Development in calculation of stressed skin effect upon experimental and numerical research results

Abstract

The opportunities of improvement in stressed skin design formulae in the European Convention for Constructional Steelwork (ECCS) publication are reviewed in this paper.
Stressed skin effect is the diaphragm action provided by the in‐plane stiffness of a diaphragm assembly. The diaphragm is composed of panel assemblies transmitting in‐plane forces to the main frames, providing considerable stabilizing effect to the building. The stiffening effect of diaphragm assemblies depends on their components: type of supporting frame, type of sheeting, number of fixings and the connection between sheeting and purlins.
This paper first discusses the results of an experimental analysis carried out in the Structural Laboratory of the Budapest University of Technology and Economics. The experimental programme aimed to study the stiffness of various diaphragm configurations. Based on the results, the principal influencing parameters are identified. The results confirm that the eccentricity of the connected members – that is out of consideration in current Eurocode provisions – play significant role in the stiffness, and thus it should be considered in design for stressed skin effect. The experimental results also served as a basis for numerical model development and calibration. The verified FE model is capable for numerical simulation of any kind of diaphragm assembly. The paper introduces the results of a parametric study aiming to extend the real experimental results by further virtual experiments.
Based on the experimental and numerical results, modifications are proposed to the current Eurocode provisions, in order to capture all influencing parameters and thus to extend the applicability of the standard design model for “non‐standard” configurations that are commonly installed in practice as well.

Full text

EUROSTEEL 2017, September 13–15, 2017, Copenhagen, Denmark
© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · CE/papers (2017)
Development in calculation of stressed skin effect upon
experimental and numerical research results
Anita Lendvai*
,a
, Attila László Joó
a
a
Budapest University of Technology and Economics, Dept.of Structural Engineering, Hungary
lendvai.anita@epito.bme.hu, joo.attila@epito.bme.hu
ABSTRACT
The opportunities of improvement in stressed skin design formulae in the European Convention for
Constructional Steelwork (ECCS) publication are reviewed in this paper.
Stressed skin effect is the diaphragm action provided by the in-plane stiffness of a diaphragm
assembly. The diaphragm is composed of panel assemblies transmitting in-plane forces to the main
frames, providing considerable stabilizing effect to the building. The stiffening effect of diaphragm
assemblies depends on their components: type of supporting frame, type of sheeting, number of
fixings and the connection between sheeting and purlins.
This paper first discusses the results of an experimental analysis carried out in the Structural
Laboratory of the Budapest University of Technology and Economics. The experimental
programme aimed to study the stiffness of various diaphragm configurations. Based on the results,
the principal influencing parameters are identified. The results confirm that the eccentricity of the
connected members – that is out of consideration in current Eurocode provisions – play significant
role in the stiffness, and thus it should be considered in design for stressed skin effect. The
experimental results also served as a basis for numerical model development and calibration. The
verified FE model is capable for numerical simulation of any kind of diaphragm assembly. The
paper introduces the results of a parametric study aiming to extend the real experimental results by
further virtual experiments.
Based on the experimental and numerical results, modifications are proposed to the current
Eurocode provisions, in order to capture all influencing parameters and thus to extend the
applicability of the standard design model for “non-standard” configurations that are commonly
installed in practice as well.
Keywords: stressed skin design, trapezoidal sheeting, experimental and numerical analysis, design
model development
1 INTRODUCTION
1.1 Previous studies
Previous international studies [1-2] showing that the current formulae used for calculating stressed
skin effect does not cover a wide range of commonly installed configurations.
Wide research program has been executed at the Budapest University of Technology and
Economics including full-scale and panel experiments [3], to examine the stiffening effect of
sheeting systems commonly applied in industrial practice.
According to ECCS [4] and Eurocode [5] methods of stressed skin design may be used only if
several necessary conditions are fulfilled. One of these criterias is that spacing of seam fasteners
between overlapping sheets should not exceed 500 mm, though in industrial practice installation of
seam fasteners are often rejected. The major difference between standard and non-standard
diaphragms is shown in Fig. 1.

© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · CE/papers (2017)
A B
Fig. 1. Standard (A) and non-standard (B) diaphragms
The purpose of this article is to show that even in these cases the sheeting has a non-negligable
stiffening effect in regards to the whole building.
1.2 Research aims
To understand the behaviour of those diaphragm configurations that are typical in everyday
construction, but are not addressed in [4], an experimental and numerical study is completed on
panels subjected to in-plane shear. Numerical model is developed and verified against the real test
results, allowing for numerical simulations replacing the real test. The model is capable for
extending the laboratory test results with non-tested configurations. The results help understanding
whether the non-standard sheeting configurations have considerable stiffening effect.
Our ultimate aim is to recommend modifications to the ECCS design method, to incorporate typical
configurations that are currently out-of-scope.
2 EXPERIMENTAL PROGRAMME
In the panel test series, altogether 18 different diaphragm configurations were tested at the
Structural Laboratory of the Budapest University of Technology, Department of Structural
Engineering. As Fig.2 shows, the test set up consists of a 3 m x 3 m diaphragm fixed to two
horizontal beams with HEA180 profiles. The beams are connected to the rigid loading frame. The
upper beam was fixed, while the lower beam was unrestrained in the in-plane horizontal direction.
Monotonically increasing in-plane load was applied to this lower beam. During the tests, the
horizontal force and the horizontal displacement of the lower beam were measured. Assessment of
these outcomes allows the calculation of the shear flexibilities of the diaphragm configurations.
Fig. 2. 3D and front view of test setup with photos

© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · CE/papers (2017)
Table 1 lists the tested configurations. Effect of the following components are investigated by these
tests:
• section size of purlins,
• section size of trapezoidal sheeting,
• number of fixings: in every corrugation, or in alternate corrugations,
• application of sheeting: only on the outer side of the purlin, or on both sides.
3 EXPERIMENTAL RESULTS COMPARED TO EUROCODE DESIGN METHOD
Shear flexibilities from tests are determined according to ECCS recommendations: the shear
stiffness of the diaphragm is the displacement of the shear diaphragm divided by the shear force.
The shear values from tests are summarized in the block Test results of Table 1.
The ECCS formulae incorporates the effect of 5 deformation components:
• distortion of the profile (c
1,1
),
• shear strain in the faces of the profile (c
1,2
),
• deformation in the sheet to support member fasteners (c
2,1
).
• deformation in the seam fasteners (c
2,2
).
• deformation in the gable connections (c
2,3
).
• axial strain in the edge members, bending in the plane of the diaphragm (c
3
).
Shear flexibility values obtained according to ECCS are listed in the last column of Table 1.
Table 1. Diaphragm configurations - experimental test results and EC shear flexibility values
Test
No. Purlins Trapezoidal
sheets
Number of
fixings
Application
of sheeting
Test results
Shear
flexibility
– EC
[mm/kN]
Difference
of mean
values of
test results
from EC
[%]
Min. shear
flexibility
[mm/kN]
Max. shear
flexibility
[mm/kN]
Mean
value of
shear
flexibility
[mm/kN]
1
Z200/1.5
LTP20/0.5
In every
corrugation Single 1.931 2.753 2.264 1.045 210.04
2
In alternate
corrugations
Single
3.285
5.333
4.066
1.841
216.96
3
Double
2.623
2.660
2.642
1.602
161.57
4
LTP45/0.5
In every
corrugation Single 3.259 4.854 3.783 1.830 203.60
5
In alternate
corrugations
Single
6.150
7.587
6.917
5.632
122.08
6
Double
3.694
4.252
3.864
3.776
101.44
7
Z250/2.0
LTP20/0.5
In every
corrugation Single 1.523 2.319 2.001 0.966 200.30
8
In alternate
corru
gations
Single
1.951
2.589
2.348
1.826
126.33
9
Double
1.469
1.836
1.623
1.587
100.15
10
LTP45/0.5
In every
corrugation Single 2.289 3.223 2.684 1.797 146.58
11
In alternate
corrugations
Single
4.425
7.698
5.662
5.627
100.03
12
Double
3.087
3.
516
3.281
3.761
86.47
13
Z300/2.0
LTP20/0.5
In every
corrugation Single 1.405 2.455 1.880 0.961 189.10
14
In alternate
corrugations
Single
1.833
3.101
2.455
1.821
132.42
15
Double
1.246
2.005
1.539
1.582
95.28
16
LTP45/0.5
In every
corrugation Single 2.270 3.077 2.571 1.796 140.57
17
In alternate
corrugations
Single
4.713
5.831
5.310
5.625
93.85
18
Double
2.821
3.571
3.223
3.774
84.67

© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · CE/papers (2017)
By comparing the test and calculated flexibilities, three major observations can be recognized:
- The stiffening effect of the investigated configurations is considerable, and promises the
utilization as diaphragm in stressed skin design.
- The ECCS method significantly underestimates the shear flexibility of the investigated
configurations; the difference varies within 14-117%, i.e. the method cannot be simply
adapted to these applications with no further modifications.
- Fig. 3 and Fig. 4 illustrate the effect of purlin section height on shear flexibility values. The
figure indicate the test results as well as the values calculated by the current ECCS
expressions. The figures well confirm that the actual behaviour is strongly dependent on the
cross-section height of the purlin: increasing purlin height yields to decreased flexibility.
This tendency is not reflected by the ECCS method.
Fig. 3. Shear stiffness results of LTP20 configurations (fixed in every corrugations) compared to ECCS values in
function of purlin section height
Fig. 4. Shear stiffness results of LTP20 configurations (fixed in alternate corrugations) compared to ECCS values in
function of purlin section height
4 NUMERICAL MODEL DEVELOPMENT AND PROGRAMME
4.1 Developed numerical model
To study of the behaviour of various sheeting configurations and thus to extend the real
experimental results, three-dimensional finite element model is developed in Ansys Workbench
environment [8], shown in Fig. 4. The upper and lower hot-rolled I-section beams as well as the
cold-formed purlins are modelled with 10-node solid elements (denoted as SOLID187 in Ansys)
with three translation degree of freedom per node. The trapezoidal sheeting is represented by 4-
node nonlinear shell elements (SHELL181 in Ansys). The connection between the purlin and the
trapezoidal sheeting is modelled with spring elements (COMBIN14); its stiffness is derived from
previous laboratory experiments discussed in [6]. The purlin-to-hot rolled profile connections are
modelled with contact elements (CONTA178), which represent contact and sliding between any

© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · CE/papers (2017)
two nodes of any types of elements. The entire assembly and the details along with meshing is
shown in Fig. 5.
Fixed supports are applied to the upper beam, while the horizontal in-plane displacement of the
bottom beam is allowed. The horizontal load is applied on the edge of the lower hot-rolled section
with SURF156 element (3-D Structural Surface Line Load Effect). The maximum load was 33 kN.
For the examination of panel stiffness, linear elastic material model with a Young’s modulus of 210
GPa is used.
Further details on the numerical model development and its verification are available in our
previous papers [6, 7].
Fig. 5. FE model of test No. 10 (Z250/LTP45)
4.2 Numerical test program
A parametric study consisting of 45 simulations is completed in order to examine the stiffening
effect of the following parameters:
• number of fixings (LTP20 trapezoidal sheeting): 81; 78; 72; 63; 54; 45; 36 fixings
• section height of trapezoidal sheeting (section types are shown in Fig. 6): 17,4; 33; 43; 60
mm
• thickness of purlin: 1; 1,5; 2; 3 mm
• thickness of sheeting: 0,5; 0,6; 0,7; 0,8; 0,9, 1,0 mm
Fig. 6. Profiles considered in the numerical parametric study

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5 RESULTS OF NUMERICAL PARAMETRIC STUDY
This section compares the result of the numerical analysis to the analytical values derived from the
current ECCS formulae, with respect to the variable parameters.
5.1 Effect of number of fixings
In this case FE model has been validated upon No. 01 and 02 panel experiments (Z200/LTP20
configurations fixed in every corrugations and alternate corrugations), see Table 1. Our results
confirm that by increasing the number of fixings to double (from 42 to 81), the shear flexibility can
be decreased by 40,4 % (Fig. 7).
The effect of number of fixings in EC formulae is taken into account by 3 parameters: p (pitch of
sheet/purlin fasteners), and β
1
and β
2
parameters which are varying in the function of fixings per
sheet width. EC resulted in about 50 % lower flexibility results than in FE model.
Fig. 7. Numerical analysis results: Shear flexibilities in function of number of fixing
5.2 Effect of the trapezoidal sheeting thickness
A comparison is made with varying trapezoidal sheet thicknesses (LTP20/Z200 configurations). It
is concluded that increasing the sheet thickness to double results in 10% lower shear flexibility in
cases where fixings are applied in every third corrugations (Fig. 8).
The role of sheet thickness is decreasing by the increase of fixing number. In case fixing is applied
in every corrugation, the shear stiffness of the thickest sheet is comparable to the thinner sheet case.
Fig. 8. Numerical analysis results: Shear flexibilities in function of sheet thickness

© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · CE/papers (2017)
5.3 Effect of trapezoidal sheeting section size
The numerical simulations prove that increased trapezoidal sheeting section height drastically
increases the shear flexibility (Fig. 9): an increase in section size from LTP20/0.5 to LTP60/0.5
results in approximately 50 % increase in flexibility. This observation is in line with the tendencies
recognized in computations based on the ECCS method; however, the ECCS method overestimates
the effect.
Fig. 9. Numerical analysis results: Shear flexibilities in function of trapezoidal sheeting section size – Z200 purlin, 36
fixings
5.4 Effect of purlin thickness
Increasing the purlin thickness yields to decreasing shear flexibility (24 %) in case of smaller
trapezoidal sheeting profile (LTP20), while increasing shear flexibility (13%) in case of deeper
profile (Fig. 10).
As per the ECCS method, purlin thickness effects the value of c
1
component; however, the total
alteration when considering the investigated thickness range is less than 2,5 %; i.e. the method
underestimates the influence of purlin thickness.
Fig. 10. Numerical analysis results: Shear flexibility in function of purlin thickness – experiments No. 02 and 05

© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · CE/papers (2017)
6 PROPOSAL
As concluded from the experimental and numerical studies, the effect of purlin-sheeting fasteners
has significant effect on shear flexibility, which is not taken into account in ECCS recommendation.
The observed influence of trapezoidal sheeting profile height is in line with the EC method.
Trapezoidal sheeting thickness does not have a great effect on flexibility. Section height and
thickness of purlin has important role in the shear flexibility; however, they are not addresses in the
ECCS recommendation.
Accordingly, the authors suggest simple modifications to the current ECCS formulae, in terms of
modifying the following components of shear flexibility: c
1,1
(profile distortion), c
2,1
(sheet to purlin
fasteners deformation) and c
3
(axial strain in edge members). The revised formulae shall include the
effect that profile distortion and sheet to purlin fasteners deformation are depending in the function
of fastener number. We have included this effect by adding a parameter which is the pitch of sheet
to purlin fasteners per pitch of corrugations (p/d
t
).
The proposed modified components are as follows:
(1)
(2)
(3)
where
a width of the shear panel in the direction perpendicular to the corrugations
A cross-sectional area of a longitudinal edge member
b depth of the shear panel in the direction parallel to the corrugations
b
1
distance between longitudinal edge members
c
1.1
, etc. component shear flexibilities
d pitch of the corrugations
E modulus of elasticity of the sheet material
H
p
height of a longitudinal edge member
K
1
and K
2
sheeting constant which is a function of the shape of the cross-section
n
p
total number of purlins (edge+intermediate)
p pitch of the sheet to purlin fasteners
s
p
slip per sheet to purlin fastener per unit load
t net sheet thickness, excluding coatings
α
1
–α
5
factors to allow for the number of purlins and sheet lengths
β
1
and β
2
factors to allow for the number of sheet to purlin fasteners per sheet width
.
Table 2. summarizes the shear flexibility values calculated by using the above modified
expressions. It can be stated, the proposed modifications yield to better fit of the calculated and the
mean actual flexibility values: the difference is 0,5-28 %, confirming the applicability of the
proposed modifications.

© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · CE/papers (2017)
Table 2. Experimental test results in comparison with values derived from proposed formulae
7 SUMMARY
This paper discussed the experimental and numerical study of sheeting panels subjected to in-plane
shear, for the purpose of the improvement of ECCS formulae regarding stressed skin design. The
investigated cases are commonly applied configurations in everyday construction, that are not
addressed in the current design provisions. An experimental programme was first conducted to
study the behaviour of such panels, followed by numerical parametric study to extend the real
experimental results by numerical simulations.
Based on the experimental observations and the results of the extended numerical study, the
following conclusions can be drawn:
- The current ECCS method does not cover the investigated configurations that are commonly
constructed in everyday practice.
- The stiffening effect of the investigated configurations is considerable, and promises the
utilization as diaphragm in stressed skin design.
- The ECCS method significantly underestimates the shear flexibility of the investigated
configurations.
- Effect of the purlin-sheeting fasteners is significant on shear flexibility, which is not taken
into account in current ECCS recommendation.
-
The observed influence of trapezoidal sheeting profile height is in line with the EC method.
-
Trapezoidal sheeting thickness does not have a great effect on flexibility.
-
Section height and thickness of purlin has important role in the shear flexibility; however,
they are not addressed in the ECCS recommendation.
Test
No. Purlins Trapezoidal
sheets
Number of
fixings
Application
of sheeting
Test results
Proposed
formulae -
Shear
flexibility
[mm/kN]
Min. shear
flexibility
[mm/kN]
Max. shear
flexibility
[mm/kN]
Mean value
of shear
flexibility
[mm/kN]
1
Z200/1.5
LTP20/0.5
In every
corrugation Single 1.931 2.753 2.264 2.932
2
In alternate
corrugations
Single
3.285
5.333
4.066
3.160
3
Double
2.623
2.660
2.642
2.078
4
LTP45/0.5
In every
corrugation Single 3.259 4.854 3.783 3.156
5
In alternate
corrugations
Single
6.150
7.587
6.917
6
.
101
6
Double
3.694
4.252
3.864
3.
905
7
Z250/2.0
LTP20/0.5
In every
corrugation Single 1.523 2.319 2.001 2.164
8
In alternate
corrugations
Single
1.951
2.589
2.348
2.7
76
9
Double
1.469
1.836
1
.623
2.092
10
LTP45/0.5
In every
corrugation Single 2.289 3.223 2.684 2.537
11
In alternate
corrugations
Single
4.425
7.698
5.662
5.479
12
Double
3.087
3.516
3.281
3.
101
13
Z300/2.0
LTP20/0.5
In every
corrugation Single 1.405 2.455 1.880 1.595
1
4
In alternate
corrugations
Single
1.833
3.101
2.455
2.
491
15
Double
1.246
2.005
1.539
2.026
16
LTP45/0.5
In every
corrugation Single 2.270 3.077 2.571 2.716
17
In alternate
corrugations
Single
4.713
5.831
5.310
5.5
69
18
Double
2.821
3.571
3.223
3.4
11

© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · CE/papers (2017)
- Modifications are proposed to the current ECCS expressions of the components of profile
distortion, sheet to purlin fasteners deformation and axial strain in edge members.
- The modified method is verified against the numerical and experimental results, and it is
concluded that these simple modifications are proven efficient for taking the above effects
into account,
- and thus the ECCS method is extended to the commonly installed configurations that were
not addressed by the provisions.
REFERENCES
[1] J. M. Davies, Developments in stressed skin design, The University of Manchester, Manchaster, UK,
2007.
[2]
Zs. Nagy, A. Pop, I. Mois, R. Ballok, Stressed skin effect on the elastic buckling of pitched roof portal
frames, Technical University of Cluj-Napoca, Romania, 2016
[3]
A. Lendvai, A. L. Joó, Shear flexibility and load bearing capacity of roof diaphragms – panel
experiments (in Hungarian), XII. Hungarian Mechanical Conference, Miskolc, Hungary, 2015
[4] ECCS. European recommendations for the application of metal sheeting acting as a diaphragm,
Brussels: European Convention for Constructional Steelwork, 1995
[5] EN 1993-1-3: Eurocode 3: design of steel structures: Part 1–3: general rules, supplementary rules for
cold-formed members and sheeting, Stage 34 draft, 2004.
[6]
A. Lendvai, A. L. Joó, Experimental research on the stiffness and load bearing capacity of purlin-
trapezoidal sheeting connection (in Hungarian), XX. International Conference, ÉPKO 2016,
Csíksomlyó, Romania, 2016
[7]
A. Lendvai, A. L. Joó, Test based finite element development for diaphragm action, Proceedings of the
International Colloqium on Stability and Ductility of Steel Structures, Timisoara, Romania, 2016
[8]
Ansys Workbench Release 14.5