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VALIDATION OF A STRUCTURAL MODEL OF A LARGE TIMBER TRUSS WITH SLOTTED-IN STEEL PLATES AND DOWELS

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VALIDATION OF A STRUCTURAL MODEL OF A LARGE TIMBER
TRUSS WITH SLOTTED-IN STEEL PLATES AND DOWELS
Pierre Landel1,2and Andreas Linderholt2
1Research Institutes of Sweden
e-mail: pierre.landel@ri.se
2Linnaeus University Sweden
e-mail: {pierre.landel, andreas.linderholt}@lnu.se
Keywords: Glued-Laminated-Timber (Glulam) truss, slotted-in steel plates and dowels con-
nection, experimental and numerical modal analysis, stiffness, damping, induced vibrations in
timber structure.
Abstract. The dynamic response to time varying loads, e.g. wind loads or earthquakes, is in
many cases decisive when designing a tall timber building. The structural parameters gov-
erning the dynamic behaviour are the mass, the damping and the stiffness. The last two pa-
rameters are not well-known at serviceability levels for timber structures in general and for
timber connections specifically. Results from forced vibration tests on single components and
on a full-scale truss for an eight-storey residential building have been analyzed. In parallel,
a detailed Finite Element (FE) model of a large Glulam truss with slotted-in steel plates and
dowels connections has been developed and simulations have been made. The damping caused
by the structural components, the embedment of fasteners and friction of mating surfaces of
components in the selected connection types is quantified experimentally. The materials’ stiff-
ness values in the model were evaluated. The results from this study bring knowledge on the
structural dynamic properties of large timber structures with mechanical connections and will
facilitate the performance prediction of new tall timber buildings for better comfort at higher
levels in environmentally friendly expansions of our cities.
4349
EURODYN 2020
XI International Conference on Structural Dynamics
M. Papadrakakis, M. Fragiadakis, C. Papadimitriou (eds.)
Athens, Greece, 23–26 November 2020
Available online at www.easdprocedia.org
EASD Procedia EURODYN (2020) 4349-4357
ISSN:2311-9020 © 2020 The Authors. Published by EASD Procedia.
Peer-review under responsibility of the Organizing Committee of EURODYN 2020.
doi: 10.47964/1120.9356.18990
Pierre Landel and Andreas Linderholt
1 INTRODUCTION
Tall timber buildings are becoming more common due to their environmental benefits and
low weights. Large engineered wood products such as Glulam members or Cross-Laminated-
Timber plates are often used. For instance, the largest column of the 18-storey Mjøst˚
arnet in
Norway, is made of glued spruce lumbers and has a cross sectional area equal to 625 x 1485
mm2. To assemble the structural elements, slotted-in steel plates and dowels are used [1].
This connection technique has traditionally been used in long-span bridges and roof structures.
Moreover, the density and the modulus of elasticity of the wood material are well known; they
are lower than the corresponding values for steel and concrete. When the height of timber
buildings rises in cities around the world, new types of challenges appear for structural design-
ers. One of them is wind-induced vibrations which appears to be annoying for the occupants
at lower heights for buildings made of timber than for traditional high-rise buildings [2]. Mass,
stiffness and damping matrices (denoted M, K and C) need to be fairly well known to accurately
predict responses of structures subjected to time varying excitations. For tall timber buildings,
it is relevant to analyze the accuracy of the mass and stiffness matrices used by structural de-
signers in FE-analysis for serviceability load levels. Unfortunately, some dynamical properties
of large timber structures are not well known [2]. The damping is the least known dynamical
property and recently started research projects aim to close the knowledge gap through ambient
vibration tests [3, 4, 5] and forced vibration tests of tall timber buildings [6].
The load distribution in timber structures depends on the stiffness of the structural elements
and the stiffness of the connections. Glulam structures are usually modeled as beam elements
with well-known stiffness but the load distribution in connections with multiple fasteners is un-
certain. The joints are often modelled either with constrains in displacement and rotation, i.e.
clamped, or only with constrains in displacement, i.e. pinned [1]. Most connections in Glulam
structures consist of many steel dowels and several slotted-in steel plates in parallel. However,
most of the experimental and numerical studies have been performed on single dowel connec-
tions. Building design codes for timber structures propose simple parameters to evaluate the
slip of single connections, e.g. [7] and [8] but better slip models for connections with multiple
fasteners and several shear planes are needed [9]. Wood is a complex material to model: high
orthotropy, inhomogeneities at different scales and large variability, and this must be consid-
ered when predicting the embedment between timber and steel [10]. Phenomenological models
for embedment have recently been developed based on the beam on foundation approach [11],
with elastic and plastic foundation modulus [12]. Such material models are suitable for beam
element models to predict deformations and load capacity. Constitutive models with non-linear
material stiffness and embedment stiffness with criteria for yielding and softening [13, 14, 15]
have also been developed recently and they are applicable to solid FE-models mainly to predict
load capacity but not focusing on the deformations at serviceability levels.
Damping in timber structures has mainly been studied experimentally through cyclic tests,
representing seismic load histories, on single components or large structures [16], but not much
through vibrational tests to assess the damping at serviceability levels [17]. Standard values of
the critical viscous damping ratio are set to 1 % and 1.5 % for timber bridges without respec-
tively with mechanical connections when designed for pedestrian induced vibrations [18].
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Pierre Landel and Andreas Linderholt
2 FORCED VIBRATION TESTS ON A LARGE TIMBER TRUSS
2.1 The Glulam truss
A truss made of Glulam members assembled with slotted-in steel plates and dowels connec-
tions has been vibrational tested in the factory where it was manufactured, in T¨
oreboda, Sweden.
It has 14 Glulam members of quality GL30c according to [19], an overall height of 18.5 m and a
width of 4.3 m. It is now part of the lateral stabilizing timber structure of a six-storey residential
building and it stands up on a concrete foundation to prevent the building from collapse in case
of strong winds. The short elements, diagonals and beams have a rectangular cross-section of
215 x 360 mm. The first column has a rectangular cross-section of 215 x 540 mm. The second
column is composed of a similar cross-section glued with 90 x 215 members on each side to
form a T-shaped cross-section. Holes, cutting and details for the Glulam members were made
with a CNC-machine. The steel plates and the dowels are made of S355JO steel quality. The
plates are 8 mm thick and weight between 8 and 37 kg. The dowels are 12 mm in diameter and
have a length of 210 mm. Each connection has two steel plates and 8 to 45 dowels hammered
in each timber member. In total there are 650 dowels and 28 steel plates in the truss. Heavy
steel feet with welded 8 mm plates, weighting 88 and 106 kg, are mounted with dowels at the
end of both columns. The overall weight of the Glulam truss including the steel elements is
4280 kg and the densities of the timber members have been measured and the mean density was
evaluated to 426.8 kg/m3.
2.2 The vibration test
When the truss was assembled, forced vibrations tests (FVT) were made at the factory. With
overhead cranes, the truss was lifted from the ground with lift straps placed close to the center
of gravity of the truss, see figure 1. Excitations were made in different directions on and close to
the steel foot of the lower column (bottom end) with a short-sledge impulse hammer. During the
tests, fourteen tri-axial piezo electrical accelerometers at the center of each truss connection and
twelve single axial accelerometers on the middle of the short Glulam elements were used. The
accelerometers, with a sensitivity of 100 mV/g (±10 %), were glued on one side of the Glulam
members. The data were recorded with an LMS data acquisition system with 56 input channels
that measured 50 accelerations in the X- Y- or Z-directions, see figure 1, and the excitation force
from the impulse hammer.
Further information on the Glulam truss properties and details of the vibration test performed
are available in paper [20].
3 A NUMERICAL MODEL OF THE LARGE TIMBER TRUSS
3.1 The 3D FE-model with solid elements
The Glulam truss has been modeled, as an FE-model, to numerically evaluate the structural
dynamic properties and compare them with the experimental results. The model was devel-
oped using the pre- and post-processor MSC Simxpert and analyzed with the FE-solver MSC
Nastran. The model consists of 1 726 778 eight-noded solid elements (CHEXA) and 523 961
six-noded solid elements (CPENTA) with a total of 2 715 641 nodes. Different element sizes
have been used with densified meshes around details such as the holes for the dowels in the tim-
ber members and the steel parts and coarser meshes in areas without complexity, see figure 2. To
ensure continuity between solid elements from the same part but with non-congruent meshes,
contact constraints paired and permanently glued slaves contact bodies to masters contact bod-
4351
Pierre Landel and Andreas Linderholt
Figure 1: The Glulam truss during a forced vibration test.
Modulus of elas-
ticity parallel to
the fiber direction
Modulus of elas-
ticity perpendicu-
lar to the fiber
Shear modulus
in the 0,90-plane
Shear mod-
ulus in the
90,90-plane
Poisson’s
ratios
E0[10.5,11.8]
in GPa
E90 = 300 MPa G0,90 = 650 MPa G90,90 =65MPa ν0,90 = 0.5
ν90,90 = 0.2
acc. to [20] acc. to [19] acc. to [19] acc. to [19] acc. to [21]
Table 1: The material properties used in the FE-models of the Glulam members.
ies with non-congruent meshes. Permanent glue contacts constrained parts of different material
together, i.e. timber member to dowel and dowel to steel plates. The MSC Nastran node-to-
segment contact method has been used and it created multi-point constraint equations among
the nodes from a slave body which met the surface of a master body. Then, the augmented
Lagrange multiplier method was used to embed constraints into the modal analysis.
Steel parts were modeled using an isotropic material model with a Young’s modulus of 210
GPa, a Poisson’s ratio of 0.3 and a density of 7850 kg/m3. The Glulam members were modeled
using an orthotropic material model with the six stiffness parameters presented in Table 1.
Two spring elements representing the hoisting loops were attached to the ground and to
several points of the upper timber column with an interpolation constraint element (RBE3).
The RBE3 elements defined the motion at a reference grid point as the weighted average of the
motions at a set of other grid points. The axial stiffness of the springs was calibrated to match
the natural frequency of the global bouncing mode in the Y-direction from the experimental
results.
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Pierre Landel and Andreas Linderholt
Figure 2: a) the FE-model representing the truss and b) the meshing details of the top-middle connection.
3.2 The numerical analysis
In a structural dynamic system without damping, the vectors of displacement, u, and accel-
eration, ¨
u, are related to the mass matrix [M], the stiffness matrix [K] and the excitation force
vector, p, according to the equation of motion:
[Mu+[K]u=p(1)
The eigenfrequencies and eigenmode shapes of the model were extracted using the normal
mode analysis in MSC Nastran implementing the block shifted Lanczos eigenvalue extraction
method. The numerical mode shapes with very low displacement out of the plane of the truss,
which is the structurally operational plane, and with eigenfrequencies between 5 and 130 Hz
were investigated.
4 COMPARISON AND DISCUSSION
During the FVT, ve eigenmodes corresponding to motion in the plane of the truss and
with eigenfrequencies between 5 Hz and 100 Hz were identified and their corresponding mode
shapes and damping values were extracted. From the numerical analysis, 23 in-plane eigen-
modes were calculated. Modal Assurance Criterion (MAC) values comparing the experimental
modes shapes ΦX
r, stemming from modal testing, to the analytical mode shapes ΦA
s, stemming
from the FE-analysis, are calculated according to equation 2 and are presented in the matrix in
figure 3.
MACr,s =X
r
TΦA
s)2
ΦX
r
TΦX
rΦA
s
TΦA
s
(2)
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Pierre Landel and Andreas Linderholt
Figure 3: A representation of the MAC matrix comparing experimental mode shapes to numerical mode shapes.
According to the MAC values, ve numerical modes (mode 1, 2, 3, 6 and 16) have high
consistency with the ve experimental modes ; their MAC values are between 0.88 and 0.99.
Table 2 presents graphical representations of the mode shapes, the eigenfrequencies, the exper-
imental damping and the MAC values of the paired eigenmodes. The numerical eigenmode 2
corresponds to a local motion of the end of the pillar and matches in both eigenfrequency and
shape the paired experimental eigenmode 2. The numerical eigenmodes 3, 6 and 16 are stiffer
and have eigenfrequencies 10 % higher than their experimental counterparts. These modes are
global bending vibration modes and are of interest when investigating structural timber trusses
aimed for stabilization against lateral forces e.g. wind loads. The total mass of the glulam and
the stiffness of the single elements are correct at a global scale. At a smaller scale, slightly
lower than the diameter of the dowels, timber presents large variability in the density and in
the orthotropic stiffnesses [22]. At this lower scale, the embedment stiffness between timber
and dowels is sensitive to the local variations of the modulus of elasticity and the shear mod-
ulus. Higher frequencies in the numerical models can signify that this embedment stiffness in
the FE-model is overestimated. Linear material model for timber with standard elastic modu-
lus stemming from clear wood testing might not be suitable. Bi-linear material models with a
yield criterion for timber friction and gaps between timber and dowels should be considered in
FE-models made of solid element to predict the dynamic properties of timber structures. The
damping ratios (relative to the critical viscous damping) from the test data of the experimental
modes 2, 3, 4 and 5 vary between 0.6 % and 1.0 %. They are lower than the damping ratios of
timber floors tested in lab [17] and the standard values for timber bridges [18].
Experimental results Numerical results
Exp. 1: 8.97 Hz and ζ1= 1.7 % Num. 1: 8.97 Hz (0%) and MAC1,1=0.99
Exp. 2: 25.25 Hz and ζ2= 0.9 % Num. 2: 26.9 Hz (+6%) and MAC2,2=0.99
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Pierre Landel and Andreas Linderholt
Exp. 3: 42.65 Hz and ζ3= 1.0 % Num. 3: 47.5 Hz (+11%) and MAC3,3=0.97
Exp. 4: 61.57 Hz and ζ4= 0.6 % Num. 6: 67.7 Hz (+10%) and MAC4,6=0.88
Exp. 5: 92.78 Hz and ζ5= 0.7 % Num. 16: 103 Hz (+11%) and MAC5,16 =0.9
Table 2: Experimental and numerical eigenmodes and their MAC values.
5 CONCLUSIONS
There is still limited knowledge on the stiffness and damping of real timber connections for
dynamic loads. This study, comparing modal data measured on a real large structure and modal
data from a detailed 3D FE-model, shows the suitability of modal analysis methods. Non-linear
embedment stiffness between timber and the dowels is likely to be important and further studies
on damping properties in timber structures must be performed to better evaluate the dissipation
of energy. The FE-model presented in this article will be further developed and reduced in
coming investigations.
6 ACKNOWLEDGEMENT
We would like to express our thanks to Moelven T¨
oreboda AB for the opportunity and the
help to measure in their factory while manufacturing had to run with a tight schedule for the
building project. The authors gratefully acknowledge the funding for the project “Tall Timber
Buildings concept studies” from Formas the Swedish Research Council for Environment,
Agricultural Science and Spatial Planning [Dnr: 942-2015-115].
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Numerical models, like the phenomenological Beam-On-Foundation (BOF) approach, have proven to be an efficient alternative to the analytical European Yield Model (EYM) for the design of dowelled timber joints according to EN 1995-1-1 (2004) (EC 5) (see e.g. Lemaître et al. (2018), Bader et al. (2016)). In contrast to the EYM, BOF-models allow not only for prediction of the load-carrying capacity, but also for prediction of the load-displacement behavior of single-dowel connections, and thus of their stiffness. This makes BOF-models predestined for the design of joints in advanced modern timber structures, which for reason of their complexity rely on a reliable prediction of the jointload-deformation behavior. BOF-models are used since the early thirties of the last century (Hager, 1930). Models of different complexity were used from simplified (i) rigid-ideal plastic models, which allow only for strength prediction (cf. Johansen (1949)); to (ii) bi-linear elastic approaches, being able to predict stiffness and strength (Sawata and Yasumura (2003), Cachim and Franssen (2009)), and (iii) nonlinear elastic models, which are optimized for numerical simulations (Lemaître et al., 2018). BOF-models might be even used for earthquake design by application of plastic, or even hysteresis models (Izzi et al. (2018), Girhammar et al. (2017)). Developers and users of such phenomenological models face the challenge to find reliable input data on the load-deformation behavior of steel dowels embedded in wood or wood-based products. Lack of input data for numerical models, like BOF, is one of the main reasons which hinders application of such models in engineering practice and in research. Since the EYM of EC 5 uses only the embedment strength (fh,EC5) but no stiffness, as input, the related European standard for embedment testing, EN 383 (2007), focuses mainly on the embedment strength determination. However, numerical modeling requires information on the entire load-displacement curve from embedment tests.The aim of this contribution is to: (i) present methods to analyze and parameterize experimental load-displacement curves for BOF-models, with embedment parameters suitable for this purpose; (ii) provide a database of embedment parameters for different wood spieces and wood products, and try to find correlations between parameters; (iii) give recommendations for embedment testing, with the aim to exploit data in numerical models.
Conference Paper
In many design codes for timber structures (e.g. Eurocode 5 and SIA 265), the stiffness of a connection is given by empirical equations for a single dowel-type fastener per shear plane. The global stiffness of the connection is then given by multiplication with the number of dowels and shear planes. In the codes cited above, the empirical equations to estimate stiffness only depend on two parameters, namely the dowel diameter and the wood density. The main difference between different codes and stiffness of different types of fasteners is the choice of the exponent on these two parameters. Development and background of empirical equations for stiffness in different codes were recently reported in Jockwer and Jorissen (2018), who analysed about one thousand double shear timber-to-timber connection tests to evaluate the influence of further parameters on stiffness, such as number of fasteners in a row, number of rows of fasteners and dowel slenderness. From this huge database, they have been able to estimate another empirical stiffness equation, that includes dowel slenderness as an additional parameter. Effects of the latter have even been reported in Lemaître et al. (2018), by using a phenomenological numerical model instead ofexperiments. Sandhaas and van de Kuilen (2017) reported that using the slip modulus Kser, calculated according to Eurocode 5 for stiffness prediction of multiple fastener joints, considerably overestimates the experimentally observed stiffness and they proposed to introduce an effective number of dowels in their design, which was also recommended in Jockwer and Jorissen (2018). This paper continues the work presented in Lemaître et al. (2018) on strength and stiffness estimations of single-fastener connections using a beam-on-foundation (BOF) modelling. In Lemaître et al (2018), the beam-on-foundation model calculations were compared to design equations of Eurocode 5, i.e. the load-carrying capacity and slip modulus. By these comparisons, the validity of the method for the design of single-fastener connections was highlighted. Moreover, effects that are not explicitly covered in the empirical design equations, namely the influence of the dowel slenderness and the nonlinear dowel diameter on the slip modulus were demonstrated. In the present paper, the same comparisons are made for multiple dowelled connections. Moreover, load distribution between dowels in this type of connection, which was shown to be non-uniform by Blass (1995), is studied by means of the BOF model. Different approaches to estimate the load distribution have been proposed by Cramer (1968), Lantos (1969) and Wilkinson (1986).