Experimental and finite element study of ultimate strength of continuous composite concrete slabs with steel decking
Abstract
Composite one-way concrete slabs with profiled steel decking as permanent formwork are commonly used in the construction industry. The steel decking supports the wet concrete of a cast in situ reinforced or post-tensioned concrete slab and, after the concrete sets, acts as external reinforcement. In this type of slab, longitudinal shear failure between the concrete and the steel decking is the most common type of failure at the ultimate load stage. Design codes require the experimental evaluation of the ultimate load capacity and longitudinal shear strength of each type of steel decking using full-scale tests on simple-span slabs. There is also no procedure in current design codes to evaluate the ultimate load capacity and longitudinal shear strength of continuous composite slabs and this is often assessed experimentally by full-scale tests. This paper presents the results of three full-scale tests up to failure on continuous composite concrete slabs cast with trapezoidal steel decking profile (KF70) that is widely used in Australia. Slab specimens were tested in four-point bending at each span with shear spans of span/4. The longitudinal shear failure of each slab is evaluated and the measured mid-span deflection, the end slip and the mid-span steel and concrete strains are also presented and discussed. Redistribution of bending moment in each slab is presented and discussed. A finite element model is proposed and verified by experimental data using interface element to model the bond properties between steel decking and concrete slab and investigate the ultimate strength of continuous composite concrete slabs.
Keywords
Continuous composite slab Cracking Deflection Longitudinal shear stress Steel decking Ultimate strengthIntroduction
Composite slabs consisting primarily of cold-formed profiled steel decking and structural concrete are increasingly used in steel-framed buildings worldwide. In this system, the steel decking is normally continuous over two-spans between the supporting steel beams and during construction the concrete is poured to form a continuous one-way composite slab.
The composite action between the steel decking and the hardened concrete is dependent on the transmission of horizontal shear stresses acting on the interface between the concrete slab and the steel decking (Abdullah and Easterling 2009; Bradford 2010; Ferrer et al. 2006; Gholamhoseini et al. 2014a). Composite action and the transmission of horizontal shear stresses at the concrete–steel interface are necessary for the steel decking to perform its role as the tension reinforcement for the system. The composite action between the concrete and the steel decking is achieved, not only by chemical bonding between the decking and the concrete, but also by mechanical interlock between the concrete and the embossments on the profiled steel decking. Further composite action can be attained by attaching shear studs or similar shear devices.
Ultimate strength of composite concrete slabs
There are two methods presented in Eurocode 4 (EN 2004) to evaluate the ultimate capacity of simple-span composite slabs, known as the ‘‘m–k’’ and ‘‘partial shear connection’’ methods.
The m–k method to evaluate the design resistance against longitudinal shear is mainly based on the numerous experimental works of Porter and Ekberg (1975, 1976) and essentially needs some tests to determine the empirical values of m and k for a certain type of steel decking.
In the partial shear connection method, the flexural capacity of the composite slab at full shear connection stage is calculated by simple plastic analysis of the section and by employing rectangular stress blocks for the concrete and profiled steel decking. Due to interface slip occurrence, to evaluate the ultimate longitudinal shear stress between steel decking and concrete slab, full-scale tests are also required in this method to determine the degree of shear connection.
As stated earlier, the steel decking is usually supplied in two-span lengths and negative reinforcement is provided on top of the supports during construction. This makes the composite slab normally continuous. Despite several studies reported in recent years on the serviceability behaviour of simple-span and continuous reinforced and steel fibre-reinforced composite slabs (Abas et al. 2013; Ackermann and Schnell 2008; Al-Deen et al. 2011; Al-Deen and Ranzi 2015; Bednar et al. 2013; Gholamhoseini et al. 2012, 2013a, b, 2014b, 2016; Gholamhoseini 2016; Gilbert et al. 2012; Kim and Jeong 2006, 2009; Lin et al. 2014a, b; Marciukaitis et al. 2006; Marimuthu et al. 2007; Mansour et al. 2015; Mirza and Uy 2012; Petkevicius and Valivonis 2010; Ranzi et al. 2013a, b), limited information is available in the literature on the assessment of their ultimate strength. For this, current codes do not present a procedure to evaluate the ultimate load capacity and longitudinal shear strength of continuous composite slabs and this is often assessed by full-scale tests. Hence, practising engineers often assume that the composite slab is simply supported and carry out the design accordingly.
This paper presents the results of three full-scale tests up to failure on continuous composite concrete slabs cast with using trapezoidal steel decking profile (KF70) that is widely used in Australia. Slab specimens were tested in four-point bending at each span with shear spans of span/4. The longitudinal shear failure of each slab is evaluated and the measured mid-span deflection (from first loading to ultimate and into the post-peak range), the end slip and the mid-span steel and concrete strains and the redistribution of bending moments are also presented and discussed. A finite element model is proposed and verified by experimental data using interface element to model the bond properties between steel decking and concrete slab and investigate the ultimate strength of continuous composite concrete slabs.
Experimental study
Overview
Each slab was 6900 mm long, with a cross section 150 mm deep and 1200 mm wide, and contained no bottom reinforcement (other than the external steel decking). The decking was formed from 0.75 mm thick grade G500 steel with a Z275 coating produced according to (Standards Australia 2011). The composite slabs were cast with the profiled steel decking as permanent formwork and the concrete was then cured for 7 days under wet hessian. For each specimen, the steel decking was completely supported on the laboratory floor during casting of the concrete to minimise initial stress or deformation in the steel decking and the deck was cleaned thoroughly before placing concrete.
It should be highlighted that the test specimens were part of a separate study on the long-term behaviour of continuous composite concrete slabs and were cracked on the interior support in that test. The complete results of that study have been reported elsewhere (Gholamhoseini et al. 2013a).
The first digit in the designation of each slab is the specimen number (1–3), and the following letter “C” indicates geometry of the slab and stands for “continuous”. The next two numbers indicate the type of decking (where 70 means KF70 decking).
Test setup and instrumentation
The test method for all tested slabs was the same. Each slab was tested with shear span of \(L_{\text{s}} { = }{{L^{\prime}} \mathord{\left/ {\vphantom {{L^{\prime}} 4}} \right. \kern-0pt} 4} = 8 40{\text{ mm}}\). Two load cells were placed underneath each support to measure the support reaction and its variation at any time. The deflection at the mid-spans and the end slip at both exterior supports were measured by LVDTs (linear variable displacement transducers). The strains in the concrete and in the steel decking were measured at selected sections on the top and bottom surfaces of slabs using 60 mm long surface-mounted strain gauges. The strain in the longitudinal reinforcement at the interior support was measured by embedded strain gauges.
The applied load and the reactions at each support were also recorded continuously throughout the tests. The applied load was measured by a load cell placed under the actuator. A schematic view of the experimental setup and the measured parameters is shown in Fig. 3.
The load was applied in a displacement control manner at a rate of 0.3 mm/min. The deformation was applied at a slow rate throughout the test to examine the complete load–deflection response, including in the post-peak unloading range. Failure was considered to have occurred when one of the spans had deflected excessively and hence, the load had dropped significantly.
Material properties
The mean compressive strength f_{cm} and modulus of elasticity E_{c} of the concrete at the age of testing were determined from tests on six standard 100 mm diameter cylinder companion specimens and were 47.9 and 33,050 MPa, respectively. At the time of testing each slab, tests were also conducted on 100 mm × 100 mm × 500 mm prisms to determine the flexural tensile strength of concrete. The mean concrete flexural tensile strength f_{ct.f} (modulus of rupture) was 4.68 MPa.
The complete stress–strain curve, elastic modulus E_{s} and yield stress f_{yp} of the steel decking were also measured from tests on three coupons cut from the sheet of decking. The yield stress f_{yp} and the elastic modulus E_{s} of the steel decking were 532 MPa and 203 GPa, respectively. Similarly, from tests on three samples of the reinforcing bars, the average values were f_{y} = 495 MPa and E_{s} = 205 GPa, respectively.
Discussion of test results
The longitudinal shear failure mode determines the post-slip strength and behaviour of composite slabs. According to the Eurocode 4 definition of ductility, the longitudinal shear behaviour is considered to be ductile if the failure load exceeds the load causing a recorded end slip of 0.1 mm by more than 10% and hence, all slabs failed in a ductile manner.
Summary of test results
Slab | P_{(0.1 mm)} (kN) | P_{max} (kN) | P_{end} (kN) | Δ_{max} (mm) | Δ_{end} (mm) | S_{max} (mm) | ε_{sm(max)} (με) | ε_{cm(max)} (με) |
---|---|---|---|---|---|---|---|---|
1-C-70 | 120.5 | 199.8 | 165.0 | E (30.9) W (31.8) | E (66.3) W (36.9) | E (17.5) W (10.8) | E (478) W (440) | E (197) W (138) |
2-C-70 | 133.8 | 213.0 | 170.5 | E (46.8) W (19.0) | E (92.4) W (17.6) | E (25.0) W (2.4) | E (1290)W (1240) | E (201) W (202) |
3-C-70 | 123.1 | 208.4 | 176.6 | E (40.4) W (21.0) | E (69.4) W (20.3) | E (19.6) W (3.6) | E (1041) W (787) | E (218) W (233) |
The maximum value of the strain in the steel decking at mid-span at the peak load was measured at the eastern span of slab 2-C-70 and was ε_{sm(max)} = 1290 με. The steel yield strain is ε_{yp} = f_{yp}/E_{s} = 2620 με and therefore, the maximum steel strain was only 49% of the yield strain. Clearly, the loss of longitudinal shear stress in all slabs prevented the steel decking from yielding and the full plastic flexural capacity could not be reached.
Bending moments redistribution
The total load in each figure is the applied load P plus the slab self-weight (3.6 kN/m) and the self-weight of the spreader beams and all packing plates used in the test and measured at the start of the test (i.e. P + 30.84 kN). The dashed straight lines in the figures represent the bending moments calculated by assuming constant stiffness along the slab and linear elastic behaviour of materials. The sagging (positive) moments are the values directly under the applied concentrated load and were calculated from statics using the measured reaction at the exterior support at the end of the slab. The hogging (negative) moment at the interior support was also calculated using the measured reaction at the exterior support of the failed span.
As stated earlier, all three slabs were cracked at mid-support under self-weight and the various sustained loading histories, prior to the commencement of these short-term load tests (Gholamhoseini et al. 2013b). Therefore, both the mid-span and mid-support moments increased linearly with load until the onset of slip. The negative moment was carried largely by the steel reinforcement in the concrete tensile zone at the top of the slab.
In slab 3-C-70, a further sudden change in the moment distribution occurred when a sudden bond slip at the steel concrete interface occurred when the total load reached 169.2 kN. At this point, the load dropped suddenly to 144.6 kN and the positive moment dropped suddenly from 26.7 to 21.2 kNm. However, the negative moment remained essentially constant as 30.8 kNm, as can be seen in Fig. 17. The drop-off in load at this point was almost totally associated with the sudden drop in positive moment. This drop-off in load was not evident in the other two slabs.
A further sudden change in the moment distribution occurred in all slabs when positive moment cracking eventually initiated bond slip at the steel concrete interface when the total load reached to about 240 kN. At this point, there was a significant drop in total load and also in the ratio of negative–positive moment as can be seen in Figs. 15, 16 and 17, respectively.
Finite element analysis
General structural modelling
The general purpose nonlinear finite element software ATENA 3D version 4.2.7 was used in the present study to investigate the ultimate strength of the composite concrete slabs tested in the laboratory. ATENA 3D programme is specifically designed for 3D nonlinear finite element analysis of solids with rigorous constitutive relationships to model the behaviour of reinforced concrete structures including concrete cracking, concrete crushing and reinforcement yielding (ATENA Program Documentation 2009).
A three-dimensional (3D) finite element model was developed to account for the material and geometric nonlinearities in the composite slabs and to investigate the ultimate strength of the continuous composite concrete slabs tested in the laboratory. The material properties for steel decking and concrete slabs were similar to the values stated earlier.
The Newton–Raphson iterative solution method was chosen. The mid-span deflection of each slab versus the total load was monitored in the analysis. Four monitoring points at the location of the applied line loads and two monitoring points at mid-span were defined to monitor the amount of total load and mid-span deflection, respectively. All of the monitoring points were defined on the top surface of each slab.
Steel plates with 50 mm thickness and 100 mm width were modelled at the load application points to simulate the steel profiles used in the laboratory experiments and to prevent high stress concentrations at these locations. The partial connection allowing slip to occur between the steel decking and concrete was considered.
Material modelling
Steel plates
Steel plates at the load application points were modelled as a linear elastic material using “CC3D Elastic Isotropic” material type with E_{s} = 200 GPa.
Steel decking
Reinforcing bar
The reinforcing bars over the interior support were modelled using “CC reinforcement” material type with elastic–fully plastic behaviour without strain hardening. There are two ways that a reinforcing bar can be modelled in ATENA; either as smeared or as discrete bar element. In smeared element modelling, the reinforcement is spread along the macroelement by assigning a reinforcement ratio, whereas in discrete bar element modelling, the reinforcing bar is modelled as one-dimensional line element with the assigned bar diameter.
The contact between the reinforcing bar and the surrounding concrete macroelement can be assigned either as perfect bond or as specified bond–slip relationship. In this study, the reinforcement bars were modelled as discrete bars with perfect bond to concrete.
Concrete slab
Concrete slab was modelled using “CC3D Nonlinear Cementitious 2” material type. This material type has the capability to consider concrete cracking; crushing and plastic behaviour. The material properties in the different stress states are presented below.
Tension before cracking
The behaviour of concrete in tension before cracking was assumed to be linear elastic, i.e., σ = E_{c}ɛ; where σ is the tensile stress in concrete, E_{c} is the initial elastic modulus of concrete and ɛ is the strain in concrete.
Tension after cracking
Compression before peak stress
Compression after peak stress
Steel decking–concrete slab contact
Finite element analysis results
A summary of the comparison between the test results and the numerical results obtained from the partial interaction analyses is presented in Fig. 27. The average measured ultimate load capacity of the three slabs was P_{u} = 207.1 kN and the result obtained from finite element modelling was P_{u} = 234.0 kN. In lieu of the expense involved with full-scale testing, the good agreement between the finite element modelling and the test results obtained in the study suggests that far less expensive numerical modelling can be used to verify the performance of continuous composite slabs.
Conclusions
The results of short-term testing up to failure of three continuous composite slabs constructed using a profiled steel decking section that is widely used in construction industry in Australia have been presented and discussed. The slabs were tested in symmetric four-point bending in each span with shear span of L′/4. For all slabs, the maximum flexural capacity was controlled by yielding of the reinforcement at the interior support with significant slip at the concrete–steel interface in the shear span, well before the fully plastic moment of the composite cross section could be reached. All slabs satisfied the ductility provisions given in Eurocode 4.
The slabs were then modelled in a finite element programme to investigate the behaviour of the slabs throughout the full range of loading and the results were compared with test results. Interface elements were used to model the bond properties between steel decking and concrete slab. Currently, the design standards do not present guidance for the design of continuous composite slabs, and full-scale testing is needed. In lieu of the expense involved with full-scale testing, the good agreement between the finite element modelling and the test results obtained in the study suggests that far less expensive numerical modelling can be used to verify the performance of continuous composite slabs.
Notes
Acknowledgements
The experimental work reported in this paper was undertaken with the steel decking material supplied from decking manufacturer Fielders Australia Pty Limited. This support is gratefully acknowledged.
Compliance with ethical standards
Conflict of interest
The author declares that he has no conflict of interest.
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