Comparison of Design Methods for Composite Slabs Using Small-scale

Shear Tests

JOSEF HOLOMEK, MIROSLAV BAJER, JIŘÍ KALA

Institute of Metal and Timber Structures, Institute of Structural Mechanics

Brno University of Technology

Veveří 95, Brno 602 00

CZECH REPUBLIC

holomek.j@fce.vutbr.cz, kala.j@fce.vutbr.cz, bajer.m@fce.vutbr.cz, http://www.fce.vutbr.cz

Abstract: - Design methods for composite slabs still require full-scale bending tests which are expensive and

space demanding. Alternatively small-scale shear tests can be used to obtain shear characteristic of the

connection. Three of the methods which are using small-scale shear tests are presented and compared in this

paper: slip-bloct test, new simplified method and built-up bars method. Small-scale shear tests performed in

laboratory are used to calculate bending resistance using these methods. The resulting resistance is compared

with previously performed four-point bending tests.

Key-Words: Built-up bars, composite slab, experiment, longitudinal shear, new simplified method, slip-block

test, small-scale tests.

1 Introduction Composite slab is a suitable solution for horizontal

load-bearing structures. Steel sheeting serves as a

permanent formwork and as a tension bearing

member after hardening of concrete. Generally there

are three global failure modes: bending, vertical shear

and horizontal shear. Bending prevail for slim slabs

with large shear spans. Vertical shear occurs rarely

for short span thick slabs. Failure mode in horizontal

shear governs for the intermediate cases. In this case

the horizontal shear resistance is not sufficient to

preserve full composite action.

The horizontal shear resistance can be provided by

prepressed embossments, self-locking shape of the

sheeting or by end restraints.

Nowadays design codes use m-k method and partial

connection method. Both of them use full scale

bending tests to determine characteristics for design.

A less expensive alternative is to use small-scale

shear tests. This kind of tests cannot include all the

effects of bent slab such as clamping, load

distribution, strain in the sheeting, etc.

Three of the methods for designing composite slabs

are introduced and compared in this paper: slip-block

test, new simplified method and built-up bars method.

The results are calculated using experiments of slip-

block test arrangement and compared with bending

tests which were previously performed in laboratory.

2 Design methods using small-scale

shear tests 2.1 Slip-Block Test Slip-block test is a simple and transparent design

method. It uses test set-up consisting horizontal shear

force H and vertical clamping force V. The specimens

are fixed by the overlapped sheeting to the base plate

and concrete block is being pushed out of it. The

clamping force is transmitted through roller bearing

to the top surface of the concrete block. Magnitude of

V is changing during the test. The aim of the test is to

obtain corresponding shear resistance H for various

levels of clamping force V. The resulting dependence

forms a line when plotting H-V diagram which is

called a “friction line”. The slope of the line

determines friction μ of the specimen and intersection

with H axis determines shear resistance of

mechanical interlock Hrib. [1]

𝐻 = 𝑏1𝐻𝑟𝑖𝑏 + 𝜇𝑉 (1)

Fig. 1 Slip-block test set-up [2]

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The specimens used by the authors of the method had

dimensions bl = 300 mm, br = 300 mm. [2]

Two options of loading procedure were presented by

the authors: V was gradually changed in steps or the

V was continuously decreased by a constant

decreasing rate. The first option meant that at first V

was 27 kN to obtain fist slip which brakes chemical

bond. Then V was changed in steps 52 kN, 42 kN,

32 kN, 22 kN and 12 kN. The step was finished when

slip increased by 1 mm. It resulted in one friction line

per each specimen. [2]

Second option brakes the chemical bond at first as

well. Than the clamping force V was continuously

decreasing from 52 kN by a constant rate and

corresponding H was recorded. It enabled to perform

several cycles of loading per each specimens and thus

obtain more friction lines. Development of friction

and resistance of mechanical interlock in relation to

magnitude of slip could be therefore observed.

However, loading jack for H had to work in position

control mode. [2]

If the shear characteristics are determined one can

calculate equilibrium horizontal shear force in the

sheeting per unit width [3]:

𝑇 =𝐻𝑟𝑖𝑏

𝑏𝑟(𝑥 + 𝐿𝑐) + 𝜇𝑅𝑢 (2)

where 𝑥 + 𝐿𝑐 is the distance from the end of the slab

to the critical cross section and Ru is the reaction

above the support which is to be calculated

iteratively. The method enables easily to take into

account effect of end anchorage by adding the

resistance to the calculated shear force T. [3]

2.2 New Simplified Method New simplified method uses pull-out test

arrangement developed by Daniels (Fig. 2). In this

set-up two specimens were fixed together through

middle plate by constant clamping force 1.6 kN.

Concrete blocks were pulled out of the sheets by

precast rods. [4]

The method uses equivalent I section for sheeting and

rectangular section for concrete.

Fig. 2 Daniels test set-up [4]

Fig. 3 Phases of behavior according to New

Simplified Method [5]

The slab behavior is described in three phases in

moment-curvature diagram (Fig. 3). For each of the

phases is calculated ultimate moment and

corresponding curvature.

Phase I finishes when first cracks occurs in the

tension part of concrete.

𝑀𝑙𝑖𝑚,1 = 𝐸𝑎𝐼𝑎,𝑒𝑞,𝑦𝜙𝑙𝑖𝑚,1 (3)

The end point of Phase II is reached when first slip

occurs. This point is also ultimate bending resistance

for profiles with brittle behavior. The solution has to

be found by iteration when considering equality of

curvature calculated from maximum strain before

cracking and curvature calculated using value of

shear resistance corresponding to first slip from

small-scale shear tests.

Phase III is developed for ductile profiles only. Its

end point is the ultimate bending resistance of the

ductile profiles. The solution is to be found using two

iterations.

Despite its name the calculation procedure is

significantly more complicated than those of the

other two methods: elasto-plastic material behavior is

considered, cross-section characteristics for cracked

section are calculated and solution have to be found

using three iterations. A calculation procedure is

needed to be set in a spreadsheet program or similar.

The procedure is described in details in [6].

2.3 Built-up Bars Method derived from general built-up bars theory

determines the bearing capacity of composite section

by dividing into layers. [4]

𝑀𝑅𝑑 = ∑ 𝑀0,𝑖𝑛𝑖=1 + ∑ 𝑇𝑅𝑑,𝑖 ⋅ 𝑐𝑖

𝑛𝑖=1 , (4)

where 𝑀0,𝑖 is a bending stiffness of a separate layer,

𝑇𝑅𝑑,𝑖 is a shear stiffness of contact between the layers

and 𝑐𝑖 is a distance from centroid of the layer to the

contact layer. In case of composite slab the section is

divided into two parts (Fig. 5). Eq. 1 is therefore

written as follows [7]:

Advances in Mathematics and Statistical Sciences

ISBN: 978-1-61804-275-0 334

Fig. 5 Scheme of forces used in the calculations [5]

𝑀𝑅𝑑 = 𝑀𝑝𝑎 + 𝑇(𝑥) ⋅ 𝑧𝑒𝑓𝑓 (5)

𝑀𝑝𝑎 is a bending resistance of the steel sheeting,

𝑇(𝑥) is a horizontal shear force and 𝑧𝑒𝑓𝑓 is lever arm

of internal forces. Value of the shear force of one of

the layers can be calculated using [7]:

𝑇(𝑥) =𝑀𝑅(𝑥)∙𝑧𝑒𝑓𝑓

𝛾(𝐸𝑝𝐼𝑝+𝐸𝑐,𝑒𝑓𝑓∙𝐼𝑐,𝑒𝑓𝑓)𝑘(𝑥). (6)

involves the influence of stiffness of each of the

layers [1]:

𝛾 =1

𝐸𝑝𝐴𝑝+

1

𝐸𝑐,𝑒𝑓𝑓𝐴𝑐,𝑒𝑓𝑓+

𝑧𝑒𝑓𝑓2

𝐸𝑝𝐼𝑝+𝐸𝑐,𝑒𝑓𝑓𝐼𝑐,𝑒𝑓𝑓 (7)

𝑀𝑅(𝑥) is a bending resistance of the section and 𝐸𝑝𝐼𝑝

is Young's modulus and moment of inertia of the

sheeting. 𝐸𝑐,𝑒𝑓𝑓 = 𝜔 ∙ 𝐸𝑐𝑚 is the Young's modulus of

concrete for calculation of bending resistance [7] and

𝐸𝑐,𝑒𝑓𝑓 = 𝜐 ∙ 𝐸𝑐𝑚 is the Young's modulus of concrete

for calculation of deflection [8]. 𝜔 is a coefficient for

the shape of the stress diagram in compression zone

of concrete flexural member (0.5 for triangular

distribution; 1.0 for rectangular distribution) and 𝜐 is

a concrete elasticity coefficient which involves

influence of cracks with increasing load [8].

𝐼𝑐,𝑒𝑓𝑓 =𝑏𝜔∙𝑥𝑚

3

3+

(𝑏−𝑏𝜔)∙ℎ𝑐3

12[1 + 12 (

𝑥𝑚

ℎ𝑐− 0,5)

2] (9)

𝑥𝑚 = 𝛽 ∙ 𝑑𝑝 (√𝜇2 +𝜇∙ℎ

𝑑𝑝− 𝜇) (10)

𝜇 = 𝜇𝑓 +𝐸𝑝∙𝐴𝑝

𝐸𝑐,𝑒𝑓𝑓∙𝑏𝜔∙𝑑𝑝 (11)

𝜇𝑓 =𝑏∙ℎ𝑐

𝑏𝜔∙𝑑𝑝 (12)

𝛽 = 1,9 − 2,6 (𝑀

𝑀𝑅𝐶)

2 (13)

𝛽 takes into account variation of equivalent

compression zone's depth (for bending resistance

calculation is equal to 1). 𝑘(𝑥) is a coefficient for

yielding of the layers and loading diagram of the slab.

For four-point bending can be expressed as [7]:

𝑘(𝑥) = 1 − [cosh((

𝑙

2−𝑎))

(∙𝑎) cosh(∙𝑙

2)

sinh( ∙ 𝑎)] (14)

is a coefficient defining the rigidity of the contact:

= √𝛼 ∙ 𝛾 (15)

𝛼 =𝑏∙𝐺𝜔

𝑧𝑒𝑓𝑓 (16)

𝐺𝜔 is the characteristic for the shear rigidity

determined from the shear tests using scheme in

Fig. 5 [9].

Fig. 5 Scheme to determine characteristics for the

shear rigidity [9]

If the characteristic for the shear rigidity is known it

is possible to calculate ultimate bending moment and

deflection for various level of loading:

𝑦 (𝑙

2) = 𝑀 (

𝑙2

8𝐸𝑒𝑓𝑓𝐼𝑒𝑓𝑓+

1

𝐷(

cosh(0,5∙𝑙)−1

2 cosh(0,5∙𝑙))) (17)

The method was derived using the results of

dovetailed sheeting tests.

The small-scale shear tests have the same

arrangement as for slip-block test. The specimens

consisted of 150 x 150 mm concrete block and

overlapped sheeting was fixed to the base plate. The

clamping force was transmitted through pneumatic

wheel. The magnitude of clamping force for the tests

taken into calculations was 5 kN. [7, 8, 9]

3 Experimental investigations Experiments were performed in laboratory of

Institute of Metal and Timber Structures in Brno

University of Technology (BUT) using the test set-

up similar to the slip-block test. Hand-operated

hydraulic cylinders were used to produce both

horizontal shear force H and vertical clamping force

V (Fig. 6). The clamping force V (was transmitted

through roller bearings.

Cofraplus 60 sheeting, 1 mm thickness, galvanized

was used in the experiments. The specimens have

width of two waves (414 mm) which enables to apply

load into one point in the middle wave. Length of

concrete block was 200 mm, length of sheeting

330 mm (Fig. 7). Thickness of the slab (height of the

specimen) was 110 mm. Sheeting was bolted to

a base plate and concrete block was pushed out of it.

Tests were performed in several options:

1) Clamping force 1.6 kN

2) Clamping force 5 kN

3) Slip-block test procedure

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Fig. 6 Test set-up before experiment (BUT)

Fig. 7 Specimen dimensions

3.1 Clamping force 1.6 kN Series with clamping force 1.6 kN was the first of the

tests with slip-block test set-up. The shear force was

applied into the half of the height of the slab which

caused an eccentricity (21 mm) of the load and

contributed to the uplift of the loaded side of concrete

for higher values of slip. The resulting diagram is in

Fig. 8. Shear resistance at the initiation of slip is taken

as 4 kN; maximum shear resistance 15 kN.

During the test of specimen 1 the clamping force

grew up to value higher than 4 kN. Resulting shear

resistance was calculated by subtracting the

difference in clamping force multiplied by coefficient

of friction 0.46 (as obtained from slip-block tests,

section 3.3). During the testing of specimens 2 and 3

the clamping force was held constant manually

(Fig. 9).

Fig. 8 Shear resistance – slip diagram for series 1

Fig. 9 Clamping force diagram for series 1

3.2 Clamping force 5 kN Resulting diagram for series with clamping force

5 kN is in Fig. 10. The shear resistance corresponding

to slip 0.5 mm was 6.6 kN and maximum shear

resistance 13.8 kN. There are two series, first with the

same eccentricity as in section 3.1 (specimens 1 – 3),

second without eccentricity (4 – 6).

Fig. 10 Shear resistance – slip diagram for series 2

0

5

10

15

20

0 2 4 6 8 10

Shea

r re

sist

ance

H[k

N]

Slip [mm]

Specimen 1

Specimen 2

Specimen 3

0,0

1,0

2,0

3,0

4,0

5,0

0 2 4 6 8 10

Cla

mp

ing

forc

e V

[kN

]

Slip [mm]

Specimen 1

Specimen 2

Specimen 3

0

2

4

6

8

10

12

14

16

18

0 2 4 6 8 10

Shea

r re

sist

ance

H[k

N]

Slip [mm]

Specimen 1

Specimen 2

Specimen 3

Specimen 4

Specimen 5

Specimen 6

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ISBN: 978-1-61804-275-0 336

Fig. 11 Clamping force diagram for series 2

Average value of maximum shear resistance with

eccentricity was 15.5 kN and without 13.8 kN. The

eccentricity has increased the shear resistance by app.

12%. The shear resistance was again calculated by

subtraction of clamping force V increment multiplied

by coefficient of friction.

3.3 Slip-block test procedure The values of clamping force were recalculated

according to ground plan of the specimens. The slip-

block test procedure was applied in several series. At

first the procedure of loading in steps was applied in

the same way as described by the authors. Next series

were performed in laboratory of Addis Ababa

Institute of Technology in Ethiopia where the

magnitude of slip for transition to next step was

decreased to 0.2 mm and the clamping force was

gradually increasing instead of decreasing. This

made possible to perform several series of loading

per specimen and obtain several friction lines for

each specimen. This comparison has shown large

dispersion of results for small slips. Therefore only

values corresponding to slip higher than 2 mm were

taken into calculations. Fig. 12 displays a friction line

coming from summation of the test results of all the

series with slip-block test procedure.

4 Comparison of results The test results are calculated considering a reference

slab loaded by four-point bending with width 1.08 m,

span 2 m and shear span 0.5 m. The real experiments

of such a slab were previously performed in

laboratory of BUT.

4.1 Slip-Block Test From the equation of friction line from Fig. 12

𝐻 = 12.95 + 0.46𝑉 (18)

Fig. 12 Friction line obtained by slip-block test

loading procedure

follows that μ = 0.46 and b1Hrib = 12.95 kN. The

length of the specimen bl = 200 mm, therefore

Hrib = 64.75 kN/m. The resultant tensile force in the

sheeting using the equation (2) is T = 181.1 kN and

considering magnitude of reaction at the support

Ru = 26.25 kN the ultimate bending moment results

in Mu = 13.12 kNm.

4.2 New Simplified Method From the results in section 3.2 follows that the input

value of shear stress corresponding to initial slip

τslip = 0.034 MPa and maximum shear stress

τmax = 0.127 MPa. Using the calculation procedure in

a spreadsheet the limiting bending moment for

phase 1 is Mlim,1 = 3.2 kNm and curvature

ϕlim,1 = 1.47E-06. The limiting bending moment for

phase 2 Mlim,2 = 3.5 kNm and curvature ϕlim,2 = 2.02E-

06. Finally the ultimate bending moment for phase 3

Mlim,3 = 17.76 kNm and curvature ϕlim,3 = 1.15E-04.

4.3 Built-up Bars Considering the results in section 3.3 and scheme in

Fig. 5 one obtains characteristic for the shear rigidity

𝐺𝜔1 = 32.0 𝑀𝑃𝑎 and 𝐺𝜔2 = 6.8 𝑀𝑃𝑎. Coefficient

for yielding of the layers k(1/4) = 0.29 and horizontal

shear force in the sheeting T(1/4) = 93.7 kN.

Considering the plastic bending moment for full

interaction calculated according to Eurocode 4

MRc = 32.2 kNm and plastic bending resistance of the

sheeting Mpa = 12.3 kNm we obtain ultimate bending

moment for the composite slab MRd = 18.1 kNm.

The built-up bars method enables easily to create load

deflection diagram. For this purpose concrete

elasticity coefficient 𝜐 and the lever arm of internal

forces zeff is calculated for each level of loading.

Resulting relationship in comparison to previously

performed four-point bending tests (static loading

and static loading after cycling) can be seen in

Fig. 15.

0

1

2

3

4

5

6

7

8

9

0 2 4 6 8 10

Cla

mp

ing

forc

e V

[kN

]

Slip [mm]

Specimen 1

Specimen 2

Specimen 3

Specimen 4

Specimen 5

Specimen 6

H = 12.95 + 0.46V

0

10

20

30

40

50

0 10 20 30 40 50 60

Shea

r re

sist

ance

H [

kN]

Clamping force V [kN]

Advances in Mathematics and Statistical Sciences

ISBN: 978-1-61804-275-0 337

Fig. 15 Load-deflection curve calculated by built-up

bars in comparison with experiment data

Design method MRd [kNm]

Slip-Block Test 13.12

New Simplified Method 17.76

Built-up Bars 18.10

four-point bending test 19.51

Table 1 Ultimate bending moment comparison

4 Conclusions Three design methods for composite slabs which use

small-scale shear tests are presented and compared in

this paper. All of them are able to assess bending

resistance of composite slabs and can be very useful

for less-expensive design of composite slabs.

Slip-block test is simple and transparent but does not

reflect changes in curvature, effect of yielding of the

sheeting and cracking of concrete.

New simplified method includes bilinear material

model, effect of cracks, longitudinal shear stress

distribution, curvature, changes in cross section

characteristics due to slip, etc. The method gives

information about behavior before ultimate limit state

is reached. The solution has to be found iteratively.

On the other side the calculation procedure is very

complicated and has to be performed in a spreadsheet

or another calculation program.

Built-up bars method takes into account cracking of

concrete, yielding of sheeting, curvature, changes of

lever arm with increasing load, etc. The calculation

procedure is not as complicated as for new simplified

method and load-deflection diagram can be easily

obtained.

From the results comparison slip-block test is the

most conservative. New simplified method and built-

up bars method give results closer to the real

experiments.

Attention should be paid on test performance to

preserve clamping force constant or to subtract the

friction force increment; to avoid eccentricity in

loading; etc. The effect of loading speed is planned to

be investigated in the upcoming tests. Results from

slip-block test set-up does not show significant

differences from those of Daniels test set-up.

However, more precise comparison would help to

find a unified approach for design using small-scale

shear tests.

Acknowledgement

This paper has been worked out under the project No.

LO1408 "AdMaS UP - Advanced Materials,

Structures and Technologies", supported by Ministry

of Education, Youth and Sports under the „National

Sustainability Programme I" and under the project

GA14-25320S.

References:

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design and behaviour of composite slabs, IABSE

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[2] Patrick, M., Poh W., Controlled test for

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[3] Patrick, M., Bridge, R., Partial shear connection

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[4] Crisinel, M. and Edder, P., New Method for the

Design of Composite Slabs, Composite

Construction in Steel and Concrete V, 2006, pp.

166-177.

[5] Crisinel, M., Marimon, F., A new simplified

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[6] Guignard, P.; Schumacher, A.; Crisinel, M.,

Etude des dalles mixtes et développement d'une

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[7] Vainiunas P., Valivonis J., Marciukaitis G.,

Jonaitis B., Analysis of longitudinal shear

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Vol. 62, Elsevier, 2006, pp. 1264–1269

[8] Marciukaitis G., Jonaitis B., Valivonis J.,

Analysis of deflections of composite slabs with

profiled sheeting up to the ultimate moment,

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[9] Valivonis J., Analysis of behaviour of contact

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Management, Vol 12, No 3, Taylor & Francis,

2006, pp. 187–194

0

5

10

15

20

25

30

35

40

45

0 10 20 30 40

Forc

e in

on

e lo

adin

g p

oin

t [k

N]

Deflection [mm]

Static 1

Static 2

After cycling 1

After cycling 2

After cycling 3

Built-up Bars

Advances in Mathematics and Statistical Sciences

ISBN: 978-1-61804-275-0 338