STRUCTURAL PERFORMANCE OF OUT-OF-PLANE MOMENT CONNECTIONS IN
THE MINOR STRENGTH AXIS OF CROSS-LAMINATED TIMBER PANELS
by
Seyed Armin Hosseini
B.Sc in Civil Engineering, Azad University, Iran, 2014
M.Sc. in Structural Engineering, Semnan University, Iran, 2018

THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF APPLIED SCIENCE
IN
ENGINEERING

UNIVERSITY OF NORTHERN BRITISH COLUMBIA
June 2024
© Seyed Armin Hosseini, 2024

Abstract
The structural performance of panel-to-panel connections in the minor strength axis of
cross-laminated timber (CLT) panels was investigated using experimental and numerical methods.
These connections are crucial for achieving two-way span action in point-supported floors of a
large structural grid. Five different connections were studied: plywood splines attached with
inclined self-tapping screws (STS), glued plywood splines, T-joints, wood X-fix shear keys, and
steel rebars.
Based on 4-point and 3-point bending tests, the glued splines had the highest rotational
stiffness, followed by the STS spline and T-joints. Steel rebar and X-fix connections had the lowest
rotational stiffness. In terms of ductility, the glued spline exhibited brittle behavior, whereas others
displayed a moderate level of ductility, while the steel rebars provided high ductility. The STS
spline and glued spline had similar bending moment capacities, with the glued spline's capacity
being affected by plywood quality. Steel rebars, T-joint, and X-fix connections had 70%, 50%, and
23% of this capacity, respectively.
Subsequently, a numerical model, validated by the experimental results, was used to
evaluate the connection demands for point-supported CLT floors in the minor direction for
different dimensions and applied loads. Increasing the rotational stiffness from 500 to 5000
kNmrad⁻¹m⁻¹ significantly improved floor structural performance, reducing the deflection by about
50%. Further increasing rotational stiffness only yielded an additional decrease in deflection of
15%. With the tested configurations, both glued and screwed splines can provide 5000
kNmrad⁻¹m⁻¹, T-joints could potentially achieve this value, while an unreasonably high number of
connectors would be necessitated for X-fix.

Page i

Table of contents
Abstract

i

Table of contents

ii

List of figures

v

List of tables

viii

Acknowledgements

ix

1

Introduction

1

1.1 Background

1

1.2 Objectives

2

1.3 Organization of thesis

2

1.4 Scope and limitations

3

Literature review

4

2.1 Wood and mass timber as structural material

4

2.2 Cross-laminated timber floors

5

2.3 Connections between CLT floor panels

6

2

3

2.3.1 Wooden shear keys

6

2.3.2 Self-tapping screws

7

2.3.3 Out-of-plane screw connections

8

2.3.4 Adhesive bonds

12

2.3.5 Hybrid connections

13

2.4 Modelling of CLT floors

14

2.5 Summary of literature review

16

Experimental investigation

18

3.1 Overview

18

Page ii

3.2 Materials

18

3.3 Specimen description

21

3.3.1 S1 - spline plate with inclined STS

21

3.3.2 S2 - glued spline plate

22

3.3.3 S3 - T-joint

22

3.3.4 S4 - X-fix

23

3.3.5 S5 - Steel rebar

24

3.4 Test methods

4

25

3.4.1 4-point bending test

25

3.4.2 3-point bending tests

27

3.4.3 Loading protocol

28

3.5 Results and discussion

28

3.5.1 Load-deflection of 4-point bending tests

28

3.5.2 Failure modes in 4-point bending tests

30

3.5.3 4-point bending test result analyses

33

3.5.4 Load-displacement behavior of 3-point bending tests

37

3.5.5 Failure modes of 3-point bending tests

38

3.5.6 3-point bending test result analyses

39

3.5.7 Reference specimen

42

Numerical investigations

43

4.1 Overview

43

4.2 Model development

44

4.3 Model validation

46

4.4 Results and discussion

48

Page iii

4.4.1 Impact of rotational stiffness on bending moment

48

4.4.2 Impact of rotational stiffness on the ULS and SLS panel utilisation

52

4.4.3 Impact of rotational stiffness on floor deflection

53

5

Recommendations for floor connection design

56

6

Conclusions

60

6.1 Summary of experimental work

60

6.2 Summary of numerical work

61

6.3 Future Research

62

References

63

Appendix A: Load-deflection response for 4-point bending tests

74

Appendix B: Load-deflection response for 3-point bending tests

77

Appendix C: Failure modes from 4-point bending tests

79

Appendix C: Failure modes from 3-point bending tests

80

Appendix D: Numerical results

83

D1: Transferred bending moment at the connecting line

83

D2: Floor deflections

87

D3: Floor utilisation ratios

91

Page iv

List of figures
Figure 1-1: CLT: (a) arrangement of lamellas, (b) major and minor direction [9] ......................... 1
Figure 1-2: Point-supported CLT floor [19] .................................................................................... 2
Figure 2-1: X-fix connector: (a) type C, (b) tensile loaded, (b) in-plane shear loaded [15] ............ 7
Figure 2-2: Edge connected shear wall: (a) arrangement of screw; (b) cross-sectional view [2] .... 7
Figure 2-3: Spline connections, (a) double spline joints and (b) internal spline joints [8] .............. 8
Figure 2-4: Edge-connected CLT panel (a) half-lapped joint (b) single-splined connections ......... 9
Figure 2-5: Spline connection with steel plate, washer, and inclined STS [19] ............................ 10
Figure 2-6: Deformed half-lapped joint (a), and simplified model with four springs (b) [9] ........ 10
Figure 2-7: Deformation in: (a) half-laps; (b) spline top loading; (c) spline bottom loading [18] 11
Figure 2-8: T-joint connection: (a) T-JOINT D40 W30, (b) and (c) example application of
different variants [37] ......................................................................................................... 12
Figure 2-9: Butt-joint bonding technology (TS3) [43]................................................................... 13
Figure 2-10: Schematic of TCC connection [53] ........................................................................... 13
Figure 2-11: Edge connected panels with serrated steel plates [54] .............................................. 14
Figure 2-12: (a) Grain orientation in lamellas and (b) homogenized orthotropic model [4] ......... 16
Figure 3-1: ASSY plus VG screws [63] ......................................................................................... 19
Figure 3-2: Plywood: (a) high-quality (grade B) and (b) low-quality (grade C) ........................... 19
Figure 3-3: X-fix-Cm Connector; (a) schematic view, (b) actual view ......................................... 20
Figure 3-4: Schematic representation of a T-joint connection utilizing the D40 W30 variant ...... 20
Figure 3-5: Spline connection with inclined STS: (a) schematic (b) photos side and bottom ....... 21
Figure 3-6: T-joint: (a) layout before installation, (b) fully installed............................................. 23

Page v

Figure 3-7: X-fix connection: (a) schematic; (b) photo bottom face ............................................. 23
Figure 3-8: Steel rebar connection: (a) schematic S5A, (b) and S5B, (c); photo S5A, (d) and S5B
............................................................................................................................................ 24
Figure 3-9: 4-point bending test: (a) schematic (dimensions in mm); (b) photo ........................... 25
Figure 3-10: Procedure for calculating ductility index .................................................................. 26
Figure 3-11: 3-point bending test: (a) schematic (dimensions in mm); (b) photo ......................... 27
Figure 3-12: Typical load-deflection curves of 4-point tests ......................................................... 30
Figure 3-13: Failure modes series S1-S4 in 4-point tests; (a) S1 tension failure in the plywood, (b)
S1 withdrawal effect in the spline plate, c) S2B, d) S2C, (e) S4 crushing perpendicular to
the grain, (f) S4 Withdrawal effects, (g) S4 ductile failure in STS, (h) S3 bottom view, (i)
S3 connecting section, (j) X-fix shear failure .................................................................... 32
Figure 3-14: Failure modes series S5: (a) S5A slot view, S5, (b) connecting section, (c) CLT
panel compression zone, (d) S5B rebar end compression zone ......................................... 33
Figure 3-15: Moment resistance of connection configurations in 4-point tests ............................. 35
Figure 3-16: Typical moment-rotation curves of 4-point tests ...................................................... 36
Figure 3-17: Rotational stiffness of connection configurations in 4-point bending tests .............. 36
Figure 3-18: Connection ductility in 4-point tests ......................................................................... 37
Figure 3-19: Load-deflection curves of 3-point bending tests ....................................................... 38
Figure 3-20: Failure modes in 3-point tests: a) S1, b) S2 plywood surface c) S3 cross section at
connecting line, d) S3 side view......................................................................................... 39
Figure 3-21: 3-point bending tests: (a) shear resistance, (b) moment resistance and (c) rotational
stiffness............................................................................................................................... 41
Figure 3-22: 3-point test of continuous panel: (a) load-displacement curve and (b) failure mode 42

Page vi

Figure 4-1: Geometry of point-supported floor: (a) top view, (b) cross section A-A along minor
direction .............................................................................................................................. 43
Figure 4-2: RFEM model of point-supported CLT floor ............................................................... 45
Figure 4-3: Models labelling convention ....................................................................................... 46
Figure 4-4: Numerical validation of experiments; (a) 3-point bending tests of solid panels, (b) 4point bending tests of S1 series, (c) 3-point bending tests of S1 series ............................. 47
Figure 4-5: Impact of Cφ on internal loads at the connecting line for floor V2_9.5-7.2_LL 1.9_e
1.0; (a) bending moment diagram, (b) shear force diagram ............................................... 48
Figure 4-6: Bending moment at connecting line V2_9.5-7.2_LL 1.9 for (a) e=0.5 m, (b) e=1.5 .. 49
Figure 4-7: Impact of Cφ and e on bending moment along minor direction for floor V2_9.57.2_LL 1.9; (a) e=500 mm, Cφ = 500, (b) e=1500 mm, Cφ = 500, (c) e=500 mm,
Continuous floor, (d) e=1500 mm, Continuous floor......................................................... 50
Figure 4-8: Impact of Cφ and e on bending moment along minor direction for floor V2_9.57.2_LL 1.9; (a) e=500 mm, Cφ = 500, (b) e=1500 mm, Cφ = 500, (c) e=500 mm,
Continuous floor, (d) e=1500 mm, Continuous floor......................................................... 51
Figure 4-9: Impact of Cφ on the ULS V2_9.5-7.2_LL 1.9; for (a) e=0.5, (b) e=1.5 ..................... 52
Figure 4-10: Impact of Cφ on the SLS ratio for V2_9.5-7.2_LL 1.9; (a) e=0.5, (b) e=1.0, (c)
e=1.5 ................................................................................................................................... 53
Figure 4-11: Influence of floor span ratio on floor deformation sensitivity for CLT grade V2 .... 54
Figure 4-12: Impact of Cφ and e on the floor deformation for floor V2_9.5-7.2_LL 1.9; (a) e=500
mm, Cφ = 500, (b) e=1500 mm, Cφ = 500, (c) e=500 mm, Continuous floor, (d) e=1500
mm, Continuous floor ........................................................................................................ 55

Page vii

List of tables
Table 3-1: Results summary from 4-point bending tests ............................................................... 34
Table 3-2: Results summary from 3-point bending tests ............................................................... 40
Table 4-1: Model parameters floor dimensions (m)....................................................................... 44
Table 4-2: Material properties for the FEM simulation (MPa) [76] .............................................. 46
Table 5-1: Design recommendation for floor V2_9-9_LL 2.4_e 1.5 ............................................. 59

Page viii

Acknowledgements
I am deeply grateful to my supervisor, Dr. Thomas Tannert for his support, valuable feedback, and
insightful guidance throughout this journey. His supervision has been instrumental in the
completion of this thesis.
I also extend my thanks to Dr. Jianhui Zhou and Dr. Md Shahnewaz for their invaluable feedback
and expert insights, which significantly enhanced the quality and depth of my research.
Furthermore, I acknowledge with gratitude the support received during the experimental phase of
this study from Brandon Sullivan, Manager of the Fast + Epp Concept Lab, and Bernhard Zarnitz,
Concept Lab Technician. Their assistance is greatly appreciated.
Finally, I would like to express my profound appreciation to my parents and sister for their
unwavering love, encouragement, and belief in me. Their support has been my anchor throughout
this endeavor.

Page ix

1

Introduction

1.1

Background

Cross-laminated timber (CLT) is an engineered wood product, produced by laminating boards in
orthogonal cross-layers. This lay-up creates major and minor strength directions (Figure 1-1). A
wide range of investigations addressed connections in CLT panels with focus on their in-plane
shear performance, with a limited number of studies on the out-of-plane performance of edgeconnected CLT floors in the major strength direction using half-lap and single-spline joints [1-9].

(a)

(b)

Figure 1-1: CLT: (a) arrangement of lamellas, (b) major and minor direction [9]

In contrast, the out-of-plane behavior of CLT panels connected in the minor axis has only been
investigated sparsely [10-13]. This behavior is especially important for point-supported CLT floors
because these depend on two-way performance with both major and minor directions providing
rotational stiffness and bending moment capacity. Point-supported CLT floors have significant
potential due to their ability to create spacious floor areas, resulting in a more flexible layout of
columns without beams compared to the one-way-span floors (Figure 1-2). However, it is
important to note that CLT exhibits lower strength and stiffness in its minor strength direction
compared to the major direction. Additionally, CLT panels are typically available in widths ranging

Page 1

from 2.4 to 3.5 meters. Therefore, edge-to-edge connections along the minor direction play a
crucial role in enabling larger open floor spaces [4], [14].
A variety of solutions are available for establishing edge connections between CLT panels. These
technologies encompass wood shear keys, like the X-fix system [15], [16], and half-lapped and
single-spline joints connected with self-tapping screws (STS) [5-8, 17, 18], which are widely
favored as mechanical fasteners due to their efficiency and cost-effectiveness.

Figure 1-2: Point-supported CLT floor [19]

1.2

Objectives

The primary objective of this study is to investigate the out-of-plane performance of connections
in the minor direction of edge-connected CLT. For this purpose, the structural performance of five
different connection options is assessed: screwed plywood splines, glued plywood splines, wooden
X-fix, T-joint, and steel rebar connection. The secondary objective is to numerically determine the
moment and shear force demand that should be met by these connections.
1.3

Organization of thesis

In Chapter 2, the state-of-the-art on the out-of-plane performance of common connection systems
for edge-connected CLT panels is reviewed. Chapter 3 presents the experimental investigations of
Page 2

edge-to-edge connections in the minor direction of CLT panels, with results that provide
fundamental information for subsequent numerical studies. In Chapter 4, the connection demands
in different possible scenarios for point-supported CLT floors are evaluated using finite element
analyses (FEA). Chapter 5 offers design recommendations based on findings from Chapters 3 and
4, assessing the behavior of connections in critical scenarios of point-supported CLT floors.
Finally, Chapter 6 summarizes the main findings and suggests areas for further research.
1.4

Scope and limitations

This study focuses on the structural performance of edge-connected CLT panels along the minor
direction subjected to quasi-static short-term out-of-plane loads. Tests involving combined,
reversed cyclic, long-term, and in-plane shear loading are beyond the scope of this work.
Furthermore, the impact of the connections on the vibration, acoustic, and fire performance of CLT
floors is not addressed in this study. The numerical modeling is limited to analyzing the linear
range of CLT floor and the connection behavior. Additionally, the boundary conditions of the
models are confined to point-supported CLT floors.

Page 3

2

Literature review

2.1

Wood and mass timber as structural material

Timber has been used for millennia due to its accessibility and workability. The use of wood also
influenced the culture and architecture of indigenous peoples in North America [20]. As a result of
the industrial revolution and the subsequent development of steel and concrete, timber was mostly
used for small-scale and residential buildings, while population growth, particularly in rural areas,
increased demand for high-rise buildings [21]. However, environmental concerns are driving the
use of sustainable building materials, such as wood and engineered wood products.
Wood is an orthotropic material; its mechanical properties are distinct along three mutually
perpendicular axes: longitudinal, radial, and tangential. The mechanical properties of wood are
influenced by natural tree growth characteristics, such as specific gravity and slope of grain, as
well as natural defects such as knots. However, thanks to stress grading, lumber can be suitable for
a wide range of applications [22]. As a hygroscopic material, wood properties are sensitive to
moisture content; it is recommended that the moisture content of wood during construction is close
to the equilibrium moisture content that it will reach during use [22], [23].
Wood is widely utilized in construction, with one of its key attractions being its smaller carbon
footprint compared to other building materials. The National Building Code of Canada (NBCC)
permits encapsulated mass timber construction up to 12 stories in height [24], and due to the
enhanced fire resistance, along with their stiffness and strength, mass timber construction with
more than six stories has become increasingly common in practice [25].

Page 4

2.2

Cross-laminated timber floors

As an engineered wood product, CLT is constructed from lumber lamellas that are glued together
in an orthogonal pattern to create the composite material. Because of this configuration, CLT panels
are a viable alternative to concrete as a structural floor and wall system [5]. In comparison to
concrete and steel, the installation of prefabricated CLT panels speeds up construction.
CLT elements can be used as plate and shell elements loaded out-of-plane and in-plane, with floors
currently being the main application. The most efficient use of CLT is taking advantage of its twoway resistance, when both major and minor directions contribute to the transfer of the loads to the
supports. A two-way spanning CLT panel is around 50% stiffer than a one-way CLT panel [26].
The assessment of rolling shear strength in CLT for point-supported flat slab systems holds
significant importance in structural design, especially considering the variations in wood species,
stress grading, and panel configurations [27]. Notably, the primary mode of failure, characterized
by crack propagation along growth rings, highlights the relationship between material properties
and structural behavior. Moreover, a nuanced correlation between lamella aspect ratio and rolling
shear strength was identified, emphasizing the necessity for refined design standards to accurately
predict shear performance [27]. Popovski et al. [28] research on point-supported CLT floors reveals
prevalent failure modes, such as: (i) compression perpendicular to grain failure at specific support
points; (ii) a combination of rolling shear and tension perpendicular to grain failure above central
support(s), particularly where bending moments were highest; and (iii) instances of partial
penetration of middle columns into the CLT floor. Importantly, critical failures tended to occur at
central support(s), coinciding with peak bending moments.

Page 5

Several studies have examined various aspects of CLT panels. Yang et al. [10] and Mestek and
Dietsch [29] studied out-of-plane shear strength of short-span panels showing different failure
modes (rolling shear and tensile failure) as a function of loading and span. Bogensperger and Jobstl
[30] employed nonlinear finite element analyses (FEA) to describe the punching shear behavior of
unreinforced CLT point-supported panels.
2.3

Connections between CLT floor panels

In a structure, while columns, beams, and floors play crucial roles in transferring loads, their
effectiveness greatly depends on the integrity provided by the connections between members [31].
In the following sub-sections, common connection technologies for CLT panels are introduced.
2.3.1 Wooden shear keys
CLT panels can be joined using wood shear keys, such as the X-fix [16]. This dovetail-shaped
connection has a wedge form that engages and self-tightens the components during installation
without the addition of metal components [28]. X-fix components are made of Beech or Birch
plywood, according to EN 13986 [31]. Based on application, this type of connector is divided into
two groups: type C and type L. The C type is used as a shear connector for butt joints but can also
resist tension loads (Figure 2-1); the L type is used to join CLT wall components. Ayansola and
Tannert [32] observed high in-plane load-carrying capacity and stiffness of X-fix connectors,
though their low ductility challenges their use in seismic applications. The connector's brittle shear
failure was shown to be the most common failure when sufficient spacing is provided.

Page 6

(a)

(b)

(c)

Figure 2-1: X-fix connector: (a) type C, (b) tensile loaded, (b) in-plane shear loaded [15]

2.3.2 Self-tapping screws
Metal dowel-type fasteners, such as nails, screws, and bolts are popular because they efficiently
distribute forces and are relatively easy to install [33]. STS, in contrast to other dowel-type
fasteners, can be installed faster because predrilling is not required [34], [35]. High strength
capacity, sharp cutting blade threads, fully threads length and surface coating eliminated extra
works on predrilling. Hossain et al. [2] studied the in-plane shear behavior of double-angled STS
assemblies in CLT and found that butt joints provide high and moderate-ductility in static and
reversed cyclic loading, respectively (Figure 2-2) [4]. Experimental tests have suggested a group
effect reduction for the performance of STS [1].

(a)

(b)

Figure 2-2: Edge connected shear wall: (a) arrangement of screw; (b) cross-sectional view [2]

Page 7

2.3.3 Out-of-plane screw connections
Spline (single, double and internal) and half-lapped joints present practical solutions for connecting
panels, transferring both in-plane and out-of-plane loads. However, achieving a precise fit during
installation can be challenging, particularly for internal splines (Figure 2-3) [8].

(a)

(b)

Figure 2-3: Spline connections, (a) double spline joints and (b) internal spline joints [8]

Subhani et al. [3] studied the flexural performance of half-lapped and single-splined CLT joints
subjected to 4-point loading (Figure 2-4). Their findings underscored the positive correlation
between lap length and moment capacity, rotational rigidity, and ductility. Specifically, extending
the lap length from 75 mm to 100 mm yielded substantial enhancements in moment capacities for
both bolted and screwed lap connections. Notably, the 100 mm lap length resulted in a 39%
increase in moment capacity for bolted connections and a 33% increase for screwed connections.
Moreover, an evident improvement in rotational rigidity and ductility accompanied the increase in
lap length. Additionally, their study highlighted the superior performance of samples featuring
single-splined connections over half-lapped joints, particularly with steel spline connections. While
increasing the thickness of spline steel plates had minimal effect on moment capacity, enlarging
bolt diameters contributed to its enhancement. Thinner steel plates exhibited better performance,

Page 8

as the rigidity of thicker plates led to localized bearing failure. Regarding plywood spline
connections, the presence of glue had little influence on bending moment, support rotation, and
rigidity, with unglued connections demonstrating better performance. However, the incorporation
of glue alongside bolts notably enhanced the ductility of plywood spline connections by 26%.

(a)

(b)

Figure 2-4: Edge-connected CLT panel (a) half-lapped joint (b) single-splined connections

Zhang et al. [5] conducted an assessment on the two-way performance of CLT panels under outof-plane loads. As depicted in Figure 2-5, the joint in the minor direction was composed of steel
plates, STS, and 45° screw washers. Their study revealed that the specimens failed at the tension
side of the connection area, specifically at the interface of the outer bottom layers, while no evident
damage was observed on other joint components. Furthermore, there was a notable and sudden
decrease in loading capacity after reaching peak load. In subsequent testing, LVL was utilized as a
replacement for steel plates. Despite experiencing an 87% decrease in stiffness compared to steel
plates in H-block tests, LVL emerged as a practical choice considering factors such as
manufacturing cost, assembly time, and fire protection. The steel plate connection exhibited a
rotational stiffness of 782 kN m/rad, accounting for 98% of the intact panel's stiffness. In contrast,
the LVL plate connection, though slightly lower, retained a commendable 92% of the full panel's
stiffness [19].

Page 9

Figure 2-5: Spline connection with steel plate, washer, and inclined STS [19]

Macpherson et al. [6] developed a model for half-lap joints using four springs arranged as
illustrated in Figure 2-6. The method was assessed using experimental testing and 3D FEA by
considering the orthotropic properties of CLT and the interaction between the screw and wood.
The model accurately predicted connection stiffness for a variety of common configurations.

(a)

(b)

Figure 2-6: Deformed half-lapped joint (a), and simplified model with four springs (b) [9]

The structural integrity and performance of CLT floors are significantly influenced by edge
connections, as revealed in recent studies [36]. These connections, such as single surface spline
and half-lapped joint, play a pivotal role in determining modal properties and dynamic responses
of CLT floors. Research highlights the sensitivity of modal properties to rotational stiffness and
emphasizes the need for accurate modeling of connections in numerical simulations. Moreover,
experimental estimation of connection stiffnesses is deemed essential for precise vibration analysis.

Page 10

Sadeghi et al. [18] investigated the out-of-plane performance of edge-to-edge connections in CLT
panels by employing STS in half-lapped and single-spline joints, with and without cup washers
(Figure 2-7). The out-of-plane behavior of a single spline connection depended on the direction of
applied moment, while half-lapped joints had the same performance in both positive and negative
moments. Employing washers beneath the screw heads in half-lapped joints with 6 mm screws
elevated maximum bending moment capacity and stiffness by 14% to 18% and 21% to 43%,
respectively. For half-lapped joints utilizing 8 mm screws, these metrics saw a more moderate
increase, ranging from 3% to 10% and 5% to 28%, respectively.

(a)

(b)

(c)

Figure 2-7: Deformation in: (a) half-laps; (b) spline top loading; (c) spline bottom loading [18]

In an experimental and numerical study, Asselstine et al. [4] concentrated on edge-connected CLT
panels along minor directions. Different configurations of screwed LVL splines were investigated
under out-of-plane bending using a 4-point loading test with the connections positioned at the
middle span with no shear. The connections achieved stiffness values close to that of the full panel.
For the connection with eight Ø8×220 mm screws at 30˚ and Ø12×260 mm screws at 45˚ on each
side, bending moments of 72 kNm/m and 52 kNm/m were transferred, respectively. Different
failure modes were observed: rolling shear and tension failures in the major layer, with withdrawal
effects being less prominent, while the latter one showed rolling shear with withdrawal effects. In

Page 11

a parallel study, Zhang et al. [5] examined inclined STS with a steel spline plate, capable of
transferring 60 kNm/m with a flexural rigidity of 1131 kNm2/m.
T-joints, depending on their type variations, can leverage high STS withdrawal resistance to
transfer tension and bending loads between two components [37]. T-joints resemble a root and
serve as focal point where the heads of multiple STS from different directions installed at different
angles converge (Figure 2-8). T-joints provide a flush surface with no protruding parts and offer
easy positioning in the borehole, enhancing the practicality of their application.

(a)

(b)

(c)

Figure 2-8: T-joint connection: (a) T-JOINT D40 W30, (b) and (c) example application of different
variants [37]

2.3.4 Adhesive bonds
Adhesive joints are a viable alternative to mechanical fasteners [38], [39]. However, there is no
standardized design guidance [41-43]. The Timber Structures 3.0 (TS3) system permits the buttjoint bonding of fibres, (Figure 2-9) [43], using a two-component Polyurethane adhesive [44]. A
bending strength up to 21 MPa was achieved for small-scale CLT panels with a width of 50 mm
and thicknesses ranging from 100 to 180 mm [45]. The performance was affected by the joint
thickness, temperature, humidity, and how the end grain was treated before they were joined.

Page 12

Figure 2-9: Butt-joint bonding technology (TS3) [43]

2.3.5 Hybrid connections
Composite construction has seen significant advancements in recent years, with Timber-Concrete
Composite (TCC) structural members garnering considerable attention [47-53]. Stieb et al. [53]
created a bending-resistant edge connection between two CLT TCC elements, termed TC Fusion
(Figure 2-10). STS are installed in the narrow faces of the CLT elements to create a lap splice, into
which concrete is poured to form a reinforced connection. Experimental tests demonstrated high
load-bearing capacity, with potential for further optimization by adjusting screw spacing or
diameter. The study also indicated that rotational stiffness exceeding 5000 kNmrad-1m-1 has
negligible effects on the structural performance of the floors.

Figure 2-10: Schematic of TCC connection [53]

Serrated steel plates offer an alternative solution for ensuring continuity between CLT panels
(Figure 2-11) [54]. These plates feature micro-teeth located along the narrow side of the panels,
which embed into the solid wood when a threaded steel rod is rotated. Such connections provide
both stiffness and a ductile failure mode [55].
Page 13

Figure 2-11: Edge connected panels with serrated steel plates [54]

2.4

Modelling of CLT floors

FEA offers the potential to minimize costly large-scale testing, provided that the model can be
validated. However, modeling CLT may pose distinct challenges due to the layup configuration
between major and minor layers, and gaps between boards, among others [56]. In the formulation
of models for the out-of-plane of CLT floor, two prevalent assumptions are typically employed.
Firstly, CLT panels are assumed to exhibit elastic behavior. Secondly, the non-linear behavior is
concentrated at the connections. It is common practice to represent CLT panels using shell
elements, while moment and shear connectors are represented using spring elements [57].
The selection between shell and solid elements is a crucial consideration. Solid elements provide a
3-D representation that requires more computational power but often delivers better accuracy,
especially for thicker plates and higher shear deformation. Linear solid elements may suffer from
shear-locking issues in geometries with significant bending deformations, leading to an
overestimation of system stiffness due to unintended shear deformations. This issue can be
addressed by using more elements through the thickness or employing quadratic solid elements,
both of which increase computational effort. The choice of element type may also depend on the
complexity of the geometry, with a fine mesh being necessary for detailed models with numerous
features, favoring the use of shell elements [58], [59]. However, shell elements offer a
Page 14

computationally efficient approach by transforming a 3D problem into a 2D, utilizing plate theory
to estimate displacements across the plate thickness. While shell elements are generally suitable
for thin plates with low shear deformation, their accuracy diminishes with thicker plates, increased
shear deformation, and concentrated loadings [58], [59].
Muster and Frangi [60] analyzed the punching performance of continuous two-way CLT pointsupported floors. The material of each layer was determined individually, and the interaction
between these layers was assumed to be without any slippage. In the FE model, there was no gap
between the lamellas, as it was determined that the precise definition of the gap between the boards
does not have a significant impact on the rolling shear stresses. These models were successfully
evaluated using RFEM [61] in 2D. Additionally, the 3D solid finite element model produced
stresses of comparable magnitude to the 2D simplified model, supporting its accuracy. The shear
stress verification presented a greater challenge. Due to the absence of nonlinearities in the
simulations and the lack of a conclusive definition for an increase in rolling shear strength for CLT
under concentrated loads, the calculated rolling shear stresses remain uncertain. Nonetheless, all
models accurately predicted rolling shear failure when considering a 50% increase in resistance.
Nevertheless, both distinct calculation methods demonstrated acceptable agreement [60].
Asselstine et al. [4] employed FEA for the two-way bending CLT panels utilizing 3D elements
with 20 nodes to represent the major and minor layers separately. To reduce computational
workload, symmetry was employed in the modeling of the beam bending setup. To address the
impact of variations in ring orientation and other inconsistencies among the individual boards in
the major and minor layers, a process of calibration was carried out. This involved the conversion
of the orthotropic properties, as illustrated in Figure 2-12.

Page 15

(a)

(b)

Figure 2-12: (a) Grain orientation in lamellas and (b) homogenized orthotropic model [4]

Mahdavifar et al. [13] employed a shell modelling approach that incorporated nonlinear interface
elements to represent the combined effects of rolling shear and bonding of the layers. The chosen
elements focused on capturing membrane and plate bending behavior while neglecting other
deformation modes. To calibrate the elastic properties, an iterative process utilizing the shear
analogy method described in CLT handbook [8] was employed. Initially, an assumed modulus of
elasticity (MOE) was selected based on established values for Douglas-fir. Then, the apparent
flexural rigidity (EI) was calculated using the shear-analogy method. Subsequently, the deflection
at peak load was compared to experimental values, and iterations were conducted by adjusting the
MOE until calculated and experimental deflections aligned. The remaining elastic properties,
including the rolling shear stiffness assigned to the interface elements, were determined based on
recommendations from the CLT handbook [8]. The linear elastic response of the model exhibited
good agreement with experimental load-displacement curves [56].
2.5

Summary of literature review

CLT panels exhibit potential for two-way action. Given the dimensional constraints of such panels,
ensuring continuity between adjacent panels, particularly in the minor direction, becomes
imperative. STS are the most common type of connection in timber structures, known for their fast
installation and cost-efficiency. In this regard, lap- and spline-joints are two common connections.
Although most previous research focused on STS, there are some alternatives with limited

Page 16

information on their structural performance. X-fix connectors can provide quick and secure
connections without the need for additional metal. Adhesively bonded connections are also an
option, providing mechanical integrity and aesthetic advantages. Assessing the out-of-plane
behavior of connections in minor directions are particularly crucial, especially in point-supported
CLT floors. However, the majority of studies to date have focused on the performance of
connections in the major direction between CLT panels, and only some studies have focused on
the out-of-plane performance of edge-connected CLT panels in the minor strength direction.
Further studies are necessary to ensure continuity in the minor direction, as neglecting the minor
direction capacity of CLT panels notably underestimates the resistance and displacement deflection
capacities of these structural components.

Page 17

3

Experimental investigation

3.1

Overview

This chapter presents the experimental investigations on edge-connections in the minor strength
axis of 7-ply CLT panels. These connections were subjected to out-of-plane 4-point and 3-point
bending loading. The work was carried out at Fast + Epp’s concept lab in Vancouver, British
Colombia. Five connection configurations were tested:
1) The first configuration (S1), screwed splines, entailed attaching plywood sheets with STS.
2) The second configuration (S2), glued splines, used glue for attachment instead of screws.
3) The third configuration, T-joints (S3), utilized the proprietary connector installed with STS.
4) The fourth connection (S4) was the X-fix, a wooden shear key with a dovetail shape.
5) Lastly, the fifth configuration (S5) involved attaching steel rebars at the bottom of the panels.
3.2

Materials

The experimental program employed CLT of V2M6 grade manufactured by Kalesnikoff in
accordance with ANSI/APA PRG 320 [62]. In this V2 grade, both longitudinal and transverse
layers were No.1/No. 2 SPF lumber. A 245 mm thick 7-layer CLT was selected for this study to
provide solutions for large two-way spans in point-supported CLT floors. The layers were 35 mm
thick, and the lamellas were 170 mm wide.
The study utilized Ø8×160 mm and Ø10×320 mm fully threaded ASSY plus VG screws with a
countersunk (CSK) head, as depicted in Figure 3-1. These screws are specifically designed for
wood-to-wood applications. SK Ø6×100 mm washer head screws were used in the glued spline
samples to clamp the plywood onto the CLT panels during adhesive curing.

Page 18

Figure 3-1: ASSY plus VG screws [63]

Two types of 18 mm (¾”) thick Baltic birch plywood panels served as splines: high-quality grade
B and low-quality grade C. Grade C permits patches, open knots, small veneer splits, veneer laps,
and small core voids (Figure 3-2). For clarity, these were designated as type B and type C.

(a)

(b)

Figure 3-2: Plywood: (a) high-quality (grade B) and (b) low-quality (grade C)

Two adhesives were utilized: LePage PL Premium Max and Titebond III. PL Premium Max,
formulated with a silane-modified polymer base, provides a compression shear strength of 9 MPa,
with an open time of 20 minutes and a curing period of 24 to 48 hours [64]. Titebond III, a polymerbased wood glue, has an open time of approximately 3-5 minutes and a total assembly time of 1015 minutes. Despite its quicker setting, it delivers a minimum bond strength of 5.5 MPa [65].
In this study, X-fix-C measuring 130 mm in length (L), 96 mm in width (w), and 90 mm in height
(h) were utilized (Figure 3-3). According to the product European technical assessment (ETA18/0254, 2020), the plywood employed in X-fix has a bending strength of 34.8 MPa, tension
strength of 36.9 MPa, and shear strength of 9.5 MPa, with a mean density of 680 kg/m³ [66].

Page 19

(a)

(b)

Figure 3-3: X-fix-Cm Connector; (a) schematic view, (b) actual view

For the T-joint connection, the D40 W30 variant was employed (Figure 2-8a), specifically designed
to enable tension and bending joints between two wooden components through dual-angle screw
fastening. This design utilizes three screws to directly transfer tensile forces from one component
to the other, as illustrated in Figure 3-4.

(a)

(b)

Figure 3-4: Schematic representation of a T-joint connection utilizing the D40 W30 variant

Two types of steel rebar were employed, both with a minimum yield strength of 400 MPa. The first
type was #4 (Ø8 mm) carbon steel (A615) grade 60 rebar, marked as NU4S60; the second type
was a Ø 10 mm epoxy rebar, labeled as grade 400W according to CSA G 30.18 [67].

Page 20

3.3

Specimen description

3.3.1 S1 - spline plate with inclined STS
The screwed spline connection consisted of two plywood sheets attached at the bottom of the CLT
panels, effectively providing a thickness equal to that of the removed CLT layer. In the minor
strength direction, the bottom (7th) layer does not transfer stresses in bending, yet the continuous
spline plates do. The plywood sheet, measuring 400 mm in length in its major direction and 600
mm in width, was connected to the panels using 12 STS on each side, installed at a 45-degree angle,
as shown in Figure 3-5. The plywood sheets were predrilled with holes for STS installation. Two
series were prepared and subsequently tested: Grade C plywood was employed for the 4-point
bending tests, whereas grade B plywood was used for the 3-point bending tests.

(a)

(b)

Figure 3-5: Spline connection with inclined STS: (a) schematic (b) photos side and bottom

Page 21

3.3.2 S2 - glued spline plate
Similar to the screwed spline, the 7th layer of the CLT panels was removed in the connection zone.
Two 17 mm thick, 400 mm long and 600 mm wide plywood sheets were glued together using
Titebond III wood glue, the resulting 35 mm thick sheet was then glued onto the CLT panels using
PL Premium Max. The minimum curing time recommended by the manufacturer, at least 24 hours
after fabrication, was met. For each specimen, approximately 175 ml of glue was applied in eleven
parallel lines across the width of the panel, ensuring an approximate 1 mm thick glue line covered
the spline and surfaces after pressing. To ensure proper compression between the CLT panel and
plywood surface, 16 SK Ø6×100 mm STS, arranged in a 4×4 pattern, were installed to clamp the
plywood onto the CLT panels. It is important to note that these STS were removed before testing.
Grade B plywood was exclusively used for the 3-point bending tests, while both grades were used
for the 4-point bending tests, with six samples from grade B and two from grade C.
3.3.3 S3 - T-joint
In these connections, four T-joints were arranged in a zigzag pattern, with a center-to-center
spacing of 120 mm along the CLT panel width, with two on the left side and two on the right side
of the connecting line, as depicted in Figure 3-6. Each T-joint was attached with two Ø8×160 mm
STS on one side at a 28˚ angle to the surface, and one Ø10 × 320 mm STS at a 30˚ angle on the
other side. To achieve a flush surface, the T-joints were installed recessed into the 7th layer,
approximately 18 mm based on the height of the T-joint.

Page 22

(a)

(b)

Figure 3-6: T-joint: (a) layout before installation, (b) fully installed

3.3.4 S4 - X-fix
This connection involved two X-fix-C shear keys to secure the panels to each other, as depicted in
Figure 3-7. The X-fix connections were positioned with a spacing of 300 mm at the center of the
panel width. Similar to spline connections, the 7th layer was removed; however, the X-fix engaged
the 6th, 5th, and part of the 4th layers (Figure 3-7a).

(a)

(b)

Figure 3-7: X-fix connection: (a) schematic; (b) photo bottom face

Page 23

3.3.5 S5 - Steel rebar
In these connections, bent steel rebars were installed into slots at the bottom of the panels,
positioned at the bottom of the 6th layer. These connections were evaluated in two variants: S5A
utilized U-shaped rebars bent at a 90˚ angle, consisting of three Φ12 mm rebars spaced at 175 mm
intervals. S5B involved four Φ10 mm rebars spaced at 120 mm bent at a 120˚ angle. To secure the
rebars in position, both ends were fixed using two flat washers and a nut (Figure 3-8).

(a)

(c)

(b)

(d)

Figure 3-8: Steel rebar connection: (a) schematic S5A, (b) and S5B, (c); photo S5A, (d) and S5B

Page 24

3.4

Test methods

3.4.1 4-point bending test
The 4-point bending tests, as shown in Figure 3-9, created a pure bending moment in a zero-shear
zone at the connecting line. The length of the two connected panels was 3450 mm, and the span,
representing the distance between two supports, was 2730 mm. The width of the panels (in the
major direction) was 600 mm. The load was applied as two lines at a distance of 495 mm from the
connection. Simple line supports without constraint of rotational movement were provided.

(a)

(b)

Figure 3-9: 4-point bending test: (a) schematic (dimensions in mm); (b) photo

Page 25

Four linear variable differential transformers (LVDTs) were installed. One pair measured the midspan deflection, and another pair measured the gap opening, with each pair positioned
perpendicular to the contact surface of the two panels located 55 mm from the bottom surface.
The rotational stiffness (CႴ) was defined from the slope of the moment-rotation curve in the range
of 10% to 40% of the peak load after the unloading cycle. The rotation is represented by the gap
angle (arc) opening of the connection, where this angle is the ratio of the gap opening at the
connection line (evaluated by two horizontal LVDTs on the panel sides) to the depth of the section.
Ductility () was defined as the ratio of ultimate displacement (𝛿𝑢 ) to yielding displacement (𝛿𝑦 ).
The displacements 𝛿𝑢 and 𝛿𝑦 were determined using the procedure shown in Figure 3-10. Line 1
(L1) is the tangent to 10% and 40% of the peak load, with a slope α relative to the horizontal axis,
while L2 passes through the peak load with a slope of α/6. The point of intersection between these
lines defined 𝛿𝑦 , and 𝛿𝑢 represents the deflection corresponding to the point where the load drops
to 80% of the peak load, as defined in section 3.5.2 [69-71].

Figure 3-10: Procedure for calculating ductility index

Page 26

3.4.2 3-point bending tests
The 3-point bending test was employed to evaluate the performance of connections under
simultaneous out-of-plane shear and out-of-plane bending moment loads, which is a scenario
commonly encountered in floor applications. The X-fix connector and rebar joints were excluded
from the 3-point bending tests because these connections are not designed to transfer out-of-plane
shear. As illustrated in Figure 3-11, the connection was positioned off-centre, located at a distance
equivalent to one-quarter of the floor span from the support.

(a)

(b)

Figure 3-11: 3-point bending test: (a) schematic (dimensions in mm); (b) photo

Page 27

The test span was 1752 mm, and the line load was applied at the midpoint of this span, extending
along the entire width of the panel. (Note: a small series of 3-point tests of continuous CLT panels
was conducted with a span of 1504 mm, and the load was applied in the centre of the span.) Five
LVDTs were installed: one pair at the center span on both sides of the panel, one LVDT at the
center of the connecting line to measure the maximum deflection of the specimens, and deflection
at the connecting line, respectively. Additionally, one pair was positioned on both sides of the
connecting line to measure the opening of the connection gap.
3.4.3 Loading protocol
The testing apparatus included a hydraulic actuator with calibrated load cell with a capacity of
350 kN. All testing followed a modified EN-26891 [71] loading protocol, employing a
displacement-controlled rate set at 8 mm/min. The specimens were subjected to loading up to 40%
of load-carrying capacity, followed by unloading to 10% of this value. After each of these stages,
the load was maintained at a constant level for 20 seconds. Subsequently, the loading was increased
until failure, defined as a 20% drop from the maximum load. The load-carrying capacity was
determined based on preliminary tests conducted for each connection series.
3.5

Results and discussion

3.5.1 Load-deflection of 4-point bending tests
Representative load-displacement curves of specimens from each connection configuration are
shown in Figure 3-12. The individual load-displacement curves are shown in Appendix A.
In the screwed spline samples (S1), generally ductile performance was observed, characterized by
three stages: a linear part up to a load of approximately 55 kN (about 70% of peak load), at an

Page 28

average deflection of 22 mm, a nonlinear part with reduced stiffness leading up to the peak load,
and a gradual drop in load-carrying capacity towards the failure point. The average maximum loadcarrying capacity of the samples was 77 kN with a Coefficient of Variation (CoV) of 4%, at an
average displacement of 42 mm.
The load-deflection characteristics of glued spline connections (S2) exhibited linear behaviour up
to peak loads, immediately followed by brittle failure. The results highlight the significant
influence of the plywood grade. Specimens featuring grade B (S2B) exhibited an average loadcarrying capacity and maximum deflection of 82 kN and 20 mm, respectively. These values
substantially decreased for the two samples fabricated with grade C (S2C) to 34 kN and 11 mm on
average.
The load-deflection curve of the T-joint (S3) can be divided into three distinct segments: an initial
linear phase, a subsequent phase characterized by reduced stiffness leading up to peak loads, and a
final segment characterized by a descent from peak loads that resulted in failure. The average loadcarrying capacity was 39 kN, corresponding to an average displacement of approximately 30 mm.
The linear range extended to a load of 19 kN equivalent to about 8 mm deflection. All samples
demonstrated a ductile behavior and the ability to experience about a 50% drop in load-carrying
capacity without experiencing any failures.
The load-deflection response of the X-fix (S4) was initially almost linear, continuing up to
approximately 70% of the peak load which averaged about 19 kN, at a deflection of 32 mm.
Subsequently, as the load-displacement curve slope gradually decreased, slight fluctuations in
loading were observed. Overall, these samples demonstrated a moderately ductile performance.

Page 29

The load-deflection behavior of the rebar joints revealed two phases. Initially, there was a stiff
phase lasting until 6% and 20% of deflection (10 mm and 40 mm) for specimens S5A and S5B,
respectively, followed by a decrease in slope. However, the load-carrying capacity remained nearly
constant during both phases. At this point, S5A and S5B reached a load-carrying capacity of 50 kN
and 67 kN, respectively, corresponding to approximately 185 mm of deflection.

100
S1

Load (kN)

80

S2B
S2C

60

S3
40

S4
S5A

20

S5B

0
0

50

100

150

200

Deflection (mm)

Figure 3-12: Typical load-deflection curves of 4-point tests

3.5.2 Failure modes in 4-point bending tests
Failure in this study was characterized by the loss of functionality within the entire system. This
occurred either when there was a 20% reduction in load-carrying capacity or when the deflection
exceeded the test setup capacity, which was approximately 185 mm (L/15). Some typical failed
specimens are shown in Figure 3-13. More photos are provided Appendix C.
The screwed spline samples (S1) displayed ductile behavior. Initial indications of damage were
discernible through noises originating from the spline plate. Two distinct failure modes were
identified: tension-induced failure in the plywood resulting in a sudden decrease in loading capacity
Page 30

(Figure 3-13a), and screw withdrawal leading to a gradual reduction in loads without abrupt failure
(Figure 3-13b). In tension failures, the gap between the spline plate surface and the 6th layer
widened symmetrically, whereas withdrawal failures exhibited a localized increase in this gap.
In all glued spline samples (S2), failure was confined to the interface between the spline plate and
the CLT panels. Samples using plywood grade B exhibited plywood failures (Figure 3-13c).
Conversely, samples with grade C plywood had failure concentrated solely within the plywood
lamella (see Figure 3-13d). Regardless of plywood type, failure was abrupt, without notable
warnings and no slip between plywood and CLT panel before peak load.
T-joint connections (S3) exhibited three distinct failure modes: i) crushing perpendicular to the
grain where T-joints meet the CLT interface; ii) withdrawal of the two short STS; and iii) bending
of the STS close to the CLT surface due to the joint rotation, as depicted in Figure 3-13e through
Figure 3-13g, respectively. Modes i) and iii) contributed to the ductility observed in the loaddisplacement response. Disassembling T-joint specimens posed considerable challenges, due to the
bent STS. The T-joint components remained intact throughout the process.
The X-fix connection (S4) is depicted in Figure 3-13h and Figure 3-13j, exhibited shear failure
parallel to the grain throughout the entire height of the X-fix. Additionally, shear failure
perpendicular to the grain is observed in the 5th layer, leading to the rotation of this layer due to
tension loads. Besides shear failure in the CLT panel layers, the X-fix itself experienced shear
damage, with cracks developing parallel to the X-fix layer in the narrow part of the X-fix.

Page 31

(a)

(b)

(c)

(e)

(d)

(f)

(h)

(g)

(i)

(j)

Figure 3-13: Failure modes series S1-S4 in 4-point tests; (a) S1 tension failure in the plywood, (b) S1
withdrawal effect in the spline plate, c) S2B, d) S2C, (e) S4 crushing perpendicular to the grain, (f) S4
Withdrawal effects, (g) S4 ductile failure in STS, (h) S3 bottom view, (i) S3 connecting section, (j) X-fix
shear failure

Page 32

In steel rebar joints (S5), the main failure mode was compression perpendicular to the grain at both
ends of the rebar where washers pushed on the CLT (Figure 3-14a). S5B showed more damage due
to smoother angles of the steel rebars, leading to larger tension loads. In contrast, S5A transferred
tension loads through the vertex of the rebars, resulting in compressive loads on the wood surface.
Failure was also evident at the bottom of the sixth layer. Imprints of the rebar ridges on the solid
wood were visible along the entire slot length. Significant gap opening concentrated compressive
forces on the first layer, leading to damage and crack formation between the first and second layers.

(a)

(b)

(c)

(d)

Figure 3-14: Failure modes series S5: (a) S5A slot view, S5, (b) connecting section, (c) CLT panel
compression zone, (d) S5B rebar end compression zone

3.5.3 4-point bending test result analyses
The results from the 4-point bending tests: loading carrying capacity (Fult), deflection (d@ult),
connection gap opening (g@ult), transferred bending moment (Mult), rotational stiffness (CႴ), and
ductility (µ) are summarized in Table 3-1.

Page 33

Table 3-1: Results summary from 4-point bending tests
S2-Glue
S1STS Grade B
Grade C

S3Tjoint

S4Xfix

A

B

Mean

76.6

77.9

32.7

39.2

18.7

50.0

67.6

Max

80.2

86.2

-

44.4

19.7

-

-

Min

72.5

68.1

-

35.6

17.4

-

-

CoV

4%

9%

-

8%

3%

-

-

Mean

33.3

35.5

15.0

17.1

8.1

21.8

29.4

Max

34.9

39.0

-

19.3

8.6

-

-

Min

31.5

30.8

-

15.5

7.5

-

-

CoV

4%

9%

-

7%

7%

-

-

Mean

42.2

19.7

10.6

31.3

30.0

185

181

Max

51.5

23.6

-

37.7

34.1

-

-

Min

33.7

17.1

-

23.3

25.8

-

-

CoV

14%

14%

-

14%

2%

-

-

Mean

5.2

0.5

0.5

3.2

6.4

48

38

Max

5.7

0.6

-

7.0

6.8

-

-

Min

4.2

0.3

-

5.0

5.8

-

-

CoV

11%

20%

-

29%

8%

-

-

Mean

3,555

47,834

24,085

2,476

853

847

486

Max

5,644

83,581

-

3,830

1,062

-

-

Min

2,347

12,900

-

1,563

533

-

-

CoV

34%

54%

-

32%

33%

-

-

Mean

2.3

≈1

≈1

3.2

2.2

10.1

2.7

Max

2.9

≈1

-

3.9

2.6

-

-

Min
CoV

1.8
21%

≈1
-

-

2.3
20%

1.9
15%

-

-

Replicates

6

6

2

6

3

1

1

Test series

Fult [kN]

Mult [kNm]

d@Fult [mm]

g@Fult [mm]

CႴ [kNmrad⁻¹]

µ

S5-Rebar

The glued spline connection (S2B) exhibited the highest bending moment capacity, followed by
the screwed spline (S1), steel rebar joint (S5), T-joint (S3), and X-fix (S4) , as depicted in Figure
3-15, with capacities at 94%, 83%, 47%, and 23% respectively, relative to series S2B. Notably, the
coefficient of variation (CoV) in bending moment capacity remained small (<10%) for all series.

Page 34

Mult (kNm)

60

40

20

0
S1

S2B

S2C

S3

S4

S5A

S5B

Figure 3-15: Moment resistance of connection configurations in 4-point tests
Samples in the S2B series demonstrated the least amount of deflection at peak load, with approx.
20 mm. In contrast, specimens in the S5 series exhibited notably higher deflection, reaching 185
mm. This deflection trend corresponded to the degree of gap opening within the connections, with
S5 samples exhibiting the widest gaps, measuring 48 mm and 38 mm for S5A and S5B,
respectively, whereas S2 registered less than 1 mm. Further, S1 exhibited an average deflection of
approximately 42 mm, while S3 and S4 displayed deflections around 31 mm at the peak load.
Variability of deflection was around 14% within most test series.
Figure 3-16 shows the typical moment-rotation curve of these connections, in which the slope of
each series represents the rotational stiffness value. As can be seen series S2 samples (glued
splines) exhibited superior rotational stiffness with 47,800 kNmrad⁻¹. Screwed connections S1 and
S3 reached roughly 3,500 kNmrad⁻¹ and 2,500 kNmrad⁻¹, respectively. Conversely, S4 (X-fix) and
S5 (rebar) connections reached rotational stiffness values less than 1,000 kNmrad⁻¹ (Figure 3-17).
However, it has to be noted, that due to the very small displacements, even minor differences
created a large variability in the rotational stiffness of the glued joints (CoV = >50%), while CoVs
for the other connection configurations were around 30%.

Page 35

Bending Moment (kN.m)

40
S1
S2B

30

S2C
20

S3
S4

10

S5A
S5B

0
0

0.01

0.02

0.03

0.04

Rotation (rad)

Figure 3-16: Typical moment-rotation curves of 4-point tests

CႴ (kNmrad⁻¹)

100,000

10,000

1,000

100
S1

S2B S2C

S3

S4

S5A

S5B

Figure 3-17: Rotational stiffness of connection configurations in 4-point bending tests

In terms of ductility, S2 exhibited a completely brittle behavior, with the yielding and failure points
coinciding. S5A demonstrated ductile performance, reaching approximately 10. Following this, S3,
S1, and S4 exhibited limited ductility of 3.2, 2.3, and 2.2, respectively. However, for S5B, the type
of failure mode and maximum deflection in the experiment prevented an accurate representation
of its ductility value, despite its deflection being almost equal to that of S5A.

Page 36

12
10

µ

8
6
4
2
0
S1

S2B

S2C

S3

S4

S5A

S5B

Figure 3-18: Connection ductility in 4-point tests

3.5.4 Load-displacement behavior of 3-point bending tests
Figure 3.16 depicts the typical load-deflection characteristics resulting from 3-point bending tests
on screwed spline (S1), glued spline (S2), and T-joint (S3) connections. The individual loaddisplacement curves are shown in Appendix B.
The spline plate with inclined STS had an initially linear response, extending up to approximately
85 kN (57% of peak load), at an average mid-span deflection of about 10 mm. Subsequently, a
nonlinear part developed up to peak load, averaging 150 kN, with an associated deflection of
approximately 26 mm. The glued spline plates exhibited a purely linear behavior until reaching an
average load-carrying capacity of 115 kN, equivalent to a deflection of 13 mm coinciding with a
sudden and abrupt failure. The T-joints encompassed a linear segment up to 50 kN and 7 mm
displacement, a second segment with reduced stiffness up to peak load of approximately 67 kN,
and a gradual decline with the capability of experiencing a 50% drop in load-carrying capacity.

Page 37

200

Load (kN)

160
S1

120

S2

80

S3

40
0
0

15

30
Deflection (mm)

45

Figure 3-19: Load-deflection curves of 3-point bending tests

3.5.5 Failure modes of 3-point bending tests
Some typical failed specimens are shown in Figure 3-20. More photos are provided in Appendix
D. For spline plate with inclined STS connections (S1), the first audible signs of damage were
detected around 70 kN, corresponding to an average mid-span deflection of 8 mm. The typical
initial damages often included separation at the second layer, occurring within or at the top or
bottom of this layer. This was followed by rolling shear failure emerging on the panel surface
between the loading point and the connecting line (Figure 3-20a).
In the glued spline connections (S2), upon reaching the peak load at approximately 115 kN,
equivalent to an average deflection of 12.6 mm, a sudden failure occurred. This failure point was
concentrated in the area where the plywood comes into contact with the CLT, involving a
combination of failures in solid wood, and plywood (Figure 3-20b).
In T-joint connections (S3), a horizontal crack appeared on the compression side of the second
layer of the right panel at the connecting line, under a load of approximately 55 kN (Figure 3-20c),
attributable to the low out-of-plane shear resistance of the connection. As the loading increased, it

Page 38

resulted in an unleveled surface at the bottom of the connecting line and a leveled surface at the
top of the sample, due to friction preventing sliding at the compression side between the two panels,
(Figure 3-20d). Furthermore, sliding caused the tearing from the corner of the seventh layer due to
the rotation of STS and T-joint, applying tension load perpendicular to the grain.

(a)

(b)

(c)

(d)

Figure 3-20: Failure modes in 3-point tests: a) S1, b) S2 plywood surface c) S3 cross section at
connecting line, d) S3 side view

3.5.6 3-point bending test result analyses
The results from 3-point bending tests on series S1, S2, S3, and S0 (solid panel) are summarized
in Table 3-2, including Mult,joint (connection bending moment capacity), d@Fult, dj@Fult (displacement
at the connecting line), g@Fult, Vult (out-of-plane shear resistance), and Cφ.
Series S1 reached the highest loading carrying capacity, shear and bending moment resistance,
exceeding that of S2 and S3 by approximately 77% and 47%, respectively (Figure 3-21 a and b).

Page 39

Concerning deflection, S2 exhibited the least deflection at about 13 mm, followed by S3 and S1,
with average deflections of 18 mm and 28 mm, respectively.

Table 3-2: Results summary from 3-point bending tests

Vult [kN]

Mult,joint [kNm]

d@Fult [mm]

djoint@Fult [mm]

g@Fult [mm]

Cφ [kNmrad⁻¹]

Page 40

Test series

S1-STS

S2-Glue

S3-Tjoint

S0-Full

Mean
Max

75.0
83.2

57.5
74.9

19.6
22.2

108.3
111.3

Min

66.3

47.7

17.8

105.0

CoV

8%

17%

9%

3%

Mean

32.8

26.2

15.4

-

Max

36.4

34.8

17.1

-

Min

29.03

22.1

13.3

-

CoV

8%

18%

9%

-

Mean

27.8

12.6

18.0

14.9

Max
Min

43.7
16.1

16.4
10.9

25.0
10.0

15.6
14.5

CoV

33%

16%

24%

4%

Mean

19.8

10.9

21.9

-

Max

23.4

13.5

31.3

-

Min
CoV

13.7
18%

10.1
13%

10.8
32%

-

Mean

4.1

0.17

5.0

-

Max

6.55

0.25

8.2

-

Min
CoV

2.18
37%

0.1
34%

2.1
41%

-

Mean

6590

32533

2869

-

Max

8522

55733

4383

-

Min

4223

17335

2104

-

CoV

22%

56%

30%

-

Replicates

6

6

6

3

40

M ult, joint (kNm/m)

V ULT (kN)

120
80
40

30
20
10
0

0
S1

S2

S3

S1

S0

(a)

S2

S3

(b)

CႴ (kNmrad⁻¹m⁻¹)

100,000

10,000

1,000

100
S1

S2

S3

(c)

Figure 3-21: 3-point bending tests: (a) shear resistance, (b) moment resistance and (c) rotational stiffness

The gap opening within the S2 series was less than 1 mm, whereas S1 and S4 both exhibited values
of approximately 5 mm. The rotational stiffness, Cφ, for series S1 and S3 was about 20% and 9%
of S2, respectively (Figure 3-21c). It is noteworthy that the variability in Cφ for S2 was notably
higher, with a CoV of 56%. Examining the CoV for shear resistance, S2 displayed the highest value
with 17%. S3, with a CoV of 9%, demonstrated a moderate degree of variability. In contrast, S0Full and S1, with CoVs of 3% and 8%, respectively, showcased lower levels of variability
compared to their means.

Page 41

3.5.7 Reference specimen
Three CLT panels without connection were tested. The load-deflection curves, shown in Figure
3-22a, reveal an initial stage, characterized by an almost linear behavior up to the peak load (on
average 217 kN at an average deflection of 15 mm), followed by a sudden drop in load-carrying
capacity. The first sign of damage at a load of 85 kN was manifested by audible cracking noises.
Initial small rolling shear cracks emerged at a load of 195 kN. As the sample approached the peak
load, rolling shear failures transpired, succeeded by delamination, as shown in Figure 3-22b.

250

Load (kN)

200
150
100
50
0
0

5

10
15
20
Deflection (mm)
(a)

25

30
(b)

Figure 3-22: 3-point test of continuous panel: (a) load-displacement curve and (b) failure mode

Page 42

4

Numerical investigations

4.1

Overview

The numerical investigation aimed to determine: i) the demand on the joints between adjacent CLT
panels in various floor scenarios; and ii) the maximum bending moment capacity that can be
transferred in the minor direction as a function of joint rotational stiffness.
In Figure 4-1, a floor consisting of three CLT panels, each with dimensions of 𝑏. 𝐿 is displayed.
The three panels were connected along the minor direction throughout the length of the panels (L),
as indicated by the dashed lines. The points indicated rectangular point supports, each 300 mm ×
300 mm in size. These supports were located in the center line of the side panels along the major
direction at a distance (e) from the edges in the major direction. Consequently, the span between
point supports was L-2·e in the major direction and 2·b in the minor direction (Table 4-1).

(a)

(b)

Figure 4-1: Geometry of point-supported floor: (a) top view, (b) cross section A-A along minor direction

Page 43

Uniform dead (DL) and live loads (LL) were applied to the floors, with the load combinations for
the ultimate limit state (ULS) and serviceability limit state (SLS), referring to the maximum loadcarrying capacity and allowable deflection, respectively [72]. Two levels of uniform live load of,
1.9 kPa and 2.4 kPa, were considered for residential and office buildings, respectively. These loads
were accompanied by a uniformly applied dead load of 1.0 kPa, excluding the self-weight of the
CLT panels, which was also considered in the analysis. The floors were designed to meet deflection
limits: L/180 for total loads and L/360 for live loads as outlined in the National Building Code of
Canada (NBCC) [73]. Additionally, the critical load combination for ULS design was
1.4·DL+1.25·LL.
The selection of rotational stiffness was based on the previous experimental findings presented in
Chapter 3, ranging from 500 to 5,000 kNmrad-1m-1. Stieb et al. [55] observed that changes in
rotational stiffness up to around 5,000 kNmrad-1m-1 were found to have a more significant impact
on floor structural performance. This observation was corroborated by initial analyses, indicating
that 500 kNmrad-1m-1 satisfies the SLS. Consequently, this study selected stiffness values of 500,
1,000, 1,500, 2,000, and 5,000 kNmrad⁻¹m⁻¹, and a continuous panel representing an infinite value.

Table 4-1: Model parameters floor dimensions (m)

4.2

b
2.4

B = 3·b
7.2

L
7.2

2.4

7.2

9.5

3.0

9.0

9.0

e
0.5 and 1.0
0.5, 1.0, and
1.5
1.5

Model development

The numerical models were developed utilizing the RFEM 6 software [61], employing the RFLaminate module for CLT. Following a sensitivity analysis, a 150 mm mesh size was chosen. The
Page 44

floor was modeled as a plate element with three degrees of freedom at each node, comprising one
translation and two rotations, as illustrated in Figure 4-2.

Figure 4-2: RFEM model of point-supported CLT floor

The point supports’ boundary conditions had their translation constrained in all directions and all
rotational degrees of freedom. The floor was treated as a single isolated unit, with no constraints
applied at the surrounding ends. The predefined surface stiffness type had the capability to transfer
both moments and membrane forces [74]. Figure 4-2 depicts an isometric view of the floor model.
To attain a precise depiction of the stress distribution at support areas, adjustments to the surface
results were specified for connection zones between columns and the floor. This involves
establishing areas that match the dimensions of the columns, simulating column performance by
averting stress concentration at the support area [75], depicted as virtual columns in Figure 4-2.
Wood was modelled as a linear elastic transverse isotropic material, accounting for the parallel and
perpendicular to the grain directions. CLT properties of grades E1 and V2 were employed in
accordance with PR-L332(C) [62]. The panels had a thickness of 245 mm, with seven 35 mm thick

Page 45

layers. The stiffness and strength parameters for these panels are provided in Table 4-2. Figure 4-3
illustrates the nomenclature employed, elucidating the CLT grade, the floor spans, the live load,
and the distance from the support centreline to the panel edge.

Table 4-2: Material properties for the FEM simulation (MPa) [76]
Major strength direction

Minor strength direction

CLT
Grade

Grade & Species

fb

E

ft

fs

Grade & Species

fb

E

ft

fs

E1

1950f-1.7E SPF

28.2

11700

15.4

0.5

No. 3 SPF

7.0

9000

3.2

0.5

V2M6

No. 1/No. 2 SPF

11.8

9500

5.5

0.5

No. 1/No. 2 SPF

11.8

9500

5.5

0.5

Figure 4-3: Models labelling convention

4.3

Model validation

The model was validated by comparing the numerical and experimental load–deflection curves.
The reference specimens (S0 series, see Figure 4-4a) represent the characteristics of CLT panels,
along with support and loading conditions, without considering any connection behavior.
Additionally, the S1 series was selected for both 4-point bending tests (Figure 4-4b) and 3-point
bending tests (Figure 4-4c). Rotational stiffness was simulated using connection test results within
the ranges of 10% to 40% and 40% to 80%. All dimensions and boundary conditions were aligned
with those employed in the experimental setup. The line supports had no rotational restrictions, and
loads were applied as line loads. When ignoring the initial alignment behaviour, the model and

Page 46

experiments align reasonably well, demonstrating the validity of the numerical model for the
present experiments within the linear range.

Numerical model

250

Load (kN)

200
150
100
50
0
0

5

10
15
Deflection (mm)

20

(a)

Numerical Model

Numerical Model

75

150

Load (kN)

200

Load (kN)

100

50
25

100
50
0

0
0

10

20
30
Deflection (mm)
(b)

40

0

5

10
15
Deflection (mm)

20

(c)

Figure 4-4: Numerical validation of experiments; (a) 3-point bending tests of solid panels, (b) 4-point
bending tests of S1 series, (c) 3-point bending tests of S1 series

Page 47

4.4

Results and discussion

4.4.1 Impact of rotational stiffness on bending moment
Figure 4-5 and Figure 4-6 depict the distribution of bending moment and shear force along the
connecting line. Consistently for all floor configurations, larger bending moments and shear forces
are observed at the ends of the connecting line compared to the midpoint. Reducing the rotational
stiffness leads to a more balanced distribution of bending moment along the connecting line. For a
floor with a Cφ of 500 kNmrad⁻¹m⁻¹, the bending moment ranges from 8.4 to 10.8 kNm/m, while
for a continuous floor (with infinite Cφ), it varies from 5.7 to 14.3 kNm/m. The smaller value of
rotational stiffness leads to a reduction at the ends of the connecting line and an increase at the
midpoint, but the average value remains constant as shown in Figure 4-5b, rotational stiffness does
not affect the internal out-of-plane shear force.

Cφ=500

Cφ=5000

Cφ=500

Cφ=infinite

Vult,joint (kN/m)

16

Mult,joint (kNm/m)

Cφ=5000

Cφ=infinite

32

12
8
4

24
16
8
0

0
0

4.75
9.5
Position along conenction (m)
(a)

0

4.75
Position along conenction (m)

9.5

(b)

Figure 4-5: Impact of Cφ on internal loads at the connecting line for floor V2_9.5-7.2_LL 1.9_e 1.0; (a)
bending moment diagram, (b) shear force diagram

Increasing the column edge distance (e) promotes a more uniform distribution of bending moments
along the connecting line, as depicted in Figure 4-6. Large e brings higher and lower bending
moment values closer to the average.
Page 48

Both ends

Middle

Both ends

Middle

20

16

Mult,joint (kNm/m)

Mult,joint (kNm/m)

20

12
8
4
0
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

16
12
8
4
0
0

(a)

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

(b)

Figure 4-6: Bending moment at connecting line V2_9.5-7.2_LL 1.9 for (a) e=0.5 m, (b) e=1.5

Figure 4-7 and Figure 4-8 display the impact of rotational stiffness (Cφ) and column edge distance
(e) on the internal bending moment distribution in the minor and major directions, respectively.
For the minor direction, an inverse relationship between rotational stiffness and uniformity of
bending moment is confirmed. As rotational stiffness decreases, the stress gradients become
smoother compared to a continuous floor. Furthermore, it can be inferred that in floors with higher
rotational stiffness, the connections located at both ends of the connecting line exert a more
significant impact on internal bending moment transmission. In continuous floors, the blue area
representing the highest bending moment is concentrated at the free edge of the middle panel.
In the major direction (Figure 4-8), transitioning from a continuous panel to 500 kNmrad⁻¹m⁻¹
increases the bending moment by only 4% at the column strip in the major direction. It is also
noteworthy that in the middle panel, the primary factor influencing the maximum bending moment
is positive bending moments along the minor direction, while in the side panels, the maximum
bending moment is usually due to negative bending moments along the same direction. The
variations in the bending moment in the major direction due to changes in rotational stiffness are
approximately one-third of those observed in the minor direction.
Page 49

(a)

(b)

(c)

(d)

Figure 4-7: Impact of Cφ and e on bending moment along minor direction for floor V2_9.5-7.2_LL 1.9;
(a) e=500 mm, Cφ = 500, (b) e=1500 mm, Cφ = 500, (c) e=500 mm, Continuous floor, (d) e=1500 mm,
Continuous floor

Page 50

(a)

(b)

(c)

(d)

Figure 4-8: Impact of Cφ and e on bending moment along minor direction for floor V2_9.5-7.2_LL 1.9;
(a) e=500 mm, Cφ = 500, (b) e=1500 mm, Cφ = 500, (c) e=500 mm, Continuous floor, (d) e=1500 mm,
Continuous floor

Page 51

4.4.2 Impact of rotational stiffness on the ULS and SLS panel utilisation
The impact of rotational stiffness on the ULS utilization (ratio of load to capacity) for bending
moment in both major and minor directions is depicted in Figure 4-9, while the SLS utilization
(ratio of deflection to deflection limit) is shown in Figure 4-10. The ULS ratio pertains to the outof-plane bending moment resistance according to CSA O86 [76]. Across all scenarios, an increase
in rotational stiffness leads to a slight reduction in the maximum ULS ratio for the major direction,
while a minor increase is discerned for the minor direction, ranging from 3% to 8%.
Comparatively, the SLS ratio exhibits heightened sensitivity to rotational stiffness, particularly at
lower values. Even slight increments in rotational stiffness result in substantial enhancements in
the SLS ratio. However, as evidenced in Figure 4-10, this effect gradually diminishes once a
rotational stiffness of around 5000 kNmrad⁻¹m⁻¹ is reached. After surpassing this point, the
influence of rotational stiffness becomes inconsequential on the floor SLS ratio (Figure 4-10).

Major direction

Minor direction

Major direction
0.60

ULS Ratio

ULS Ratio

1.10

Minor direction

0.90
0.70
0.50

0.50
0.40
0.30

0.30

0.20

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)
(a)

Infinite
7500

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)
(b)

Figure 4-9: Impact of Cφ on the ULS V2_9.5-7.2_LL 1.9; for (a) e=0.5, (b) e=1.5

Page 52

Infinite
7500

L/360

L/180

1.25

1.25

1.00

1.00

SLS Ratio

SLS Ratio

L/360

0.75
0.50

L/180

0.75
0.50
0.25

0.25
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

(a)

0

2500

5000

Infinite
7500

Cφ (kNmrad⁻¹m⁻¹)
(b)

Figure 4-10: Impact of Cφ on the SLS ratio for V2_9.5-7.2_LL 1.9; (a) e=0.5, (b) e=1.0, (c) e=1.5

4.4.3 Impact of rotational stiffness on floor deflection
The sensitivity of floor deflection to rotational stiffness at various floor span aspect ratios is
illustrated in Figure 4-11. The vertical axis represents the ratio of edge-connected floor deflection
(Uz,ec) to continuous floor deflection (Uz,c), while the horizontal axis represents changes in
rotational stiffness. Consequently, each line on this graph demonstrates the impact of rotational
stiffness on floor deflection, scaled against a continuous floor, for each analyzed floor scenario.
The results underscore the significance of floor aspect ratio: floors with smaller span ratios exhibit
much higher sensitivity to rotational stiffness, particularly at lower levels of rotational stiffness.
For example, considering 500 kNmrad⁻¹m⁻¹ rotational stiffness, the maximum deformation for
floors with span aspect ratios of 1.0 and 1.8 is 2.2 and 1.3 times higher than the maximum
deformation of a continuous floor, respectively.

Page 53

2.60

Span ratio=1.00
Span ratio=1.35

UZ,EC/UZ,C

2.20

Span ratio=1.56
1.80

Span ratio=1.77

1.40
1.00
0

2500
Cφ (kNmrad⁻¹m⁻¹)

5000

Figure 4-11: Influence of floor span ratio on floor deformation sensitivity for CLT grade V2

In Figure 4-12, the influence of rotational stiffness and the floor span ratio on the deformation
pattern shape of the floor is depicted. In Figure 4-12d, for the continuous floor, the two-way
performance is enhanced, especially when the floor span ratio approaches 1:1. In contrast, in Figure
4-12c, the continuous floor deflects similarly to a one-way floor due to the larger span ratio. For
edge-connected floors, as shown in Figure 4-12a and Figure 4-12b, reducing the rotational stiffness
significantly impacts the floor deformation shape, resulting in opposite outcomes to those seen in
continuous floors. Consequently, while the distinction between two-way and one-way action in
floor behavior depends on the floor aspect ratio, influencing the floor's deformation pattern and
load distribution direction, for edge-connected floors, the significance of the floor aspect ratio can
be diminished or rendered less effective based on the value of rotational stiffness. Consequently, it
can be asserted that edge-connected floors with a lower value of rotational stiffness tend to exhibit
cranking in two directions, indicating a proclivity towards one-way action characterized by a
cylindrical deformation shape, even when the aspect ratio of these floors falls within the range
typical of two-way floors.

Page 54

(a)

(b)

(c)

(d)

Figure 4-12: Impact of Cφ and e on the floor deformation for floor V2_9.5-7.2_LL 1.9; (a) e=500 mm, Cφ
= 500, (b) e=1500 mm, Cφ = 500, (c) e=500 mm, Continuous floor, (d) e=1500 mm, Continuous floor

Page 55

5

Recommendations for floor connection design

In addressing the need for continuity in the minor direction, the required numbers of connections
to satisfy both ULS and SLS criteria, pertaining to load-carrying capacity and stiffness respectively,
need to be determined. Achieving a floor behavior closely resembling continuity is paramount.
Through the present numerical evaluations, it was established that enhancing rotational stiffness
up to 5000 kNmrad⁻¹m⁻¹ significantly enhances floor performance, reducing deflection by
approximately 50%. However, further increasing rotational stiffness to attain a fully rigid
connection (continuous floor) only marginally decreases deflection by 15%. Hence, a target
rotational stiffness of 5000 kNmrad⁻¹m⁻¹ is deemed appropriate to approach continuous floor
behavior. As an example, two critical floors with longer possible spans including V2_9-9_LL 2.4_e
1.5, and V2_9.5-7.5_LL 1.9_e 0.5 were evaluated.
Screwed splines (S1), with 20 screws per meter (test result), achieved a bending moment capacity
(Mult) of roughly 55 kNm/m and a rotational stiffness (CႴ) of close to 6,000 kNmrad⁻¹m⁻¹ in the 4point bending test. In the 3-point bending test, the S1 reached Mult=53 kNm/m, a shear capacity
(Vult) of 125 kN/m, and a rotational stiffness of 11,000 kNmrad⁻¹m⁻¹. While plywood splines failed
in the 4-point bending tests, CLT shear strength governed failure in the 3-point bending tests and
the connection element remained undamaged. Therefore, for evaluating floor demand, the results
of the 3-point bending test are deemed critical, even though the rotational stiffness surpassed the
target in the 4-point bending test, with approximately 36% of the connection bending moment
capacity satisfying the floor demand. Based on the experimental data, using 17 screws per m still
meets the target rotational stiffness, with 40% utilization of the connection bending moment
capacity fulfilling the floor demand. Employing only nine screws per m still satisfies both the ULS
and SLS criteria, utilizing approximately 80% of the connection capacity to meet these
Page 56

requirements. However, it is noteworthy that utilizing 80% of the connection capacity, while
technically feasible, is not recommended due to the mean values utilized for this connection design.
For the glued splines (series S2), the outcome of the 3-point bending test serves as the primary
design criterion. Under simultaneous out-of-plane bending moment and shear load, Mult decreased
by 26% (Mult = 44 kNm/m, Vult = 96 kN/m) compared to the 4-point bending tests. Despite
variations in plywood grade, the rotational stiffness of the connection consistently remained
significantly higher than CႴ,t. For the S2B series, which incorporates plywood measuring 220
mm/m long along the CLT panel's minor direction, utilizing 80% of the capacity allows the
connection to meet floor demands while ensuring CႴ > 5000 kNmrad⁻¹m⁻¹. However, based on the
tested connections configuration (400 mm/m long), satisfying the floor demand requires utilizing
only 45% of the connection bending moment capacity.
Utilizing six T-joints per meter in the S3 series allows for meeting floor demands by utilizing 78%
and 64% of the bending moment and shear capacity of the connection, respectively (Mult = 23
kNm/m, Vult = 29 kN/m, CႴ = 3700 kNmrad⁻¹m⁻¹). Increasing the number of T-joints to nine per
meter results in Mult = 35 kNm/m, Vult = 44 kN/m, and CႴ = 5500 kNmrad⁻¹m⁻¹, which represents
the maximum number of T-joints that can be utilized in a zigzag position within one meter [37].
However, increasing the length of the two STS that connect the panels would increase the
withdrawal resistance. It is important to note that the spacing of T-slots depends on the length of
the STS, as this spacing prevents intersecting of the STS.
As for the S4 series, according to the ETA-18/0254 [66] by considering a minimum edge distance
of 150 mm and a connector spacing of 300 mm, maximum of three X-fix connectors can be

Page 57

installed per meter, providing Mult = 12.1 kNm/m, CႴ = 1275 kNmrad⁻¹m⁻¹ which does not meet
the ULS and SLS requirements.
Regarding floor V2_9.5-7.2_LL 1.9_e 0.5 the connection should be capable of providing Mult =
15.5 kNm/m, Vult = 27.5 kN/m, which is the average value within one meter of the critical area of
the connecting line (connecting line edges) due to the uneven distribution of forces and minimum
rotational stiffness of CႴ,min=2000 kNmrad⁻¹m⁻¹ to satisfy SLS ratio. In this way, for connection S1
series with minimum eight STS per meter (Mult = 21.8 kNm/m, Vult = 50 kN/m, CႴ = 4400
kNmrad⁻¹m⁻¹) the connection utilizes 71% of the connection bending moment capacity. However,
by utilizing fifteen STS per meter (Mult = 41.0 kNm/m, Vult = 93.7 kN/m, CႴ = 7950 kNmrad⁻¹m⁻¹)
the floor behavior can be much closer to a continuous floor as 38% of the connection capacity
meets the demand.
For the S2B series, featuring plywood measuring 180 mm/m long in its major direction, utilizing
80% of the capacity enables the connection to meet floor demands while maintaining CႴ > 5000
kNmrad⁻¹m⁻¹. However, with a plywood measuring 360 mm/m long in its major direction, the floor
demand is satisfied by CႴ, utilizing 40% of the connection capacity meets the floor demand.
Regarding S3 series utilizing five T-joints per meter in the S3 series allows for meeting floor
demands while utilizing 78% and 64% of the bending moment and shear capacity of the connection,
respectively (Mult = 19.2 kNm/m, Vult = 24.5 kN/m, CႴ = 3100 kNmrad⁻¹m⁻¹). By utilizing nine Tjoint per meter resulting in Mult = 35 kNm/m, Vult = 44 kN/m, and CႴ = 4900 kNmrad⁻¹m⁻¹, which
meets the floor demand by utilizing 45% and 63% of the connection bending and shear capacity,
respectively.

Page 58

Table 5-1 presents the summary results for design recommendations. For example, in the case of
floor V2_9-9_LL 2.4_e 1.5 which is one of the evaluated critical scenarios suggests that connection
series S1 and S2 have the capability to achieve rotational stiffness close to or higher than the target
rotational stiffness, utilizing up to 80% of their connection capacity, although about 40% of their
capacity meets the floor demand. In comparison, using 9 T-joints per meter with the same STS
detailing can achieve higher than target rotational stiffness by utilizing approximately 40% of the
connection capacity. However, meeting the floor demand would require utilizing about 55% of the
connection capacity.

Table 5-1: Design recommendation for floor V2_9-9_LL 2.4_e 1.5
Connection series

S1 (Screwed spline)

S2 (Glued spline)
S3 (T-joint)

Page 59

Cφ (kNmrad-1m-1)
10%-40%

40%-80%

Connection capacity
utilization (%)

20 STS

10900

4660

36

17 STS

9300

3980

40

9 STS

4950

2110

80

400×600 mm / 175 ml

54200

23380

45

220×600 mm / 96 ml

29800

12850

80

9 T-joint
6 T-joint

6190
4120

2130
1420

55
78

Connection detailing

6

Conclusions

6.1

Summary of experimental work

The research conducted in this thesis delves into the out-of-plane behavior of connections in the
minor direction of edge-connected CLT floor segments. The structural performance of five distinct
connections was assessed: glued-on plywood spline, plywood spline attached with inclined screws,
wooden X-fix, T-joints, and steel rebar.
1. Utilizing glued splines with a rotational stiffness exceeding 5000 kNmrad⁻¹m⁻¹, approaches the
bending stiffness of a solid panel, making it an appropriate choice to meet SLS requirements.
2. The plywood quality significantly influences the structural performance of glued spline
connections within the S2 series. In comparison to the S2B series, the S2C samples exhibited
approximately 50% lower values for Fult, Mult, d@ult, and CႴ. Moreover, CႴ remained
significantly superior to other connection types even after the S2B series.
3. Screw spline connections are less sensitive to the quality of plywood. This observation is
supported by the fact that both the S1 series (screwed spline plate) and S2C utilized the same
grade of plywood. Despite this, the load-bearing capacity and moment resistance of the S1
series are comparable to those of the S2B series.
4. The T-joint (S3) remained intact and reusable. Compared to screwed joints, T-joints exhibited
about half the out-of-plane bending moment and one-fourth the shear capacity. In the 3-point
bending tests, the T-joints exhibited sliding along the connecting line.
5. The X-fix connector (S4) exhibited ductile performance. However, its rotational stiffness was
very small; its bending moment capacity was only about half of the S2C series.

Page 60

6. Steel rebars were able to transfer 74% of the maximum bending moment compared to screwed
and glued splines. However, owing to their lower rotational stiffness, their deformation
capacity is multiple times greater than that of the screw splines. Therefore, they could be
considered a solution to add robustness of the connections between floor panels.
6.2

Summary of numerical work

The secondary objective was to evaluate the impact of rotational stiffness on floor performance
using numerical modeling. A range of scenarios for point-supported CLT floors, considering
variations in rotational stiffness, span, and loading conditions was explored.
1. While higher rotational stiffness can enhance floor structural performance, particularly in terms
of serviceability, the impact of rotational stiffness gradually diminishes. Based on the results,
up to about 5000 kNmrad⁻¹m⁻¹ could be considered as the upper limit (target rotational
stiffness), beyond which the results become less sensitive to changes in rotational stiffness. An
increase in rotational stiffness resulted in higher bending moments being transferred at both
ends of the connection compared to the middle. Consequently, depending on the stiffness of
the connection, additional connectors at both ends of the connecting line may be required.
2. Increasing the rotational stiffness results in the transfer of a major portion of the bending
moment to both ends of the connecting line. Therefore, when utilizing a stiffer connection to
approach continuous flooring, the detailing of the joints at both ends of the connecting line may
require more attention.
3. In edge-connected floor systems, the floor aspect ratio is not the predominant factor
determining the transition to two-way action. The magnitude of rotational stiffness also exerts
a direct influence on the shift between one-way and two-way action.

Page 61

4. Based on the floor analysis and experimental results, the tested connection configurations
screwed spline (S1) and glued spline (S2) were capable of providing values close to or higher
than the target rotational stiffness (5000 kNmrad-1m-1), while utilizing approximately 40% of
the connection capacity to meet the required demand. T-joint can meet the target demands;
however, more research is needed to define the optimum compromise between number of
connectors and length of STS used to install them. The X-fix connector exhibited moderately
ductile performance; however, its rotational stiffness and bending moment capacity is
insufficient for out-of-plane moment connections.
6.3

Future Research

Drawing upon the findings of this research, further experimental and numerical investigations
focusing on edge-connected CLT floors should aim to advance the development of connections
that address a broader spectrum of structural performance, constructability, and cost-effectiveness.
1. Testing of hybrid connections combining glued spline with screws or steel rebar is
recommended. This combination could add the ductile performance of steel rebar to
complement the stiffness of the glued joint. Such experiments provide insights into their
behavior, aiding in the development of resilient structural solutions for CLT floor applications.
2. Assessing the structural performance of the connection under simultaneous out-of-plane and
in-plane loads since the connections are subjected to the biaxial loading.
3. Conducting experiments on a larger scale, capable of simulating real two-way action scenarios.
4. Evaluating the long-term loading performance, particularly for glued spline joints, is crucial.

Page 62

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Appendix A: Load-deflection response for 4-point bending tests
100
S1-STS-01
80

S1-STS-02

Load (kN)

S1-STS-03
60

S1-STS-04
S1-STS-05

40

S1-STS-06

20
0
0

20

40

60

80

100

120

Deflection (mm)
100
S2-GlueB-01
80

S2-GlueB-02

Load (kN)

S2-GlueB-03
60

S2-GlueB-04
S2-GlueB-05

40

S2-GlueB-06

20
0
0

5

10

15

20

Deflection (mm)

Page 74

25

30

50
S2-GlueC-01

40

Load (kN)

S2-GlueC-02
30
20
10
0
0

5

10

15

Deflection (mm)
25
S3-Xfix-01

Load (kN)

20

S3-Xfix-02
S3-Xfix-03

15
10
5
0
0

20

40

60

Deflection (mm)

Page 75

80

100

60

S4-Tjoint-01

Load (kN)

S4-Tjoint-02
S4-Tjoint-03

40

S4-Tjoint-04
S4-Tjoint-05
S4-Tjoint-06

20

0
0

20

40

60

80

Deflection (mm)
80
S5-RebarA-01

Load (kN)

60

S5-RebarB-01

40

20

0
0

50

100
Deflection (mm)

Page 76

150

200

Appendix B: Load-deflection response for 3-point bending tests
200
S11-STS-01
160

S11-STS-02

Load (kN)

S11-STS-03
120

S11-STS-04
S11-STS-05

80

S11-STS-06

40
0
0

20

40

60

80

Deflection (mm)
160
S21-Glue-01
S21-Glue-02
S21-Glue-03
S21-Glue-04
S21-Glue-05
S21-Glue-06

Load (kN)

120

80

40

0
0

5

10
Deflection (mm)

Page 77

15

20

100
S61-Tjoint-01
S61-Tjoint-02

80

Load (kN)

S61-Tjoint-03
60

S61-Tjoint-04
S61-Tjoint-05

40

S61-Tjoint-06

20
0
0

10

20

30

40

50

Deflection (mm)

250
S01-Full-01

Load (kN)

200

S01-Full-02
S01-Full-03

150
100
50
0
0

5

10

15

20

Deflection (mm)

Page 78

25

30

Appendix C: Failure modes from 4-point bending tests

Page 79

S2B-1

S2B-2

S2B-3

S2B-4

S2B-5

S2B-6

S2C-1

S2C-2

Appendix C: Failure modes from 3-point bending tests

Page 80

S1-1

S1-2

S1-3

S1-4

S1-5

S1-6

Page 81

S2-1

S2-2

S2-3

S2-4

S2-5

S2-6

Page 82

S3-1

S3-2

S3-3

S3-4

S3-5

S3-6

Appendix D: Numerical results
D1: Transferred bending moment at the connecting line
Both ends

Middle

Both ends
20

Mult,joint (kNm/m)

Mult,joint (kNm/m)

16
12
8

4
0

16
12
8
4
0

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

0

E1_7.2-7.2_LL 1.9_e 0.5
Both ends

Middle

Infinite
7500

Both ends

Middle

16

16

Mult,joint (kNm/m)

Mult,joint (kNm/m)

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_7.2-7.2_LL 2.4_e 0.5

20

12
8
4
0

12
8
4
0

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

0

E1_9.5-7.2_LL 1.9_e 0.5
Both ends

Middle

Infinite
7500

Both ends

Middle

Mult,joint (kNm/m)

16

12
8
4
0

12
8
4
0

0

Page 83

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_7.2-7.2_LL 1.9_e 1.0

16

Mult,joint (kNm/m)

Middle

Infinite
2500
5000
7500
Cφ (kNmrad⁻¹m⁻¹)
E1_7.2-7.2_LL 2.4_e 1.0

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)
E1_9.5-7.2_LL 1.9_e 1.0

Infinite
7500

Both ends

Middle

Both ends

16
12
8
4
0
2500
5000
Cφ (kNmrad⁻¹m⁻¹)

8
4

Infinite
7500

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_9.5-7.2_LL 2.4_e 1.0

E1_9.5-7.2_LL 1.9_e 1.5

Both ends

Both ends

Middle

16

20

12

16

Mult,joint (kNm/m)

Mult,joint (kNm/m)

12

0
0

8
4
0

Infinite
7500

Middle

12
8
4
0

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

E1_9.5-7.2_LL 2.4_e 1.5

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_9.0-9.0_LL 1.9_e 1.5

Both ends

Middle

Mult,joint (kNm/m)

24
20
16
12
8
4
0
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_9.0-9.0_LL 2.4_e 1.5

Page 84

Middle

16

Mult,joint (kNm/m)

Mult,joint (kNm/m)

20

Infinite
7500

Infinite
7500

Middle

Both ends
20

12

16

Mult,joint (kNm/m)

Mult,joint (kNm/m)

Both ends
16

8
4
0

12
8
4
0

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

0

V2_7.2-7.2_LL 1.9_e 0.5
Both ends

Middle

Both ends

16

Mult,joint (kNm/m)

Mult,joint (kNm/m)

Infinite
7500

Middle

16

12
8
4
0

12
8
4
0

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

0

V2_9.5-7.2_LL 1.9_e 0.5
Both ends

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

V2_7.2-7.2_LL 1.9_e 1.0

Middle

Both ends

Middle

16

Mult,joint (kNm/m)

16

Mult,joint (kNm/m)

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_7.2-7.2_LL 2.4_e 0.5

20

12
8
4
0

12
8
4
0

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

V2_7.2-7.2_LL 2.4_e 1.0

Page 85

Middle

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_9.5-7.2_LL 1.9_e 1.0

Infinite
7500

Both ends

Middle

Both ends

16
12
8
4
0

12
8
4
0

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_9.5-7.2_LL 2.4_e 1.0

Infinite
7500

V2_9.5-7.2_LL 1.9_e 1.5

Middle

Both ends

16

20

12

16

Mult,joint (kNm/m)

Mult,joint (kNm/m)

Both ends

8
4

0

Middle

12
8
4

0
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

V2_9.5-7.2_LL 2.4_e 1.5

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_9.0-9.0_LL 1.9_e 1.5

Both ends

Middle

Mult,joint (kNm/m)

24

20
16
12
8
4
0
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_9.0-9.0_LL 2.4_e 1.5

Page 86

Middle

16

Mult,joint (kNm/m)

Mult,joint (kNm/m)

20

Infinite
7500

Infinite
7500

Column strip major direction
Column strip minor direction
Maximum deflection

40

Deflection (mm)

Deflection (mm)

D2: Floor deflections

30
20
10
0

80

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

40
30
20
10
0
0

Column strip major direction
Column strip minor direction
Maximum deflection

Column strip major direction
Column strip minor direction
Maximum deflection

20
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

40
30
20

10
0

Infinite
7500

0

Column strip major direction
Column strip minor direction
Maximum deflection

30
20
10

0
2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

E1_7.2-7.2_LL 2.4_e 1.0

Page 87

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

E1_7.2-7.2_LL 1.9_e 1.0

Deflection (mm)

Deflection (mm)

E1_9.5-7.2_LL 1.9_e 0.5

0

Infinite
7500

E1_7.2-7.2_LL 2.4_e 0.5

40

40

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_7.2-7.2_LL 1.9_e 0.5

60

0

50

Infinite
7500

Deflection (mm)

Deflection (mm)

0

Column strip major direction
Column strip minor direction
Maximum deflection

Column strip major direction
Column strip minor direction
Maximum deflection

50
40
30
20
10

0
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_9.5-7.2_LL 1.9_e 1.0

Infinite
7500

60

Deflection (mm)

Deflection (mm)

Column strip major direction
Column strip minor direction
Maximum deflection

40
20
0

50

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

30
20

10
0
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_9.5-7.2_LL 1.9_e 1.5

Column strip major direction
Column strip minor direction
Maximum deflection

Column strip major direction
Column strip minor direction
Maximum deflection

30
20
10
0
Infinite
7500

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Deflection (mm)

E1_9.5-7.2_LL 2.4_e 1.5

80

60
40
20
0
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_9.0-9.0_LL 1.9_e 1.5
Column strip major direction
Column strip minor direction
Maximum deflection

80
60
40
20
0
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_9.0-9.0_LL 2.4_e 1.5

Page 88

Infinite
7500

E1_9.5-7.2_LL 2.4_e 1.0

40

0

40

Infinite
7500

Deflection (mm)

Deflection (mm)

0

Column strip major direction
Column strip minor direction
Maximum deflection

Infinite
7500

Infinite
7500

40

Deflection (mm)

Deflection (mm)

Column strip major direction
Column strip minor direction
Maximum deflection

30
20
10
0

80

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

40
30
20
10
0
0

Column strip major direction
Column strip minor direction
Maximum deflection

Column strip major direction
Column strip minor direction
Maximum deflection

20

0
2500
5000
Cφ (kNmrad⁻¹m⁻¹)

40
30
20
10

0

Infinite
7500

0

Column strip major direction
Column strip minor direction
Maximum deflection

30
20
10
0
2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

V2_7.2-7.2_LL 2.4_e 1.0

Page 89

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

V2_7.2-7.2_LL 1.9_e 1.0

Deflection (mm)

Deflection (mm)

V2_9.5-7.2_LL 1.9_e 0.5

0

Infinite
7500

V2_7.2-7.2_LL 2.4_e 0.5

40

40

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_7.2-7.2_LL 1.9_e 0.5

60

0

50

Infinite
7500

Deflection (mm)

Deflection (mm)

0

Column strip major direction
Column strip minor direction
Maximum deflection

Column strip major direction
Column strip minor direction
Maximum deflection

60
40
20
0
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_9.5-7.2_LL 1.9_e 1.0

Infinite
7500

60

Deflection (mm)

Deflection (mm)

Column strip major direction
Column strip minor direction
Maximum deflection

40
20
0

50

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

30
20
10
0
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_9.5-7.2_LL 1.9_e 1.5

Column strip major direction
Column strip minor direction
Maximum deflection

Column strip major direction
Column strip minor direction
Maximum deflection

30
20
10

0
2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

Deflection (mm)

V2_9.5-7.2_LL 2.4_e 1.5

50
40
30
20
10

0
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_9.0-9.0_LL 1.9_e 1.5
Column strip major direction
Column strip minor direction
Maximum deflection

80
60

40
20
0
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_9.0-9.0_LL 2.4_e 1.5

Page 90

Infinite
7500

V2_9.5-7.2_LL 2.4_e 1.0

40

0

40

Infinite
7500

Deflection (mm)

Deflection (mm)

0

Column strip major direction
Column strip minor direction
Maximum deflection

Infinite
7500

Infinite
7500

D3: Floor utilisation ratios

Major direction

Minor direction

Major direction
1.00

ULS Ratio

ULS Ratio

1.00
0.90
0.80
0.70

0.80

0.60
0

Infinite
2500
5000
7500
Cφ (kNmrad⁻¹m⁻¹)
E1_7.2-7.2_LL 1.9_e 0.5

Major direction

0

Minor direction

Minor direction

ULS Ratio

0.80

1.00
0.80

0.70
0.60
0.50

0.60

0.40
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

0

E1_9.5-7.2_LL 1.9_e 0.5
Major direction

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

E1_7.2-7.2_LL 1.9_e 1.0

Minor direction

Major direction

Minor direction

0.80

ULS Ratio

0.80

ULS Ratio

Infinite
2500
5000
7500
Cφ (kNmrad⁻¹m⁻¹)
E1_7.2-7.2_LL 2.4_e 0.5

Major direction

1.20

ULS Ratio

0.90

0.70

0.60

0.70
0.60
0.50

0.70
0.60
0.50

0.40

0.40
0

Page 91

Minor direction

Infinite
7500

2500
5000
Cφ (kNmrad⁻¹m⁻¹)
E1_7.2-7.2_LL 2.4_e 1.0

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)
E1_9.5-7.2_LL 1.9_e 1.0

Infinite
7500

Major direction

Minor direction

Major direction
0.90

ULS Ratio

ULS Ratio

0.90

0.80
0.70

0.80
0.70
0.60

0.60

0.50
0

Infinite
7500

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

0

E1_9.5-7.2_LL 2.4_e 1.0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

E1_9.5-7.2_LL 1.9_e 1.5

Minor direction

Major direction

0.90

1.00

0.80

0.90

ULS Ratio

ULS Ratio

Major direction

0.70
0.60

Minor direction

0.80
0.70
0.60

0.50

0.50
0

Infinite
7500

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_9.5-7.2_LL 2.4_e 1.5

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_9.0-9.0_LL 1.9_e 1.5

Major direction

Minor direction

ULS Ratio

1.00
0.90
0.80
0.70
0.60
0.50

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_9.0-9.0_LL 2.4_e 1.5

Page 92

Minor direction

Infinite
7500

Infinite
7500

Major direction

Minor direction

Major direction
0.70

ULS Ratio

ULS Ratio

0.60

0.50
0.40

0.60
0.50
0.40

0.30

0.30
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

0

V2_7.2-7.2_LL 1.9_e 0.5

Major direction

Minor direction

Major direction

ULS Ratio

ULS Ratio

Infinite
7500

Minor direction

0.50

0.90
0.70
0.50

0.45
0.40
0.35

0.30

0.30
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

0

V2_9.5-7.2_LL 1.9_e 0.5

Major direction

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

V2_7.2-7.2_LL 1.9_e 1.0

Major direction

Minor direction

Minor direction

0.80

ULS Ratio

0.50

ULS Ratio

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_7.2-7.2_LL 2.4_e 0.5

1.10

0.45
0.40
0.35

0.60
0.40
0.20

0.30

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

V2_7.2-7.2_LL 2.4_e 1.0

Page 93

Minor direction

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_9.5-7.2_LL 1.9_e 1.0

Infinite
7500

Major direction

Minor direction

Major direction
0.60

ULS Ratio

ULS Ratio

1.00
0.80
0.60
0.40

0.50
0.40
0.30

0.20

0.20
0

Infinite
7500

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

0

V2_9.5-7.2_LL 2.4_e 1.0

Major direction

Minor direction

Major direction

Infinite
7500

Minor direction

0.60

ULS Ratio

ULS Ratio

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_9.5-7.2_LL 1.9_e 1.5

0.60
0.50
0.40
0.30

0.50
0.40
0.30

0.20

0.20
0

Infinite
7500

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_9.5-7.2_LL 2.4_e 1.5

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_9.0-9.0_LL 1.9_e 1.5

Major direction

Minor direction

ULS Ratio

0.70
0.60
0.50
0.40
0.30
0.20
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_9.0-9.0_LL 2.4_e 1.5

Page 94

Minor direction

Infinite
7500

Infinite
7500

L/180

L/360

1.00

1.00

0.75

0.75
SLS Ratio

SLS Ratio

L/360

0.50
0.25
0.00
2500
5000
Cφ (kNmrad⁻¹m⁻¹)

0.25

Infinite
7500

0

E1_7.2-7.2_LL 2.4_e 0.5

L/360

L/360

L/180

Infinite
7500

L/180

1.00

1.00

SLS Ratio

0.75

0.75
0.50
0.25
0.00

0.50
0.25
0.00

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

0

E1_9.5-7.2_LL 1.9_e 0.5
L/360

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

L/180

L/360

1.00

1.00

0.75

0.75

0.50
0.25
0.00

Infinite
7500

E1_7.2-7.2_LL 1.9_e 1.0

SLS Ratio

SLS Ratio

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_7.2-7.2_LL 1.9_e 0.5

1.25

SLS Ratio

0.50

0.00
0

L/180

0.50
0.25
0.00

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

E1_7.2-7.2_LL 2.4_e 1.0

Page 95

L/180

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_9.5-7.2_LL 1.9_e 1.0

Infinite
7500

L/360

L/180

L/360

1.25

1.00
0.75
SLS Ratio

SLS Ratio

1.00
0.75
0.50
0.25
0.00

0.50
0.25
0.00

0

Infinite
7500

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

0

E1_9.5-7.2_LL 2.4_e 1.0
L/360

L/180

L/360

Infinite
7500

L/180

1.50
1.25

SLS Ratio

0.75

SLS Ratio

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_9.5-7.2_LL 1.9_e 1.5

1.00

0.50
0.25

1.00
0.75
0.50
0.25

0.00

0.00
0

Infinite
7500

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_9.5-7.2_LL 2.4_e 1.5

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_9.0-9.0_LL 1.9_e 1.5
L/360

L/180

1.50

SLS Ratio

1.25
1.00
0.75
0.50
0.25
0.00
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

E1_9.0-9.0_LL 2.4_e 1.5

Page 96

L/180

Infinite
7500

Infinite
7500

L/360

L/180

L/360

1.00

1.25
1.00
SLS Ratio

SLS Ratio

0.75
0.50
0.25

0.50

0.00
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

0

V2_7.2-7.2_LL 2.4_e 0.5

L/360

L/360

L/180

Infinite
7500

L/180

1.00

1.25

0.75

SLS Ratio

1.00
0.75
0.50
0.25
0.00

0.50
0.25
0.00

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

0

V2_9.5-7.2_LL 1.9_e 0.5
L/360

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

V2_7.2-7.2_LL 1.9_e 1.0

L/180

L/360

1.00

L/180

1.25
1.00

SLS Ratio

0.75

SLS Ratio

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_7.2-7.2_LL 1.9_e 0.5

1.50

SLS Ratio

0.75

0.25

0.00

0.50
0.25

0.75
0.50
0.25

0.00

0.00
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

Infinite
7500

V2_7.2-7.2_LL 2.4_e 1.0

Page 97

L/180

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_9.5-7.2_LL 1.9_e 1.0

Infinite
7500

L/360

L/180

L/360

1.25

1.00
0.75
SLS Ratio

SLS Ratio

1.00
0.75
0.50
0.25
0.00

0.50
0.25
0.00

0

Infinite
7500

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

0

V2_9.5-7.2_LL 2.4_e 1.0
L/360

L/180

L/360

Infinite
7500

L/180

1.50
1.25

SLS Ratio

0.75

SLS Ratio

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_9.5-7.2_LL 1.9_e 1.5

1.00

0.50
0.25

1.00
0.75
0.50
0.25

0.00

0.00
0

Infinite
7500

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_9.5-7.2_LL 2.4_e 1.5

0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_9.0-9.0_LL 1.9_e 1.5
L/360

L/180

1.50

SLS Ratio

1.25
1.00
0.75
0.50
0.25
0.00
0

2500
5000
Cφ (kNmrad⁻¹m⁻¹)

V2_9.0-9.0_LL 2.4_e 1.5

Page 98

L/180

Infinite
7500

Infinite
7500