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TEST BASED FINITE ELEMENT DEVELOPMENT FOR DIAPHRAGM
ACTION
Anita Lendvai, Attila L. Joó
Budapest University of Technology and Economics, Department of Structural Engineering
Abstract: Lightweight roof and wall structural systems are widely used for industrial type steel
buildings and it has been recognised that assembled systems of profiled sheeting and purlins
show strong resistance to loads acting in their own plane. In our experimental research the pur-
pose was to determine the stiffness and strength in widely used structural configurations of
trapezoidal sheeting and purlins without additional stiffeners. To improve the Eurocode formu-
las a series of panel experiments (18 tests altogether) were carried out where 3 m x 3 m dia-
phragms were examined in different configurations for static load. Based on the test series a
shell finite element based modelling method has been developed in ANSYS environment to be
able to follow the real behaviour.
1. Introduction
In the past few years numerous research work [7] [8] has been carried out internationally and
by a research group at the Budapest University of Technology and Economics: Young Scientific
Conference work [1] and diploma work [2] as well, in order to amend the inaccuracy of the
existing Eurocode formulas calculating the stressed skin effect, the stiffening effect of dia-
phragms built up of purlins and trapezoidal sheets [3] [4] [5]. The inaccuracy might cause un-
derestimation of the whole building’s stiffness in earthquake related areas [6].
In order to be able to examine the diaphragm stiffness first a test series has been carried
out from which we could get exact panel stiffness data for each specimen, as well as the load
bearing capacity and failure types. Our aim was to develop and verify a shell finite element
based numerical model in ANSYS upon these results, so we will be able to follow the real
behaviour of the diaphragm, and extend the results to any different, non-examined section sizes
which might be relevant in engineering practice.
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The International Colloquium on Stability and Ductility of Steel Structures, Timisoara, Romania
2. The test series
2.1 The test set-up
The 3-dimensional view of the test set up can be seen on Fig. 1, the loading frame is built up
from horizontal HEA180 beams fixed to the vertical SHS columns. Between the SHS columns
2 U160 bracings have been applied in order to provide a stable loading frame to which we have
built up the diaphragms. The purlins were fixed to the HEA beams, and the trapezoidal sheets
were fixed straight to the purlins. There were no additional bracing applied in the diaphragms.
A static horizontal load has been applied by a hydraulic jack to the right side of the bottom
HEA180 beam until the total failure mechanism of the diaphragm.
The overall size of the test series is also included in Fig. 1. The distance of the horizontal
HEA180 beams is 3 m, to which the vertical purlins has been fixed in 1.5 metres distance. The
overall size of the trapezoidal sheet is 3 m x 3 m. Measured parameters were the horizontal
deflection and the horizontal force loaded by the hydraulic jacks, besides that the failure types
of the panels has been examined during the tests.
Fig. 1: Test set-up 3D and front view
2.2 Execution of test series
During the design of the test series the most important parameters were the examination of the
effect of the purlin’s size and trapezoidal sheet’s profile height, the number of fixings and the
effect of sheeting used only the outer or both side of the purlins (inner and outer side).
For this reason we have planned 18 different configurations, the below structural elements
have been used in our test series:
trapezoidal sheets: LTP20/0.5; LTP45/0.5 (see Fig. 2 for sheet profiles)
purlins: Z200/1.5; Z250/2.0; Z300/2.0 (see Fig. 2 for purlin profiles)
number of fixings: in every through or in every alternate through
usage of trapezoidal sheeting: only one side (outside) or both sides of the purlins (sheets
fixed only to purlins, no fixings applied between two sheets)
Test based finite element development for diaphragm action
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Fig. 2: Lindab trapezoidal sheet- and purlin profiles applied in the test series
3. Evaluation of test results
3.1 Method of evaluation
During the test series the horizontal displacements of the bottom HEA beam has been measured,
and the corresponding force values. These data ranges have been illustrated on a typical force-
displacement diagram.
In Fig. 3 the test results of the panel experiment No. 7 (see Table 1) can be seen: in this
configuration LTP20 sheets outside has been fixed to the Z250 purlins in every alternate
through. The panel has been loaded 8-times, in which the load has been increased in every load-
step until the failure of panels (exceeding the plastic range). In Fig. 4 the appearance of local
failure types are marked, and according to the thick trend line the stiffness of the panels has
been determined. Type of failures are shown in Fig. 4.
Fig. 3: Diagram of the panel test No. 7.
During the panel experiments we have defined the typical local failure types with descrip-
tion and photo documentation, which will be presented in detail in the next chapter.
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The International Colloquium on Stability and Ductility of Steel Structures, Timisoara, Romania
3.2 Typical failure types
The failure types have been numbered in order to later references. In most cases the combination
of failure types has been determined, see Fig. 4 for pictures of the failure modes.
The bottom line of the panels has been subjected to an increasing horizontal load, and in
most cases the failure of the panel has been started with the increase of the opening between
the attached sheets, after – depending on panel strength – other local failure types has been
appeared. In stronger panel constructions – for example in panels with fixings in every through
– another typical local failure type appeared: distortional buckling of the purlin’s upper end.
During the tests we have experienced horizontal and vertical curvature of the sheet edge as well.
Typically the end failure of the panel was caused by hole elongation around the self-drilling
screws. As a conclusion, depending on the stiffness of the specified construction, the local fail-
ure type started with either the purlin’s distortional buckling or the increasing opening between
the sheets, and the horizontal or vertical distortional of sheet edges. The end failure type was
mostly the hole elongation around fixings. The failure of the self drilling has not occurred dur-
ing testing.
Fig. 4: Typical failure types from left to right: increasing opening between sheets, distortional
buckling of purlins, horizontal- and vertical curvature of sheet edges, hole elongation
3.3 Panel stiffnesses
In Table 1 we have summarized the load carrying capacities and calculated panel stiffnesses,
which are based on the trend line, shown in Fig. 3.
In general the conclusion is that for the most stiff constructions, including double sided
sheets (inner and outer side fixed sheets), and the number of fixing has a great effect on panel
stiffness. For example in the tests made of the smallest purlin section and trapezoidal sheets
(see Table 1., test No. 1-3), the simple and in every through fixed construction (No.1) is still
Test based finite element development for diaphragm action
5
stiffer than the construction made of double sheets, but which are fixed only in every alternate
through.
Table 1: Load carrying capacities and stiffnesses from the test series
Test
No.
Purlins
Trapezoidal
sheets
Number of fix-
ings
Application
of sheeting
Panel stiff-
ness
(kN/mm)
1
Z200/1.5
LTP20/0.5
In every through
Single
0.4327
2
In every alternate
through
Single
0.1875
3
Double
0.3812
4
LTP45/0.5
In every through
Single
0.2281
5
In every alternate
through
Single
0.1459
6
Double
0.2826
7
Z250/2.0
LTP20/0.5
In every through
Single
0.4274
8
In every alternate
through
Single
0.3605
9
Double
0.5688
10
LTP45/0.5
In every through
Single
0.3187
11
In every alternate
through
Single
0.2056
12
Double
0.2945
13
Z300/2.0
LTP20/0.5
In every through
Single
0.4086
14
In every alternate
through
Single
0.3842
15
Double
0.5947
16
LTP45/0.5
In every through
Single
0.3800
17
In every alternate
through
Single
0.1967
18
Double
0.3260
4. Finite element analysis
4.1 Finite element model
In order to examine the stiffness of the diaphragms, a non-linear finite element analysis has
been performed using ANSYS. The frame itself with the HEA180 beams and the different pur-
lins have been modelled by the use of SOLID187 element type, the trapezoidal sheets were
modelled by SHELL181 element type. On the top HEA180 beam fixed supports have been
applied, while on the bottom HEA180 beam fixed support have been applied in axis ‘X’ and
‘Y’, while free displacement has been allowed in axis ‘Z’.
The complexity of the semi-rigid connection due to self-drilling screws between the purlins
and sheeting has been established by laboratory tests, where the stiffness of a connection were
determined by tension tests on the purlin and sheeting materials and self-drilling screws. From
these laboratory tests we could achive the connection’s stiffness, which has been used for
BUSHING JOINT element type, which has six degrees of freedom, three translations and three
rotations, all of which can potentially be characterized by their rotational and translational de-
grees of freedom as being free or constrained by stiffness. Depending on the type of the dia-
phragm each node in the middle of the trapezoidal sheet’s through has been connected to the
purlin’s flange node.
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The International Colloquium on Stability and Ductility of Steel Structures, Timisoara, Romania
The purlin and hot rolled steel connections are modelled with CONTA178 elements, which
represent contact and sliding between any two nodes of any types of elements). The horizontal
load has been applied on the edge of the hot rolled HEA180 section with SURF156 element (3-
D Structural Surface Line Load Effect).
Table 2: Properties of the finite elements used, see Fig. 1 for x, y, z axes
SHELL181
SOLID187
CONTA178
Description
Four-node element
with six degrees of
freedom at each node
3-D 10-Node Tetra-
hedral Structural
Solid
Two node element with
three degrees of freedom
at each node with
translations in the X, Y,
and Z directions
Number of
nodes
4
10
2
Degrees of
freedom
x, y, and z translational
and rotational dis-
placements
x, y, and z transla-
tional displacements
x, y, and z translational dis-
placements
For the material properties we have applied 235 MPa yield stress for the hot rolled steel
sections, 350 MPa yield stress for the trapezoidal sheets, and 360 yield stress for the purlins.
The applied Young modulus is 210000 MPa.
For the examination of panel stiffnesses’ linear elastic material model has been used. The
entire assembly and the details along with meshing is shown in Fig. 5. The load is horizontally
applied by steps on the side of the bottom HEA180 beam, and the deflection of the bottom
HEA180 beam has been monitored besides the local failure types in comparison with the labor-
atory results. As elastic range has been examined, imperfections are not included which have
small effect on panel stiffness.
Fig. 5: Meshed diaphragm (No.1. test set up)
4.2 Model behavior
During numerical modelling the typical model behaviour in the elastic range has been exam-
ined. Compared to our laboratory experiments we have experienced all the failure types de-
scribed in 3.2 except the hole elongation (see Fig. 6), which is a typical plastic failure type and
needs more detailed modelling of the surroundings of the self-drilling screws. Therefore further
Test based finite element development for diaphragm action
7
examination will be executed to define the load bearing capacity of the sheeting. So we con-
centrated on the stiffness comparison with the test results.
In stiffer configurations we have experienced Type 1 and 2 behaviour modes in Fig. 4 (in-
creasing opening between sheets, and distortional buckling of purlin’s end), though in less stiff
diaphragms Type 3 and 4 has been experienced (vertical and horizontal curvature of sheets
edges), similarly to laboratory experiments.
Fig. 6: Vertical sheet curling in the FEM model
4.3 Comparison of the stiffnesses of the experimental tests and FEA
In Fig. 7 the results of test No 2. can be seen, where the panel stiffnesses in elastic range have
been compared. The laboratory test result has given the result of 0.1875 kN/mm stiffness, com-
pared to the ANSYS numerical model value, which is 0.1807 kN/mm. The difference between
the two results is ~4 %, which is a reasonable difference in respect of the complex behavior.
All other models showed similar behavior.
Fig. 7: Comparison of diaphragm stiffnesses: ANSYS numerical model and laboratory test
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The International Colloquium on Stability and Ductility of Steel Structures, Timisoara, Romania
5. Summary
In our panel experimental test series and FE-modelling of them we have got experiences as
follows: the typical failure types in FE-model showed similar types as in tests: firstly the defor-
mation of the sheets, and secondly the distortional mode of the purlin ends. The failure of the
self-drilling screws and its surroundings has not been modelled in any cases. In our numerical
analyses the calculated stiffness has been verified with the laboratory tests.
Summarizing the panel stiffness results the stiffest constructions were the configurations
with double side applied sheets in higher profiled purlins configurations (Z250 and Z300). Dur-
ing application of small profiled sheet and purlin this effect is not valid (combining Z200 and
LTP20), in this case the single sides sheets in the every through fixed version was the stiffest
construction.
In general it can be determined that the application of smaller profiled sheets (LTP20) in-
creases the panel stiffness, compared to the higher profiled ones (LTP45). This is valid for all
the tests.
After verification of ANSYS model in the elastic range our next aim is to improve the
numerical model in plastic range around the self-drilling screws to be able to follow the dia-
phragm’s real behaviour, during which the model will be verified upon the diaphragm’s load
bearing capacity. After the verification we are planning to generalize the test series, in which
by the help of virtual tests we can determine the panel stiffness and load bearing capacity for
other configurations as well.
References
[1] Á. Kenéz, A. Rácz “Stiffening effect of trapezoidal sheetings on steel halls”, Young Sci-
entific Conference (in Hungarian), supervisors: L. Dunai, A. L. Joó, BME Department of
Structural Engineering, 2014.
[2] P. Schaul “Stiffening effect of trapezoidal sheetings on the behaviour of steel halls”, MSc.
diplomawork (in Hungarian), supervisor: A. L. Joó, I. Kotormán, BME Department of
Structural Engineering, 2013.
[3] P.K.A. Yiu “BRANZ study report. Profiled sheet steel claddings as diaphragms – General
review”, Building Research Association, New Zealand, 1987.
[4] Larry D. Luttrell, “Strength and behaviour of light-gage steel shear diaphragms”, Cornell
University, Ithaca, New York, 1967.
[5] J. Michael Davies “Developments in stressed skin design”, The University of Manchester,
Manchaster, UK, 2007.
[6] Torsten Höglund “Stabilisation by stressed skin diaphragm action”, Swedish Institute of
Steel Construction, Stockholm, 2002.
[7] Andrzej Wrzeslen, James B.P.Lim, Yixiang Xu, I.A MacLeod, R.M. Lawson “Effects of
stressed skin action on the behaviour of cold-formed steel portal frames “, Engineering
Structures, 2015.
[8] Olli Ilveskoski “Stabilization of steel structures by sandwich panels”, HAMK University
of Applied Sciences, Hämeenlinna, Finland, 2015
