Longitudinal shear strength prediction for steel-concrete composite slabs with additional reinforcement bars

Journal of Constructional Steel Research 166 (2020) 105908

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Journal of Constructional Steel Research

Longitudinal shear strength prediction for steel-concrete composite slabs with additional reinforcement bars Luiz Gustavo Fernandes Grossi, Carol Ferreira Rezende Santos ⁎, Maximiliano Malite Department of Structural Engineering, Sao Carlos Engineering School, University of Sao Paulo, Av. Trabalhador Sao-carlense, 400, Sao Carlos, SP 13566-590, Brazil

a r t i c l e

i n f o

Article history: Received 29 July 2019 Received in revised form 11 December 2019 Accepted 12 December 2019 Available online xxxx Keywords: Composite structures Composite slab Shear bond behaviour Longitudinal shear failure m-k method

a b s t r a c t This paper presents an experimental and analytical study of composite slabs with additional reinforcement bars. The analytical model is based on m-k method and is able to estimate the longitudinal shear capacity of composite slabs with additional reinforcement bars. A total of 11 simply supported specimens with different additional reinforcement rates and shear span length were tested. All slabs showed ductile longitudinal shear behavior. Composite slabs with additional reinforcement bars exhibited greater ductility and load capacity than corresponding specimens without additional reinforcement bars. The analytical model was verified against experimental data and showed good agreement with test results. © 2019 Published by Elsevier Ltd.

1. Introduction Concrete-steel composite slabs are one of the most popular floor system types used in steel frame buildings. They are composed of coldformed profiled steel decking and structural concrete, which after concrete casting works together to support the external actions. In this system, the performance of the steel-concrete interface on the transmission of longitudinal shear stresses is determinant to develop the composite action between steel decking and concrete slab [1–7], affecting the connection degree between these two materials, the failure mode and, consequently, the carrying load capacity of composite slabs. In concrete-steel composite slabs, the steel decking has two main roles: acts as permanent formwork before the casting and as positive tension reinforcements after the casting carrying the tensile stress induced by external actions throughout the life of the structure [1,2,5]. If the strength provided by the steel decking is not adequate, the tensile reinforcement area must be increased which can be achieved by increasing the thickness of steel decking or including additional reinforcement bars in the concrete slab [2,4,8–10]. The additional reinforcements bars insertion instead of increasing of steel decking thickness is advantageous in situations where it is desired to adopted the same thickness of the steel sheeting along the floor system or when the supplier only has steel decking of a certain thickness.

⁎ Corresponding author. E-mail addresses: [email protected] (C.F.R. Santos), [email protected] (M. Malite).

https://doi.org/10.1016/j.jcsr.2019.105908 0143-974X/© 2019 Published by Elsevier Ltd.

Thus, the additional reinforcing bars should be added only in the regions along the floor where the steel decking thickness is insufficient. In addition to steel decking, concrete slab and, if used, additional reinforcement, a welded wire mesh is included in the top of concrete slab for cracking control due to restrained shrinkage or for fire-resistance purposes [5]. In Fig. 1 is show a composite slab with additional reinforcement. The longitudinal shear bond failure is the most common failure mode in simply supported composite slabs for span lengths and slab heights commonly used in building construction [7,11,12]. That failure mode occurs in slabs in a partial interaction regime and is due to the degradation of the resistant capacity of the steel-concrete interface to transmit the horizontal shear stresses along the shear span [6], preventing the maximum bending capacity of composite slabs could be achieved [13,14]. The composite slabs with longitudinal shear bond failure can be classified as ductile or fragile behavior and exhibit significant relative slipping between concrete slab and steel decking at the failure. According Ferrer et al. [4], for shear failure ductility, it is desired that the maximum resistance to longitudinal shear should be achieved after large slip has been developed. Several researchers has evaluated numerically and experimentally the longitudinal shear bond failure on simply supported composite slabs without additional reinforcement [2,4,11,15]. However, the mechanical behavior of composite slabs with additional reinforcement never been investigated, as consequence, the structural behavior of this system remains unknown. The standard codes [10,16–20] presents two methods to evaluate the longitudinal shear strength of simply supported composite slabs:

2

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considers the additional reinforcement area as a variable would eliminate the need to carry out specimens tests with differents additional reinforcement areas. In this paper, an analytical model to evaluate the longitudinal shear capacity of composite slabs with additional reinforcement is developed. The analytical model consists of an extension of m-k method applied to slabs without additional reinforcement, therefore, experimental results obtained for slabs with additional reinforcement are not necessary. In other words, in the proposed analytical model the same constants m and k determined by the composite slabs without additional reinforcement are used and the additional reinforcement area is admited as a variable, thus, experimental tests on composite slabs with additional reinforcement are not necessary. The analytical model was validated based on flexure tests of composite slabs with and without additional reinforcement for different shear span length and additional reinforcement area.

Fig. 1. Components of composite slab with additional reinforcement.

2. Analytical model: longitudinal shear bond model The m-k method described in Eurocode 4 [16] for evaluation of composite slabs longitudinal shear strength without additional reinforcement consists of model adaptation developed by Porter and Ekberg [22]. In m-k method, the constants m e k Eq. (1) are determined by linear regression of experimental data obtained from four-point bending tests on two different groups of full-scale specimens for two different length of shear span, short span and long span, as shown in Fig. 2. Vu m  AF ¼ þk b dF b  Ls

ð1Þ

where Vu is the ultimate shear force i.e. the support reaction under the ultimate test load; b is the width of composite slab; dF is the effective depth of composite slab (i.e the depth of the mid-axis on the steel decking measured from top of the slab); AF is the nominal cross-section area of the steel decking; Ls length of shear span; m and k constants obtained by linear regression of experimental data. The analytical model developed in this study is based on m-k method (Fig. 2), in which the additional reinforcement contribution is considered in Eq. (1), resulting in a new m-k straight line whose constants m and k are the same determined from composite slabs without additional reinforcement. The Fig. 3 shows a free body diagram of the shear span of the slabs and the internal force distribution at the critical section (at applied load position) of composite slab with additional reinforcement at failure. In order to simplify, only part of the cross section A-A of the composite slab was shown in Fig. 3. In Fig. 3, the constant dF is the effective depth of composite slab; ds is depth of mid-axis on additional reinforcement bars measured from the top of slab; Vu is the ultimate shear force; Ls is the length of shear span; a is the depth of neutral axis in concrete slab with partial connection; tc is the height of concrete slab above of upper flange of the steel decking; Nc is the compression force in the concrete slab; Ns is the total traction force in additional reinforcement bars; Na is the traction force in steel

Fig. 2. The m-k straight line of composite slabs.

m-k method and partial shear connection method (PSC) [7], both originally developed to composite slabs without additional reinforcement and that require experimental data obtained from full-scale tests [12,21]. Full scale laboratory tests are necessary because the longitudinal shear strength is dependent on the geometry of the particular type of steel decking, including size and spacing of embossment on the steel decking, the slab slenderness and the mechanical properties of steel decking and concrete slab. The m-k method can be used for composite slabs with ductile and brittle longitudinal shear behavior, while the PSC method should only be used for composite slabs with ductile longitudinal behavior. For evaluation of the longitudinal shear strength of composite slabs with additional reinforcement from the current methods (m-k and PSC), it is necessary that experimental tests be carried out for each additional reinforcement area, impacting directly the experimental cost and time spent into laboratory. The proposition of an analytical model that

A Vu

Nc

-

-

ds dF

-

Cracking

a-

A-A

tc

Ls

Vu

A

Fig. 3. Free body diagram of the shear span and internal force distribution on section A-A.

Na Ns

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because of this Na is limited by longitudinal shear strength of steelconcrete interface. The longitudinal shear force strength on interface is provided by mechanical interlock between the concrete and the embossments on steel decking (Fn) and by friction (Fa) given as Fa = fa ⋅ Ls ⋅ b, where fa corresponds to the mean value for longitudinal shear stress on interface due to friction between the steel decking and the concrete slab. As proposed by Schuster and Ling [23], in the design codes to composite without additional reinforcement, the longitudinal shear force strength provided by mechanical interlock is weighted by relationship AF/b and fn/b = m and fa = k is adopted. The same was done in the analytical model proposed in this present work. From this, the Eq. (4) is obtained, which is given in terms of mean values.

Vu (kN)

60 40 20 0 0

100

200

300

400

3

500

As (mm2 ) Fig. 4. Ultimate shear force versus additional reinforcement bars area obtained by Grossi [8].

decking which is limited by longitudinal shear capacity of steel-concrete interface. The Eq. (2) is obtained from equilibrium of external and internal moments in the section A-A illustrated in Fig. 3, where Ns is defined as Ns = As ⋅ fyb, since As is total area of additional reinforcement bars and fyb is the yield strength of additional reinforcement bars. So, in the analytical model proposed, it is admitted that the yield stress was achieved by all bars of additional reinforcement. This condition occurs only for reinforcement bars rates below 1.4% (which is usual range), where the rate is given by the relationship between the additional reinforcement area and the concrete area above the upper flange of the steel decking. This rate is equivalent to the relationship z / dF = 0.5, where z is the depth of plastic neutral axis at mid span of composite slab with additional reinforcement bars, which can be obtained from equilibrium of internal forces in the section at mid span admitting the composite slab with additional reinforcement bars in full interaction according the analytical model decribed in Appendix. In composite slabs without additional reinforcement bars is common to consider that in the longitudinal shear bond failure the depth of plastic neutral axis in concrete slab at partial connection is close to the upper concrete surface and because of this the thickness of the concrete above the steel decking is negligible. The same consideration can be admitted for composite slabs with reinforcement bars rates below 1.0%, so a/2 ≪ dF and a/2 ≪ ds and the Eq. (2) results in Eq. (3).   a a V u Ls ¼ N a d F − þ Ns ds − 2 2

ð2Þ

V u Ls ¼ N a ðd F Þ þ Ns ðds Þ

ð3Þ

Similar to composite slabs without additional reinforcement, the traction force in steel decking (Na) is equilibrated by resulting longitudinal shear force that acts between concrete and steel decking and

Vu m  AF Ns  ds ¼ þkþ b  dF b  Ls b  d F  Ls

ð4Þ

As the failure mode is by longitudinal shear bond failure, the compression force value in concrete slab (Nc) will be Ns bNc bNc with traction force in steel decking (Na) given by Na = Nc − Ns. This is only possible if Nc NNs þ Npa , where Nc is the compression force in concrete slab to a = tc and Npa is the plastic traction force of steel decking given as Npa = AF ⋅ fy. The Eq. (4) corresponds to Eq. (1) with addition of term corresponding to the contribution of additional reinforcement (second term in the right side of Eq. (4)). However, the constants m and k values are the same for two equations. From Eq. (4), it can be observed the direct relationship between the ultimate shear force (Vu) and the traction force in the additional reinforcement (Ns), indicating that the increasing in load capacity of composite slabs is proportional to the additional area (As). The relationship between ultimate shear force and additional reinforcement bars area obtained by Grossi [8] is shown in Fig. 4. 3. Experimental study setup Four-point bending tests was carried out in 11 specimens of composites slabs, 4 with additional reinforcement bars and 7 without additional reinforcement bars. The setup relative to geometry, boundary conditions and specimens applied load without additional reinforcement was determined according to recommendations of Eurocode 4 [16] for m-k method. In the specimens were varied the shear span length Ls (450 mm e 900 mm), the length of the internal span L (1800 mm e 3600 mm), the height h (120 mm e 180 mm) and the additional reinforcement area (1.87 cm2–6 bars with diameter 6,3 mm and 4.71 cm2–6 bars with diameter 10,0 mm). The main parameters and the wire mesh used in each slab are summarized in Table 1. In Table 1, the letters S and L indicate short span (Ls = 450 mm) and long span (Ls = 900 mm), respectively. The next numbers xxx/xx

Table 1 Dimensions, wire mesh and additional reinforcement bars area in specimens. Specimen designation

Dimensions (b × L × h) (mm)

Ls (mm)

dF (mm)

dF Ls

Mesh wire diameter/spacing

Additional reinforcement bars area As (cm2)

P1S – 120/00 P2S – 120/00 P3S – 120/00 P4L – 180/00 P5L – 180/00 P6L – 180/00 P7L – 180/00 P8S – 120/1.87 P9S – 120/4.71 P10L – 180/1.87 P11L – 180/4.71

920 × 1800 × 120 930 × 1800 × 120 930 × 1800 × 120 925 × 3600 × 180 930 × 3600 × 180 930 × 3600 × 180 930 × 3600 × 180 925 × 1800 × 120 925 × 1800 × 120 930 × 3600 × 180 930 × 3600 × 180

450 450 450 900 900 900 900 450 450 900 900

87.5 87.5 87.5 147.5 147.5 147.5 147.5 87.5 87.5 147.5 147.5

0.19 0.19 0.19 0.16 0.16 0.16 0.16 0.19 0.19 0.16 0.16

4.2 mm/150 mm 4.2 mm/150 mm 4.2 mm/150 mm 4.2 mm/100 mm 4.2 mm/100 mm 4.2 mm/100 mm 4.2 mm/100 mm 4.2 mm/150 mm 4.2 mm/150 mm 4.2 mm/100 mm 4.2 mm/100 mm

– – – – – – – 1.87 4.71 1.87 4.71

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L.G.F. Grossi et al. / Journal of Constructional Steel Research 166 (2020) 105908 Table 3 Material properties of concrete. Specimen

All specimens

Concrete Average compressive strength fcm (MPa)

Average tensile strength fct (MPa)

Elastic modulus Eci (GPa)

18.90

2.06

18.12

Fig. 5. Dimensions (in mm) of the MD65 steel decking profile.

indicate the height h in mm and the additional reinforcement bars area As in cm2, respectively. The term dF/Ls refers to composite slabs compactness. The same steel decking with trapezoidal profiled MD65 with nominal thickness t = 0.76 mm, thickness without zinc coating, and section area of AF = 912 mm2 was used in all specimens. The shape and dimensions of steel decking are shown in Fig. 5. The geometric and material properties of steel decking are shown in Table 2. The material properties of steel decking were measured from tensile tests on 6 coupons cut from steel decking. The tensile test was performed as recommended in ASTM A370 [24]. The mean values of compressive strength (fcm), indirect tensile strength (fct) and initial elastic modulus (Eci) of the concrete at 28 days age used in specimens was determined from tests on 6 specimens of 100 mm diameter cylinder and 200 mm height and the mean values are shown in Table 3. The yield stress (fyb) and the ultimate stress (fub) of additional reinforcement bars reinforcement bars were also measured from tests and the mean values are shown in Table 4. The experimental schematic view setup and the instrumentation positions are illustrated in Fig. 6. The specimens were simply supported with a roller support at one end and a pin support at the other end. Displacement transducers (DT) were used in each slab to record the deflection at mid-span and the end slip between steel decking and concrete slab at each end of slabs. The strains were measured only in the specimens P1S – 120/00, P4L – 180/00 and the slabs with additional reinforcement using strain gages (SG), which were placed on the upper flange and lower flange of steel decking, on top surface of concrete slab and on 2 bars of the additional reinforcement, in specimens with additional reinforcement, in the sections (S1, S2 e S3) indicated in Fig. 6, allowing to obtain the strain distribution in these sections. The load was applied by a hydraulic jack of 500 kN capacity with displacement control technique at a rate of 0.01 mm/s until 0.05 mm/s and distributed to the top surface of each slab at each loading point using a spreader beam, according to Fig. 6. The loading history, deflections, end slips and strains were recorded at a rate of 1 register for second. The setup test configuration before the test and the details of end slip and mid span DTs are shown in Fig. 7 and Fig. 8, respectively. 4. Results and discussion 4.1. Experimental results The Applied Load versus Mid-span deflection curves of the specimens without additional reinforcement bars are shown in Fig. 9. The mid span deflections were obtained from the mid span DT shown in Fig. 8a. According to the Eurocode 4 [16] definition of ductility, all specimens failed in a ductile manner. In Fig. 9, three different behaviors related to the degree of connection between the steel decking and concrete slab (full, partial and

null) can be identified along the slabs loading history. At beginning of loading, the composite slabs were in full interaction and show linear relation between Applied Load versus Mid-span deflection, became nonlinear with the load increasing due to cracking of the concrete. As the load increases, the shear stress at the steel-concrete interface exceeded the shear strength promoted by the initial adhesion, resulting in stiffness reduction characterized by a sudden drop of load verified in the Applied load versus Mid-span deflection curves shown in Fig. 9. As a consequence of the change from the full connection regime to the partial connection regime, wide cracks formed below the applied line loads as can be seen in Fig. 10a, which propagated rapidly until reaching the position of the welded wire mesh, and first slip occurs between the two materials. After the first slip, due to mechanical interlocking and friction, the slabs supported load increases until the longitudinal shear bond failure occurred along the shear span. With the increase of load, the relationship between applied load and deflection became more nonlinear and flexural cracks formed in the constant moment region. At the peak load, significant end slip was observed in all slabs as can be seen in Fig. 10b. After peak load, the composite slabs assume the null connection regime and no shear forces are transferred between steel-concrete interface, resulting in a sudden drop in applied load and abrupt increases in relative slip and deflection. A little vertical separation between the steel decking and the concrete slab along the shear span was observed at the test ending. The specimens with short span showed higher ultimate shear strength than specimens with long span, confirming that slenderness is an important parameter that influences the ultimate capacity of composite slabs [12,21,25]. The described behavior was also observed in other studies [2,5,13]. The Applied Load versus Mid-span deflection curves of the specimens with and without additional reinforcement are compared in Fig. 11. It can be seen that additional reinforcement insertion improved structural behavior of the composite slabs, promoting increased on ductility, stiffness, and carrying load capacity, resulting in a significant increase in the ultimate load and deflection correspondent to the peak load. The stiffness reduction due the change from full to partial connection degree was less evident in the specimens with additional reinforcement than in specimens without additional reinforcement. Furthermore, the sudden drop in the Applied Load versus Mid-span deflection curves was not observed on specimens with additional reinforcement. Differences related to the opening and distribution concrete cracking and to the post-peak behavior were also noticed. In the specimens with additional reinforcement, the presence of additional reinforcement contributed to reduce the cracks opening and the postpeak behavior became more ductile, indicating the effective contribution of the reinforcement bars at the post-peak region. Experimental results are summarized in Table 5. The weight of the specimens, of the loading system and of the spreader beam were considered in the determination of the ultimate shear force Vu of all

Table 2 Geometrical and average mechanical properties of steel decking. Deck profile

Thickness t (mm)

Section area A'F (mm2/m)

Height centroid ys (mm)

Moment of inertia Is (mm4/m)

Yield strength fy (MPa)

Ultimate strength fu (MPa)

Elastic modulus Es (GPa)

MD65

0.76

1061.00

32.50

832.70

367.10

445.60

198.00

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5

Table 4 Material properties of additional reinforcement bars. Slab

Additional reinforcement bars

All specimens a b

Yield strengtha fyb1 (MPa)

Yield strengtha fyb2 (MPa)

Elastic modulusb Eb1 (GPa)

Elastic modulusb Eb2 (GPa)

622.00

601.80

198.00

198.00

fyb1 and fyb2: yield stress of the additional reinforcement bars with diameter of 6.3 mm and 8.0 mm, respectively. Eb1 and Eb2: initial elastic modulus of the additional reinforcement bars with diameter of 6.3 mm and 8.0 mm, respectively.

P

Ls = L/4

50 Ls = L/4

S2

Applied Load (kN)

40 S1

S3

DT

DT

300 650

DT

For Ls = 450 mm For Ls = 900 mm

100

300 650 100

L

A-A

SG

A

30 (P1S-120/00) (P1S-120/00) (P2S-120/00) (P4L-180/00) (P5L-180/00) (P6L-180/00) (P7L-180/00)

20 10

SG

0

20

0 SG

SG

h

10

20

30

40

Mid span deflection (mm)

34 SG

SG

Fig. 9. Applied Load versus Mid-span deflection curves of the specimens without additional reinforcement.

SG

SECTIONS S1, S2, S3 Fig. 6. Test setup, transducer displacements (DT) and strain gages (SG) positions. Dimensions in mm.

Fig. 7. Setup test configuration.

specimens, in which the values adopted were: 5.2 kN, for slabs with Ls = 450 mm, and 14.3 kN, for slabs with Ls = 900 mm. In Table 5, the variables P0,1 e δ0,1 correspond to the load and the deflection relative to slip of 0,1 mm; Pmax e δmax correspond to peak load and the deflection

at peak load; Mu is the ultimate mid span moment in the middle of the span and Mp is the theoretical ultimate moment associated to total connection, calculated in the reinforced specimens according to the analytical model proposed by Grossi [8] described in Appendix. The peak load and load at which slip occurs (P0,1) were increased by the insertion of additional reinforcement bars as shown in Table 5. It is known that the initial end slip occurs due broke of the longitudinal shear strength promoted by the chemical bond and is consequence of various small local slips that results in global slip along the shear span. Thus, as the cracks openings in the specimens with additional reinforcement were smaller when compared with specimens without additional reinforcement bars, a greater loading was necessary in order to form a sufficient amount of microcracks to result in the onset of slip. The longitudinal shear ductility, given by the relation Pmax/P0,1, the initial stiffness of Applied Load versus Mid-span deflection curves and peak load Pmax increases with increasing of additional reinforcement area. The increases in the initial stiffness and in the peak load are directly related to the increase of positive reinforcement area in the composite slabs. The increase in longitudinal shear ductility may be explained by the reduction of the loss of stiffness, due the change of full to partial connection, promoted by the contribution of additional reinforcement bars, which, according Ferrer et al. [4], is a desirable

Fig. 8. a) Mid span DT; b) End slip DT.

6

L.G.F. Grossi et al. / Journal of Constructional Steel Research 166 (2020) 105908

160

160

140

140

120

120

Applied Load (kN)

Applied Load (kN)

Fig. 10. Four-point bending tests: a) wide crack bellow the applied line load; b) end slip at failure.

100 80 60

(P1S-120/00) (P2S-120/00) (P2S-120/00) (P8S-120/1.87) (P9S-120/4.71)

40 20 10

20

30

40

50

60

80 60

(P4L-180/00) (P5L-180/00) (P6L-180/00) (P7L-180/00) (P10L-180/1.87) (P11L-180/4.71)

40 20

0 0

100

0

70

0

10

Mid span deflection (mm)

20

30

40

50

60

70

Mid span deflection (mm)

a)

b)

Fig. 11. Applied Load versus Mid-span deflection curves of tested specimens, Ls:a) 450 mm; b) 900 mm.

phenomenon in the composite slabs because it avoids that the longitudinal shear failure is fragile type. In the Fig. 12, the initial end slip load (P0,1), longitudinal shear ductility (Pmax /P0,1) and the ultimate shear force (Vu) are related to additional reinforcement area (Asl). The relationships were weighted according to the slenderness of the slab (λ) which is given by the relation Ls/dF. The initial end slip load (P0,1), the longitudinal shear ductility (Pmax /P0,1) and the ultimate shear force (Vu) varied linearly with the additional reinforcement area (see Fig. 12). For the initial end slip load (P0,1), the increase was 46% for Asl = 1.87 cm2 and 97% for Asl = 4.71 cm2, in composite slabs with Ls = 450 mm, and of 61% for Asl = 1.87 cm2 and 135% for Asl = 4.71 cm2, in slabs with Ls = 900 mm. Regarding to the longitudinal shear ductility (Pmax/P0,1), the increase in the specimens with Ls = 450 mm was 36% and 158% corresponding to Asl = 1.87 cm2 and Asl = 4.71 cm2, respectively. In the slabs with Ls = 900 mm, the increase was 45% for Asl = 1.87 cm2 and 75% for

Asl = 4.71 cm2. In the slabs with Ls = 450 mm, the ultimate shear force (Vu) increases 92% for Asl = 1.87 cm2 and 194% for Asl = 4.71 cm2. For slabs with Ls = 900 mm, this increase was of 93% and 210% for Asl = 1.87 cm2 and Asl = 4.71 cm2, respectively. The Applied Load versus End slip displacement curves of the tested are shown in Fig. 13. The end slip displacements were measured by end slip DT illustrated in Fig. 8b. Similar to the specimens without additional reinforcement, all specimens with additional reinforcement exhibited longitudinal shear failure with ductile behavior. Significant relative slippage at the end of the slabs was observed at the failure, which the greater values were presented by the specimens with larger additional reinforcement area and the smaller ones by the specimens without additional reinforcement. The tensile strains in upper and lower flanges of the steel decking and the compressive strains in the top surface of the concrete slab at section S1 and S2 of the specimen P1–120/00 are presented in Fig. 14.

Table 5 Summary of test results. Slab designation

P0, 1 (kN)

Pmax (kN)

Vu (kN)

P max P 0;1

Mu (kN.cm)

δ0,1mm(mm)

δmax(mm)

Mu Mp

P1S – 120/00 P2S – 120/00 P3S – 120/00 P4L – 180/00 P5L – 180/00 P6L – 180/00 P7L – 180/00 P8S – 120/1.87 P9S – 120/4.71 P10L – 180/1.87 P11L – 180/4.71

32.3 24.7 27.7 19.6 22.7 20.1 23.3 41.3 55.6 34.5 50.4

46.6 47.7 47.4 28.8 32.6 27.8 28.1 95.3 149.0 70.1 121.0

25.9 26.5 26.3 21.6 23.5 21.1 21.2 50.3 77.1 42.2 67.7

1.4 1.9 1.7 1.5 1.4 1.4 1.2 2.3 2.7 2.0 2.4

1165.5 1192.5 1183.5 1944.0 2115.0 1899.0 1908.0 2263.5 3469.5 3798.0 6093.0

4.9 4.3 4.2 6.1 7.8 7.1 9.4 6.6 6.30 8.01 7.10

12.4 14.2 14.1 17.1 17.5 15.1 18.0 27.0 29.8 38.0 54.0

0.45 0.46 0.45 0.42 0.46 0.41 0.41 0.68 0.80 0.63 0.75

L.G.F. Grossi et al. / Journal of Constructional Steel Research 166 (2020) 105908

7

350 y

P0.1

(kN)

300

29.56 x 149.7

R2

0.99

250 y

200

37.26 x 134.53

R2

0.99

150

Ls= 450 mm Linear Fit Ls= 450 mm Ls= 900 mm Linear Fit Ls= 900 mm

100 50 0 0

2

4

6 2

Additional reinforcement bars area As (cm )

a) 500

16

/ P0.1 Pmax

1.29 x 8.92

R2

R2 y

12

y

400

0.94 1.1x 9.03

R2

55 x 143 0.99

y

300

Ls= 450 mm Linear Fit Ls= 450 mm Ls= 900 mm Linear Fit Ls= 900 mm

10 8

59 x 139

R2

0.94

Vu

y

14

0.99 Ls= 450 mm Linear Fit Ls= 450 mm Ls= 900 mm Linear Fit Ls= 900 mm

200 100 0

0

2

4

6

Additional reinforcement bars area As (cm2)

b)

0

2

4

6

Additional reinforcement bars area As (cm2)

c)

Fig. 12. Curves: a) P0,1 ∙λ versus Asl; b) Pmax ∙λ/P0,1 versus Asl; c) Vu ∙λ versus Asl.

Until the first slip load, the strains distribution in section S1 (Fig. 14a) indicated the existence of only 1 neutral axes outlined within in the cross section, which is typical of full connection regime. Before the first slip, tensile strains were recorded by SG11, however, after the onset of slip, the compression strains were recorded by the SG11 which indicates the existence of 2 neutral axes in the cross section, characterizing the partial connection regime (Fig. 14a). As result of the change of total to partial connection occurs stiffness reduction which is identificated in Fig. 14 by the change in the slope of the strains distribution. After the section S1, the change from the total to partial connection regime also occurred in the section S2 of the specimen P1–120/00. Comparing the measured strains on sections S1 and S2 in Fig. 14, it can be seen that the higher values of strains on steel decking were recorded by the SG10 and SG12 positioned in the lower flange of the steel decking at section S1 located in the shear span on the side where the first slip occurred. Although the moment is not maximum in the region of section S1, the strains in this section were greater than those recorded in section S2 due the stiffness reduction along the shear span caused by the the change of total to partial connection regime. The specimen P5L-180/00 showed similar behavior to the specimen P1S-120/00, except that in section S2 of the specimen P1S-120/00 occurred, after the section S1, the change from the total to partial connection regime and this did not occur in the specimen P5L- 180/00. The strains distribution in the steel decking, concrete slabs and additional reinforcement in section S2 of the specimens P8S – 120/1.87, P9S – 120/4.71, P10L – 180/1.87 and P11L – 180/4.71 are shown in the Fig. 15 and Fig. 16, respectively. In this slabs, instead of the specimens without reinforcement bars, the largest strains in the steel decking and in the additional reinforcement bars occurred in section S2 located in the mid span (Fig. 15 and Fig. 16). This is due to the fact that in the

specimens with additional reinforcement bars, the stiffiness reduction due to the change in the connection regime was less impacting in the global behavior and, because of this, the highest values of steel strain occurred in the region of maximum moment. The Figs. 15 and 16 shows that after the first slip the strains measured in the reinforcement bars became larger than those measured in the steel decking, which was expected because, after onset slip, the interaction between the steel decking and the concrete slab gradually decreases with the decreases with increasing load. Thus, the reinforcement bars in composite slabs with additional reinforcement contribute to support the tensile forces in the concrete slab. In addition, it was observed that steel decking strains were larger in the slabs with short span and with higher additional reinforcement rate. In the specimens with additional reinforcement and in P1S - 120/00, local buckling appeared in the upper flange and lower flange of the steel decking in vicinity of the applied loads, in the side where the first slip occurred, indicating local yielding of the steel decking. In the specimens with additional reinforcement, the larger strains measured in the steel decking was higher than the mean value of the steel decking yield strain obtained from the uniaxial tensile test (εy = 1800 με). Despite of the strain measured in the steel decking of the P1S - 120/00 (shown in Fig. 14) was smaller than steel decking yield strain (εy = 1800 με), local buckling was noticed in the bending tests. This occur because the strains in the specimens were obtained in sections in the shear span distant 150 mm/250 mm from the applied load points, in which the moment is less than the maximum moment. The local buckling in the specimen P1S - 120/00 is shown in Fig. 17. The Mmax/Mp ratios of all specimens is shown in Table 5 and indicates that longitudinal shear failure prevented all specimens from reaching the full plastic bending capacity. The Mmax/Mp ratios varied from 0.41

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L.G.F. Grossi et al. / Journal of Constructional Steel Research 166 (2020) 105908

50

40

Applied Load (kN)

Applied Load (kN)

40 30 20

(P1S-120/00-Right side) (P1S-120/00-Left side) (P2S-120/00-Right side) (P2S-120/00-Left side) (P3S-120/00-Right side) (P3S-120/00-Left side)

10 0 0

2

4

6

8

30

20

(P4L-180/00-Right side) (P4L-180/00-Left side) (P5L-180/00-Right side) (P5L-180/00-Left side) (P6L-180/00-Right side) (P6L-180/00-Left side) (P7L-180/00-Right side) (P7L-180/00-Left side)

10

0 10

0

2

End slip (mm)

140

140

120

120

100 80 60 (P8S-120/1.87-Right side) (P8S-120/1.87-Left side) (P9L-120/4.71-Right side) (P9L-120/4.71-Left side)

0 0

2

4

6

8

10

b) Ls = 900 mm 160

Applied Load (kN)

Applied Load (kN)

a) Ls = 450 mm

20

6

End slip (mm)

160

40

4

8

100 80 60 40

(P10L-180/1.87-Right side) (P10L-180/4.71-Left side) (P11L-180/1.87-Right side) (P11L-180/4.71-Left side)

20 0 10

End slip (mm)

c) Ls = 450 mm

0

2

4

6

8

10

End slip (mm)

d) Ls = 900 mm

Fig. 13. Applied Load versus End slip curves of specimens without additional reinforcement bars, a) Ls = 450 mm and b) Ls = 900 mm; with additional reinforcement bars, c) Ls = 450 mm and d) Ls = 900 mm.

to 0.46 in the specimens without additional reinforcement and from 0.63 to 0.80 in the specimens with additional reinforcement. In the usual composite slabs, the typical values of Mmax/Mp ratio are less than 0.6 [1,21,26,27]. Clearly, the additional reinforcement insertion contributed to greater use of full plastic bending capacity of the composite sections when compared against specimens without additional reinforcement, resulting in better use of steel decking and concrete strength. At failure, the measured strains in the additional reinforcements bars were greater than the mean steel bars yield strain (εyb1 = 3140 με and εyb2 = 3000 με) determined from the uniaxial tensile

test. The mean concrete crushing strain obtained in uniaxial compression test was εyd = 2190 με, so, the concrete compressive strength was only achieved in the specimens P10L - 180/1.87 and P11L 180/4.71. The experiment setup after the test of specimens with and without additional reinforcement is compared in Fig. 18. It can be observed that more flexural cracks were formed in specimens with additional reinforcement than in specimens without additional reinforcement, which was expected due the greater applied load on the slabs with additional reinforcement.

Fig. 14. Strain slope in steel decking and concrete slab of the specimen P1–120/00 in the sections: a) S1; b) S2.

L.G.F. Grossi et al. / Journal of Constructional Steel Research 166 (2020) 105908

100

9

160 140

60

S2

E6

E7

E21

E22 E14 E15

E13

40

s (E13 e E15) s (E14) c (E6 e E7) s (E21 e E22)

20

0 -2000

-1000

0

1000

2000

3000

Applied Load (kN)

Applied Load (kN)

80

120 100 S2

80

E6

E7

E21

E22

s (E13 e E15) s (E14) c (E6 e E7) s (E21 e E22)

40 20 0 -2000

4000

E14 E15

E13

60

-1000

0

1000

2000

3000

4000

Strain ( )

Strain ( )

a)

b)

Fig. 15. Applied load versus strain in mid span (section S2) of specimens P8S – 120/1.87 e P9S – 120/4.71.

100

160 140

60

S2

40

E7

E21

E22

E13

E14 E15 s (E13 e E15) s (E14) c (E6 e E7) s (E21 e E22)

20

0 -2000

E6

-1000

0

1000

2000

3000

4000

Strain ( )

Applied Load (kN)

Applied Load (kN)

80

120 100 S2

80

E7 E22 E14 E15

E13

60

s (E13 e E15) s (E14) c (E6 e E7) s (E21 e E22)

40 20 0 -2000

E6 E21

-1000

0

1000 2000 Strain ( )

a)

3000

4000

b)

Fig. 16. Applied load versus strain in mid span (section S2) of specimens P10L – 180/1.87 e P11L – 180/4.71.

4.2. Analytical model validation The analytical model proposed in item 2 was validated against experimental data, previously presented in Table 5, therefore, the coefficients m and k in Eqs. (1) and (4) should be determined from the mean values. The straight line m-k shown in Fig. 19 and

Fig. 17. Local buckling in the steel decking in the specimen P1S - 120/00.

given by the Eq. (5) was determined from experimental data of the specimens without additional reinforcement. The value obtained were m = 151 N / mm2 and k = −0.005 N / mm2, with correlation coefficient R = 0.99. Based on the coefficients m, k and Eq. (4), the straight line m-k was determined for the specimens with additional reinforcement expressed by the Eq. (6). The condition Ns bNc bN c was verified and satisfied by all specimens with additional reinforcement, where the variable Ns in Eq. (6) is given by Ns = As ⋅ fyb as described in item 2. Vu 151  A F ¼ −0:005 b  dF b  Ls

ð5Þ

Vu 151  A F Ns  ds ¼ −0:005 þ b  dF b  Ls b  d F  Ls

ð6Þ

The experimental ultimate shear force (Vue) and the analytical ultimate shear force (Vua) estimated from Eq. (6), based on the analytical model proposed in item 2, are compared in Table 6. The maximum difference between the experimental and analytical results of specimens with additional reinforcement was 5% for the specimen P10L - 180/ 1.87, demonstrating good agreement between the experimental and analytical results and the suitability and adequacy of proposed analytical model.

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L.G.F. Grossi et al. / Journal of Constructional Steel Research 166 (2020) 105908

Fig. 18. Experimental setup after test: a) without and b) with additional reinforcement bars.

In the evaluation of the proposed analytical model based in the experimental data, the coefficients m and k in Eqs. (5) and (6) was determinated from mean values. In projects, the m-k straight line obtained from specimens without additional reinforcement must be determined based on the procedures indicated in the standards. Furthermore, the partial safety factors recommended in the normative codes should be introduced in the analytical model proposed and presented in Eq. (4).

0,4

mm2)

0,3

Vu b dF

151 AF b Ls

0.005

Vu bd

0,2 0,1 Test data Average test data m-k method

0,0 -0,1 0,0

0,5

1,0

1,5

AF /bLs

(103)

2,0

5. Conclusions

2,5

Fig. 19. Analysis for m-k method.

Table 6 Comparison between the experimental and analytical ultimate shear force. Slab designation

Nsl (kN)

Vue (kN)

Vua (kN)

V ue V ua

P1S – 120/00 P2S – 120/00 P3S – 120/00 P4L – 180/00 P5L – 180/00 P6L – 180/00 P7L – 180/00 P8S – 120/1.87 P9S – 120/4.71 P10L – 180/1.87 P11L – 180/4.71

– – – – – – – 116.0 112.6 292.2 283.6

25.9 26.5 26.3 21.6 23.5 21.1 21.2 50.3 77.1 42.2 67.7

26.3

0.98 1.01 1.00 0.99 1.06 0.96 0.97 1.04 0.96 1.05 1.01

21.9

48.5 80.4 40.0 67.0

In the current paper, an analytical model to estimate the ultimate shear force of composite slabs with additional reinforcement from constants m and k determinated by specimens without additional reinforcement was developed. To validate the analytical model, an experimental study was also conducted in which different rates of additional reinforcement were tested. Although the insertion of additional reinforcement does not directly affect the local behavior of steel-concrete interface, significant changes in the global behaviour promoted by the additional reinforcement was observed. The experimental results showed the insertion of additional reinforcement improved the structural behavior of composite slabs, promoting increase on carrying load capacity and on longitudinal shear ductility, which allowed a greater use of plastic bending capacity of the composite sections, resulting in better use of the steel decking and concrete slab strength. Differences on cracking and post-peak behavior were also noted. It is seen that the post-peak behavior was more ductile and that the cracking presented smaller opening and evolved more slowly than in the specimens without additional reinforcement. Also, it was observed in the specimens with additional reinforcement that after the first slip, the additional reinforcement bars contributed more than the steel decking to support the tensile forces induced by positive bending moment.

L.G.F. Grossi et al. / Journal of Constructional Steel Research 166 (2020) 105908

a 2-

a-

-

tc

ysl

y

-

-

ds dF

. MR ¼ Npa  y þ Ns  ysl expanding M R ¼ Npa  ðd F −0:5  aÞ þ Ns  ðds −0:5  aÞ

ðA:2Þ

ii) Plastic neutral axis between the upper face of steel decking and the mid-axis of the additional reinforcement bars (tc ≤ a b ds) This situation can be subdivided into two cases. In the first the plastic neutral axis is below of the upper face of the steel decking and above the centroid of the steel decking given the force distribution shown in Fig. A.2, where Nc ≥Ns , Na = Nc − Ns, Np1 is the resulting compressive force of part of the steel decking and Np2 the resulting tensile resulting force of part of the steel decking. In the second case the plastic neutral axis is located between the centroid of the steel decking and the midaxis of the additional reinforcement bars and results in the force distribution shown in Fig. A.3. For second case Nc bNs and Na = Ns − Nc. Note that for both cases, the resistant bending moment is given by the sum of the moments of parts I and part II which results in the Eq. (A.3). The difference between this two cases in the calculation of y and Mpr variables is associated to the signal Nc and Ns that can be simplified assuming the absolute value of Na which result in the same equations for both cases. From simplification, the variables y and Mpr can be obtained by the Eqs. (A.4) and (A.5), respectively. tc 2

Nc

Mp

y

Na ysl

a-

(II) M pr

(I)

Nc N p1 N p2

-

tc

0,85f cd

Ns

Ns

Fig. A.2. Plastic neutral axis located in the steel decking: Case 1.

N p1 N p2 Ns

Na

tc 2

Nc

y

Nc

ysl

a-

-

(II)M pr

(I)

0,85f cd

tc

In composite slabs with full connection, the shear stresses are fully transferred between concrete slab and steel decking and the strain distribution along the cross-section of composite slab can be assumed as linear and continuous [4]. Composite slabs without additional reinforcement bars can fail with the plastic neutral axis located in the concrete slab (a b tc) or below the upper flange of the steel decking (a ≥ tc). In composite slabs with additional reinforcement bars, the plastic neutral axis can be located in the concrete slab (a b tc), between the upper face of the steel decking and mid-axis of the additional reinforcement bars (tc ≤ a b ds) or between the mid-axis of the additional reinforcement and the lower flange of the steel decking (a N ds). In addition, it is possible that the plastic neutral axis is located in the mid-axis of the additional reinforcement bars (a = ds). In practice, the situations where the plastic neutral axis is located in the mid-axis of the additional reinforcement bars (a = ds) or between the mid-axis of the additional reinforcement and the lower flange of the steel decking (a N ds) are impossible because they requires a combination of highest rates of additional reinforcement bars and very thin thickness concrete slab. Therefore, the fomulations corresponding to these situations will not be presented in this manuscript but can be consulted in Grossi [8], for the other situations (a b tc and tc ≤ a b ds) the theoretical ultimate moment equations are shown in sequence. The proposed equations were obtained from rigid plastic analysis, considering the yielding of

ðA:1Þ

-

Appendix A. Analytical model to predict the theoretical ultimate moment of composite slabs with additional reinforcement bars with full connection

Mp


a ¼ Npa þ N s =ð0; 85  f cd  bÞ

-

The authors acknowledge to National Council for Scientific and Technological Development (CNPq) and Modular Building Systems for donating the specimens. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.

N pa

Fig. A.1. Plastic neutral axis located in the concrete slab.

ds dF

Acknowledgements

Nc

Ns

-

None.

0,85f cd

-

Declaration of Competing Interest

the materials in composite slab section and neglecting the tensile strength of concrete, similar to what was considered by Stark and Brekelmans [28] in the developed of the theoretical ultimate moment equations of the composite slabs without additional reinforcement bars. i) Plastic neutral axis located in the concrete slab (a b tc) This situation occurs when Nc NNpa þ Ns, where Nc ¼ 0; 85  f cd  b  t c to a = tc, Npa = AF ⋅ fy and Ns = As ⋅ fyb. The Eqs. (A.1) and (A.2) correspond to the depth of neutral axis in concrete slab (a) and the theoretical ultimate moment (Mp) for composite slabs with full connection.

ds dF

Regarding the analytical model, it was seen that it was able to accurately predict the carrying load capacity of specimens tested in the laboratory, demonstrating the suitability of proposed model to predicted the carrying load capacity of composite slabs with additional reinforcement. It is important to emphasize that the analytical model was validated only with experimental results of composite slabs with ductile behavior, being necessary, therefore, to evaluate the accuracy of the analytical model for composite slabs with fragile behavior. The two main advantages of the proposed analytical model are described in sequence. First, as it is a simple model, can be easily used by designers. Second, as the constants m and k determined from specimens without additional reinforcement are used in proposed model, flexure bending tests of composite slabs with additional reinforcement are not necessary, which reduces the time and costs spent in laboratory. To use the analytical model in design projects, the constants m and k must be defined according to the guidelines described in design standards. Furthermore, the partial safety factors recommended by design codes have to be included in the proposed analytical model. As a suggestion for future investigations, it recommended the evaluation: of different rates of additional reinforcement bars; of slenderness in composite slabs with additional reinforcement bars; comparison between composite slabs with same positive reinforcement area but with different steel decking thickness and, consequently, different additional reinforcement area. In addition, it is suggested that the analytical model proposed in this paper be evaluated for composite slabs with fragile behavior.

11

Mp

Ns

Fig. A.3. Plastic neutral axis located in the steel decking: Case 2..   tc M R ¼ N c  y þ Ns ds −y− þ M pr 2 .   jN c −N s j M pr ¼ 1; 25 M pa 1− ≤M pa N pa y ¼ ht −0; 5t c −ep þ ep −e


jN c −N s j N pa

ðA:3Þ ðA:4Þ ðA:5Þ

It should be noted that the case 2 of is very unlikely because, similar to the situations where a = ds and a N ds, it require a very thin thickness concrete slab and a highest rate of additional reinforcement bars. Thus,

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L.G.F. Grossi et al. / Journal of Constructional Steel Research 166 (2020) 105908

the formulation was only cited in this document to show the complete formulation of the problem. References [1] A. Gholamhoseini, R.I. Gilbert, M.A. Bradford, Z.T. Chang, Longitudinal shear stress and bond-slip relationships in composite concrete slabs, Eng. Struct. 69 (2014) 37–48, https://doi.org/10.1016/j.engstruct.2014.03.008. [2] A. Gholamhoseini, A. Khanlou, G. MacRae, A. Scott, S. Hicks, R. Leon, An experimental study on strength and serviceability of reinforced and steel fibre reinforced concrete (SFRC) continuous composite slabs, Eng. Struct. 114 (2016) 171–180, https://doi. org/10.1016/j.engstruct.2016.02.010. [3] M. Ferrer, F. Marimon, M. Crisinel, Designing cold-formed steel sheets for composite slabs: an experimentally validated FEM approach to slip failure mechanics, ThinWalled Struct. 44 (2006) 1261–1271, https://doi.org/10.1016/j.tws.2007.01.010. [4] M. Ferrer, F. Marimon, M. Casafont, An experimental investigation of a new perfect bond technology for composite slabs, Constr. Build. Mater. 166 (2018) 618–633, https://doi.org/10.1016/j.conbuildmat.2018.01.104. [5] F.M. Abas, R.I. Gilbert, S.J. Foster, M.A. Bradford, Strength and serviceability of continuous composite slabs with deep trapezoidal steel decking and steel fibre reinforced concrete, Eng. Struct. 49 (2013) 866–875, https://doi.org/10.1016/j.engstruct.2012. 12.043. [6] V.V. Degtyarev, Strength of composite slabs with end anchorages. Part I: analytical model, J. Constr. Steel Res. 94 (2014) 150–162, https://doi.org/10.1016/j.jcsr.2013. 10.005. [7] H. Cifuentes, F. Medina, Experimental study on shear bond behavior of composite slabs according to Eurocode 4, J. Constr. Steel Res. 82 (2013) 99–110, https://doi. org/10.1016/j.jcsr.2012.12.009. [8] L.G.F. Grossi, Sobre o Comportamento Estrutural e o Dimensionamento de Lajes Mistas de Aço e Concreto com Armadura Adicional, 275f. Dissertação (Mestrado). Escola de Engenharia de São Carlos, Universidade de São Paulo, São Carlos 2016, p. 2016. [9] DD ENV 1992-1-1:1992, Eurocode 2: Design of Concrete Structures-Part 1. General Rules and Rules for Buildings-(Together with United Kingdom National Application Document), Br. Stand, 1992 194. [10] A.B.D.N. TÉCNICAS, NBR 8800:, Projeto de estruturas de aço e de estruturas mistas de aço e concreto de edifícios. Rio de Janeiro, www.abnt.org.br 2008. [11] J.D. Ríos, H. Cifuentes, A. Martínez-De La Concha, F. Medina-Reguera, Numerical modelling of the shear-bond behaviour of composite slabs in four and six-point bending tests, Eng. Struct. 133 (2017) 91–104, https://doi.org/10.1016/j.engstruct. 2016.12.025.

[12] R. Abdullah, W.S. Easterling, New evaluation and modeling procedure for horizontal shear bond in composite slabs, J. Constr. Steel Res. 65 (2009) 891–899, https://doi. org/10.1016/j.jcsr.2008.10.009. [13] X. Li, X. Zheng, M. Ashraf, H. Li, Experimental study on the longitudinal shear bond behavior of lightweight aggregate concrete – closed profiled steel sheeting composite slabs, Constr. Build. Mater. 156 (2017) 599–610, https://doi.org/10.1016/j. conbuildmat.2017.08.108. [14] Y.H. Wang, J.G. Nie, Analytical model for ultimate loading capacities of continuous composite slabs with profiled steel sheets, Sci. China Technol. Sci. 58 (2015) 1956–1962, https://doi.org/10.1007/s11431-015-5877-1. [15] M.M. Florides, K.A. Cashell, Numerical modelling of composite floor slabs subject to large deflections, Structures. 9 (2017) https://doi.org/10.1016/j.istruc.2016.10.003. [16] CEN (European Committee for Standardization) Eurocode 4, H E U R O P E a N N I O N, Brussels, 2004. [17] AMERICAN SOCIETY OF CIVIL ENGINEER, ANSI/ASCE 3–-91, Standard for the Structural Design of Composite Slabs. New Yok, New York, United State, 1992nd ed., 1992 1992. [18] ANSI, SDI, C-2011 Standard for Composite Steel Floor Deck - Slabs, 2012. [19] C. Steel, CSSBI 12M-2017: Standard for Composite Steel Deck, Can. Sheet Steel Build. Inst., 2017 7. [20] AS/NZS4600, Draft for public comment Australian/New Zealand standard, 2016, 2003. [21] R. Abdullah, A.B.H. Kueh, I.S. Ibrahim, W.S. Easterling, Characterization of shear bond stress for design of composite slabs using an improved partial shear connection method, J. Civ. Eng. Manag. 21 (2015) 720–732, https://doi.org/10.3846/13923730. 2014.893919. [22] M.L. Porter, J.C.E. Ekberg, Design recommendatios for steel deck floor slabs, ASCE, J. Struct. Div. 102 (1976) 2121–2136. [23] W.C. Schuster, R.M. Ling, Mechanical interlocking capacity of composite slabs, Missouri University of Science and Technology (Ed.), 5th - Int. Spec. Conf, Cold-Formed Steel Struct, Missouri ST 1980, p. 23. http://scholarsmine.mst.edu/isccss%0D. [24] ASTM, A370, Standard Test Methods and Definitions for Mechanical Testing of Steel Products, 2017https://doi.org/10.1520/A0370-14.2. [25] R. Abdullah, V.P. Paton-cole, W.S. Easterling, F. Asce, Quasi-static analysis of composite slab, Malaysian, J. Civ. Eng. 19 (2007) 1–13. [26] Y.C. Kan, L.H. Chen, T. Yen, Mechanical behavior of lightweight concrete steel deck, Constr. Build. Mater. 42 (2013) 78–86, https://doi.org/10.1016/j.conbuildmat.2013. 01.007. [27] S. Chen, X. Shi, Shear bond mechanism of composite slabs - a universal FE approach, J. Constr. Steel Res. 67 (2011) 1475–1484, https://doi.org/10.1016/j.jcsr.2011.03.021. [28] J.W.B. Stark, J.W.P.M. Brekelmans, Plastic Design of Continuous Composite Slabs, Struct. Eng. Int. 6 (1990) 47–53, https://doi.org/10.2749/101686696780495914.