Behaviour and design of composite beams subjected to sagging bending and axial compression

Journal of Constructional Steel Research 110 (2015) 29–39

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Journal of Constructional Steel Research

Behaviour and design of composite beams subjected to sagging bending and axial compression G. Vasdravellis a,⁎, B. Uy b, E.L. Tan c, B. Kirkland b a b c

Institute for Infrastructure and Environment, Heriot-Watt University, United Kingdom Centre for Infrastructure Engineering and Safety, University of New South Wales, Australia Institute for Infrastructure Engineering, University of Western Sydney, Australia

a r t i c l e

i n f o

Article history: Received 28 May 2014 Accepted 16 March 2015 Available online xxxx Keywords: Steel–concrete composite beam Finite element analyses Combined loading Experiments Design

a b s t r a c t This paper presents an experimental and numerical study on the ultimate strength of steel–concrete composite beams subjected to the combined effects of sagging (or positive) bending and axial compression. Six full-scale composite beams were tested experimentally under sagging bending and increasing levels of axial compression. A nonlinear finite element model was also developed and found to be capable of accurately predicting the nonlinear response and the combined strength of the tested composite beams. The numerical model was then used to carry out a series of parametric analyses on a range of composite sections commonly used in practice. It was found that the sagging moment resistance of a composite beam is not reduced under low-to-moderate axial compression, while it significantly deteriorates under high axial compression. Sectional rigid plastic analyses confirmed the experimental results. The moment–axial force interaction does not change significantly between full and partial shear connection. Based on the experimental and numerical results, a sagging moment–axial compression interaction law is proposed which will allow for a more efficient design of composite beams. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction Steel–concrete composite construction is a very efficient structural method for framed buildings, bridges, and stadia, due to several wellestablished advantages that it provides compared to other structural types. The optimal combination of the individual properties of structural steel and concrete, results in structures that are safe, robust, and economic. Steel–concrete composite beams are an ideal solution for building floors or bridge decks due to the increased speed of construction and flexibility that they offer. Moreover, the restraining effect of the concrete slab provides increased resistance to global (out-ofplane) instability failure modes, which are common in non-restrained steel beams. Steel–concrete composite beams are increasingly being used in situations where they can be subjected to the simultaneous actions of flexure (sagging or hogging bending moments) and axial forces (tensile or compressive). Some representative examples include: a) diaphragmatic forces due to lateral (wind or seismic) loading on composite floor beams; b) high-rise frames where the effects of wind or seismic loading may impose large axial forces to the beams of the building; c) structures where inclined members are used, e.g. stadia beams or inclined parking ramp approaches; and d) cable stayed bridges, where the inclined ⁎ Corresponding author. E-mail address: [email protected] (G. Vasdravellis).

http://dx.doi.org/10.1016/j.jcsr.2015.03.010 0143-974X/© 2015 Elsevier Ltd. All rights reserved.

cables and traffic loads may introduce large axial forces to the supporting composite deck [1]. The current structural provisions for composite construction, e.g. AISC 360-10 [2], AS2327.1 [3] and Eurocode 4 [4], do not provide a unified method for the design of composite beams under combined actions; instead, they refer the designer to rules established for bare steel sections. However, the behaviour of a composite beam differs substantially from that of a bare steel section; therefore, the moment–axial load interaction in composite beams deserves further investigation. Despite the large amount of available experimental data on the flexural behaviour of composite beams (see for example [5–7]), experimental data on the behaviour of composite beams under combined loading is limited. The combined effects of bending and shear force in composite beams were studied experimentally by Nie et al. [8], and numerically, using the finite element method (FEM), by Liang et al. [9,10]. The authors recently studied the shear strength and moment–shear interaction in compact composite beams using experimental tests supplemented by parametric numerical analyses [11]. In that study, the high degree of conservatism in current structural codes is highlighted, and design models for the shear strength and moment–shear interaction are proposed. The performance of composite beams under combined bending and torsion was studied by Nie et al. [12] through experiments on eleven steel–concrete composite beams. The effect of torsion on straight and curved beams was also studied by Tan and Uy [13,14]. Their research provided experimental data for the effects of torsion on

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composite beams with both full and partial shear connection. Based on the tests, design equations for ultimate limit analysis of composite beams are proposed. This paper presents an experimental and numerical study on the ultimate strength of steel–concrete composite beams subjected to the simultaneous actions of sagging bending and axial compression. This study is the last part of a larger research project aiming to evaluate the axial force–moment interaction response of composite beams under all combinations of axial compression or tension and sagging or hogging bending moments. Previous studies by the authors investigated the behaviour and design of composite beams under tension and hogging bending [15], tension and sagging bending [16], and compression and hogging bending [17]. The experimental interaction curves resulting from those studies are summarised in Fig. 1 along with the interaction curves obtained by numerical analyses using the FEM. The quadrant that is studied in this paper is specified in the same figure. The results of six full-scale tests on composite beams under sagging bending and various levels of axial compression are presented first. Details of a nonlinear FEM model that was developed and validated against the experimental results are given next. The model was found to be capable of predicting the nonlinear response and the ultimate failure modes of the tested beams with reasonable accuracy. The developed numerical model was further used to carry out a series of parametric analyses on a range of composite sections commonly used in practice. It was found that the sagging moment resistance of a composite beam is not reduced when a low-to-moderate axial compression acts on the section, while it significantly deteriorates when the axial compression is high. The sagging moment–axial compression interaction diagram does not change when the minimum, according to EC4, partial shear connection is used. Based on the experimental and numerical results a simple design model is proposed for use in practice. 2. Experimental programme 2.1. Test specimens Six full-scale composite beams were designed and tested. The tested beams are denoted as CB1 to CB6. Specimens CB1 and CB6 were tested under pure sagging bending and pure axial compression, respectively, while specimens CB2 to CB5 were tested under combined sagging bending and progressively increasing levels of axial compression. The relevant geometry and details of the specimens are shown in Fig. 2. All specimens were constructed with a 600 mm wide and 120 mm deep concrete slab connected to an UB203x133x30 steel beam section (equivalent to an IPE270 or W40 profile). The composite action was achieved by welding 19 mm-diameter, 100 mm-long headed shear This study

Axial force (kN)

2000

1000 M- and Compression

0

M- and Tension

M+ and Compression M+ and Tension

-1000 Tests FEM

-2000

-200

-100

0

100

200

300

Moment (kNm) Fig. 1. Complete moment–axial force interaction diagram resulting from tests and FEM analyses.

stud connectors in a single line along the centre of the top flange of the steel beam. The number of shear studs was calculated in order to achieve partial shear connection between the slab and the beam. The degree of shear connection (β) achieved is 0.5 if the nominal value of the strength of a shear stud is used, and 0.6 if the actual strength resulting from the pushout tests (described later) is used. A group of three studs was welded near the supports to transfer the longitudinal shear without premature shear failure in the cases where high axial compression was applied. Longitudinal and transverse reinforcement was also placed in the concrete slab in the arrangement shown in Fig. 2. Two 10 mm-thick web stiffeners were welded to the beam web at the point of the axial load application to prevent premature buckling due to the concentrated load. 2.2. Material property tests Concrete and steel material property tests were performed to obtain the actual strength of the materials. Concrete tests consisted of standard cylinder compressive tests and flexural splitting tests. The latter aimed to determine the flexural tensile strength of the concrete. 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 Tables 1 and 2. Tensile tests were conducted on coupons cut out from the flanges and web of the steel beams as well as the reinforcing bars. The values obtained from the tests for the 0.2% proof stress, tensile stress (i.e. maximum nominal stress), and Young's modulus are reported in Table 3. The load–slip behaviour of the shear studs was evaluated by conducting three push-out tests according to the Eurocode 4 procedure [4]. The push-out specimens were constructed using concrete from the same batches as the one used to form the steel–concrete composite beams in the main experimental programme. The resulting load–slip curves showed that the average strength of one shear stud is about 108 kN, the average maximum slip is 14.1 mm, and the average slip at maximum load is 10.1 mm. 2.3. Experimental setup The experimental setup is shown in Fig. 2. The composite beams were simply supported at the two ends and a combination of hydraulic actuators was used to apply simultaneous sagging bending and axial compression to the composite beam specimens. The free span of the beams was 4000 mm for CB1 and 4950 mm for the rest of the tests, as indicated in Fig. 2. The vertical load was applied at the midspan using a 1000 kN — capacity hydraulic actuator with a stroke of 250 mm. The axial compression was applied using four 800 kN — capacity hydraulic actuators placed horizontally and in parallel, imposing a controlled displacement at the one end of the beam, while the other end was restrained in the horizontal direction. This system was capable of applying a maximum 3200 kN axial load, and the stroke was 200 mm. In specimens CB2 and CB3, the axial load was applied to the beam through a plate welded to the steel beam section. Thus, the load was transferred to the composite section via the shear connectors. However, this setup resulted in premature failure of the (already weak) shear connection, and, therefore, in beams CB4, CB5, and CB6 the axial compression was transferred to the composite beam section using a triangular spreader plate of height equal to the composite section, as schematically shown in Fig. 2. In this way, the loaded area was the area of the steel beam plus a portion of the slab area equal to the width of the spreader plate times the depth of the slab. 2.4. Instrumentation A set of linear variable differential transformers (LVDTs), load cells, and strain gauges was used to monitor the experimental behaviour of the beams, as shown in Fig. 2. LVDTs were placed at the midspan and

G. Vasdravellis et al. / Journal of Constructional Steel Research 110 (2015) 29–39

31

“East”

“West”

Fig. 2. Geometric details, test setup and instrumentation of the testing procedure.

at the quarter points of each tested beam, measuring vertical deflections. The steel beam–concrete slab interface slip was also recorded using LVDTs appropriately placed at the ends, quarter points and midpoint of each tested beam. The applied vertical and horizontal loads were measured by load cells positioned between the hydraulic actuators and the specimen. Strain gauges were used to measure the development of strains in the steel beam and reinforcing bars. Strain gauges were located in sets of seven through each cross-section with one set at midspan and one set at each quarter point.

2.5. Test procedure The beam CB1 was loaded in pure sagging bending and, hence, it was only subjected to a vertical load. In specimens CB2 to CB5, the vertical load was applied in incremental steps of 10% of the theoretical design strength of the composite section. To obtain different levels of axial compression, the increments of applied axial load were varied. Both loads were increased until failure of specimen was reached. Beam CB6 was tested in pure axial compression and only the axial loading rig was used to apply the load. In this test, the vertical actuator was positioned in contact with the top side of the slab in order to prevent the development of second-order bending at the midspan. The ultimate Table 1 Material test results for concrete in compression.

bending moment achieved in each tested beam was calculated taking into account the equilibrium of the external forces acting on it. 3. Theoretical analysis 3.1. Rigid plastic analysis Sectional rigid plastic analysis (RPA) was used as a simplified tool to predict the combined strength of the composite beams. Fig. 3a shows the assumed stress distribution throughout the composite section for the case of pure sagging bending. When an axial force is present, the location of the plastic neutral axis is varied along the height of the section. The resulting sagging bending moment and axial compression are then calculated taking as centre of rotation the plastic centroid of the composite section, as shown in Fig. 3b. For comparison purposes with the experimental values, no partial safety factors were assumed and the average material strength resulting from the material tests was used in the calculation of the internal forces. 3.2. Finite element model The FEM model that was used to simulate the tests of the composite beams under sagging bending and axial compression is based on the Table 2 Material test results for concrete in tension.

Age at testing (days)

Compressive strength (N/mm2)

Age at testing (days)

Tensile strength (N/mm2)

7 14 21 28 38

12 17 21 24 23

31 34 38 41 45

3.65 4.07 3.33 3.86 3.93

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Table 3 Material test results for steel. Coupon

Sample no.

0.2% proof stress (N/mm2)

Tensile strength (N/mm2)

Modulus of elasticity (×103 N/mm2)

Flange

1 2 3 4 Average 1 2 3 4 Average 1 2 3 Average

362 370 371 361 366 369 383 379 378 377 571 518 516 535

537 538 545 536 539 545 549 544 546 546 665 618 631 638

203 223 208 217 213 211 216 207 203 209 202 192 202 199

Web

Reinforcement

basic assumptions used in the numerical analyses described in [16], where a FEM model was developed for the modelling of composite beams under sagging bending and axial tension. The FEM model was modified to account for axial compression, and the main features and modelling characteristics are presented in the following sections. The model relies on the use of the commercial software Abaqus [19]. 3.2.1. 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 modelled using eight-node solid elements with incompatible modes, namely C3D8I. The reinforcing bars were modelled as 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 to the plane of symmetry. An overview of the mesh and a schematic representation of the various modelling assumptions are depicted in Fig. 4. 3.2.2. Interactions To model the reinforcement in the slab the embedded element technique was used. 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,

Fig. 4. Details of the finite element mesh used for modelling the composite beams.

it is assumed that a perfect bond exists between the reinforcing bars and the surrounding concrete. A contact interaction was applied in 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 was used while the “hard” contact without friction was specified as the contact property. 3.2.3. Material properties The stress–strain relations obtained from material tests were used to model the steel material for the beam and the reinforcing bars. A plastic material with isotropic hardening law was used as the constitutive law for all the steel parts of the model. Fig. 5a and b shows the true stress versus logarithmic strain laws used (as required by Abaqus). The concrete material stress–strain relationship was calibrated according to the values obtained from the concrete cylinder and flexural splitting tests. The stress–strain curve for compression follows the formula proposed by Carreira and Chu [20], while the tensile behaviour is assumed to be linear up to the uniaxial tensile stress provided by the material test. The adopted stress–strain law is plotted in Fig. 5c. The post-failure behaviour is modelled using the tension-stiffening option and by determining a linear relation until stress is zero at a strain value of 0.05. This value is used to avoid numerical problems in the computational procedure while accuracy is not affected considerably. The damaged plasticity model was used to model the concrete behaviour. The shear connectors were modelled as spring elements. The nonlinear spring element SPRING2 was employed to connect a beam flange node with a slab node at the interface at the same positions where the shear connectors were welded to the specimen, as schematically shown in Fig. 4. The force slip law for the spring element was derived from the push-out tests on the 19 mm-diameter shear connectors. A piecewise linear curve was fitted to the experimental curve and defined as the force–slip law for the springs, as shown in Fig. 5d. 3.2.4. Loading and solution method The vertical load was applied as an imposed displacement on the top of the beam flange, 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, as in the experimental procedure.

Fig. 3. Stress distribution according to RPA: a) pure sagging bending; and b) assumed stress distribution resulting to axial compression and sagging moment in the section (PNA = plastic neutral axis).

3.2.5. Failure criteria Failure of the composite beams during the FEM analyses was identified by establishing specific failure criteria corresponding to the ultimate strength of the various section components. In particular, failure of the composite beam in the simulation was identified by one of the following situations: a) concrete crushing; b) shear connection failure; and

G. Vasdravellis et al. / Journal of Constructional Steel Research 110 (2015) 29–39

b) Reinforcement steel 800

800

True stress (MPa)

True stress (MPa)

a) Structural steel 600 400 200 0 0

33

0.1

600 400 200 0

0.2

0

0.05

Log strain

0.1

Log strain

d) Shear stud force – slip law

c) Concrete

120

Load per stud (kN)

Stress (MPa)

10 0 -10 -20 -30 -20

-10

0

10

100 80 60 40 SPRING PUSH TESTS

20 00

Strain (x10e3)

2

4

6

8

10

12

14

Slip (mm)

Fig. 5. Material stress–strain laws adopted in the finite element model.

c) buckling (local or global) of the steel section in the cases of high axial compression. Concrete crushing was defined when the principal compressive strain at a point reached the crushing strain, equal to 0.004. Shear connection failure was defined when the recorded slip at a shear connector reached a value of 6 mm [21]. Buckling of steel components can be explicitly captured in Abaqus, and therefore it was identified from the deformed shape of the model.

4. Results and discussion 4.1. Observations and failure modes A summary of the main failure modes and ultimate strengths of the tested composite beams is presented in Table 4. The experimental pure sagging moment and axial compression capacities are denoted as Mu and Nu, respectively. The axial compression levels applied to specimens CB2, CB3, CB4 and CB5 are equal to 11, 28, 52, and 84% Nu, respectively. Three failure modes were observed during the tests, depending on the level of the applied axial compression, i.e., ductile failure, shear connection failure, and local buckling of the steel beam's flange and web. Ductile failure consisted of gradual concrete crushing taking place in the slab and large tensile stresses developing in the steel beam. Shear connection failure was identified by the recorded slip at the slab–steel beam interface and the formation of large cracks throughout the slab

at the locations of the failed shear studs. Local buckling was associated with the application of high axial compression. Fig. 6 shows typical failure modes observed during the tests. CB1 experienced a ductile failure mode, as shown in Fig. 6a. A maximum slip of 16 mm recorded at the specimen's east end indicates that shear connection failure also occurred as a result of the weak supplied shear connection. The beam ultimately failed due to concrete crushing and cracking at the midspan and the response was characterized by high ductility. Specimens CB2 and CB3 were subjected to axial compression loads equal to 229 kN (11% Nu) and 593 kN (28% Nu), respectively (see Table 4). The dominant failure mode of both specimens was the shear connection failure. The maximum recorded slips were 40 mm at the west end (Fig. 2) of CB2 end 26 mm at the east end of CB3. Fig. 6b shows that large cracks were formed throughout the slab at the positions of the shear stud failures and the loss of shear connection resulted in the slab uplifting and separating from the steel beam at large imposed deformations. The shear connection failure was sudden in these beams and propagated very fast through the shear span. Specimen CB4 was subjected to moderate bending moment and an axial load approximately half of the section's axial capacity. CB4 experienced shear connection failure but this was not premature to reaching the strength predicted by the RPA. This behaviour will be further discussed later. The LVDT at the east end measured an end slip equal to 27 mm. The ultimate moment was calculated as 243 kNm with an axial load equal to 1105 kN (52% Nu).

Table 4 Failure modes and experimental ultimate strengths of composite beams. Specimen

Loading

Failure mode

Moment at failure (kNm)

Axial force (kN)

CB1 CB2 CB3 CB4 CB5 CB6

Pure positive bending Positive bending axial compression Positive bending axial compression Positive bending axial compression Positive bending axial compression Axial compression only

Ductile Shear connection failure Shear connection failure Crushing/ductile Local buckling Local buckling

222 (Mu) 190 (−14% Mu) 175 (−20% Mu) 242 (+10% Mu) 125 (−43% Mu) 41 (−81% Mu)

0 229 (11% Nu) 593 (28% Nu) 1105 (52% Nu) 1791 (84% Nu) 2144 (Nu)

Mu: Positive moment resistance; Nu: Pure compression strength.

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G. Vasdravellis et al. / Journal of Constructional Steel Research 110 (2015) 29–39

a)

b)

c)

d)

Fig. 6. Typical failure modes of the specimens: a) crushing of slab of specimen CB1; b) shear connection failure (CB2); c) local buckling (CB5); and d) concrete crushing at the axial load application region (CB6).

The loading of specimen CB5 resulted in very high axial compression. The LVDTs recorded 22 mm of slip at the east end. The ultimate midspan moment was calculated as 126 kNm and the axial load was 1790 kN (84% Nu). Local buckling of the bottom and top flanges at the eastern quarter was also observed and is shown in Fig. 6c. The concrete crushing and cracking at the east end of the beam where the triangular plates restricted the end slip is shown in Fig. 6d. Specimen CB6 was subjected to pure axial compression. The vertical actuator was placed as a fixed point to measure the midspan reaction. Based on the measured reaction at the midspan, the ultimate midspan moment was calculated as 41 kNm with an axial compression equal to 2144 kN. The specimen failed due to local buckling of the bottom flange at the eastern quarter similar to specimen CB5 and showed comparable concrete crushing and cracking modes as shown in Fig. 7c and d. 4.2. Force–deformation behaviour Fig. 7a shows the moment versus midspan deflection response of specimen CB1 along with the numerical response predicted by the FEM model. The beam has sustained a vertical load equal to 215 kN, ultimate moment 215 kNm, and the ultimate deflection is 197 mm. The force deformation response shows that the ductility of beam CB1 is very high, reaching a value of 8 (defined as δu / δy, where δu is the ultimate deflection and δy is the deflection at first yield). The moment achieved experimentally is less than the moment resistance of the beam calculated by the RPA assuming full shear connection (FSC), and greater than the moment resistance calculated by the RPA using β = 0.6, which is the theoretical value of the experimental degree of shear connection. The experimental strength (215 kNm) is about 19% greater than the value given by RPA with β = 0.6 (180 kNm) using the experimental material yield stresses. This is attributed to material strainhardening behaviour which is not taken into account by the RPA.

Experimental and numerical axial compression versus axial displacement curves for the beam CB6 are plotted in Fig. 7b. The experimental curve shows the total stroke displacement as recorded by the actuator against the total axial force in the steel beam and, hence, it does not include any possible local flexibilities or minor local yielding effects. For this reason, the initial stiffness of the experimental curve is significantly smaller than the numerical one. The ultimate axial compressive strength of CB6 is 2144 kN, considerably larger than the 1370 kN axial capacity of the steel profile, based on the actual material values.

4.3. Interaction diagram Fig. 8 shows the sagging moment versus axial compression interaction diagram obtained from the experimental results along with the results obtained using the RPA. RPA was performed according to the procedure described in Section 3.1 for both FSC and PSC with β = 0.6, i.e. as in the experimental beams. The experimental moment capacities of beams CB2 and CB3 are significantly reduced with respect to CB1. The moment reduction is 14% for CB2 and 20% for CB3 with respect to Mu (Table 4). These two beams experienced early shear connection failure, which propagated fast through the entire shear span (Fig. 6b). The additional plates added to specimens CB4 and CB5 limited the slip at the load application point and, therefore, resulted in an increased strength with respect to that of CB2 and 3. As shown in Fig. 8 and Table 4, CB4 reached an ultimate moment capacity 10% higher than that of CB1 reaching the value predicted by the RPA for FSC. The moment capacity of CB5 is reduced by 43% to the pure moment capacity due to the high axial compression that resulted in buckling failure. The combined strengths of beams CB5 and CB6 are in close agreement with the RPA for PSC, as shown in Fig. 8.

G. Vasdravellis et al. / Journal of Constructional Steel Research 110 (2015) 29–39

4.4. FEM model validation

250

Force (kN)

200 150 100

Test CB1

50

FEM 0 0

100

200

Midspan deflection (mm)

Axial compression (kN)

b)

2500 2000 1500 1000

0

a)

Test

500

The ability of the FEM model to accurately predict the combined strength of a composite beam is evaluated by simulating the experimental tests. The cases of pure sagging bending and pure axial compression are first simulated followed by the combined loading cases. Fig. 7a shows that the FEM model is in very good agreement with the experimental force–deflection response of specimen CB1, both in terms of initial stiffness and ultimate moment capacity. The stiffness and sagging moment strength predicted by the model are 7.05 kN/mm and 211 kNm, respectively, which are very close to the experimental values of 6.8 kN/mm and 215 kNm. The model predicts with reasonable accuracy the axial compressive strength of the composite section; the predicted axial compressive strength is 2114 kN, which is about 4% lower than the experimental one (2144 kN). The difference in initial stiffness is due to the reasons associated with the internal flexibility of the loading system, as mentioned previously. Fig. 9a shows the experimental interaction data points and the results of the FEM analyses for two cases: a) the axial load applied to the steel beam section only (denoted as Case 1); and b) the axial load applied both to the steel section and the portion of the slab above the steel section (denoted as Case 2). The first case simulates the experimental loading of specimens CB2 and 3 and the second one the experimental loading of specimens CB4 to 6, where the additional plates were included. Inspection of the results reveals that the experimental strengths of specimens CB2 and CB3 are close to the first numerical

3000

FEM 0

10

20

30

40

Axial displacement (mm) Fig. 7. a) Moment versus midspan deflection response of CB1; and b) axial compression versus axial displacement response of CB6.

From the experimental interaction data points it is concluded that: a) composite beams with weak shear connection have significantly reduced ultimate moment capacity due to early and fast-propagating fracture of the shear studs; and b) application of high axial compressive force in the form of a ‘column’ can delay the early shear connection failure and result in an increased sagging moment strength under a moderate applied axial compression. Since the data from the experiments is limited, a numerical analysis using the developed FEM model is conducted in this study to further clarify the behaviour and ultimate combined strength of composite beams under sagging bending and axial compression.

Axial compression (kN)

a)

2000

CB5 CB4

1000

CB3 CB2 0

b)

0

Tests FEM N to steel FEM N to S+C

1

5

CB5 CB4

0.5 4

1000

CB3 CB2

3 2

100

0

1

0 0

300

1.5

N/Nu

2000

CB1

100 200 Moment (kNm)

CB6

Tests RPA FSC RPA PSC

6

Tests FEM N to steel FEM N to S+C

CB6

3000

Axial compression (kN)

35

200

300

CB1 0

0.5

1

1.5

M/Mu

Moment (kNm) Fig. 8. Comparison of tests results with RPA.

Fig. 9. Sagging moment–axial compression interaction diagrams resulting from the tests and the FEM analysis: a) actual values; and b) non-dimensional form.

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G. Vasdravellis et al. / Journal of Constructional Steel Research 110 (2015) 29–39

a) Case 1-FSC

simulation case, whereas the combined strengths of CB4, CB5, and CB6 agree with the numerical curve resulting from the second case. Fig. 9b shows the interaction results in a non-dimensional form, i.e. the moment is divided by Mu and the axial force by Nu. The non-dimensional plots show that: a) the moment capacity is not reduced for values of axial compression less than approximately 30% Nu when the axial load is applied only to the steel section (Case 1); and b) the moment capacity is slightly increased for applied axial compression less than approximately 40% Nu when the axial load is applied to both the steel section and the slab (Case 2). The results are in agreement with the RPA analyses. The FEM model is considered as reliable since it is in good agreement with the experimental observations and, thus, it is further used to generalise the results of this study to a wider range of composite sections.

Axial compression (kN)

6000

IPE300 IPE360 IPE400 IPE450 IPE500 IPE550 IPE600

4000

2000

0

0

1000

2000

3000

Moment (kNm)

5. Parametric study

b) Case 1-PSC

5.1. Parametric beam designs

Axial compression (kN)

6000

The design example chosen incorporated a steel–concrete composite building consisting of a reinforced concrete core and a composite steel frame, as shown in Figs. 1 and 11. In such a structural system, seismic or wind loading can produce high axial compression to the composite beams that are bearing to the concrete core. Thus, a design situation of combined compression and sagging bending may arise in the case of simply supported composite beams. The composite beams of the prototype building are designed according to Eurocode 4 provisions [4]. A 120 mm slab is assumed to act compositely with the steel sections. The main parameter that affects the design is the span length of the composite beams and, accordingly, the effective width of the slab. Assuming office/commercial use [18], the dead load of the structure is DL = 4.0 kN/m2 and the live load is LL = 5.0 kN/m2. The ultimate limit state design load combination is taken according to Eurocode 1 [18] as 1.35 ∗ DL + 1.5 ∗ LL. For the parametric study, the span length L values range from 6 to 15 m. The effective width of the slab, beff (defined according to Eurocode 4 [4]) ranges from 1.5 to 3 m. A summary of the parametric beam designs is given in Table 5. For comparison reasons, the steel sections are given in both European shapes (IPE) and Universal Beam (UB) designations, but IPE sections are used in the FEM analyses. (See Fig. 10.)

4000

2000

0

0

1000

2000

3000

Moment (kNm) Fig. 11. Sagging moment–axial compression interaction for: a) Case 1-FSC; and b) Case 1-PSC.

interaction curve. Then, each beam was subjected to sagging bending moment using an imposed displacement at the midspan and various levels of axial compression, ranging from 10% to 80% of the ultimate axial strength of the steel section. The compressive load was applied to the composite beam according to the two cases described previously, i.e. axial load applied to the steel section only (Case 1), and axial load to the steel section and part of the concrete slab (Case 2). Both FSC and PSC with β = 0.5 were considered. Thus, four analysis results are presented and denoted as: Case 1-FSC; Case 1-PSC; Case 2-FSC; and Case 2-PSC.

5.2. Interaction diagrams The parametric beams were first subjected to pure sagging moment and pure axial compression to determine the two extreme values of the

b) Static system andinternal

a) Structure andloading Concrete core

IPE300 IPE360 IPE400 IPE450 IPE500 IPE550 IPE600

force diagrams

g, q w

g, q

w

[M] +

H

-

L

L Fig. 10. The design example.

[N]

G. Vasdravellis et al. / Journal of Constructional Steel Research 110 (2015) 29–39 Table 5 Details of the parametric beam designs.

37

a) Case 2-FSC beff (m)

UB305x165x40 (IPE300) UB356x171x57 (IPE360) UB457x152x60 (IPE400) UB457x152x82 (IPE450) UB457x191x98 (IPE500) UB533x210x109 (IPE550) UB610x229x125 (IPE600)

6 8 9 10 12 13 15

1.5 2.0 2.25 2.5 3.0 3.0 3.0

Fig. 11 shows the resulting interaction diagrams for Case 1-FSC (Fig. 11a) and Case 1-PSC (Fig. 11b). Fig. 11a shows that, in the case of a strong shear connection between the slab and the steel beam, the sagging moment strength of a composite beam is not reduced due to the simultaneous action of a low-to-moderate axial compression applied to the steel section. For higher compression levels, however, the moment capacity is significantly reduced. Most of the interaction diagrams (mainly those relating to the higher beam sections) follow a quasi-bilinear shape. The results of the PSC case generally confirm this outcome, but with slightly faster reduction of the sagging moment capacity, as observed in Fig. 11b. The faster reduction is due to early failure of the shear connection. In addition, in the case of PSC, the interaction shape follows a nonlinear shape. Fig. 12 shows the non-dimensional forms of the Case 1-FSC (Fig. 12a) and Case 1-PSC (Fig. 12b) analyses. It is shown that most of the Case 1-FSC interaction curves can be approximated with a bilinear diagram, where the limiting value of axial compression is about 30–35% Nu. The Case 1-PSC interaction results

8000

Axial compression (kN)

L (m)

IPE300 IPE360 IPE400 IPE450 IPE500 IPE600

6000 4000 2000 0

0

1000

2000

3000

Moment (kNm)

b) Case 2-PSC 8000

Axial compression (kN)

Beam section

IPE300 IPE360 IPE400 IPE450 IPE500 IPE600

6000 4000 2000 0

0

1000

2000

3000

Moment (kNm) Fig. 13. Sagging moment–axial compression interaction for: a) Case 2-FSC; and b) Case 2-PSC.

a) Case 1-FSC 1.5

N/Nu

1

0.5

0 0

0.5

1

1.5

M/Mu

b) Case 1-PSC

are more consistent and can be approximated with a second or higher degree polynomial curve. The value of axial compression where the reduction in moment capacity starts is about 25–30% Nu. Fig. 13 shows the results of the parametric analyses for the Case 2-FSC (Fig. 13a) and Case 2-PSC (Fig. 13b). The resulting interaction curves indicate that there is a slight increase in sagging moment strength when a low-to-moderate axial compression is applied to the composite section of both fully- and partially-shear connected beams. For higher levels of axial compression the moment strength is drastically reduced up to Nu. Fig. 14 shows the non-dimensional form of the Case 2 results. It is observed that the interaction shape is consistent for both the FSC and PSC cases and can be approximated with a bilinear curve. The level of axial compression where the moment capacity starts to deteriorate is about 40% Nu in both cases.

1.5 5.3. Axial compression strength

N/Nu

1

0.5

0 0

0.5

1

1.5

M/Mu Fig. 12. Non-dimensional plot of the interaction for: a) Case 1-FSC; and b) Case 1-PSC.

Fig. 15 shows the ratio of the axial compressive strength resulting from the FEM analysis on the parametric beams (NFEM) to the calculated strength based on RPA. Nsteel is the axial strength of the steel section alone and NC is the axial compressive strength of the portion of the slab which is axially loaded. Fig. 15a shows that in Case 1 the composite axial compressive strength is in average 20% higher than Nsteel. In this case, the additional compressive force is transferred to the slab through the shear connection. Fig. 15b shows that in Case 2 the ultimate compressive strength of a composite beam is in average 30% higher than the one calculated according to RPA. In both cases, local reinforcement with web and flange plates is assumed to be present so that premature local buckling is prevented. Lateral support of the beam that prevents

38

G. Vasdravellis et al. / Journal of Constructional Steel Research 110 (2015) 29–39

a) Case 2-FSC

a)

1.5

1.5

1

N/Nu

N/Nu

1

0.5

0.5

Design 0

0

0.5

1

0

1.5

0

M/Mu

0.5

1

1.5

M/Mu

b)

b) Case 2-PSC

1.5

1.5

1

N/Nu

N/Nu

1

0.5

0.5

Design 0 0

0.5

1

1.5

0

M/Mu

0

0.5

1

1.5

M/Mu Fig. 14. Non-dimensional plot of the interaction for: a) Case 2-FSC; and b) Case 2-PSC. Fig. 16. Non-dimensional interaction of parametric beams for both FSC and PSC: a) compression applied to the steel section only; and b) compression applied to the steel section and part of the slab.

global instability is also assumed. Thus, it is reasonable and conservative for design purposes to calculate the compressive design strength of a composite section, NU, as the sum of the compressive strengths of the loaded areas (steel and/or slab), i.e.: N U ¼ Nsteel ¼ As f y

6. Proposed design model Based on the experimental results and the numerical analyses, a design model is proposed for composite beams subjected to sagging bending and axial compression. Figs. 12 to 15 show that the interaction curves are slightly different when the axial compression is applied to the steel section only and when the axial compression is applied to both the steel section and the concrete slab, whereas the difference in the non-dimensional shape of the interaction is minimal between the FSC and PSC cases. Therefore, the results are grouped in two categories for design purposes: a) axial compression applied to the steel section only; and b) axial compression applied to both the steel section and

ð1Þ

for Case 1

0

N U ¼ NC þ Nsteel ¼ 0:85 f c Ac þ As f y

ð2Þ

for Case 2

where As is the steel beam section area, fy the yield strength of steel, Ac the loaded concrete area, and fc′ the compressive (cylinder) strength of concrete.

a)

b) 1.6

1.6

1.4

1.4

1.2

1.2

1

1

0.8

0.8 0.6

0.6 200

400

Beam height (mm)

600

200

400

600

Beam height (mm)

Fig. 15. Ratios of axial compression strength of the parametric beams to the nominal strength: a) Case 1; and b) Case 2.

G. Vasdravellis et al. / Journal of Constructional Steel Research 110 (2015) 29–39

the concrete slab, irrespectively of the degree of shear connection. Fig. 16 shows the two sets of results. In the same graphs, the design equations are superimposed and denoted as “Design”. A bilinear equation is proposed for the interaction of sagging bending and axial compression in a composite beam: M ¼ MU ; ð1−γ Þ

ð3Þ

for N b γNU

M N þ ¼ 1:0; MU NU

for N N γNU

ð4Þ

γ = 0.3, if N applied to steel section only γ = 0.4, if N applied to both the steel section and the concrete slab (i.e. a column type loading). Mu is the plastic moment resistance of the composite section, and NU is calculated according to Eqs. 1 and 2. The proposed design model assumes that the sagging moment capacity of a composite section is not reduced when a predefined level of axial compression acts simultaneously. The level of axial compression is 30% when the axial force is applied to the steel section and 40 % when the axial force is applied to both the steel section and part of the concrete slab. For greater values of axial compression, the moment capacity is linearly reduced until NU. The proposed bilinear model is reasonably conservative, as can be seen from Fig. 16. The proposed design model is intended to provide the ultimate design strength of the composite section under sagging bending and compression. The design model applies to class 1 or 2 compact composite beams, and not to slender beams or girders. In addition, global instability failure modes (lateral torsional buckling, LTB) are not included, although they are unlikely to occur under sagging bending. If the applied axial force requires LTB check, then these checks should be performed according to current codes of practice. 7. Conclusions This paper presented the results of an experimental and numerical investigation on the ultimate strength of steel–concrete composite beams subjected to the combined effects of sagging (or positive) bending moment and axial compression. The experimental results along with the numerical parametric study allowed for the derivation of an interaction law and a simple model was proposed for the practical design of composite beams. Based on the research outcomes presented herein the following conclusions are drawn: • The experiments have shown that a weak shear connection leads to premature shear connection failure when the axial compression is applied to the steel section only. This early failure results in a significantly reduced ultimate moment capacity even when a low axial compression is applied to the beam. Application of the axial force to both the steel section and the slab through stiffening plates resulted in a significant increase in moment capacity of the beams. • Sectional rigid plastic analysis, with modifications to account for axial compression, was performed and the results are in reasonable agreement with the tests. Thus, a rigid plastic analysis can be safely used for the prediction of the combined strength of composite beams. • A nonlinear finite element model was developed and found accurate in predicting the combined strength of the tested composite beams. The developed model can be used for the detailed modelling of the nonlinear behaviour of composite beams under generalised loading. • Parametric analyses on a wide range of composite sections commonly used in practice showed that the interaction is slightly different depending on the load application area of the compression force. • The sagging moment capacity of a composite beam is not reduced when an axial compressive load lower or equal to 30% of the plastic axial capacity of the steel section is introduced through the steel section.

39

• The sagging moment capacity of a composite beam is slightly increased when an axial compressive load lower or equal to 40% of the plastic axial capacity of the steel section is applied to both the steel section and part of the concrete slab. • A design model is proposed for the design of composite beams under sagging bending and compression. The model assumes no reduction of the moment capacity up to a predefined level of axial compression depending on the axially loaded area, whereas it assumes a linear reduction for greater axial compression values. • This study completes the results of the total bending moment–axial compression interaction in steel–concrete composite beams. The research results presented herein along with those presented in the previous studies by the authors have shown that it is important to account for the axial force in calculating the ultimate bending resistance of a composite section, and that different rules may apply in each combination, i.e. axial compression or tension combined with sagging or hogging bending. The proposed design models aim to cover the existing gap in the current codes of practice and facilitate a more efficient design of composite structures.

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 all the technical staff of the Structures Laboratory at the University of Western Sydney for their valuable assistance with the experimental work. References [1] Uy B. Applications, behaviour and design of composite steel–concrete structures. Adv Struct Eng Sep. 2012;15(9):1559–72. [2] ANSI/AISC 360-10, specification for structural steel buildings. One East Wacker Drive, Suite 700, Chicago, Illinois, 60601-1802: American Institute of Steel Construction; 2010. [3] Standards Australia, AS2327.1-2003. Composite structures. Part 1: simply supported beams. Sydney, NSW 2001. Standards Australia International Ltd; 2003. [4] British Standards Institution, BS EN 1994-1-1:2004. Eurocode 4: Design of composite steel and concrete structures — Part 1-1: General rules and rules for buildings, vol. 3. London: British Standards Institution; 2009. [5] Chapman J, Balakrishnan S. Experiments on composite beams. Struct Eng 1964; 42(11):369–83. [6] Barnard PR, Johnson RP. Ultimate strength of composite beams. ICE Proc Jan. 1965; 32(2):161–79. [7] Yam LCP, Chapman JC. The inelastic behaviour of simply-supported composite beams of steel and concrete. ICE Proc Jan. 1968;41(4):651–83. [8] Nie J, Xiao Y, Chen L. Experimental Studies on Shear Strength of Steel–Concrete Composite Beams, vol. 130; No. 8; 2004 1206–13. [9] Liang QQ, Asce M, Uy B, Bradford MA, Ronagh HR. Strength Analysis of Steel–Concrete Composite Beams in Combined Bending and Shea, vol. 131; No. 10; 2005 1593–600. [10] Liang QQ, Uy B, Bradford MA, Ronagh HR. Ultimate strength of continuous composite beams in combined bending and shear. J Constr Steel Res Aug. 2004;60(8):1109–28. [11] Vasdravellis G, Uy B. “Shear strength and moment–shear interaction in steel– concrete composite beams”. ASCE J Struct Eng 2014;140(11). http://dx.doi.org/10. 1061/(ASCE)ST.1943-541X.0001008. [12] Nie J, Tang L, Cai CS. Performance of steel–concrete composite beams under combined bending and torsion. J Struct Eng Sep. 2009;135(9):1048–57. [13] Tan EL, Uy B. Experimental study on curved composite beams subjected to combined flexure and torsion. J Constr Steel Res Aug. 2009;65(8–9):1855–63. [14] Tan EL, Uy B. Experimental study on straight composite beams subjected to combined flexure and torsion. J Constr Steel Res Apr. 2009;65(4):784–93. [15] Vasdravellis G, Uy B, Tan EL, Kirkland B. The effects of axial tension on the hoggingmoment regions of composite beams. J Constr Steel Res Jan. 2012;68(1):20–33. [16] Vasdravellis G, Uy B, Tan EL, Kirkland B. The effects of axial tension on the saggingmoment regions of composite beams. J Constr Steel Res May 2012;72:240–53. [17] Vasdravellis G, Kirkland B, Tan EL, Uy B. Behaviour and design of composite beams subjected to negative bending and compression. J Constr Steel Res 2012;79:34–47. [18] British Standards Institution, BS EN 1991: 2002. Eurocode 1: Actions on structures — Part 1-1: General actions — Densities, self-weight, imposed loads for buildings, vol. 3. London: BSI; March 2010. [19] Abaqus 6.12. Abaqus documentation. RI, USA: Dassault Systèmes, Providence; 2011. [20] Carreira DJ, Chu KH. Stress–strain relationship for plain concrete in compression. ACI J Proc 1985;82(11):797–804. [21] Oehlers D, Bradford MA. Elementary behaviour of composite steel and concrete structural members. Oxford: Butterworth-Heinemann; 1999.