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705
WOOD RESE ARCH
65 (5): 2020
705-714
STRENGTH AND STIFFNESS OF MECHANICALLY
JOINTED CLT PANELS LOADED BY SHEAR IN PLANE
L V, P K
C T U P
C R
(R D )
ABSTRACT
This article is focused on research into the racking strength and stiffness of mechanically
jointed cross laminated timber shear walls considering the inf luence of fasteners between the
layers of boards on the stiffness of panels. The work includes an experimental analysis and
analytical model. The experimental analysis included tests of the shear wall panels, tests of the
specimens to determine the stiffness at the joint of the layers and material tests. The analytical
model based on the component method allows the determination of the racking strength and
horizontal displacement of the shear wall in dependence on the number of layers and the number
of fasteners in the joint of layers, parameters of the anchorage to the substructure and applied
external load. The outputs of the numerical model and the results of the experiments agree
relatively well. The largest relative displacement error is 18%.
KEY WORDS: Cross laminated timber (CLT), wall panels, racking strength, racking stiffness,
fasteners, component method.
INTRODUCTION
Massive plate construction systems made of cross laminated timber are becoming more
and more used for multi-storey construction. There is a European product standard, EN 16351
(2015), but it is still necessary to develop technical standards that would give designers the basis
for designing structures from this product. The research of glued CLT has been the subject
of activity of scientific teams for many years (Mestek et al. 2008, Schickhofer et al. 2010,
Bogensperger et al. 2010, Gagnon and Pirvu 2011, Kreuzinger and Sieder 2013, Brandner et al.
2017, Song et al. 2019, Wie et al. 2020). The most common method of joining layers is by all-over
gluing. An alternative to the gluing process is the usage of mechanical fasteners. Nowadays, only
the method for surfaces from mutually flexible jointed layers (DIN 1052 2008) can be used to
design this system. However, this method does not take into account the effect of wall anchoring
or the plasticity of the fasteners, and the empirically determined values of the slip modulus are
doi:/10.37763/wr.1336-4561/65.5.705714
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WOOD R ESEARC H
higher than the values measured during the tests. General relationships of the theory of elasticity
and models of torsionally rigid joints describing the distribution of forces and stresses in the joints
in relation to the arrangement of fasteners (Racher 1995) can be used to create a more suitable
model. The verification of the racking strength of wall panels is therefore based on the assessment
of the shear strengths in the joints of the layers. Blaß and Görlacher (2002) and Jöbstl et al. (2004)
investigated the strength and stiffness in torsional shear of a glued joint between perpendicularly
oriented boards. Flaig and Meyer (2014) focused on the creation of a test method for a more
accurate determination of the slip modulus in glued joints.
The racking strength and stiffness of shear walls are significantly inf luenced by the type
of anchoring to the substructure, which must ensure the transmission of tensile and shear forces
induced by the horizontal load in plane of the wall (Fragiacomo et al. 2011, Hummel et al. 2013,
Gavric et al. 2015). Jára (2018) dealt with the issue of anchoring sandwich shear wall panels of
wooden buildings. The analytical model compiled using a component method is included in
this research. With increasing horizontal loads on the wall, the model considers the shift of the
centre of rotation in the panel anchorage and the related gradual activation of tensile anchors.
The method of components in research of structure was also used by Wald et al. (2000), Brühl
and Kuhlmann (2012) and Sabatka et al. (2014).
This paper presents the results of experimental analysis and the description of an analytical
model for determining the racking strength and stiffness of wall panels made of mechanically
jointed cross-laminated timber.
MATERIAL AND METHODS
Experimental analysis
Three types of tests were performed in the experimental analysis. The first type was the test
of the racking strength and stiffness of the wall panel. The rotation of the joints between the
layers and thus the shear deformation of the whole panel depends on the rigidity of the lamella
connection. The second type was therefore the test for determining the torsional stiffness of the
layers’ joint and the slip modulus of fasteners in dependence on the number of layers and the
number of fasteners in the joint. The third type were material tests to determine the modulus of
elasticity, bending strength and density of wooden boards.
The EN 594 (2011) was used to perform and evaluate the rack ing strength and stiffness
of the wall panel. The applied horizontal and vertical loads as well as horizontal and vertical
displacements of the specimen were recorded during the tests. Three specimens with dimensions
of 3 000 x 2 520 x 81 mm were used. The panels consisted of three layers of boards 27 mm thick
and 170 mm wide. Two galvanized screws 5 x 80 mm were used to join the layers in each board
crossing. The characteristic values of a 5% quantile of the stiffness Ks,k and the load-bearing
capacity Fv, k were determined from the results of the experiments.
The tests for the determination of stiffness in the joints of the layers were carried out
according to the EN 26891 (1991). The specimens were placed in steel test equipment during
the experiment. The design of the test equipment is based on tests to determine the slip modulus
in the joint of glued boards (Meyer and Flaig 2014). The value of the applied loading force and
mutual rotation of the boards were recorded during the experiments. Five series of test specimens
with five identical specimens in each series were used to determine the joint stiffness. The
specimens consisted of boards with dimensions of 170 x 27 x 500 mm joined together by screws
5 x 80 mm. The number of lamellae in the specimens and the number of screws in each shear
plane between the lamellae are listed in Tab. 1.
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Tab. 1: Experimental program for the determination of stiffness in joints of layers.
Test series A_2L B_2LS C_3L D_3LS E_5L
Number of lamellae in each specimen 2 2 3 3 5
Number of screws in each shear plane 2 4 2 4 2
The maximum torsional moment Mmax,exp, the torsional stiffness of the layers’ joint Kr,s er,i ,e xp,
the slip modulus of the fasteners Kser,i, exp and the maximum load per one cut of the fastener
FM,i,max,exp were determined from the measured data.
All test specimens were conditioned in a standard laboratory environment. Three basic
parameters were evaluated to determine wood material properties: modulus of elasticity parallel to
grain, 5% quantile of density and characteristic value of bending strength. The dynamic modulus
of elasticity was determined by a non-destructive ultrasonic method. The static modulus of
elasticity was then determined from the dynamic modulus of elasticity. To determine the bending
strength, the boards were subjected to a 4-point bending test. The material characteristics of the
Würth screws were taken from the ETA-11/0190 (2013).
The output of the layers’ joint stiffness tests and the material tests were the values used as
input data for the analytical model. The data obtained from the shear wall tests were used for the
validation of the analytical model.
Analytical model
The shear wall was divided into a system of f ive components to create the model: screw
joint of layers in shear (a1), vertical boards in compression parallel to the grain (a2), bottom wall
plate in compression perpendicular to the grain (a3), bolt joint of the anchor and the panel in
shear (a4) and base of the steel anchor in bending (a5). The stiffness and load-bearing capacity
are determined for each component in dependence on its geometric arrangement, material
characteristics and type of stress. The racking strength of the wall corresponds to the component
with the lowest load-bearing capacity. To determine the displacement in plane of the wall, the
components are assembled into a corresponding relationship, taking into account the applied load
and the geometric arrangement of the wall. The displacement at the top of the wall is composed
from the displacement including the stiffness effect of the connection between the layers (a1) and
from the displacement caused by the rotation of panel in its anchorage (a2 - a5). Due to the free
rotation of the lamella ends and also due to the low stiffness of the joint between the layers in
relation to the bending and shear stiffness of the lamellae, the wall displacement caused by the
bending and shear stress of the lamellae is negligible and was not considered in the analytical
model.
RESULTS AND DISCUSSION
Tests of shear walls
A mutual torsional displacement of the board between the layers due to the grain embedment
by fasteners, the deformation of the tensile panel anchor and the grain embedment by the bolts
connecting the panel to the anchor occurred during the loading of panels. The evaluation of the
racking strength and stiffness of shear wall panels is presented in Tab. 2.
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WOOD R ESEARC H
Tab. 2: Racking strength and stiffness of shear wall panels.
Test
specimen
Ks,exp Ks,avg Ks,k Fv,max Fv, avg Fv,k
(N.mm-1)(N.mm-1)(N.mm-1)(kN) (kN) (kN)
S_1 510
582 358
33.65
32.13 26.20S_2 651 30.06
S_3 585 32. 67
Tests of layers’ joint
The cur ves describing the dependences of the joint rotation on the torsional moment are
presented in Fig. 1. The values of the torsional stiffness and load bearing capacity of the joints
increase in proportion to the increasing number of shear planes and the number of fasteners. If
the dependences of the load and displacement of the screws are related to one cut of fastener, the
curves of the dependences are almost identical for all series (Fig. 2). The summary of the mean
values of load-bearing capacities and stiffnesses of joints is shown in Tab. 3.
Fig. 1: Comparison of joint rotation to torsional
moment dependence.
Fig. 2: Comparison of displacement and load
dependencies of the fastener.
Tab. 3: Summary of load-bearing capacities and stiffnesses of test series A – E.
Test series Mmax, exp (kNm) FM,i,max ,exp (N) Kr,ser, i,ex p Kser, i,exp (N.mm-1)
A_2L 0.52 3 083.79 17.9 0 1 242.87
B_2LS 0.99 2 911.33 30.93 1 074 .20
C_3L 1.00 2 94 7.86 24.22 841.05
D_3LS 1.95 2 873. 39 51.42 892.80
E_5L 1.89 2 786.07 52.95 919. 29
Analytical model
To determine the displacement of the panel affected by the stiffness in the joint of the layers
(a1), the dependence between the horizontal load of the panel Fv and the force acting on one cut
of the fastener is found. The stiffness of component a1 can be expressed as:
(1)
where: Kser is the slip modulus of the fastener, r is the distance of the fastener from the centre
of the joint rotation, m is the number of the shear planes, n is the number of fasteners, a0 is the
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Vol. 65 (5): 2020
number of boards along the panel length, a90 is the number of boards along the panel height,
hCLT is the height of the panel and Kr, ser,CLT is the torsional stiffness of the layers’ joint.
To determine the stiffness of the compressed components a2 and a3, the elastic behavior
and dependence for normal stress and relative elongation were considered. The stiffness of
components a2 and a3 can be expressed for the triangular stress distribution in the compressed
zone of the wall anchor as:
(2)
where: Emean,a 2(3) is the modulus of elasticity parallel to the grain (a2) and perpendicular to the
grain (a3), dlam,0 is the thickness of the board, a is the length of the compressed zone, p is the
reduction factor of the loaded area and hak ,a 2(3) is the active length of the elements a2 and a3.
Components a2 and a3 are considered as lines and the stiffnesses are therefore apply to
1 mm of component length. Components a4 and a5 are considered as points. The stiffness of the
component a4 is determined using the Kser slip module:
(3)
where: n is the number of bolts in the joint and m is the number of shear planes.
The component a5 is considered as a pair of symmetrical consoles, loaded by forces at the free
ends. The stiffness of a component is expressed as:
(4)
where: E is the modulus of elasticity in tension of the steel, I is the moment of inertia of the
console and L is the length of the console.
The panel rotation depends on the rotational stiffness Kα,CLT including the inf luence of the
stiffness of components a2 - a5. The connection of components a2 and a3 in the compression zone
as well as a4 and a5 in the tension zone is considered to be serial. Within the rotational stiffness
Kα,CLT, the components in the compression and tension zone are in parallel connection. The
stiffness in the compression zone Kc is expressed as:
(5)
The stiffness of the tensile anchor Kt,i, taking into account the displacement δ0 given by the
tolerance of the bolt hole and the tensile force in the anchor Ft,i, is based on the relation:
(6)
The rotational stiffness Kα,CLT is determined as:
(7)
where: n is the number of anchors loaded in tension and st,i is the distance of the anchor from
the center of wall rotation.
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WOOD R ESEARC H
The function describing the course of the horizontal displacement at the top of the wall was
divided into three intervals defined by the values of the horizontal load:
(8)
The first interval describes the state when the whole bottom wall plate is stressed in
compression due to the vertical load on the panel. The second inter val defines the state when
the horizontal limit load Fv, 0 compensating the effect of vertical loading is exceeded and the
outermost anchor of the panel begins to be stressed by tension. Within the third interval, the
stiffness of the layers’ joint is reduced and the slip modulus of the fasteners Kser is replaced by
the slip modulus Ku, determined as Ku = 2/3 Kser. After reaching the horizontal limit load and
activating the rotational stiffness, the wall displacement is determined based on a set of equations,
including the vertical and moment equilibrium condition and the relationship for the horizontal
displacement at the top of the panel. The vertical lifts of the panel u, the horizontal displacement
of the panel v and the length of the compression zone a are unknown.
The torsional moments and shear forces are distributed uniformly over the fasteners, similar
to glued CLT (Blaß and Flaig 2012). The load of one cut of the fastener is based on the vector sum
of the forces from the torsional moment FM and from the shear force FQ. Depending on the shear
resistance of one cut of the fastener in the vertical and horizontal lamella Fv,R, the load-bearing
capacity of the panel FV, a1 ,m ax can be determined as:
(9)
where: an is the distance of the fasteners from the center of joint rotation in the x-axis and bCLT
is panel width.
Components a2 and a3 do not affect the load-bearing capacity of the wall, because after
the local exceeding of the compressive strength of the board, the shear wall is able to withstand
the increasing horizontal load. The load-bearing capacity of component a4 is given by the shear
resistance of the bolts. The load-bearing capacity of component a5 is based on the moment of
resistance of the steel anchor base. The ma ximum tensile force in the anchor must be less than or
equal to the maximum load capacity of components a4 and a5:
(10)
where: at is the angle of panel rotation, nr is the number of rows of fasteners, nef is the effective
number of fasteners in a row, Fv,a4,R is the shear resistance of one cut of the fastener, Wy is the
cross-sectional modulus of the anchor base and fy is the yield strength of steel.
Comparison of experimental results with analytical model outputs
The test data of wall panels were averaged for a clearer graphical comparison of the results.
The comparison of the displacement curves is shown in Fig. 3.
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Fig. 3: Comparison of experimental results with analytical model outputs at the end of the compression
zone of anchorage (left), at the end of the tensile zone of anchorage (middle) and at the top of the wall
(right).
The largest absolute difference in horizontal displacements at the top of the panel is
12.5 mm (relative error of 18%). The absolute difference of the maximum resistances is 1.1 kN
(relative error of 3.5%). By comparing the experimental data with the outputs of method for
surfaces from mutually f lexible jointed layers (DIN 1052 2008), the largest absolute difference in
displacements of 47 mm (313%) and resistances of 2.3 kN (7.7%) is obtained. If the slip modulus
of the fasteners from the standard is replaced by stiffness obtained from the tests of layers’ joints,
the maximum absolute difference in displacements is 11 mm (16%).
CONCLUSIONS
The analytical model for determining the load-bearing capacity and deformation of the shear
wall made of mechanically jointed cross-laminated timber was compiled and the obtained data
were validated using the results of the tests of three wall panels. The maximum relative difference
in deformations is 18% and resistances is 3.5%.
The deformation in the wall plane is most signif icantly affected by the stiffness of the contact
between the layers. Based on the performed stiffness tests in the joint of layers, it can be stated
that the values of torsional stiffness and load-bearing capacity of joints increase in proportion to
the increasing number of shear planes and the number of fasteners. The differences in the average
values of the slip modulus of the fasteners are up to 9% for the series of specimens corresponding
to the common layup of wall panels.
ACKNOWLEDGMENTS
This work has been supported by the project TE02000077 Smart Regions - Buildings and
Settlements Information Modelling, Technology and Infrastructure for Sustainable Development
and by the project COST LD15077 Mechanically jointed cross laminated timber (CLT).
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REFERENCES
1. Bogensperger, T., Moosbrugger, T., Silly, G., 2010: Verification of CLT-plates under loads
in plane. In: Proceedings of the 11th conference WCTE 2010 (ed. Ceccotti, A.). National
Research Council, Trentino Pp 1-9.
2. Blaß, H.J., Flaig, M. 2012: Stabförmige Bauteile aus Brettsperrholz. K IT Scientific
Publishing, Karlsruhe, 171 pp.
3. Blaß, H.J., Görlacher, R., 2002: Zum Trag- und Verformungsverhalten von
Brettsperrholzelementen bei Beanspruchung in Plattenebene. Bauen mit Holz 104(11):
34-41.
4. Brandner, R., Dietsch, P., Dröscher, J., Schulte-Wrede, M., Kreuzinger, H., Sieder,
M., 2017: Cross laminated timber (CLT) diaphragms under shear: Test configuration,
properties and design. Construction and Building Materials 147: 312-327.
5. Brühl, F., Kuhlmann, U., 2012: Connection ductility in timber structures considering
the moment-rotation behavior. In: Proceedings of the 12th conference WCTE 2012.
Auckland Pp 136-145.
6. DIN 1052, 2008: Entwurf, Berechnung und Bemessung von Holzbauwerken – A llgemeine
Bemessungsregeln und Bemessungsregeln für den Hochbau.
7. EN 16351, 2015: Timber structures. Cross laminated timber. Requirements.
8. EN 26891, 1991: Timber structures. Joints made with mechanical fasteners. General
principles for the determination of strength and deformation characteristics.
9. EN 594, 2011: Timber structures. Test methods. Racking strength and stiffness of timber
frame wall panels.
10. ETA 11/0190, 2013: Self-tapping screws for use in timber constructions.
11. Fragiacomo, M., Dujic, B., Sustersic, I., 2011: Elastic and ductile design of multi-storey
crosslam massive wooden buildings under seismic actions. Engineering Structures 33(11):
3043-3053.
12. Gagnon, S., Pirvu, C., 2011: CLT handbook: Cross-laminated timber. Vancouver, British
Columbia: FPInnovations, 380 pp.
13. Gavric, I., Fragiacomo, M., Ceccotti, A., 2015: Cyclic behaviour of typical metal connectors
for cross-laminated (CLT) structures. Materials and Structures. 48(6): 1841-1857.
14. Hummel, J., Flatscher, G., Seim, W., Schickhofer, G., 2013: CLT wall elements under
cyclic loading - Details for anchorage and connection. In: COST Action FP1004
(ed. Harris, R., Ringhofer, A., Schickhofer, G.). University of Bath, Bath, Pp 152-165.
15. Jára, R., 2018: Anchoring of load-bearing sandwich panels of timber buildings. Dissertation.
Czech Technical University in Prague, Prague, 90 pp.
16. Jöbstl, R.A., Bogensperger, T., Schickhofer, G., Jeitler, G., 2004: Mechanical behaviour
of two orthogonally glued boards. In: Proceedings of the 8th conference WCTE 2004.
Finnish Association of Civil Engineers. Helsinki, Pp 357-364.
17. Kreuzinger, H., Sieder, M., 2013: Basic test method for valuation of shear strength of cross
laminated timber. Bautechnik 90(5): 314-316.
18. Mestek, P., Kreuzinger, H., Winter, S., 2008: Design of Cross Laminated Timber (CLT).
In: Proceedings of the 10th conference WCTE 2008. TU Munich, Munich, Pp. 156-163.
19. Meyer, N., Flaig, M., 2014: A new test configuration to determine the slip modulus of
connections between crosswise bonded boards. In: COST FP1004 (ed. Schober, K.).
University of Bath, Bath, Pp 77-84.
713
Vol. 65 (5): 2020
20. Racher, P., 1995: Moment-resisting joints. In: Timber engineering - Principles for design
(ed. Blaß, H.J., Sandhaas, C.). KIT Scientific Publishing, Karlsruhe, Pp 491-508.
21. Sabatka, L., Wald, F., Kabeláč, J., Gödrich, L., Navrátil, J., 2014: Component based
finite element model of structural connections. In: Proceedings of the 12th International
Conference on Steel, Space and Composite Structures. Prague, Pp 337-344.
22. Schickhofer, G., Bogensperger, T., Moosbrugger, T., 2010: BSP Handbuch: Holz-
Massivbauweise in Brettsperrholz. Verlag der TU Graz. Graz, 440 pp.
23. Song, Y.J., Lee, I.H., Hong, S.I., 2019: Evaluation of horizontal shear performance of larch
CLT walls according to the edge connection shape. Wood Research 64(2): 213-222.
24. Wald, F., Mareš, J., Sokol, Z., Drdácký, M., 2000: Component method for historical timber
joints. In: The Paramount Role of Joints into the Reliable Response of Structures (eds.
Banitopoulos, C.C., Wald, F.). NATO Science Series. Dordrecht, Pp 417-425.
25. Wie, P., Wang, B.J., Li, Z., Ju, R., 2020: Development of cross-laminated timber (CLT)
products from stress graded Canadian hem-fir. Wood Research 65(2): 335-346.
*L V, P K
C T U P
F C E
T /
P
C R
*Corresponding author: lukas.velebil@cvut.cz
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