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Experimental study on the longitudinal shear bond behavior of lightweight aggregate concrete – Closed profiled steel sheeting composite slabs
Construction and Building Materials 156 (2017) 599–610
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Experimental study on the longitudinal shear bond behavior of lightweight aggregate concrete – Closed profiled steel sheeting composite slabs Xin Li a, Xiaoyan Zheng a,⇑, Mahmud Ashraf b, Haitao Li a a b
College of Civil Engineering, Nanjing Forestry University, Nanjing 210037, China School of Engineering and Information Technology, The University of New South Wales at the Australian Defence Force Academy, Northcott Drive, Canberra ACT 2612, Australia
h i g h l i g h t s A new type of LWAC – Closed profiled steel sheeting Composite Slab is proposed. Specific slab configurations produce better composite actions and a new mode failure. The validities of existing methods for the new type of composite slab are confirmed.
a r t i c l e
i n f o
Article history: Received 9 May 2017 Received in revised form 13 August 2017 Accepted 17 August 2017
Keywords: Composite slab Lightweight aggregate concrete Closed profiled steel sheeting Longitudinal shear bond strength
a b s t r a c t Composite slabs with ordinary concrete and typical profiled steel sheeting are quite common in construction industry. This paper presents full-scale experiments conducted on a new type of composite slab produced from lightweight aggregate concrete and closed profiled steel sheeting (LCCS). A total of 11 simply supported specimens were tested to investigate the structural behavior of this new type of composite slab with special emphasis on their failure modes. Whilst shear bond failure is the common failure type for typical composite slabs with sheet sheeting, a new type of failure was observed herein where slabs failed with showing remarkable bending capacity, and significant end slips was observed in long-span slabs. In addition to m-k method and PSC method, which are typically used for composite slabs with normal weight concrete, three other techniques such as slenderness method, PSC composite beam method and force equilibrium method were used to assess the longitudinal shear bond strength of LCCS. The ultimate carrying capacity and the shear bond stress predicted using slenderness method and force equilibrium method showed very good agreement with test results; PSC composite beam method may underestimate the longitudinal shear bond strength, but still can be used as an optional method. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Composite slabs consisting of cold-formed profiled steel sheeting and structural concrete are one of the most popular types of floor system used in steel framed buildings. The main advantages of this concrete-steel composite slabs are the reduction of selfweight and simplification of the construction process. The profiled steel sheeting acts as a permanent formwork before casting and as tension reinforcements after casting; the standard scaffolding and propping systems are not required [1]. Lightweight aggregate concrete (LWAC) is now considered as a useful construction material due to significant reduction in self⇑ Corresponding author. E-mail address: [email protected] (X. Zheng). http://dx.doi.org/10.1016/j.conbuildmat.2017.08.108 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.
weight as well as providing better performance in thermal insulation (low density), fire resistance, acoustic isolation and reduction in lateral force due to earthquake when compared with normal weight concrete (NWC) [2,3]. Hence, introduction of LWAC into concrete-steel composite slabs could produce an improved structural system. However, very limited numbers of studies are currently available on composite slabs with LWAC and profiled steel sheeting, especially those using closed profiled steel sheeting. The longitudinal shear bond failure is reported to be the most common failure mode in composite slabs. Significant end slips occur between concrete and profiled steel sheeting interfaces well ahead of reaching its ultimate bending capacity [4]. The failure mode is determined by composite actions which are dependent on the transmission of longitudinal shear bond stress due to pure bond, mechanical interlocking and friction as well as several other
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factors including material properties of concrete, geometry and thickness of steel sheeting, slenderness ratio of the slab, loading arrangement and shear connectors [5–7]. In this paper, the failure mode of a new type composite slab with LWAC and closed profiled steel sheeting (LCCS) is investigated. A mixed failure mode is found and defined. The methods (m-k method, PSC method, slenderness method, PSC composite beam method and force equilibrium method) for evaluating the longitudinal shear bong strength are compared and confirmed to be valid on the new type composite slabs.
Existing methods for assessing the longitudinal shear bond strengths are mainly based on slabs with NWC and trapezoidal profiled steel sheeting. Eurocode 4 suggests using m-k method and Partial Shear Connection method (PSC). Both of these two methods require experimental data obtained from full-scale tests because the composite action is strongly dependent on the particular geometry type of the sheeting. In addition to these methods, the current paper also considered Slenderness method, PSC Composite Beam method and Force Equilibrium method to check their suitability for the new type of composite slab investigated herein. All considered design rules are briefly discussed in the following paragraphs. 2.1. The m-k method The semi-empirical based m-k method was developed by Schuster [8], Porter and Ekberg [9,10], and is adopted in ASCE [11] and Eurocode 4 [12]. The values of m and k are obtained by using linear regression but are only applicable to specific slab configurations as expressed in Eq. (1).
Ap m þk cv s bLs
bdp
su ¼
Nc bðLs þ L0 Þ
ð2Þ
If extra support reaction is considered:
su ¼
N c lV t bðLs þ L0 Þ
ð3Þ
The partial interaction connection moment resistances of composite slabs M can be calculated by:
2. Theories of longitudinal shear bond strength
V 1;Rd ¼
the surface area of the interface between concrete and steel sheeting along the overall length of the shear span, the longitudinal shear bond strength su can be calculated as:
ð1Þ
where V1,Rd is the design shear resistance; Ls is the length of the shear span; Ap is the nominal cross-section of the steel sheeting; b and dp are the width and effective depth of slab, respectively; cvs is the partial safety factor i.e. 1.25 for the slab as defined in Eurocode 4. 2.2. The PSC method PSC method (Fig. 1), which is based on a clear mechanical model, is an alternative to the m-k method but should only be used for composite slabs with ductile longitudinal shear behavior as outlined in Eurocode 4. It is assumed that the mean value for the ultimate longitudinal shear stress su is constant and is uniformly distributed throughout
M ¼ Nc z þ M pr
ð4Þ
z ¼ h 0:5x ep þ ðep eÞg
ð5Þ
Mpr ¼ 1:25Mpa ð1 gÞ
ð6Þ
where Nc is the actual compression force in concrete; L0 is the overhanging length beyond the support; l is the default value of the friction coefficient to be taken as 0.5; Vt is support reaction under the ultimate test load; z is the moment lever arm; h is the overall thickness of the slab; e and ep are the distance from centroidal axis and plastic neutral axis of the effective area of the steel sheeting to its lower flange fiber, respectively; Mpr and Mpa are reduced plastic moment resistance and plastic moment of the effective cross section of the steel sheeting, respectively; g is the degree of shear connection defined as g = Nc/Ncf obtained from test; Ncf is the maximum compression force in concrete at fully interaction connection. 2.3. The slenderness method Slenderness method, which is a modified version of PSC method, considers the thickness of steel sheeting and the slenderness ratio of slab (shear span length to effective depth of slab ratio, Ls/dp). Considerable studies reported by [6,13,14] showed that the longitudinal shear bond strength su varies with the slenderness ratio Ls/ dp and is represented as a function of slab slenderness. The Slenderness method was derived based on the following assumptions: (1) The moment lever arm z, differs very slightly from the effective depth of the slab dp; (2) The overhanging length L0 doesn’t have any considerable effect on slab behavior, and hence is usually negligible. Eq. (4) can be written as:
VLs ¼ sðLs þ L0 Þbdp þ M pr
ð7Þ
Rearranging Eq. (7) and substituting into Eq. (1):
sdp ¼ m
Ap dp kbdp Ls M pr þ b ðLs þ L0 Þ bðLs þ L0 Þ
ð8Þ
If the overhanging length L0 is ignored, the second term of the right side in Eq. (8) becomes a constant s regardless of the Mpr value as explained by Abdullah [6]
sdp ¼ p
Fig. 1. Mechanical model of PSC method.
Ap dp þs bLs
ð9Þ
Eq. (9) was also obtained by Chen [15] by using a different experimental linear regression method. For a specific type of profiled steel sheeting, the ratio of expansion length w to the width of the slab b is constant, and can be written as w = ib = Ap/t, where i is a constant. The new equation changes into:
X. Li et al. / Construction and Building Materials 156 (2017) 599–610
sdp ¼ p
itdp þs Ls
ð10Þ
As seen from Eq. (10), the slenderness equation has the same form and can be compared directly with the m-k method as it employs the concept of linear interpolation into modified PSC method. The slope p and the intercept s are obtained from linear regression.
2.4. The PSC composite beam method PSC Composite Beam method is proposed to assess the capacity of Partial Shear Connection beam in Chinese Code for design of steel structures [16]. Figs. 1 and 2 show the mechanical model and equilibrium relationships used in this method. It is used only to investigate the feasibility for the new type of LCCSs. The area of the steel sheeting compression zone Ac and the partial shear connection moment resistance Mu can be expressed as:
Ac ¼ ðAp f y Nc Þ=2f y
ð11Þ
M u ¼ Nc y1 þ 0:5ðAp f y Nc Þy2
ð12Þ
Thus, su can be calculated using Eq. (2) and Eq. (3).where y1 is the moment lever arm; y2 is the distance between the steel sheeting centroid positions of tensile zone and compressive zone. fy is the yield strength of the steel sheeting.
2.5. The force equilibrium method The force equilibrium method is also a PSC based method, and was first used to calculate the relationship between the longitudinal shear bond strength and the end slip in bending test reported by An [17]. The results of su versus s curves are widely used in numerical modelling. When compared with the PSC method, the primary difference lies in using the geometry and mechanics of materials relationships to calculate the reduced plastic moment resistance of the sheeting Mpr, as shown in Fig. 3.
L 2Ls ðd1 þ d2 Þ 1 Mpr ; ¼ ¼ Ls R Es I s R
ð13Þ
d1 þ d2 Es Is Ls ðL 2Ls Þ
ð14Þ
M pr ¼
Thus, su can be calculated using Eq. (2) and Eq. (3).where d1 and d2 are the deflections measured under each side of applied load line; Es and Is are the elasticity modulus and inertia moment of the steel sheeting.
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3. Setup for the experimental study Eleven different configurations for a new type of composite slab with closed profiled steel sheeting and shale ceramisite lightweight aggregate concrete were investigated. The shape for all profiles was the same as shown in Fig. 4; Geometric and material properties for the considered profiles are shown in Table 1. LWAC was mixed with shale ceramisite (gravel type, Fig. 5), medium grained sand, water and Portland cement. The strengthgrade and grain-size distribution of the shale ceramisite were 700 and 5–20 mm, respectively. Mix proportion used in concrete is shown in Table 2, which produced approximately 30% lighter concrete, LWAC (1823 kg/m3) when compared with that of NWC (2500 kg/m3). The profiled steel sheeting was cleaned before casting, and was completely supported on the floor during casting in order to reduce uncertainties that could affect the shear bond strength, and to minimize the initial stress and deformation in the slab. It acts as a permanent formwork before casting, and as tension reinforcement after casting [5]. Only distribution reinforcement was included to tackle shrinkage and temperature effects. Three standard 150 mm 150 mm 300 mm prism specimens and six 150 mm cubic specimens were tested at 28 days to determine the elastic modulus and the mean compressive strength of concrete. The slabs were 720 mm wide and 2.2 m (short span)/3.8 m (long span) in length consisting of a 100 mm overhang from each support. The thickness of the slabs were 120 mm, 150 mm and 180 mm with the same shear span length Ls = L’/4. The main parameters of each slab are summarized in Table 3. STS-S1.2-150 and STS-L1.2-150 were two contrasting specimens with U16 mm studs were arc welded through the sheeting on the steel plate as shear connectors. Designation of the specimens represent experiment type – span length (S/L) and profile thickness (1.2/1.0/0.8) – design thickness of the slab. The abbreviations ST and STS mean the Static Test and the Static Test with Studs, respectively. L and S refer to long span and short span, respectively. Figs. 6–8 show the schematic of the experimental setup with measurement parameters. The load was applied at L’/4 using a 300 kN electro-hydraulic servo jack with displacement control technique at a rate of 0.5 mm/min for the short-span and 1.0 mm/min for the long-span. Slabs were simply supported with a pin and a roller support applied at each end. Slips at each end, deflections under the applied load lines and strains at mid-span were measured by the LVDTs and TDS530. 4. Discussion of the test results 4.1. The failure procedure The main results recorded from the conducted tests are summarized in Table 4. Pcr is the initial cracking load determined by
Fig. 2. The cross-section equilibrium relationships.
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Fig. 3. The geometry and mechanics of materials relationships.
Fig. 4. Shape of steel sheeting.
hearing the noise of the concrete cracking; Ps is the load causing an end slip of 0.1 mm. Figs. 9 and 10 show the mid-span deflection versus mid-span moment curves. All slabs showed somewhat similar failure pattern. At the beginning of loading, the profiled steel sheeting worked well with the LWAC. Deflection increased linearly with applied loading within elastic range showing fully composite action. The initial concrete cracks occurred after the interface lost its chemical bonding, which was obvious through continuous crushing noise. The indentations and flanges on the sheeting kept transmitting the longitudinal shear stress after the initial cracking by mechanical interlocking and friction. The composite slab deformed inelasticity, whilst the deflection increased nonlinearly with increase in applied load. The mean initial cracking load was 0.21 Pu for short-span slabs, 0.16 Pu for long-span slabs and 0.3 Pu for slabs with studs. Initial end slip occurred after a specific percentage of the applied load and resulted in a sudden transition as shown in Figs. 11 and 12. This transition is due to the interface separation between steel sheeting and concrete, which is also marked by the observed fluctuations. Nevertheless, the specific shape of the closed profiled steel sheeting, in this study, embedded its flanges in the concrete providing a better ductile performance. They were able to support the increscent load as well as consequent deflection and slips. The mean initial end slip load was 0.50 Pu for short-span slabs, 0.62 Pu for long-span slabs, 0.76 Pu for short-span slab with studs and 0.86 Pu for long-span slab with studs.
The concrete cracks reached the upper fiber of the slab when the applied load reached its ultimate magnitude. The main crack for each slab was fully developed under one side of the applied load line, and the interface separation was observed along the entire shear span, which eventually caused the applied load to gradually decrease but mid-span deflection and end slips kept increasing. All slabs showed ductile failure modes; end studs were effective in complementing the ultimate carrying capacity and the mid-span deflections in all slabs in addition to reducing the end slips in longspan slabs. 4.2. The ultimate limit state and failure modes The ultimate load carrying capacities and failure modes of slabs are shown in Table 5, where Mu is the ultimate mid-span moment obtained from test, Mp,rm is the bending resistance of the section at full shear connection stage, and Smax is the end slip at ultimate mid-span moment. The slenderness ratio Ls/dp showed a clear influence on the ultimate carrying capacities. Abdinasir [6,18] reported that for a NWCtrapezoidal profiled steel sheeting composite slab, the reaction force drops exponentially with increasing slenderness within a certain range and changes slowly with continued increasing slenderness. Similar phenomenon was observed in LCCSs as shown in Fig. 13, which clearly shows that the slenderness ratio is a significant factor in assessing load carrying capacities for all types of concrete-steel sheeting composite slabs. The steel sheeting thickness showed a significant influence on the ultimate carrying capacity of the slab with same depth, as shown in Fig. 14. The increments of Mu were about 23% in both short-span slab and long-span slab when the steel sheeting thickness changed from 0.8 mm to 1.0 mm, whilst stable trends from 1.0 mm to 1.2 mm. That is, with the increase of steel sheeting thickness, the ultimate carrying capacity may stabilize; this effect
Table 1 Geometric and material properties of profile steel sheeting. Sheet profile
Thickness (mm)
Moment of inertia (cm4/m)
Section modulus (cm3/m)
Yield strength (MPa)
Elastic modulus (GPa)
YX66-240-720
0.8 1.0 1.2
84.24 111.13 132.70
17.55 23.62 28.24
230 234 232
182 185 180
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is very important for usual profiles when design the configurations of the slab. All short-span slabs without studs, ST-S1.2-180, ST-S1.2-150, ST-S1.0-150, ST-S0.8-150 showed longitudinal shear failure modes; they failed before reaching the theoretical plastic bending capacity. Mu/Mp,rm ratios varied from 0.77 to 0.93 with a mean of 0.85, which is larger than the typical ratio for normal type concrete-steel composite slabs with a mean value less than 0.6 [3,5,6,15]. This indicates that the new type of LCCSs may provide better composite actions when compared against typical NWCsteel sheeting composite slabs. Slabs with studs showed bending failure modes; Mu/Mp,rm ratio and end slip Smax for STS-S1.2-150 were 1.24 and 1.38 mm, respectively, whilst those for STS-L1.2-150 were 1.12 and 1.13 mm, respectively. When compared with similar slabs without studs (ST-S1.2-150 and ST-L1.2-150), STS-S1.2-150 had a similar end slip but a greater carrying capacity of 50.3% and a larger mid-span
Fig. 5. Typical shape of the ceramisite lightweight aggregate.
Table 2 Mix proportion of LWAC. Grade
Material consumption of concrete/m3(kg) Cement
Sand
Shale ceramisite
Water
LC30
420
720
400
200
Nominal density (kg/m3)
fck,cube (MPa)
fcd (MPa)
Elastic modulus (GPa)
1823
43.7
20.6
26.3
Note: fck,cube is the characteristic compressive strength of concrete. fcd is the design value of the concrete compressive strength.
Table 3 Dimensions and geometrical properties of each slab. Slab designation
Dimensions b L h (mm)
t (mm)
End anchorage (studs)
Ap (mm2)
Ls (mm)
dp (mm)
Slenderness ratio (Ls/dp)
ST-S1.2-180 ST-S1.2-150 ST-L1.2-150 ST-L1.2-120 ST-S1.0-150 ST-L1.0-150 ST-S0.8-150 ST-L0.8-150 ST-L0.8-120 STS-S1.2-150 STS-L1.2-150
720 2200 167 720 2200 147 720 3800 148 720 3800 120 720 2200 153 720 3800 148 720 2200 147 720 3800 142 720 3800 110 720 2200 145 720 3800 151
1.2 1.2 1.2 1.2 1.0 1.0 0.8 0.8 0.8 1.2 1.2
– – – – – – – – – n=3 n=3
1500 1500 1500 1500 1250 1205 1000 1000 1000 1500 1500
500 500 900 900 500 900 500 900 900 500 900
149.7 129.7 130.7 102.7 135.7 130.7 129.7 124.7 92.7 127.7 133.7
3.34 3.85 6.89 8.76 3.68 6.89 3.86 7.22 9.71 3.92 6.73
Note: n is the number of the studs used in each end.
Fig. 6. The experiment setup and measurement parameters.
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Fig. 7. The experiment setup before test.
Fig. 9. Mid-span deflection versus moment curves (short span).
Fig. 8. The experiment setup after test.
deflection of 8.3%; STS-L1.2-150 had a significant decreasing of end slip about 89%, a moderate increasing of carrying capacity about 26.1% and a prominent rising of mid-span deflection about 21.0%. The long-span slab ST-L1.2-150, Mu/Mp,rm = 0.91, failed in a longitudinal shear failure with a larger end slip of 10.05 mm. Other long span slabs ST-L1.2-120, ST-L1.0-150, ST-L0.8-150 and STL0.8-120 exceeded the theoretical full plastic bending capacity with Mu/Mp,rm varying between 1.04 and 1.14, showing significant
Fig. 10. Mid-span deflection versus moment curves (long span).
end slips with Smax varying between 6.28 mm and 10.35 mm. Observed failure modes showed a combination of bending failure accompanied by obvious end slips as shown in Figs. 8 and 15. This
Table 4 The main results from the tests. Slab designation
ST-S1.2-180 ST-S1.2-150 ST-L1.2-150 ST-L1.2-120 ST-S1.0-150 ST-L1.0-150 ST-S0.8-150 ST-L0.8-150 ST-L0.8-120 STS-S1.2-150 STS-L1.2-150
Carrying capacity
The initial cracking of concrete
The initial end slip
Pu (kN)
Mu (kNm)
Pcr (kN)
Mcr (kNm)
Mcr/Mu
Ps (kN)
Ms (kNm)
Ms /Mu
146.28 130.84 82.23 78.12 127.27 81.37 103.15 65.48 45.85 196.70 103.72
36.57 32.71 37.00 35.15 31.82 36.62 25.79 29.47 20.63 49.18 46.67
33.32 27.03 11.02 8.69 27.81 13.83 25.21 16.69 8.90 35.33 13.39
8.33 6.76 4.96 3.91 6.95 6.22 6.30 7.51 4.01 8.83 6.02
0.23 0.21 0.14 0.12 0.19 0.18 0.20 0.21 0.16 0.30 0.29
58.69 69.41 46.15 52.65 47.81 55.95 63.90 35.82 28.04 149.72 89.46
14.67 17.35 20.77 23.69 11.95 25.18 15.97 16.12 12.58 37.43 40.26
0.40 0.53 0.56 0.67 0.38 0.69 0.62 0.55 0.61 0.76 0.86
Mean value 1 Coefficient of variation 1 Mean value 2 Coefficient of variation 2 Note: Mean value 1 and Coefficient of variation 1 calculated from short-span slabs without end studs. Mean value 2 and Coefficient of variation 2 calculated from long-span slabs without end studs.
0.21 0.08 0.16 0.22
0.50 0.23 0.62 0.10
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Fig. 11. End slip versus mid-span moment curves (short span).
Fig. 13. Relationships between slenderness ratio and ultimate reaction force.
Fig. 14. Steel sheeting thickness versus Mu in 150 mm slabs. Fig. 12. End slip versus mid-span moment curves (long span).
type of failure mode is a new observation and has been categorized as a ‘mixed mode failure’, in which slab has a remarkable bending capacity but suffers significant end slip at failure; following are the possible reasons for this new type of failure. (1) LWAC has a lower elasticity modulus of 26.3 GPa, in this study, which is about 80% of NWC with similar strength. Lower elasticity modulus facilitates in releasing internal
stress of concrete, which makes it more effective in improving the synergetic deform performance between LWAC and steel sheeting. (2) The geometry of closed profiled steel sheeting produced a strong bond between the concrete and the steel profile. The upper flanges of the steel profile were encased within LWAC making those even stiffer, and the inverted triangular shape restrained the interface separation during deformation. These two materials deformed uniformly along the
Table 5 The ultimate carrying capacities and failure modes of the slabs. Slab designation
Ls/dp
Mu (kNm)
Vu (kN)
Mp,rm (kNm)
Mu/Mp,rm (kN)
Smax (mm)
Failure mode
ST-S1.2-180 ST-S1.2-150 ST-L1.2-150 ST-L1.2-120 ST-S1.0-150 ST-L1.0-150 ST-S0.8-150 ST-L0.8-150 ST-L0.8-120 STS-S1.2-150 STS-L1.2-150
3.34 3.85 6.89 8.76 3.68 6.89 3.86 7.22 9.71 3.92 6.73
36.57 32.71 37.00 35.15 31.82 36.62 25.79 29.47 20.63 49.18 46.67
73.14 65.42 41.12 39.06 63.64 40.68 51.58 32.74 22.92 98.35 51.86
47.30 40.34 40.63 30.89 36.58 35.07 27.74 26.56 19.20 39.64 41.67
0.77 0.81 0.91 1.14 0.87 1.04 0.93 1.11 1.07 1.24 1.12
1.74 1.30 10.05 6.68 1.69 10.35 1.24 9.47 6.28 1.38 1.13
Shear bond failure Shear bond failure Shear bond failure Mixed failure Shear bond failure Mixed failure Shear bond failure Mixed failure Mixed failure Bending failure Bending failure
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Closed type profiled steel sheeting used in the current study possessed a lower height of centroid, and hence provided a larger moment lever arm in the composite slab action ensuring that the material properties were fully utilized. Fig. 16 clearly shows that all long-span slabs reached steel yield strain. Overall, the better composite action played a significant role in all types of LCCSs resulting in mixed failure in long-span slabs, which is different from observations reported from normal type concrete-steel sheeting composite slabs [2,3,5–7,13–15,18–20]. 4.3. The serviceability limit state Fig. 15. The significant slip at the long-span slab end.
Fig. 16. Steel deck strain at mid-span versus mid-span moment.
vertical axis as well as transmitted shear bond stress longitudinally through the effects of chemical bonding, mechanical interlocking and friction. (3) Concrete between the upper and the lower flanges of the steel sheeting was under multiaxial stress conditions because of the constraints from the surrounding sheeting.
In Chinese Code for design of concrete structures [21], the same deflection limits are stipulated both NWC and LWAC structures. L’/200 for ordinary constructions and L’/250 for constructions with higher deflection requirements. In BS 5950-4, the recommended limit for the maximum deflection of composite slabs due to imposed load is the lesser value between L’/350 and 20 mm. Obtained test results are shown in Table 6. The t versus M/Mu ratios from same overall thickness 150 mm slabs are shown in Fig. 17. The M/Mu ratio can be an evaluation of the utilization rate of material strength, where negligible difference was observed between 1.2 mm and 0.8 mm steel sheeting slabs. However, the sunken trends in 1.0 mm steel sheeting slabs, especially in short-span, indicated that same overall thickness slabs with 0.8 mm and 1.2 mm steel sheeting made better use of material properties than 1.0 mm steel sheeting when the slab resistance is controlled by its deflection limit. Fig. 18 shows the h versus M /Mu ratios of each slab. The rates of M/Mu increase were similar in 1.2 mm steel sheeting slabs, ST-S1.2180 and ST-S1.2-150, ST-L1.2-150 and ST-L1.2-120, regardless of span lengths, whilst those for 0.8 mm steel sheeting slabs were slower (ST-L0.8-150 and ST-L0.8-120). When the deflections reached specified limits of L’/200 and L’/250, the mean M/Mu values for short-span slabs were 0.84 and 0.75 respectively, whilst those for long-span slabs were 0.52 and 0.43 respectively. Lower moment ratio ensures higher safety capacity beyond the serviceability limit state. Even smaller values were observed in slabs with end studs. In short, steel sheeting thickness t may influence the evaluation of the utilization rate of material strength, while slab overall
Table 6 The deflections from the tests. Slab designation
ST-S1.2-180 ST-S1.2-150 ST-L1.2-150 ST-L1.2-120 ST-S1.0-150 ST-L1.0-150 ST-S0.8-150 ST-L0.8-150 ST-L0.8-120 STS-S1.2-150 STS-L1.2-150
Carrying capacity
f = l/200
Pu (kN)
Mu (kNm)
Pl/200 (kN)
Ml/200 (kNm)
Ml/200/Mu
f = l/250 Pl/250 (kN)
Ml/250 (kNm)
Ml/250/Mu
146.28 130.84 82.23 78.12 127.27 81.37 103.15 65.48 45.85 196.70 103.72
36.57 32.71 37.00 35.15 31.82 36.62 25.79 29.47 20.63 49.18 46.67
140.53 111.27 48.38 33.59 86.93 45.11 87.84 36.75 21.42 134.77 50.83
35.13 27.82 21.77 15.12 21.73 20.30 21.96 16.54 9.64 33.69 22.88
0.96 0.85 0.59 0.43 0.68 0.55 0.85 0.56 0.47 0.69 0.49
130.65 101.53 42.12 26.47 76.57 37.98 75.51 29.76 17.57 109.62 40.50
32.66 25.38 18.96 11.91 19.14 17.09 18.88 13.39 7.91 27.41 18.23
0.89 0.78 0.51 0.34 0.60 0.47 0.73 0.45 0.38 0.56 0.39
Mean value 1 Coefficient of variation 1 Mean value 2 Coefficient of variation 1 Note: Mean value 1 and Coefficient of variation 1 calculated from short-span slabs without end studs. Mean value 2 and Coefficient of variation 2 calculated from long-span slabs without end studs.
0.84 0.14 0.52 0.12
0.75 0.16 0.43 0.16
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Fig. 17. t versus M/Mu ratios.
Fig. 18. h versus M/Mu ratios.
thickness h and clear span length of slab L’ may affect the rate of increase. Short-span slab with thicker h and t could have better utilization rate in the serviceability limit state. The current limits will impede the fully use of material properties, especially overconservative in long-span slab and slab with studs. 5. Methods of analysis Considering the particular combining forms and different failure modes in the new type of LCCSs, the feasibilities of assessing the longitudinal shear bond strength by using traditional methods are discussed below. 5.1. Comparison between m-k method and slenderness method The linear regression of the predictions obtained using m-k method and slenderness method are shown in Figs. 19 and 20.
The main parameters used in linear regression and the results from the equations are summarized in Table 7. 5.1.1. The m-k equation The linear regression equation for m-k method is shown in Eq. (15). With m = 159.61 N/mm2 and k = 0.22, correlation coefficient R = 0.9385.
Ap V 1;Rd ¼ bdp 159:61 þ 0:22 bLs
ð15Þ
5.1.2. The shear-bond slenderness equation The closed profile steel sheeting used in the tests has same expansion length w = 1250 mm and slab width b = 720 mm. Ap/ b = 1.736t, and hence the Eq. (10) can be express as:
sdp ¼ 1:736p
tdp þs Ls
ð16Þ
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sdp ¼ 165:13
tdp þ 29:12 Ls
ð17Þ
Outcomes obtained from previous studies on composite slabs showed that the m-k method is a reliable tool in predicting the strength of composite slabs despite its semi-empirical formulation without any clear mechanical model. On the other hand, the slenderness method is a modified PSC method based on the schematic diagram as shown previously in Fig. 1. By introducing some assumptions and simplifications, a direct comparison between modified PSC method and m-k method is now possible. When the predicted strengths were compared against obtained test results, the m-k method produced a mean of 1.005 with a standard deviation of 0.060, whilst those for the slenderness method were 1.008 and 0.070, respectively. This clearly showed that ultimate carrying capacities predicted using the slenderness method were almost the same as those predicted using the m-k method for the new type of LCCSs. The effects of end studs should, however, be considered separately, otherwise an underestimation of the load carrying capacity will be observed as shown in Table 7 (STS-S1.2-150 and STS-L1.2150).
Fig. 19. The m-k curves of slabs without end studs.
5.2. Shear bond stress value calculated from different methods
Fig. 20. The p-s curves of slabs without studs.
The linear regression equation for slenderness method is shown in Eq. (17). With p = 95.12 MPa, s = 29.12 MPa mm, correlation coefficient R = 0.8986.
Table 8 summarizes the shear bond strength su that were calculated using different methods introduced in this paper. Fig. 21 shows t versus su curves form the same overall thickness 150 mm slabs. The shear bond strengths obtained from slenderness method su, p-s almost proportionately increased as the t was changed from 0.8 mm to 1.2 mm, as shown in Fig. 21. A similar trend was reported by [19] based on an experimentally validated FE investigation. The short-span slabs produced higher su than long-span slabs with thin slabs giving more su than relatively thick slabs (ST-S1.2-180 and ST-S1.2-150, ST-L1.2-150 and ST-L1.2-120, STL0.8-150 and ST-L0.8-120). In short, a short-span slab with relatively thin overall thickness and relatively thicker steel sheeting produced better shear bond strength, which is consistent with previous research on similar topics. The shear bond strengths calculated using the PSC method su,PSC and those obtained using the slenderness method su,p-s are nearly the same confirming the validity of the slenderness method as a modified PSC method. It is also confirmed that both the m-k method and the PSC method are valid to estimate the longitudinal shear bond strength of the new type of LCCSs.
Table 7 Design parameters and results from m-k method and slenderness method. Slab designation
Mtest
The m-k method
The shear bond slenderness method
m = 159.61
ST-S1.2-180 ST-S1.2-150 ST-L1.2-150 ST-L1.2-120 ST-S1.0-150 ST-L1.0-150 ST-S0.8-150 ST-L0.8-150 ST-L0.8-120 STS-S1.2-150 STS-L1.2-150 Mean value Standard deviation
36.57 32.71 37.00 35.15 31.82 36.62 25.79 29.47 20.63 49.18 46.67
k = 0.221
p = 95.12
s = 29.12
cvs V/bdp
Ap/bLs
Mm-k
Mm-k/Mtest
s dp
itdp/Ls
Mp-s
Mp-s/Mtest
0.85 0.88 0.55 0.66 0.81 0.54 0.69 0.46 0.43 1.34 0.68
0.0042 0.0042 0.0023 0.0023 0.0035 0.0019 0.0028 0.0015 0.0015 0.0042 0.0023
38.22 33.11 40.04 31.46 30.31 35.87 24.83 30.24 22.48 32.60 40.96
1.05 1.01 1.08 0.89 0.95 0.98 0.96 1.03 1.09 0.66 0.88
86.39 77.67 55.62 60.83 77.21 56.71 64.31 46.47 33.95 129.07 75.40
0.62 0.54 0.30 0.24 0.47 0.25 0.36 0.19 0.14 0.53 0.31
37.23 33.59 38.11 31.72 30.78 34.85 25.49 29.94 24.16 32.92 38.74
1.02 1.03 1.03 0.90 0.97 0.95 0.99 1.02 1.17 0.67 0.83
1.005 0.060
Note: The mean and standard deviation values were obtained from slabs without studs; cvs = 1.25. Mm-k and Mp-s were the ultimate mid-span moments calculated from Eq. (1) and Eq. (10).
1.008 0.070
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X. Li et al. / Construction and Building Materials 156 (2017) 599–610 Table 8 The shear bond stress from different methods. Slab designation
su,p-s
su,PSC
su,beam
su,FE
su,p-s/su,PSC
su,beam/su,PSC
su,FE/su,PSC
Mtest
MFE
MFE/Mtest
ST-S1.2-180 ST-S1.2-150 ST-L1.2-150 ST-L1.2-120 ST-S1.0-150 ST-L1.0-150 ST-S0.8-150 ST-L0.8-150 ST-L0.8-120 STS-S1.2-150 STS-L1.2-150
0.59 0.62 0.44 0.50 0.54 0.41 0.49 0.38 0.46 0.59 0.62
0.58 0.60 0.43 0.59 0.57 0.43 0.50 0.37 0.37 0.58 0.60
0.54 0.55 0.37 0.46 0.51 0.37 0.43 0.31 0.28 0.54 0.55
0.61 0.55 0.44 – 0.49 0.42 0.50 0.38 – 0.82 0.48
1.02 1.03 1.02 0.85 0.95 0.95 0.98 1.03 1.24 1.02 1.03
0.93 0.92 0.86 0.78 0.89 0.86 0.86 0.84 0.76 0.93 0.92
1.05 0.92 1.02 – 0.86 0.98 1.00 1.03 – 1.41 0.80
36.57 32.71 37.00 35.15 31.82 36.62 25.79 29.47 20.63 49.18 46.67
38.88 29.57 38.56 – 28.22 35.99 26.37 30.11 – 42.16 42.54
1.06 0.90 1.04 – 0.89 0.98 1.02 1.02 – 0.86 0.91
1.008 0.100
0.855 0.055
0.979 0.063
Mean value Standard deviation
0.989 0.063
Note: The mean and standard deviation values were calculated from slabs without studs.
su,FE was the maxima in su versus s curves calculated from force equilibrium method.
Fig. 21. Steel sheeting thickness t versus shear bond stress su curves.
Fig. 23. The su versus s curves of long-span slabs.
Figs. 22 and 23 show the su versus s curves, which are important to be used in finite element analysis [22], determined using the force equilibrium method. The maximum values of the shear bond stress su,FE for each slab are included in Table 8 showing very good agreement with test results for both short and long span slabs without end studs. The best advantage, in contrast to the PSC method, is the parameters that contribute to the shear bond property such as the steel sheeting strain, support friction, end connection conditions and curvature have already been included implicitly in the shear bond property [14]. The MFE/Mtest ratios, 0.86 in STS-S1.2-150 and 0.91 in STS-L1.2-150, were relatively more accuracy because of the existence of additional end studs had been considered. 6. Conclusions
Fig. 22. The su versus s curves of short-span slabs.
It is worth noting that the shear bond strengths calculated using the PSC beam method were always smaller than those determined using the PSC methods. Although the mean value was 0.855, the PSC beam method was still valid as its minimum standard deviation of 0.055. A proportionality factor of 1.15 is advised herein.
The current paper presented detailed experimental investigations on a new type composite slab with lightweight aggregate concrete. The considered LCCS showed better composite actions than the traditional concrete-steel sheeting composite slabs offering ductile failure for all tested slabs. The specific shape of the profiled steel sheeting combined with LWAC produced a new ‘mixed mode failure’ in long span slabs. If the slab was controlled by strength, the ultimate carrying capacities of slabs with the same depth stabilized with the increasing steel sheeting thickness from 1.0 mm to 1.2 mm, but if the slab
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was controlled by the deflection, slabs with 1.0 mm steel sheeting showed relatively lower utilization rate of material strength. All methods analyzed in this study for assessing the longitudinal shear bond strength of the new type LCCSs are comparable, and proven to be valid in both shear bond failure mode and new mix failure mode. Following observations were made in regards to the considered analysis techniques: the m-k method is a reliable tool in predicting the strength of composite slabs, but it is a semiempirical formulation without any clear mechanical model. The PSC method is based on a clear mechanical model, but additional supports or end connectors’ effects should be considered separately. The slenderness method is a modified PSC method, which can be used easily by using linear regression, but its accuracy depends heavily on the obtained s. The PSC composite beam method may underestimate the longitudinal shear bond strength, but still can be used as an optional method. The force equilibrium method has included the parameters that contribute to the shear bond property and the obtained su versus s curves can be used in finite element analysis. However, the complex measurement data from the tests may lead to some fluctuations to the accuracy of results. Acknowledgement The study in this paper is based upon work supported by A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). The writers gratefully acknowledge Nan KUAI, Cong GU, Hangzhou CHANG, Jian CHEN, Fengyu LI, Bohan JIN, Xiaocan SUO and others from the Nanjing Forestry University and the UNSW at ADFA for helping with this work. References [1] S.A. de Andrade et al., Standardized composite slab systems for building constructions, J. Constr. Steel Res. 60 (3) (2004) 493–524. [2] S. Chandra, L. Berntsson, Lightweight Aggregate Concrete, Elsevier, 2002. [3] Y.-C. Kan, L.-H. Chen, T. Yen, Mechanical behavior of lightweight concrete steel deck, Constr. Build. Mater. 42 (2013) 78–86.
[4] P. Mäkeläinen, Y. Sun, The longitudinal shear behaviour of a new steel sheeting profile for composite floor slabs, J. Constr. Steel Res. 49 (2) (1999) 117–128. [5] A. Gholamhoseini et al., Longitudinal shear stress and bond–slip relationships in composite concrete slabs, Eng. Struct. 69 (2014) 37–48. [6] R. Abdullah et al., Characterization of shear bond stress for design of composite slabs using an improved partial shear connection method, J. Civil Eng. Manage. 21 (6) (2015) 720–732. [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. [8] R.M. Schuster, Strength and behavior of cold-rolled steel-deck-reinforced concrete floor slabs, 1970. [9] M.L. Porter, C.E. Ekberg Jr, Design recommendations for steel deck floor slabs, 1975. [10] M. Porter, C. Ekberg Jr, Design recommendations for steel deck floor slabs, J. Struct. Div. 102 (ST11) (1976). [11] Standard for the Structural Design of Composite Slabs and Standard Practice for Construction and Inspection of Composite Slabs, ASCE, 1994. [12] EN C., 1–1. Eurocode 4: Design of Composite Steel and Concrete Structures— Part 1.1: General Rules and Rules for Buildings, European Committee for Standardization, Brussels, 2004. [13] R. Abdullah, W.S. Easterling, Elemental bending test and modeling of shear bond in composite slabs, Compos. Constr. Steel Concr. VI (2011) 138–150. [14] R. Abdullah, W.S. Easterling, New evaluation and modeling procedure for horizontal shear bond in composite slabs, J. Constr. Steel Res. 65 (4) (2009) 891–899. [15] S. Chen, X. Shi, Z. Qiu, Shear bond failure in composite slabs—a detailed experimental study, Steel Compos. Struct. 11 (3) (2011) 233–250. [16] C. Code, Code for Design of Steel Structures, in GB 50017–2003, Beijing, China, 2003. [17] L. An, Load bearing capacity and behaviour of composite slabs with profiled steel sheet, 1993. [18] Y. Abdinasir, R. Abdullah, M. Mustaffa, Modelling of shear bond with cohesive element and slenderness study of composite slabs, in: Proceedings of Joint Conference of the 8th Asia Pacific Structural Engineering & Construction Conference (APSEC) and 1st International Conference on Civil Engineering Conference (ICCER), APSEC-ICCER 2012, 2012. [19] M. Ferrer, F. Marimon, M. Crisinel, Designing cold-formed steel sheets for composite slabs: an experimentally validated FEM approach to slip failure mechanics, Thin-Walled Struct. 44 (12) (2006) 1261–1271. [20] K. Hossain et al., High performance composite slabs with profiled steel deck and engineered cementitious composite-strength and shear bond characteristics, Constr. Build. Mater. 125 (2016) 227–240. [21] Standard, C., Code for design of concrete structures, Standard GB50010-2002, Ministry of Construction of the People’s Republic of China, Beijing, China, 2002. [22] J.D. Ríos, H. Cifuentes, M.D.L. Concha, et al., Numerical modelling of the shearbond behaviour of composite slabs in four and six-point bending tests, Eng. Struct. 133 (2017) 91–104.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Experimental study on the longitudinal shear bond behavior of lightweight aggregate concrete – Closed profiled steel sheeting composite slabs Xin Li a, Xiaoyan Zheng a,⇑, Mahmud Ashraf b, Haitao Li a a b
College of Civil Engineering, Nanjing Forestry University, Nanjing 210037, China School of Engineering and Information Technology, The University of New South Wales at the Australian Defence Force Academy, Northcott Drive, Canberra ACT 2612, Australia
h i g h l i g h t s A new type of LWAC – Closed profiled steel sheeting Composite Slab is proposed. Specific slab configurations produce better composite actions and a new mode failure. The validities of existing methods for the new type of composite slab are confirmed.
a r t i c l e
i n f o
Article history: Received 9 May 2017 Received in revised form 13 August 2017 Accepted 17 August 2017
Keywords: Composite slab Lightweight aggregate concrete Closed profiled steel sheeting Longitudinal shear bond strength
a b s t r a c t Composite slabs with ordinary concrete and typical profiled steel sheeting are quite common in construction industry. This paper presents full-scale experiments conducted on a new type of composite slab produced from lightweight aggregate concrete and closed profiled steel sheeting (LCCS). A total of 11 simply supported specimens were tested to investigate the structural behavior of this new type of composite slab with special emphasis on their failure modes. Whilst shear bond failure is the common failure type for typical composite slabs with sheet sheeting, a new type of failure was observed herein where slabs failed with showing remarkable bending capacity, and significant end slips was observed in long-span slabs. In addition to m-k method and PSC method, which are typically used for composite slabs with normal weight concrete, three other techniques such as slenderness method, PSC composite beam method and force equilibrium method were used to assess the longitudinal shear bond strength of LCCS. The ultimate carrying capacity and the shear bond stress predicted using slenderness method and force equilibrium method showed very good agreement with test results; PSC composite beam method may underestimate the longitudinal shear bond strength, but still can be used as an optional method. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Composite slabs consisting of cold-formed profiled steel sheeting and structural concrete are one of the most popular types of floor system used in steel framed buildings. The main advantages of this concrete-steel composite slabs are the reduction of selfweight and simplification of the construction process. The profiled steel sheeting acts as a permanent formwork before casting and as tension reinforcements after casting; the standard scaffolding and propping systems are not required [1]. Lightweight aggregate concrete (LWAC) is now considered as a useful construction material due to significant reduction in self⇑ Corresponding author. E-mail address: [email protected] (X. Zheng). http://dx.doi.org/10.1016/j.conbuildmat.2017.08.108 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.
weight as well as providing better performance in thermal insulation (low density), fire resistance, acoustic isolation and reduction in lateral force due to earthquake when compared with normal weight concrete (NWC) [2,3]. Hence, introduction of LWAC into concrete-steel composite slabs could produce an improved structural system. However, very limited numbers of studies are currently available on composite slabs with LWAC and profiled steel sheeting, especially those using closed profiled steel sheeting. The longitudinal shear bond failure is reported to be the most common failure mode in composite slabs. Significant end slips occur between concrete and profiled steel sheeting interfaces well ahead of reaching its ultimate bending capacity [4]. The failure mode is determined by composite actions which are dependent on the transmission of longitudinal shear bond stress due to pure bond, mechanical interlocking and friction as well as several other
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factors including material properties of concrete, geometry and thickness of steel sheeting, slenderness ratio of the slab, loading arrangement and shear connectors [5–7]. In this paper, the failure mode of a new type composite slab with LWAC and closed profiled steel sheeting (LCCS) is investigated. A mixed failure mode is found and defined. The methods (m-k method, PSC method, slenderness method, PSC composite beam method and force equilibrium method) for evaluating the longitudinal shear bong strength are compared and confirmed to be valid on the new type composite slabs.
Existing methods for assessing the longitudinal shear bond strengths are mainly based on slabs with NWC and trapezoidal profiled steel sheeting. Eurocode 4 suggests using m-k method and Partial Shear Connection method (PSC). Both of these two methods require experimental data obtained from full-scale tests because the composite action is strongly dependent on the particular geometry type of the sheeting. In addition to these methods, the current paper also considered Slenderness method, PSC Composite Beam method and Force Equilibrium method to check their suitability for the new type of composite slab investigated herein. All considered design rules are briefly discussed in the following paragraphs. 2.1. The m-k method The semi-empirical based m-k method was developed by Schuster [8], Porter and Ekberg [9,10], and is adopted in ASCE [11] and Eurocode 4 [12]. The values of m and k are obtained by using linear regression but are only applicable to specific slab configurations as expressed in Eq. (1).
Ap m þk cv s bLs
bdp
su ¼
Nc bðLs þ L0 Þ
ð2Þ
If extra support reaction is considered:
su ¼
N c lV t bðLs þ L0 Þ
ð3Þ
The partial interaction connection moment resistances of composite slabs M can be calculated by:
2. Theories of longitudinal shear bond strength
V 1;Rd ¼
the surface area of the interface between concrete and steel sheeting along the overall length of the shear span, the longitudinal shear bond strength su can be calculated as:
ð1Þ
where V1,Rd is the design shear resistance; Ls is the length of the shear span; Ap is the nominal cross-section of the steel sheeting; b and dp are the width and effective depth of slab, respectively; cvs is the partial safety factor i.e. 1.25 for the slab as defined in Eurocode 4. 2.2. The PSC method PSC method (Fig. 1), which is based on a clear mechanical model, is an alternative to the m-k method but should only be used for composite slabs with ductile longitudinal shear behavior as outlined in Eurocode 4. It is assumed that the mean value for the ultimate longitudinal shear stress su is constant and is uniformly distributed throughout
M ¼ Nc z þ M pr
ð4Þ
z ¼ h 0:5x ep þ ðep eÞg
ð5Þ
Mpr ¼ 1:25Mpa ð1 gÞ
ð6Þ
where Nc is the actual compression force in concrete; L0 is the overhanging length beyond the support; l is the default value of the friction coefficient to be taken as 0.5; Vt is support reaction under the ultimate test load; z is the moment lever arm; h is the overall thickness of the slab; e and ep are the distance from centroidal axis and plastic neutral axis of the effective area of the steel sheeting to its lower flange fiber, respectively; Mpr and Mpa are reduced plastic moment resistance and plastic moment of the effective cross section of the steel sheeting, respectively; g is the degree of shear connection defined as g = Nc/Ncf obtained from test; Ncf is the maximum compression force in concrete at fully interaction connection. 2.3. The slenderness method Slenderness method, which is a modified version of PSC method, considers the thickness of steel sheeting and the slenderness ratio of slab (shear span length to effective depth of slab ratio, Ls/dp). Considerable studies reported by [6,13,14] showed that the longitudinal shear bond strength su varies with the slenderness ratio Ls/ dp and is represented as a function of slab slenderness. The Slenderness method was derived based on the following assumptions: (1) The moment lever arm z, differs very slightly from the effective depth of the slab dp; (2) The overhanging length L0 doesn’t have any considerable effect on slab behavior, and hence is usually negligible. Eq. (4) can be written as:
VLs ¼ sðLs þ L0 Þbdp þ M pr
ð7Þ
Rearranging Eq. (7) and substituting into Eq. (1):
sdp ¼ m
Ap dp kbdp Ls M pr þ b ðLs þ L0 Þ bðLs þ L0 Þ
ð8Þ
If the overhanging length L0 is ignored, the second term of the right side in Eq. (8) becomes a constant s regardless of the Mpr value as explained by Abdullah [6]
sdp ¼ p
Fig. 1. Mechanical model of PSC method.
Ap dp þs bLs
ð9Þ
Eq. (9) was also obtained by Chen [15] by using a different experimental linear regression method. For a specific type of profiled steel sheeting, the ratio of expansion length w to the width of the slab b is constant, and can be written as w = ib = Ap/t, where i is a constant. The new equation changes into:
X. Li et al. / Construction and Building Materials 156 (2017) 599–610
sdp ¼ p
itdp þs Ls
ð10Þ
As seen from Eq. (10), the slenderness equation has the same form and can be compared directly with the m-k method as it employs the concept of linear interpolation into modified PSC method. The slope p and the intercept s are obtained from linear regression.
2.4. The PSC composite beam method PSC Composite Beam method is proposed to assess the capacity of Partial Shear Connection beam in Chinese Code for design of steel structures [16]. Figs. 1 and 2 show the mechanical model and equilibrium relationships used in this method. It is used only to investigate the feasibility for the new type of LCCSs. The area of the steel sheeting compression zone Ac and the partial shear connection moment resistance Mu can be expressed as:
Ac ¼ ðAp f y Nc Þ=2f y
ð11Þ
M u ¼ Nc y1 þ 0:5ðAp f y Nc Þy2
ð12Þ
Thus, su can be calculated using Eq. (2) and Eq. (3).where y1 is the moment lever arm; y2 is the distance between the steel sheeting centroid positions of tensile zone and compressive zone. fy is the yield strength of the steel sheeting.
2.5. The force equilibrium method The force equilibrium method is also a PSC based method, and was first used to calculate the relationship between the longitudinal shear bond strength and the end slip in bending test reported by An [17]. The results of su versus s curves are widely used in numerical modelling. When compared with the PSC method, the primary difference lies in using the geometry and mechanics of materials relationships to calculate the reduced plastic moment resistance of the sheeting Mpr, as shown in Fig. 3.
L 2Ls ðd1 þ d2 Þ 1 Mpr ; ¼ ¼ Ls R Es I s R
ð13Þ
d1 þ d2 Es Is Ls ðL 2Ls Þ
ð14Þ
M pr ¼
Thus, su can be calculated using Eq. (2) and Eq. (3).where d1 and d2 are the deflections measured under each side of applied load line; Es and Is are the elasticity modulus and inertia moment of the steel sheeting.
601
3. Setup for the experimental study Eleven different configurations for a new type of composite slab with closed profiled steel sheeting and shale ceramisite lightweight aggregate concrete were investigated. The shape for all profiles was the same as shown in Fig. 4; Geometric and material properties for the considered profiles are shown in Table 1. LWAC was mixed with shale ceramisite (gravel type, Fig. 5), medium grained sand, water and Portland cement. The strengthgrade and grain-size distribution of the shale ceramisite were 700 and 5–20 mm, respectively. Mix proportion used in concrete is shown in Table 2, which produced approximately 30% lighter concrete, LWAC (1823 kg/m3) when compared with that of NWC (2500 kg/m3). The profiled steel sheeting was cleaned before casting, and was completely supported on the floor during casting in order to reduce uncertainties that could affect the shear bond strength, and to minimize the initial stress and deformation in the slab. It acts as a permanent formwork before casting, and as tension reinforcement after casting [5]. Only distribution reinforcement was included to tackle shrinkage and temperature effects. Three standard 150 mm 150 mm 300 mm prism specimens and six 150 mm cubic specimens were tested at 28 days to determine the elastic modulus and the mean compressive strength of concrete. The slabs were 720 mm wide and 2.2 m (short span)/3.8 m (long span) in length consisting of a 100 mm overhang from each support. The thickness of the slabs were 120 mm, 150 mm and 180 mm with the same shear span length Ls = L’/4. The main parameters of each slab are summarized in Table 3. STS-S1.2-150 and STS-L1.2-150 were two contrasting specimens with U16 mm studs were arc welded through the sheeting on the steel plate as shear connectors. Designation of the specimens represent experiment type – span length (S/L) and profile thickness (1.2/1.0/0.8) – design thickness of the slab. The abbreviations ST and STS mean the Static Test and the Static Test with Studs, respectively. L and S refer to long span and short span, respectively. Figs. 6–8 show the schematic of the experimental setup with measurement parameters. The load was applied at L’/4 using a 300 kN electro-hydraulic servo jack with displacement control technique at a rate of 0.5 mm/min for the short-span and 1.0 mm/min for the long-span. Slabs were simply supported with a pin and a roller support applied at each end. Slips at each end, deflections under the applied load lines and strains at mid-span were measured by the LVDTs and TDS530. 4. Discussion of the test results 4.1. The failure procedure The main results recorded from the conducted tests are summarized in Table 4. Pcr is the initial cracking load determined by
Fig. 2. The cross-section equilibrium relationships.
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Fig. 3. The geometry and mechanics of materials relationships.
Fig. 4. Shape of steel sheeting.
hearing the noise of the concrete cracking; Ps is the load causing an end slip of 0.1 mm. Figs. 9 and 10 show the mid-span deflection versus mid-span moment curves. All slabs showed somewhat similar failure pattern. At the beginning of loading, the profiled steel sheeting worked well with the LWAC. Deflection increased linearly with applied loading within elastic range showing fully composite action. The initial concrete cracks occurred after the interface lost its chemical bonding, which was obvious through continuous crushing noise. The indentations and flanges on the sheeting kept transmitting the longitudinal shear stress after the initial cracking by mechanical interlocking and friction. The composite slab deformed inelasticity, whilst the deflection increased nonlinearly with increase in applied load. The mean initial cracking load was 0.21 Pu for short-span slabs, 0.16 Pu for long-span slabs and 0.3 Pu for slabs with studs. Initial end slip occurred after a specific percentage of the applied load and resulted in a sudden transition as shown in Figs. 11 and 12. This transition is due to the interface separation between steel sheeting and concrete, which is also marked by the observed fluctuations. Nevertheless, the specific shape of the closed profiled steel sheeting, in this study, embedded its flanges in the concrete providing a better ductile performance. They were able to support the increscent load as well as consequent deflection and slips. The mean initial end slip load was 0.50 Pu for short-span slabs, 0.62 Pu for long-span slabs, 0.76 Pu for short-span slab with studs and 0.86 Pu for long-span slab with studs.
The concrete cracks reached the upper fiber of the slab when the applied load reached its ultimate magnitude. The main crack for each slab was fully developed under one side of the applied load line, and the interface separation was observed along the entire shear span, which eventually caused the applied load to gradually decrease but mid-span deflection and end slips kept increasing. All slabs showed ductile failure modes; end studs were effective in complementing the ultimate carrying capacity and the mid-span deflections in all slabs in addition to reducing the end slips in longspan slabs. 4.2. The ultimate limit state and failure modes The ultimate load carrying capacities and failure modes of slabs are shown in Table 5, where Mu is the ultimate mid-span moment obtained from test, Mp,rm is the bending resistance of the section at full shear connection stage, and Smax is the end slip at ultimate mid-span moment. The slenderness ratio Ls/dp showed a clear influence on the ultimate carrying capacities. Abdinasir [6,18] reported that for a NWCtrapezoidal profiled steel sheeting composite slab, the reaction force drops exponentially with increasing slenderness within a certain range and changes slowly with continued increasing slenderness. Similar phenomenon was observed in LCCSs as shown in Fig. 13, which clearly shows that the slenderness ratio is a significant factor in assessing load carrying capacities for all types of concrete-steel sheeting composite slabs. The steel sheeting thickness showed a significant influence on the ultimate carrying capacity of the slab with same depth, as shown in Fig. 14. The increments of Mu were about 23% in both short-span slab and long-span slab when the steel sheeting thickness changed from 0.8 mm to 1.0 mm, whilst stable trends from 1.0 mm to 1.2 mm. That is, with the increase of steel sheeting thickness, the ultimate carrying capacity may stabilize; this effect
Table 1 Geometric and material properties of profile steel sheeting. Sheet profile
Thickness (mm)
Moment of inertia (cm4/m)
Section modulus (cm3/m)
Yield strength (MPa)
Elastic modulus (GPa)
YX66-240-720
0.8 1.0 1.2
84.24 111.13 132.70
17.55 23.62 28.24
230 234 232
182 185 180
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is very important for usual profiles when design the configurations of the slab. All short-span slabs without studs, ST-S1.2-180, ST-S1.2-150, ST-S1.0-150, ST-S0.8-150 showed longitudinal shear failure modes; they failed before reaching the theoretical plastic bending capacity. Mu/Mp,rm ratios varied from 0.77 to 0.93 with a mean of 0.85, which is larger than the typical ratio for normal type concrete-steel composite slabs with a mean value less than 0.6 [3,5,6,15]. This indicates that the new type of LCCSs may provide better composite actions when compared against typical NWCsteel sheeting composite slabs. Slabs with studs showed bending failure modes; Mu/Mp,rm ratio and end slip Smax for STS-S1.2-150 were 1.24 and 1.38 mm, respectively, whilst those for STS-L1.2-150 were 1.12 and 1.13 mm, respectively. When compared with similar slabs without studs (ST-S1.2-150 and ST-L1.2-150), STS-S1.2-150 had a similar end slip but a greater carrying capacity of 50.3% and a larger mid-span
Fig. 5. Typical shape of the ceramisite lightweight aggregate.
Table 2 Mix proportion of LWAC. Grade
Material consumption of concrete/m3(kg) Cement
Sand
Shale ceramisite
Water
LC30
420
720
400
200
Nominal density (kg/m3)
fck,cube (MPa)
fcd (MPa)
Elastic modulus (GPa)
1823
43.7
20.6
26.3
Note: fck,cube is the characteristic compressive strength of concrete. fcd is the design value of the concrete compressive strength.
Table 3 Dimensions and geometrical properties of each slab. Slab designation
Dimensions b L h (mm)
t (mm)
End anchorage (studs)
Ap (mm2)
Ls (mm)
dp (mm)
Slenderness ratio (Ls/dp)
ST-S1.2-180 ST-S1.2-150 ST-L1.2-150 ST-L1.2-120 ST-S1.0-150 ST-L1.0-150 ST-S0.8-150 ST-L0.8-150 ST-L0.8-120 STS-S1.2-150 STS-L1.2-150
720 2200 167 720 2200 147 720 3800 148 720 3800 120 720 2200 153 720 3800 148 720 2200 147 720 3800 142 720 3800 110 720 2200 145 720 3800 151
1.2 1.2 1.2 1.2 1.0 1.0 0.8 0.8 0.8 1.2 1.2
– – – – – – – – – n=3 n=3
1500 1500 1500 1500 1250 1205 1000 1000 1000 1500 1500
500 500 900 900 500 900 500 900 900 500 900
149.7 129.7 130.7 102.7 135.7 130.7 129.7 124.7 92.7 127.7 133.7
3.34 3.85 6.89 8.76 3.68 6.89 3.86 7.22 9.71 3.92 6.73
Note: n is the number of the studs used in each end.
Fig. 6. The experiment setup and measurement parameters.
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Fig. 7. The experiment setup before test.
Fig. 9. Mid-span deflection versus moment curves (short span).
Fig. 8. The experiment setup after test.
deflection of 8.3%; STS-L1.2-150 had a significant decreasing of end slip about 89%, a moderate increasing of carrying capacity about 26.1% and a prominent rising of mid-span deflection about 21.0%. The long-span slab ST-L1.2-150, Mu/Mp,rm = 0.91, failed in a longitudinal shear failure with a larger end slip of 10.05 mm. Other long span slabs ST-L1.2-120, ST-L1.0-150, ST-L0.8-150 and STL0.8-120 exceeded the theoretical full plastic bending capacity with Mu/Mp,rm varying between 1.04 and 1.14, showing significant
Fig. 10. Mid-span deflection versus moment curves (long span).
end slips with Smax varying between 6.28 mm and 10.35 mm. Observed failure modes showed a combination of bending failure accompanied by obvious end slips as shown in Figs. 8 and 15. This
Table 4 The main results from the tests. Slab designation
ST-S1.2-180 ST-S1.2-150 ST-L1.2-150 ST-L1.2-120 ST-S1.0-150 ST-L1.0-150 ST-S0.8-150 ST-L0.8-150 ST-L0.8-120 STS-S1.2-150 STS-L1.2-150
Carrying capacity
The initial cracking of concrete
The initial end slip
Pu (kN)
Mu (kNm)
Pcr (kN)
Mcr (kNm)
Mcr/Mu
Ps (kN)
Ms (kNm)
Ms /Mu
146.28 130.84 82.23 78.12 127.27 81.37 103.15 65.48 45.85 196.70 103.72
36.57 32.71 37.00 35.15 31.82 36.62 25.79 29.47 20.63 49.18 46.67
33.32 27.03 11.02 8.69 27.81 13.83 25.21 16.69 8.90 35.33 13.39
8.33 6.76 4.96 3.91 6.95 6.22 6.30 7.51 4.01 8.83 6.02
0.23 0.21 0.14 0.12 0.19 0.18 0.20 0.21 0.16 0.30 0.29
58.69 69.41 46.15 52.65 47.81 55.95 63.90 35.82 28.04 149.72 89.46
14.67 17.35 20.77 23.69 11.95 25.18 15.97 16.12 12.58 37.43 40.26
0.40 0.53 0.56 0.67 0.38 0.69 0.62 0.55 0.61 0.76 0.86
Mean value 1 Coefficient of variation 1 Mean value 2 Coefficient of variation 2 Note: Mean value 1 and Coefficient of variation 1 calculated from short-span slabs without end studs. Mean value 2 and Coefficient of variation 2 calculated from long-span slabs without end studs.
0.21 0.08 0.16 0.22
0.50 0.23 0.62 0.10
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Fig. 11. End slip versus mid-span moment curves (short span).
Fig. 13. Relationships between slenderness ratio and ultimate reaction force.
Fig. 14. Steel sheeting thickness versus Mu in 150 mm slabs. Fig. 12. End slip versus mid-span moment curves (long span).
type of failure mode is a new observation and has been categorized as a ‘mixed mode failure’, in which slab has a remarkable bending capacity but suffers significant end slip at failure; following are the possible reasons for this new type of failure. (1) LWAC has a lower elasticity modulus of 26.3 GPa, in this study, which is about 80% of NWC with similar strength. Lower elasticity modulus facilitates in releasing internal
stress of concrete, which makes it more effective in improving the synergetic deform performance between LWAC and steel sheeting. (2) The geometry of closed profiled steel sheeting produced a strong bond between the concrete and the steel profile. The upper flanges of the steel profile were encased within LWAC making those even stiffer, and the inverted triangular shape restrained the interface separation during deformation. These two materials deformed uniformly along the
Table 5 The ultimate carrying capacities and failure modes of the slabs. Slab designation
Ls/dp
Mu (kNm)
Vu (kN)
Mp,rm (kNm)
Mu/Mp,rm (kN)
Smax (mm)
Failure mode
ST-S1.2-180 ST-S1.2-150 ST-L1.2-150 ST-L1.2-120 ST-S1.0-150 ST-L1.0-150 ST-S0.8-150 ST-L0.8-150 ST-L0.8-120 STS-S1.2-150 STS-L1.2-150
3.34 3.85 6.89 8.76 3.68 6.89 3.86 7.22 9.71 3.92 6.73
36.57 32.71 37.00 35.15 31.82 36.62 25.79 29.47 20.63 49.18 46.67
73.14 65.42 41.12 39.06 63.64 40.68 51.58 32.74 22.92 98.35 51.86
47.30 40.34 40.63 30.89 36.58 35.07 27.74 26.56 19.20 39.64 41.67
0.77 0.81 0.91 1.14 0.87 1.04 0.93 1.11 1.07 1.24 1.12
1.74 1.30 10.05 6.68 1.69 10.35 1.24 9.47 6.28 1.38 1.13
Shear bond failure Shear bond failure Shear bond failure Mixed failure Shear bond failure Mixed failure Shear bond failure Mixed failure Mixed failure Bending failure Bending failure
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Closed type profiled steel sheeting used in the current study possessed a lower height of centroid, and hence provided a larger moment lever arm in the composite slab action ensuring that the material properties were fully utilized. Fig. 16 clearly shows that all long-span slabs reached steel yield strain. Overall, the better composite action played a significant role in all types of LCCSs resulting in mixed failure in long-span slabs, which is different from observations reported from normal type concrete-steel sheeting composite slabs [2,3,5–7,13–15,18–20]. 4.3. The serviceability limit state Fig. 15. The significant slip at the long-span slab end.
Fig. 16. Steel deck strain at mid-span versus mid-span moment.
vertical axis as well as transmitted shear bond stress longitudinally through the effects of chemical bonding, mechanical interlocking and friction. (3) Concrete between the upper and the lower flanges of the steel sheeting was under multiaxial stress conditions because of the constraints from the surrounding sheeting.
In Chinese Code for design of concrete structures [21], the same deflection limits are stipulated both NWC and LWAC structures. L’/200 for ordinary constructions and L’/250 for constructions with higher deflection requirements. In BS 5950-4, the recommended limit for the maximum deflection of composite slabs due to imposed load is the lesser value between L’/350 and 20 mm. Obtained test results are shown in Table 6. The t versus M/Mu ratios from same overall thickness 150 mm slabs are shown in Fig. 17. The M/Mu ratio can be an evaluation of the utilization rate of material strength, where negligible difference was observed between 1.2 mm and 0.8 mm steel sheeting slabs. However, the sunken trends in 1.0 mm steel sheeting slabs, especially in short-span, indicated that same overall thickness slabs with 0.8 mm and 1.2 mm steel sheeting made better use of material properties than 1.0 mm steel sheeting when the slab resistance is controlled by its deflection limit. Fig. 18 shows the h versus M /Mu ratios of each slab. The rates of M/Mu increase were similar in 1.2 mm steel sheeting slabs, ST-S1.2180 and ST-S1.2-150, ST-L1.2-150 and ST-L1.2-120, regardless of span lengths, whilst those for 0.8 mm steel sheeting slabs were slower (ST-L0.8-150 and ST-L0.8-120). When the deflections reached specified limits of L’/200 and L’/250, the mean M/Mu values for short-span slabs were 0.84 and 0.75 respectively, whilst those for long-span slabs were 0.52 and 0.43 respectively. Lower moment ratio ensures higher safety capacity beyond the serviceability limit state. Even smaller values were observed in slabs with end studs. In short, steel sheeting thickness t may influence the evaluation of the utilization rate of material strength, while slab overall
Table 6 The deflections from the tests. Slab designation
ST-S1.2-180 ST-S1.2-150 ST-L1.2-150 ST-L1.2-120 ST-S1.0-150 ST-L1.0-150 ST-S0.8-150 ST-L0.8-150 ST-L0.8-120 STS-S1.2-150 STS-L1.2-150
Carrying capacity
f = l/200
Pu (kN)
Mu (kNm)
Pl/200 (kN)
Ml/200 (kNm)
Ml/200/Mu
f = l/250 Pl/250 (kN)
Ml/250 (kNm)
Ml/250/Mu
146.28 130.84 82.23 78.12 127.27 81.37 103.15 65.48 45.85 196.70 103.72
36.57 32.71 37.00 35.15 31.82 36.62 25.79 29.47 20.63 49.18 46.67
140.53 111.27 48.38 33.59 86.93 45.11 87.84 36.75 21.42 134.77 50.83
35.13 27.82 21.77 15.12 21.73 20.30 21.96 16.54 9.64 33.69 22.88
0.96 0.85 0.59 0.43 0.68 0.55 0.85 0.56 0.47 0.69 0.49
130.65 101.53 42.12 26.47 76.57 37.98 75.51 29.76 17.57 109.62 40.50
32.66 25.38 18.96 11.91 19.14 17.09 18.88 13.39 7.91 27.41 18.23
0.89 0.78 0.51 0.34 0.60 0.47 0.73 0.45 0.38 0.56 0.39
Mean value 1 Coefficient of variation 1 Mean value 2 Coefficient of variation 1 Note: Mean value 1 and Coefficient of variation 1 calculated from short-span slabs without end studs. Mean value 2 and Coefficient of variation 2 calculated from long-span slabs without end studs.
0.84 0.14 0.52 0.12
0.75 0.16 0.43 0.16
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Fig. 17. t versus M/Mu ratios.
Fig. 18. h versus M/Mu ratios.
thickness h and clear span length of slab L’ may affect the rate of increase. Short-span slab with thicker h and t could have better utilization rate in the serviceability limit state. The current limits will impede the fully use of material properties, especially overconservative in long-span slab and slab with studs. 5. Methods of analysis Considering the particular combining forms and different failure modes in the new type of LCCSs, the feasibilities of assessing the longitudinal shear bond strength by using traditional methods are discussed below. 5.1. Comparison between m-k method and slenderness method The linear regression of the predictions obtained using m-k method and slenderness method are shown in Figs. 19 and 20.
The main parameters used in linear regression and the results from the equations are summarized in Table 7. 5.1.1. The m-k equation The linear regression equation for m-k method is shown in Eq. (15). With m = 159.61 N/mm2 and k = 0.22, correlation coefficient R = 0.9385.
Ap V 1;Rd ¼ bdp 159:61 þ 0:22 bLs
ð15Þ
5.1.2. The shear-bond slenderness equation The closed profile steel sheeting used in the tests has same expansion length w = 1250 mm and slab width b = 720 mm. Ap/ b = 1.736t, and hence the Eq. (10) can be express as:
sdp ¼ 1:736p
tdp þs Ls
ð16Þ
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sdp ¼ 165:13
tdp þ 29:12 Ls
ð17Þ
Outcomes obtained from previous studies on composite slabs showed that the m-k method is a reliable tool in predicting the strength of composite slabs despite its semi-empirical formulation without any clear mechanical model. On the other hand, the slenderness method is a modified PSC method based on the schematic diagram as shown previously in Fig. 1. By introducing some assumptions and simplifications, a direct comparison between modified PSC method and m-k method is now possible. When the predicted strengths were compared against obtained test results, the m-k method produced a mean of 1.005 with a standard deviation of 0.060, whilst those for the slenderness method were 1.008 and 0.070, respectively. This clearly showed that ultimate carrying capacities predicted using the slenderness method were almost the same as those predicted using the m-k method for the new type of LCCSs. The effects of end studs should, however, be considered separately, otherwise an underestimation of the load carrying capacity will be observed as shown in Table 7 (STS-S1.2-150 and STS-L1.2150).
Fig. 19. The m-k curves of slabs without end studs.
5.2. Shear bond stress value calculated from different methods
Fig. 20. The p-s curves of slabs without studs.
The linear regression equation for slenderness method is shown in Eq. (17). With p = 95.12 MPa, s = 29.12 MPa mm, correlation coefficient R = 0.8986.
Table 8 summarizes the shear bond strength su that were calculated using different methods introduced in this paper. Fig. 21 shows t versus su curves form the same overall thickness 150 mm slabs. The shear bond strengths obtained from slenderness method su, p-s almost proportionately increased as the t was changed from 0.8 mm to 1.2 mm, as shown in Fig. 21. A similar trend was reported by [19] based on an experimentally validated FE investigation. The short-span slabs produced higher su than long-span slabs with thin slabs giving more su than relatively thick slabs (ST-S1.2-180 and ST-S1.2-150, ST-L1.2-150 and ST-L1.2-120, STL0.8-150 and ST-L0.8-120). In short, a short-span slab with relatively thin overall thickness and relatively thicker steel sheeting produced better shear bond strength, which is consistent with previous research on similar topics. The shear bond strengths calculated using the PSC method su,PSC and those obtained using the slenderness method su,p-s are nearly the same confirming the validity of the slenderness method as a modified PSC method. It is also confirmed that both the m-k method and the PSC method are valid to estimate the longitudinal shear bond strength of the new type of LCCSs.
Table 7 Design parameters and results from m-k method and slenderness method. Slab designation
Mtest
The m-k method
The shear bond slenderness method
m = 159.61
ST-S1.2-180 ST-S1.2-150 ST-L1.2-150 ST-L1.2-120 ST-S1.0-150 ST-L1.0-150 ST-S0.8-150 ST-L0.8-150 ST-L0.8-120 STS-S1.2-150 STS-L1.2-150 Mean value Standard deviation
36.57 32.71 37.00 35.15 31.82 36.62 25.79 29.47 20.63 49.18 46.67
k = 0.221
p = 95.12
s = 29.12
cvs V/bdp
Ap/bLs
Mm-k
Mm-k/Mtest
s dp
itdp/Ls
Mp-s
Mp-s/Mtest
0.85 0.88 0.55 0.66 0.81 0.54 0.69 0.46 0.43 1.34 0.68
0.0042 0.0042 0.0023 0.0023 0.0035 0.0019 0.0028 0.0015 0.0015 0.0042 0.0023
38.22 33.11 40.04 31.46 30.31 35.87 24.83 30.24 22.48 32.60 40.96
1.05 1.01 1.08 0.89 0.95 0.98 0.96 1.03 1.09 0.66 0.88
86.39 77.67 55.62 60.83 77.21 56.71 64.31 46.47 33.95 129.07 75.40
0.62 0.54 0.30 0.24 0.47 0.25 0.36 0.19 0.14 0.53 0.31
37.23 33.59 38.11 31.72 30.78 34.85 25.49 29.94 24.16 32.92 38.74
1.02 1.03 1.03 0.90 0.97 0.95 0.99 1.02 1.17 0.67 0.83
1.005 0.060
Note: The mean and standard deviation values were obtained from slabs without studs; cvs = 1.25. Mm-k and Mp-s were the ultimate mid-span moments calculated from Eq. (1) and Eq. (10).
1.008 0.070
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X. Li et al. / Construction and Building Materials 156 (2017) 599–610 Table 8 The shear bond stress from different methods. Slab designation
su,p-s
su,PSC
su,beam
su,FE
su,p-s/su,PSC
su,beam/su,PSC
su,FE/su,PSC
Mtest
MFE
MFE/Mtest
ST-S1.2-180 ST-S1.2-150 ST-L1.2-150 ST-L1.2-120 ST-S1.0-150 ST-L1.0-150 ST-S0.8-150 ST-L0.8-150 ST-L0.8-120 STS-S1.2-150 STS-L1.2-150
0.59 0.62 0.44 0.50 0.54 0.41 0.49 0.38 0.46 0.59 0.62
0.58 0.60 0.43 0.59 0.57 0.43 0.50 0.37 0.37 0.58 0.60
0.54 0.55 0.37 0.46 0.51 0.37 0.43 0.31 0.28 0.54 0.55
0.61 0.55 0.44 – 0.49 0.42 0.50 0.38 – 0.82 0.48
1.02 1.03 1.02 0.85 0.95 0.95 0.98 1.03 1.24 1.02 1.03
0.93 0.92 0.86 0.78 0.89 0.86 0.86 0.84 0.76 0.93 0.92
1.05 0.92 1.02 – 0.86 0.98 1.00 1.03 – 1.41 0.80
36.57 32.71 37.00 35.15 31.82 36.62 25.79 29.47 20.63 49.18 46.67
38.88 29.57 38.56 – 28.22 35.99 26.37 30.11 – 42.16 42.54
1.06 0.90 1.04 – 0.89 0.98 1.02 1.02 – 0.86 0.91
1.008 0.100
0.855 0.055
0.979 0.063
Mean value Standard deviation
0.989 0.063
Note: The mean and standard deviation values were calculated from slabs without studs.
su,FE was the maxima in su versus s curves calculated from force equilibrium method.
Fig. 21. Steel sheeting thickness t versus shear bond stress su curves.
Fig. 23. The su versus s curves of long-span slabs.
Figs. 22 and 23 show the su versus s curves, which are important to be used in finite element analysis [22], determined using the force equilibrium method. The maximum values of the shear bond stress su,FE for each slab are included in Table 8 showing very good agreement with test results for both short and long span slabs without end studs. The best advantage, in contrast to the PSC method, is the parameters that contribute to the shear bond property such as the steel sheeting strain, support friction, end connection conditions and curvature have already been included implicitly in the shear bond property [14]. The MFE/Mtest ratios, 0.86 in STS-S1.2-150 and 0.91 in STS-L1.2-150, were relatively more accuracy because of the existence of additional end studs had been considered. 6. Conclusions
Fig. 22. The su versus s curves of short-span slabs.
It is worth noting that the shear bond strengths calculated using the PSC beam method were always smaller than those determined using the PSC methods. Although the mean value was 0.855, the PSC beam method was still valid as its minimum standard deviation of 0.055. A proportionality factor of 1.15 is advised herein.
The current paper presented detailed experimental investigations on a new type composite slab with lightweight aggregate concrete. The considered LCCS showed better composite actions than the traditional concrete-steel sheeting composite slabs offering ductile failure for all tested slabs. The specific shape of the profiled steel sheeting combined with LWAC produced a new ‘mixed mode failure’ in long span slabs. If the slab was controlled by strength, the ultimate carrying capacities of slabs with the same depth stabilized with the increasing steel sheeting thickness from 1.0 mm to 1.2 mm, but if the slab
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was controlled by the deflection, slabs with 1.0 mm steel sheeting showed relatively lower utilization rate of material strength. All methods analyzed in this study for assessing the longitudinal shear bond strength of the new type LCCSs are comparable, and proven to be valid in both shear bond failure mode and new mix failure mode. Following observations were made in regards to the considered analysis techniques: the m-k method is a reliable tool in predicting the strength of composite slabs, but it is a semiempirical formulation without any clear mechanical model. The PSC method is based on a clear mechanical model, but additional supports or end connectors’ effects should be considered separately. The slenderness method is a modified PSC method, which can be used easily by using linear regression, but its accuracy depends heavily on the obtained s. The PSC composite beam method may underestimate the longitudinal shear bond strength, but still can be used as an optional method. The force equilibrium method has included the parameters that contribute to the shear bond property and the obtained su versus s curves can be used in finite element analysis. However, the complex measurement data from the tests may lead to some fluctuations to the accuracy of results. Acknowledgement The study in this paper is based upon work supported by A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). The writers gratefully acknowledge Nan KUAI, Cong GU, Hangzhou CHANG, Jian CHEN, Fengyu LI, Bohan JIN, Xiaocan SUO and others from the Nanjing Forestry University and the UNSW at ADFA for helping with this work. References [1] S.A. de Andrade et al., Standardized composite slab systems for building constructions, J. Constr. Steel Res. 60 (3) (2004) 493–524. [2] S. Chandra, L. Berntsson, Lightweight Aggregate Concrete, Elsevier, 2002. [3] Y.-C. Kan, L.-H. Chen, T. Yen, Mechanical behavior of lightweight concrete steel deck, Constr. Build. Mater. 42 (2013) 78–86.
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