. AS 2327.1-2004. Sydney (Australia); 2004. [4] ANSI/AISC 360-05. Specification for structural steel buildings. Chicago (IL, USA): American Institute of Steel Construction; 2005. [5] Chapman JC, Balakrishnan S. Experiments on composite beams. Struct Eng 1964;42(11):369–83. [6] Ansourian P. Experiments on continuous composite beams. Proc Inst Civ Engr Part 2 1982;73(1):26–51. [7] Nie J, Fan J, Cai CS. Experimental study of partially shear connected composite beams with profiled sheeting. Eng Struct 2008;30(1):1–12. [8] Uy B, Bradford MA. Cross-sectional deformation of prestressed composite tee-beams. Struct Eng Rev 1993;5(1):63–70. [9] Uy B. Long term behaviour of composite steel-concrete beams prestressed with high strength steel tendons. Advances in Steel Structures (ICASS '96); 1996. p. 419–24. [10] Nie J, Tang L, Cai CS. Performance of steel-concrete composite beams under combined bending and torsion. J Struct Eng 2009;135(9):1048–57. [11] Tan EL, Uy B. Experimental study on straight composite beams subjected to combined flexure and torsion. J Constr Steel Res 2009;65(4):784–93. [12] Tan EL, Uy B. Experimental study on curved composite beams subjected to combined flexure and torsion. J Constr Steel Res 2009;65(8–9):1855–63. [13] Baskar K, Shanmugam NE. Steel-concrete composite plate girders subject to combined shear and bending. J Constr Steel Res 2003;59(4):531–57. [14] Elghazouli AY, Treadway J. Inelastic behaviour of composite members under combined bending and axial loading. J Constr Steel Res 2008;64(9):1008–19. [15] Uy B, Tuem HS. Behaviour and design of composite steel-concrete beams under combined actions. Eighth International Conference on Steel–Concrete Composite and Hybrid Structures (ICSCCS 2006), Harbin, China; 2006. p. 286–91. [16] Vasdravellis G, Uy B, Tan EL, Kirkland B. The effects of axial tension on the hogging moment regions of composite beams. J Constr Steel Res 2012;68(1):20–33. [17] ABAQUS. User's manual, version 6.9. Pawtucket, RI: Karlsson & Sorenson; 2005. [18] Deric JO, Bradford MA. Elementary behaviour of composite steel and concrete structural members. Oxford: Butterworth-Heinemann; 1999. [19] Carreira DJ, Chu KH. Stress–strain relationship for plain concrete in compression. ACI J Proc 1985;82(11):797–804. [20] Byfield MP, Nethercot DA. Material and geometric properties of structural steel for use in design. Struct Eng 1997;75(21):363–7. [21] Eurocode 3. Design of steel structures. London (UK): British Standards Institution; 2005.