Experimental and Analytical Behaviour of Composite Slabs: Emanuel Lopes Rui Simões
Experimental and Analytical Behaviour of Composite Slabs: Emanuel Lopes Rui Simões
Experimental and Analytical Behaviour of Composite Slabs: Emanuel Lopes Rui Simões
Rui Simões*
ISISE, Civil Engineering Department, University of Coimbra, Coimbra, Portugal
(Received March 21, 2007, Accepted May 21, 2008)
Abstract. The Eurocode 4 presents some negative aspects in the design of composite slabs by the m-k
Method or the Partial Connection Method. On one hand, the component chemical adherence is not accounted for
in the connection between the profiled steel sheet and the concrete. On the other hand, the application of these
methods requires some fitting parameters that must be determined by full scale tests. In this paper, the Eurocode
4 methods are compared with a method developed at the Federal Polytechnic School of Lausanne, based on pull-
out tests, which can be a valid alternative. Hence, in order to calculate the necessary parameters for the three
methods, several tests have been performed such as the full scale test described in Eurocode 4 and pull-out tests.
This last type of tests is of small dimensions and implicates lower costs. Finally, a full-scale test of a steel-
concrete composite slab with a generic loading is presented, with the goal of verifying the analytical formulation.
Keywords: composite slabs; curvature; longitudinal shear; shear span; slip phenomenon; moment-curva-
ture relation; pull-out test; full-scale test; small-scale test.
1. Introduction
A composite slab is a structural element composed by a cold formed steel sheet in connection with
concrete (Fig. 1). The profiled sheeting can have several functions, among others: i) offer an immediate
working platform; ii) acts as a stay-in-place formwork and iii) acts as slab reinforcement.
There are two different phases to consider in design: i) Formwork-profiled sheeting as shuttering and
working platform and ii) Composite slab-after the concrete hardening the steel sheet combines
structurally with concrete.
A composite slab may collapse in three different ways: vertical shear, longitudinal shear or bending
(usually steel sheet yielding). For building spans between 2 and 4.5 m, the main failure mode is the
longitudinal shear.
Besides the brief description of the methods predicted in the European rules (EN 1994-1-1 2007) for
the evaluation of the longitudinal shear resistance of composite slabs, it is the objective of this paper: i)
to describe the experimental tests carried out to obtain results to calibrate the semi-empirical parameters
for the application of previous methods; ii) to apply and calibrate a new model (developed by Crisinel
and Carvajal 2002), designated in this paper by the New Simplified Method and iii) to evaluate the
*Corresponding author, E-mail: rads@dec.uc.pt
362 Emanuel Lopesa and Rui Simões
accuracy of the two type of methods, when compared with experimental results.
Vt Ap ⎞
-------
- = m ⎛⎝ -------
-⎠ + k (1)
bd p bLs
where: Vt is the support reaction measured during the test; b is the width of the slab; dp is the depth of
the centroidal axis of the profiled sheet measured from the slab top; Ap is the cross sectional area of the
profiled sheet and Ls is the shear span.
Although the m-k Method presents simple design equations, it has some disadvantages: i) It’s a semi-
empirical method with small physical meaning; ii) it does not exploit the longitudinal shear resistance
guaranteed by end anchorage or by bearing friction and iii) the method requires the execution of a
minimum of six composite slabs full-scale tests.
EN 1994-1-1 presents an additional method to verify the sagging moment resistance of ductile slabs
in partial connection: the Partial Connection Method (Bode 1990). This method is similar to the one
used in composite beams design. When compared to m-k Method, it is possible to point out some
advantages: it presents a physical basis and it’s also more intuitive. The method has its basis on a
graphic that relates the bending moment with the shear connection degree (Fig. 3). The longitudinal
shear strength τu is determined from a full-scale tests series, through the Eq. (2):
η N cf
τu = ------------------------
- (2)
b ( Ls + Lo )
η N cf – µ V t
τu = ------------------------
- (3)
b ( Ls + Lo )
where: η represents the shear connection degree of the tested slab; Ncf represents the compressive
normal force applied in concrete with full shear connection; Lo is the cantilever length of the slab near
the support and µ is the friction coefficient. The remaining symbols have the already mentioned
meanings.
The Partial Connection Method guarantees more economical designs because it takes advantage of
the profiled sheets ductile behaviour with good mechanical interlock and large spans. However, there
are some disadvantages to mention: i) The method is only applicable to ductile slabs; ii) it requires full-
scale tests in composite slabs and iii) it is impossible to extrapolate test results for slabs with a smaller
span and if the same is done for composite slabs with a larger span the procedure will be too secure.
2.2. The New Simplified Method
Recently, in the Federal Polytechnic School of Lausanne, in order to verify composite slabs behaviour
in partial connection, a new method was developed - The New Simplified Method (Crisinel and
Carvajal 2002). This method does not rely on full-scale tests or on numerical simulation and can be
applied to all types of composite slabs, fragile or ductile, and to all types of profiled sheeting.
This method is based on the determination of the moment-curvature relation of all composite slabs
critical sections. The moment-curvature relation immediately allows knowing the slabs maximum
resistant moment in partial connection. The deflection of the slab can be determined through the
integration of the critical sections curvature.
The steel sheeting-to-concrete connection properties are determined from small-scale pull-out tests,
similar to the ones Daniels and Crisinel accomplished (Daniels and Crisinel 1988). The longitudinal
shear strength is guaranteed by chemical bond (τslip) and mechanical interlock (τmax).
Figs. 4 and 5 represent the results (stress-displacement relation) of Pull-Out Tests of composite slabs
with fragile and ductile behaviour, respectively. They also represent the adopted behaviour for the
analytical model (interrupted line) in both cases.
The analytical model takes into account the physical components of the steel-concrete connection,
which are chemical bond and mechanical interlock (from the pull-out tests results), friction near support
and end anchorage.
The physical model which represents the slab in this method is similar to the one that represents a
composite beam. The profiled sheeting is modelled as an I section with the same area and inertia of the
original sheeting section. The same procedure is used in concrete, though it is modelled as a rectangular
section. The real section transformation of the composite slab into the modelled section is represented
in Figs. 6 and 7.
Fig. 4 Stress- displacement relation of a Pull-Out Test of a composite slab with fragile behaviour
Experimental and Analytical Behaviour of Composite Slabs 365
Fig. 5 Stress- displacement relation of a Pull-Out Test of a composite slab with ductile behaviour
As referred, the New Simplified Method is based on the determination of a tri-linear moment-
curvature relation at the critical section of the composite slab (Fig. 8).
The line segments represented on the diagram are associated to each phase of the composite slab
behaviour, in particular:
366 Emanuel Lopesa and Rui Simões
Phase I. Linear elastic behaviour - Total interaction between steel and concrete and no concrete
cracking.
This phase has the following assumptations: a) linear elastic behaviour; b) concrete not cracked; c)
total interaction between steel and concrete; d) steel extension equal to concrete extension and e) the
equivalent steel section of the concrete determined by the relation between the modules of elasticity of
steel and concrete.
The first phase of the moment-curvature relation ends after the first crack in concrete. Point I is
determined.
Phase II. Elastic or elasto-plastic behaviour - Concrete cracking and total interaction between steel
and concrete.
After Point I of the moment-curvature relation, the critical section in study is cracked. The moment-
curvature relation is now with a cracked elastic or elasto-plastic behaviour. The assumptions of this
phase are:
a) if the steel and concrete stresses are below yield and characteristic stresses, respectively, the
section is in elastic behaviour; if not, it is in elasto-plastic behaviour;
b) cracked concrete;
c) total interaction between steel and concrete; this indicates that the longitudinal stress is inferior
to τslip;
d) steel extension equal to concrete extension.
The second phase ends when the first slip occurs. The longitudinal stress equals τslip and Point II is
defined.
Phase III. Non-linear elasto-plastic behaviour - Concrete cracking and partial connection between
steel and concrete.
When Point II of the moment-curvature relation is reached, the slip between steel and concrete
becomes effective. In that moment the third phase of the moment-curvature relation begins. This phase
only happens with ductile slabs.
Normally, Point III of the moment-curvature relation represents the complete rupture of the
composite connection (infinite slip between steel and concrete).
The assumptions of this phase are:
a) cracked concrete and effective slip between steel and concrete;
b) the rupture of the connection (or of one of their components) implicates the rupture of the
Experimental and Analytical Behaviour of Composite Slabs 367
composite slab;
c) after slip, concrete and steel have the same curvature.
For non-ductile composite slabs the second point represents the point of collapse, which means that
the maximum moment has been attained. For slabs with ductile behaviour, the third point indicates that
maximum mechanical longitudinal shear stress has been attained, which represents the rupture of the
slab (infinite slip).
In this method it is possible to consider the effect of supplementary parameters, such as friction and
end anchorage.
The initial test lasted at least three hours and was composed by 5000 cycles. It was controlled by
strength and the upper and lower load limits applied were, respectively, 0.6 Wt and 0.2 Wt. The
subsequent test was controlled by displacement until rupture and lasted at least one hour.
The tests main goal is to determine Vt and Mtest (maximum moment applied on the test) in order to
calculate m, k and τu. It is also important to measure the end slip, because it allows the determination of
the behaviour of the steel-concrete connection (ductile or non-ductile). With this purpose, the models
were instrumented (Figs. 12 and 13) and the variables indicated in the Table 1 were measured.
Tension tests (according to EN 10 002-1) were performed in specimens obtained from the flanges and
webs of profiled sheets, in order to determine the real properties of the steel. From these tests the
average values of yield stress, ultimate stress and elasticity modulus were attained. Four cylindrical
specimens (∅150 × 300 mm) were made for each slab, with the purpose to investigate the concrete
compressive strength.
The full-scale tests results are represented through load/displacement curves, particularly the
following: i) load/midspan deflection curve; ii) load/end slip curve and iii) load/stress in profiled sheet
curve (Lopes 2005).
Experimental and Analytical Behaviour of Composite Slabs 369
Tables 2 and 3 present load or displacement values which represent slab behavioural changes, such
as: the maximum load applied to the slab (Wt); the first crack load (W1crack); the first and second end slip
load (W1slip, W2slip); the load in which end slip is equal to 0.1 mm (W0.1 mm); the cyclic load limits (0.2Wt
−0.6Wt); the load for a midspan deflection of L/350 (WL/350); the midspan deflection for maximum
370 Emanuel Lopesa and Rui Simões
applied load (δWt); the midspan deflection at the end of the test (δmax); the midspan deflection when first
crack and the first and second end slip occur (δ1crack, δ1slip, δ2slip) and the end slip for maximum applied
load (SlipFmax). Fig. 14 shows the load decrease in the slab 2 when the first and second end slip
occurred. From the tests analysis it is important to mention that the maximum load applied to the slab is
Experimental and Analytical Behaviour of Composite Slabs 371
almost twice the load that causes total detachment of the concrete (which occurs when W = W2slip).
The detachment between steel sheeting and concrete occurs from the section where the load is
applied until the support, which implies that when end slip takes place there are sections closer to the
load application zones that already present a significant slip.
The load/midspan curves of both slabs groups (L = 2200 mm and L = 3500 mm), including the
average stiffness on-going, are shown in Figs. 15 and 16.
3.1.2. m and k parameters
Table 4 indicates the sum of all applied loads, including the self weight (Wt) and the reaction in the
slab supports (Vt).
Eq. (4) and Eq. (5), respectively, define the abscise and the ordinate of the points that belong to
groups A and B.
x = A p / ( bL s ) (4)
y = Vtk / ( bd p ) (5)
The m and k values are, respectively, the slope and the origin ordinate of the line defined by the
characteristic points of groups A and B, described in Fig. 17.
372 Emanuel Lopesa and Rui Simões
Fig. 15 Load vs. midspan deflection of slabs 1, 2 and 3 (without the cycles)
Fig. 16 Load vs. midspan deflection of slabs 4, 5 and 6 (without the cycles)
Table 4 Summary of the composite slabs design and applied loads
Slab model L (mm) Self weight (N) Wt (N) Vt (N)
1 2200 6414 113104 56552
2 2200 6414 114164 57082
3 2200 6463 108303 54151
4 3500 10039 91879 45940
5 3500 10116 100816 50408
6 3500 10116 104126 52063
than 10% (Wt > 1.1 W0.1 mm). τu,Rd has been determined from slab models 4, 5 and 6.
The slab has a sagging moment resistance of Mp,Rm in total connection. However, the effectively
maximum applied moment during the test, Mtest, can be determined through the product of Vt, by the
shear length Ls. Those values are indicated in the Table 5, as well as Mtest / Mp,Rm relation value. From
the partial connection diagram of the slab (Fig. 18) it is possible to calculate the shear connection
degree (η ) and the longitudinal shear strength (τ u ) for each test (Table 6). Characteristic longitudinal
shear strength (τu,Rk) is calculated after a statistic model application (defined in the Annex D of EN
1990) to the values of each slab longitudinal shear strength (τu). Table 7 represents the characteristic
(τu,Rk) and the design (τu,Rd) values of the longitudinal shear strength, with and without friction.
Table 5 Moment applied during the test
Slab model Mtest (kNm) Mtest / b (kNm/m) Mtest / Mp.Rm
4 40.197 44.124 0.6460
5 44.107 48.416 0.7089
6 45.555 50.006 0.7321
3.2. Test results and parameters calculation according to the New Simplified Method
The tests to determine τslip and τmax parameters will now be presented. These tests concern to
ComFlor 70 profiled sheeting (with a nominal thickness of 1.20 mm). The function of those parameters
is to quantify the connection between steel sheet and concrete, in order to apply the New Simplified
Method (Crisinel and Carvajal 2002).
The specimens are composed by two ribs of the profiled sheeting (placed in opposite ways),
intercalated by two steel sheets (5 mm thickness). Two concrete blocks are attached on the two opposite
sides of the profiled sheets. The tension force (applied on top of the profiled sheets) is transferred to the
specimens’ base by four bar ∅12 with a 495 mm length, anchored in concrete. The specimens have the
dimensions and shape indicated in Fig. 19. The connection between profiled sheets and steel sheets
with a 5 mm thickness, as well as the connection between profiled sheets is made by bolting. Fig. 19
shows also the specimens immediately after concrete cover (Lopes 2005).
Figs. 20 and 21 display the test scheme, as well as its components. According to Daniels and Crisinel
1988, a pair of horizontal forces, with a total intensity of 0.16 kN, should be applied to specimens. The
goal is to simulate the self weight of the concrete acting as a vertical load on the profiled sheet of the
slab. The measured values were: the tension force (Ftot), the horizontal forces applied (H1, H2) and the
relative slip between profiled sheets and the concrete blocks (C1, C2). The effective instrumentation is
represented in Fig. 22.
By analysing Table 8, it is possible to compare maximum shear resistance before first slip (Fslip) and
in failure (Fmax).
Longitudinal shear strength before the first slip (τslip) and for maximum force (τmax), are determined
through the Eqs. (6):
F slip F max
τslip = -----------
-; τmax = -----------
- (6)
2 lb bs 2 lb bs
where bs represents the distance between the centres of profiled sheeting ribs and lb the concrete blocks
height. The obtained values are: τslip = 183.5 kPa and τmax = 295.7 kPa.
Experimental and Analytical Behaviour of Composite Slabs 375
In the analysis of the mentioned slabs group by the New Simplified Method, it is necessary to use the
connection resistances determined by pull-out tests; they are the following:
Experimental and Analytical Behaviour of Composite Slabs 377
τslip = 183.54 kPa and τmax = 295.68 kPa. Fig. 23 presents the application of the New Simplified Method
for the slabs group here analysed (L = 3500 mm). With this method it is possible to obtain the moment-
curvature relation for the critical section (maximum sagging moment section).
378 Emanuel Lopesa and Rui Simões
In the application of the New Simplified Method, two curves were determined: one curve in which
the additional resistance due friction (with the value of 0.5 proposed in EN1994-1-1) is considered and
another where that resistance is ignored.
From the analysis of the graphic in Fig. 23 it is possible to observe that friction consideration rises the
resistant moment for Points II and III, and reduces Point III curvature.
The test structural scheme is represented in Fig. 24. Assuming that there is a linear variation of the
curvature between the support and the section where the load is applied (New Simplified Method
critical section) it is possible (by curvature integration) to determine the slab midspan deflection,
without needing to know the stress level in the section (elastic, elasto-plastic, ...).
The midspan deflection is given by Eq. (7):
δ midspan = ( φ ( x ) M ) dx = 11
------ φ ⋅ L2 (7)
∫L
96
Fig. 24 Structural scheme for the EN 1994-1-1 composite slabs full scale tests
Experimental and Analytical Behaviour of Composite Slabs 379
where M represents the virtual moment due to a vertical linear load applied at midspan.
For the slabs group in study, Table 12 indicates the moments, the curvature and the midspan
deflection for the three points of the moment-curvature relation.
For the same structural scheme (Fig. 24) it is possible to obtain, from the maximum moment, the total
load W applied to the slab.
By comparing the midspan load-deflection relation (disregarding slabs self weight) subjected to two
symmetrical loads, with the results obtained from the New Simplified Method, it was possible to attain
the graphic in Fig. 25. Additionally, the approximated behaviour of the slabs was introduced in the
same graphic (Lopes and Simões 2006).
Through the analysis of the curves presented in Fig. 25 it is possible to observe that the maximum
moment foreseen by the New Simplified Method approaches the maximum moment applied to the
slabs if the resistance by friction is not considered. In this case the maximum resistant moment is
practically identical to the minor maximum moment applied in the slabs group. If the friction additional
resistance is taken into account the method provides unsafe resistant moments.
In relation to stiffness, the method simulates accurately the composite slabs behaviour (when
subjected to two symmetrical linear loads), as long as the additional resistance guaranteed by friction is
Table 12 Maximum moment, critical section curvature and midspan deflection for the groups of slabs with a
3500 mm span, determined by the New Simplified Method
Span Friction is taken in Moment-curvature Mmax Curvature φ W δ midspan
[mm] consideration? relation points [kNm] [1/m] [kN] [mm]
Point I 6.59 0.000922 15.06 1.29
3500 No Point II 17.54 0.006343 40.09 8.90
Point III 35.82 0.064896 81.87 91.09
Point I 6.59 0.000922 15.06 1.29
3500 Yes Point II 18.02 0.006519 41.19 9.15
Point III 47.95 0.044211 109.6 62.06
Fig. 25 Load vs. midspan deflection of the group of slabs with L = 3500 mm
380 Emanuel Lopesa and Rui Simões
taken into consideration. Until Point II, the friction has small influence on the method; however, from
this point and as long as the rupture occurs by longitudinal shear, this implies a smaller curvature
needed to attain the maximum resistant moment (in partial connection). This is the main reason for the
big difference between the midspan deflections foreseen by the method when friction is considered and
when it is not.
the deformation caused by the temporary prop removal (estimated in 1.53 mm for short-term loading).
The effective resistance reserve of the composite slab, determined by the Eq. (8), concerning to the
effort Ei at the ultimate limit state, is presented in Table 16.
E Rupture – E ULS
R Resis tan ce E = ----------------------------------
-, (8)
,
i
E ULS
In conclusion, should be referred that the tested slab presented a longitudinal shear resistance higher
than predicted, essentially due to: i) the real shear length is higher than predicted; ii) the slab was
designed through the m-k method; iii) load applied in many points increases the longitudinal shear
resistance (Veljkovic 1998) and iv) if the thickness increases, the longitudinal shear resistance of the
slab also increases (Luttrell 1987).
5.2 Comparison between the experimental results and the analytical methods
In the analysis of the behaviour of the composite slab by the studied analytical methods, the average
connection resistance values and the material properties were used, considering safety partial factors
(γap, γvs and γc) with unitary values.
In order to calculate the midspan deflection from the curvature of the critical section (provided by the
New Simplified Method), it is necessary to integrate the curvatures presuming, in a simplified way, that
the curvature displays a linear variation between the support and the midspan section (critical section).
In this case, the test structural scheme is the one presented in Fig. 28 and the midspan deflection is
given by Eq. (9):
Table 16 Effective composite slab resistance
Effort Ei Effective resistance (%)
VEd 59.4
MEd 93.8
Experimental and Analytical Behaviour of Composite Slabs 383
δ midspan = ( φ ( x ) M ) dx
1- φ ⋅ L2
= ----- (9)
∫L
12
where M represents the virtual moment caused by a vertical linear load applied at midspan.
From the moment-curvature relation for the ultimate and serviceability limit states it is possible to
relate the critical section moment with the midspan deflection (Fig. 29).
Short-term loading is considered for the midspan deflection calculation, according to
EN 1994-1-1. When the deflection is calculated by curvature integration (New Simplified Method) it’s
enough to replace the bending moment applied to the slab, for each limit state, in Fig. 29 to determine
the midspan deflection. The determined values are represented on Table 17.
Through the Table 17 analysis it is possible to verify that all analytical methods provide values for the
midspan deflection closer to the measured ones for serviceability limit state load. However, the New
Simplified Method provides more accurate values in this particular case.
When the ultimate limit state load is reached, the composite slab was quite cracked and the concrete
component was between the linear (elastic) and the nonlinear state. Due to this fact, the deflection value
Fig. 29 Bending moment vs. midspan deflection of the slab (New Simplified Method)
384 Emanuel Lopesa and Rui Simões
Table 17 Comparison between the foreseen midspan deflection and the measured one during test
Midspan deflection (mm)
Bending moment – without New Simplified Method
Limit states slab self weight Measured (Curvature integration)
[kNm] from test EN 1994-1-1
Without friction With friction
SLS 19.35 3.14 3.45 3.48 3.73
ULS 43.52 18.68 14.59 13.07 8.28
foreseen in EN 1994-1-1, calculated in elastic range, is lower than the measured one.
The New Simplified Method presents good results in the prevision of the serviceability limit state
midspan deflection, because the equivalent composite section is in linear elastic state until point II. A
similar situation occurred during the test of the composite slab.
The ultimate limit state bending moment occurs between Points II and III of the bending moment-
midspan deflection relation. Above the Point II, the deflection obtained by the New Simplified Method
is very different from the real one. However, in an ultimate limit state analysis of a structural element,
the deformation is only relevant if it induces second order effects, which is not the case.
In the analysis of the composite slab until rupture, the New Simplified Method and the Partial
Connection Method takes into account the additional resistance guaranteed by friction. This option was
made because in this phase the support reaction is significant.
The shear length of the slab changed during the test, between the limits L/4 (distributed load) and L/2
(linear load at midspan). This variation is particularly significant from the instant that the distributed
load becomes constant; this is, from the final of the ultimate limit state phase.
For the test rupture load, the shear length Ls calculated by EN 1994-1-1 is equal to 1.54 m. For this
length, the New Simplified Method indicates a resistant moment of 76.49 kNm, with an equivalent
steel section plastification of approximately 46.4%. This moment is 28.6% lower than the effectively
applied moment in the slab. Fig. 30 presents the composite slab moment-curvature relation for shear
lengths higher than 1.54 m; from this figure, it’s possible to verify that the resistant moment depends on
the assumed shear length. However, it is not possible to exceed the moment of 86.65 kNm (88.1% of
the maximum moment applied to the slab) because the entire steel equivalent section achieved the
yielding stress.
The shear length calculation according to EN 1994-1-1, in general, leads to conservative results.
Indeed, the cracks induced by longitudinal shear and the New Simplified Method results (Fig. 30)
indicate a shear length with a value near to 1.8 m, therefore, very different from the value of 1.54 m
calculated by EN 1994-1-1.
Fig. 31 presents a partial connection diagram. The maximum resistant moment obtained by the Partial
Connection Method is 87.51 kNm (conditioned by the total yielding of the steel sheet). In this case, that
moment is attained for a resistant length closer to the shear length foreseen by the EN 1994-1-1, equal
to 1.54 m. The longitudinal shear strength that fits the Partial Connection Method (τu), with or without
friction, is determined for a shear length that is according to the procedure indicated in EN 1994-1-1.
This can justify why the values are so close.
Both methods indicated for the calculation of the partial connection moments presents very similar
maximum moments, although for very different shear lengths.
In a design situation, when only one shear length is defined, the moments determined by the two
methods would be very different; for example, considering Ls = 1.54 m, the resistant moment determined
Experimental and Analytical Behaviour of Composite Slabs 385
Fig. 30 Moment-curvature relation of the equivalent section of the composite slab for several shear lengths
Fig. 31 Partial Connection Diagram (EN 1994-1-1) of the final composite slab
by the New Simplified Method is 14.4% lower than the resistant moment determined by the Partial
Connection Method (Lopes 2006).
6. Conclusions
The experimental tests were performed in a particular composite slab configuration to obtain the
parameters necessary to the application of the analytical methods for slip resistance analysis. These
tests also allowed to get some conclusions about its behaviour. All the tested slabs presented a ductile
behaviour; in general, the maximum load applied to the slabs was almost twice the load that causes total
detachment of the concrete.
From the comparison of the tests results with the analytical methods it is possible to draw the
386 Emanuel Lopesa and Rui Simões
following main conclusions: i) the New Simplified Method and the EN 1994-1-1 present realistic
values for the serviceability limits state midspan deflection; ii) the maximum resistant moment obtained
by the New Simplified Method is quite closer to the applied moment of the slabs subjected to two
symmetrical linear loads, as long as the additional resistance guaranteed by friction is not considered;
iii) in the Partial Connection Method and in the New Simplified Method the maximum resistant
moment of the final composite slab was conditioned by the sheet plastification, confirming the tested
slab collapse mode; iv) the Partial Connection Method and the New Simplified Method demonstrate
that if the shear length increases, the resistant moment in partial connection also increases and v) on the
contrary, the m-k Method indicates that the resistance decreases when the shear length increases;
therefore the use of that method in slabs design, with shear lengths different from the ones that allow to
determine the m and k values, should be prudent.
According the results of this research work, the method developed at the Federal Polytechnic School
of Lausanne, here designated by “New Simplified Method” based on pull-out tests, can be a valid
alternative to the methods of EN1994-1-1; however, this conclusion must be confirmed with further
applications to real cases.
Acknowledgments
The authors would like to thank Corus Portugal, in particular to Architect Fernando Mourão, for the
supply of the profiled sheets.
Thanks and recognition is also given to Professor Michel Crisinel, from the Federal Polytechnic
School of Lausanne, who provided study elements essential to understand the New Simplified Method.
Nomenclature
b Width of the slab
b1, b2, b3 Geometrical parameters in an equivalent composite slab section
b1,0 Width of the rib of the profiled steel sheeting
b3,0 Width of the bottom of the concrete rib
beq,c Equivalent width of the concrete in a composite slab
borig Width of the slab for calculation
bs Distance between the centres of profiled sheeting ribs
dp Depth to the centroidal axis of the profiled sheet measured from the slab top
e Level of elastic neutral axis
ep Level of plastic neutral axis
fcm Ultimate strength of the concrete
fyp Yield strength of the steel sheet
heq,c Equivalent thickness of the concrete in a composite slab
hp Overall depth of the profiled steel sheeting
ht, h, htot Overall thickness of a composite slab
k Fitting parameter of the m-k Method
lb Concrete blocks height
m Fitting parameter of the m-k Method
Experimental and Analytical Behaviour of Composite Slabs 387
s Slip displacment
t1, t2 Geometrical parameters in an equivalent composite slab section
tp Thickness of the steel sheeting
Ap Cross sectional area of the profiled sheet
C1 Relative slip between profiled sheets and the concrete blocks in the pull-out tests
C2 Relative slip between profiled sheets and the concrete blocks in the pull-out tests
Ecm Young modulus of the concrete
ERupture Force in the rupture
EULS Force in the ultimate limite states
F Total vertical load in a slab according EC4
P Load
Fmax Maximum shear force resistance determined in the pull-out tests
Fslip Shear force resistance before slip determined in the pull-out tests
Ftot Total tension force in the pull-out tests
H1 Horizontal force applied in the pull-out tests
H2 Horizontal force applied in the pull-out tests
L Slab span
Lo Cantilever length of the slab near the support
Ls Shear span
Lx Resistant length
Mpla Plastic moment of steel sheet
Mp,Rm Sagging moment resistance
Mtest Maximum moment applied on the test
M Bending moment
M Virtual moment due to a vertical linear load
Nc Compressive normal force applied in concrete
Ncf Compressive normal force applied in concrete with full shear connection
RResistance,Ei Effective resistance corresponding to the effort Ei
SlipFmax End slip for maximum applied load
SWspec Self weight of the specimen
Vl,Rd Design shear resistance
Vt Support reaction; transverse shear
Vtk Characteristic value of the support reaction
W Total vertical load
W0.1 mm Load in which end slip is equal to 0.1 mm
W1crack First crack load
W1slip First end slip load
W2slip Second end slip load
WL/350 Load for a mid-span deflection of L/350
Wt Maximum load P applied in the test
δ Deflection
δ1crack Mid-span deflection when the first crack occur
δ1slip Mid-span deflection when the first end slip occur
388 Emanuel Lopesa and Rui Simões
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