EXPERIMENTAL VERIFICATION OF ANALYTICAL STRENGTH AND DEFORMATION
METHODS FOR SINGLE AND MULTI-PANEL NAILED CLT SHEAR WALLS
by
Milvio Sanchez Baptista Junior
B.Sc., São Paulo State University, Brazil, 2020

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

UNIVERSITY OF NORTHERN BRITISH COLUMBIA
July 2022
© Milvio Sanchez Baptista Junior, 2022

Abstract
Cross-laminated timber (CLT) is becoming a feasible alternative as structural material for midand high-rise buildings. Although CLT walls are appropriate for resisting lateral loads from wind
and earthquakes, the current provisions in the Canadian Standard for Engineering Design in
Wood lack analytical expressions for estimating their resistance and deflection.
In this thesis, the performance of nailed single and couple CLT shear walls is investigated by
comparing UNBC test data with the strength and stiffness predictions using analytical proposals.
Four methods are considered: Method A (Casagrande et al. 2017), considers the minimum
strength value of the hold-down and the vertical fasteners; Method B (Shahnewaz et al. 2019),
which accounts for the rocking resistance of all connectors; Method C (Masroor et al. 2020) which
accounts for the bi-axial behaviour of connectors; and Method D (Nolet et al. 2019) which
describes the elastic-perfectly plastic behaviour of CLT shear walls while neglecting the bi-axial
behaviour of brackets.
The best match for the elastic behaviour of the nailed shear walls was achieved using Method B,
while Method C reasonably predicted the inelastic shear wall behaviour. With the validation
against test results, designers should consider using either method depending on the design
intentions. Future research should aim at either extending Method B (Shahnewaz et al. 2019)
towards the inelastic behaviour or improving Method C (Masroor et al. 2020) in the elastic range.

ii

Table of Contents
Abstract

............................................................................................................................ ii

List of Figures .................................................................................................................... vii
List of Tables ..................................................................................................................... xiv
List of Abbreviations ........................................................................................................ xvi
List of Symbols ............................................................................................................... xviii
Acknowledgments ........................................................................................................... xxii
Chapter 1: Introduction ....................................................................................................... 1
1.1. Motivation .................................................................................................................... 1
1.2. Objectives .................................................................................................................... 1
1.3. Thesis Overview .......................................................................................................... 2
1.4. Scope and Limitations .................................................................................................. 2
Chapter 2: Literature Review .............................................................................................. 3
2.1. Construction Industry’s Environmental Impacts ............................................................ 3
2.2. Wood as a Structural Material ...................................................................................... 4
2.2.1. Solid wood ............................................................................................................ 4
2.2.2. Engineered Wood Products and Mass-Timber...................................................... 5
2.2.3. Cross-Laminated Timber (CLT) ............................................................................ 6
2.2.4. Timber Connections.............................................................................................. 7
2.3. Lateral Load Resisting Systems ................................................................................... 9
2.3.1. Lateral Loads ........................................................................................................ 9
2.3.2. Overview of Lateral Load Resisting Systems ...................................................... 10
2.4. Tall and Hybrid Wood Buildings ................................................................................. 12

iii

2.5. Cross-Laminated Timber Shear Walls........................................................................ 13
2.5.1. Overview ............................................................................................................ 13
2.5.2. Connections in CLT Shear Walls ........................................................................ 14
2.5.3. CLT Shear Wall Kinematic Motions .................................................................... 16
2.5.4. Previous Research on CLT Shear Walls ............................................................. 19
2.5.5. Analytical Models for CLT Shear Walls ............................................................... 23
2.6. Design Provisions for CLT Shear Walls ..................................................................... 25
2.6.1. Design Provisions in Canada .............................................................................. 25
2.6.2. Design Provisions in the United States ............................................................... 27
2.6.3. Design Provisions in Europe ............................................................................... 28
2.6.4. Recent Proposal for Capacity-Based Design of CLT Shear Walls....................... 29
2.7. Summary of Literature Review ................................................................................... 30
Chapter 3: Analytical Methods for CLT Shear Wall Design ............................................ 32
3.1. Strength Assessment Methods .................................................................................. 32
3.1.1. Overview ............................................................................................................ 32
3.1.2. Pei et al. (2012) .................................................................................................. 34
3.1.3. Tomasi (2013) .................................................................................................... 35
3.1.4. Wallner-Novak et al. (2013) ................................................................................ 36
3.1.5. Gavric and Popovski (2014) ................................................................................ 37
3.1.6. Casagrande et al. (2017) .................................................................................... 39
3.1.7. Shahnewaz et al. (2019) ..................................................................................... 43
3.1.8. Nolet et al. (2019) ............................................................................................... 46
3.1.9. Masroor et al. (2020) .......................................................................................... 48
3.2. Stiffness Analytical Approaches ................................................................................. 52
3.2.1. Overview ............................................................................................................ 52

iv

3.2.2. Wallner-Novak et al. (2013) ................................................................................ 53
3.2.3. Gavric et al. (2015) ............................................................................................. 53
3.2.4. Hummel et al. (2016) .......................................................................................... 55
3.2.5. Casagrande et al. (2017) .................................................................................... 56
3.2.6. Shahnewaz et al. (2020) ..................................................................................... 57
3.2.7. Masroor et al. (2020) .......................................................................................... 60
3.3. Design Examples ....................................................................................................... 62
3.3.1. Rationale for Method Selection ........................................................................... 62
3.3.2. Examples ............................................................................................................ 63
3.3.3. Results ............................................................................................................... 67
3.3.4. Discussion .......................................................................................................... 74
Chapter 4: Comparison of Analytical Methods and Test Results .................................. 77
4.1. UNBC CLT Shear Wall Test Data with Nailed Connections ....................................... 77
4.1.1. Materials and Methods ....................................................................................... 77
4.1.2. Shear Wall Test Results ..................................................................................... 82
4.2. Model Input Parameters ............................................................................................. 83
4.3. Evaluation of the Elastic Strength of Nailed CLT Shear Walls .................................... 85
4.3.1. Results ............................................................................................................... 85
4.3.2. Shear-uplift Interaction........................................................................................ 88
4.3.3. Discussion .......................................................................................................... 89
4.4. Evaluation of the Elastic Displacement of Nailed CLT Shear Walls ............................ 95
4.4.1. Results ............................................................................................................... 95
4.4.2. Discussion .......................................................................................................... 98
4.5. Inelastic Response of Nailed Multi-panel CLT Shear Walls ...................................... 104
4.5.1. Results ............................................................................................................. 104

v

4.5.2. Discussion ........................................................................................................ 108
Chapter 5: Conclusions................................................................................................... 115
5.1. Summary ................................................................................................................. 115
5.2. Future Research ...................................................................................................... 119
References ....................................................................................................................... 121
Appendix A: Elastic Strength Results ............................................................................ 136
Appendix B: Elastic Displacement Results .................................................................... 151
Appendix C: Inelastic Response of Multi-panel CLT Shear Walls ................................ 166

vi

List of Figures
Figure 2.1. Engineered Wood Products a) Glulam; b) PSL; c) LSL; d) LVL (Green and Taggart,
2017) ......................................................................................................................................... 6
Figure 2.2. a) CLT layup (Breneman, 2016); b) Major (lengthwise) and minor (widthwise) axes
direction and orientation of the outer fibers (Karacabeyli & Gagnon, 2019) ................................ 7
Figure 2.3. Typical timber connections: a) Nails; b) Screws; c) Bolts; d) Self-Tapping Screws; e)
Self-Drilling Dowels; f) Nail plate (proHolz, 2003) ....................................................................... 8
Figure 2.4. Different structural responses of lateral loading (Vessby, 2008) ..............................10
Figure 2.5. Lateral Load Resisting Systems for timber, steel, and concrete buildings (CCPIA,
2021) ........................................................................................................................................11
Figure 2.6. a) The Stadthaus (Hurst, 2020); b) The Wood Innovation and Design Centre (MGA,
2014); c) Brock Commons (Thomas, 2017)...............................................................................13
Figure 2.7. CLT shear wall: a) single panel and b) coupled panel (Shahnewaz et al. 2019), and
c) CLT connections (i) wall-to-wall and floor-to-floor; (ii) wall-to-floor; (iii) wall to foundation
(Brandner et al. 2016) ...............................................................................................................14
Figure 2.8. a) Half-Lap joint; b) Spline joint, c) Butt joint (MTC, 2019) .......................................15
Figure 2.9. Hold-down and shear angle bracket connected to a CLT wall and a concrete floor,
showing the load-carrying direction (SIMPSON Strong-Tie, 2019) ............................................16
Figure 2.10. a) Bending deformation; b) Shear deformation; c) Sliding Deformation; d) Rocking
Deformation (Lukacs et al., 2019) .............................................................................................17
Figure 2.11. Lateral deflection due to rocking (Henriksson and Rosenberg, 2019) ....................18
Figure 2.12. Different types of rocking behaviours (a) Coupled-Wall Behaviour; (b) Intermediate
Behaviour; (c) Single-Wall Behaviour (Nolet et al., 2019) ..........................................................19

vii

Figure 2.13. a) SOFIE project (Ceccotti et al., 2013); b) CLT house before loading (Popovski and
Gavric, 2016); c) NHERI Shake Table (Pei et al., 2019) ............................................................23
Figure 3.1. Shear wall layout for Pei et al. (2012) method (Lukacs et al., 2019). .......................34
Figure 3.2. Description of the “stress block” method (Lukacs et al., 2019).................................36
Figure 3.3. Shear wall layout for Wallner-Novak et al. (2013) method (Lukacs et al., 2019) ......37
Figure 3.4. a) Analytical models used for determining the lateral resistance of CLT shear walls; b)
Distribution of reaction forces in a coupled CLT wall; c) Iterative procedure; d) Circular shear-uplift
interaction (Gavric and Popovski, 2014) ....................................................................................38
Figure 3.5. a) Deformed shape of SW; b) Deformed shape of CP (Casagrande et al., 2017) ....40
Figure 3.6. a) Sliding for CP with angle bracket and hold-down; b) Rocking for CP with angle
bracket and 2-hold-downs; c) Combined rocking-sliding for CP with angle bracket and 2-holddowns (Shahnewaz et al., 2019) ...............................................................................................43
Figure 3.7. The ratio of sliding to rocking deformation for different aspect ratios with SW with angle
bracket and with angle bracket and hold-downs (Shahnewaz et al., 2019)................................44
Figure 3.8. a) Idealized Multi-panel CLT shear wall notation; b) Elastic-plastic force-displacement
curve for CPEL-SWPL (Nolet et al., 2019) ................................................................................46
Figure 3.9. Inelastic diagram of multi-panel CLT shear walls (Masroor et al., 2020) ..................51
Figure 3.10. Rigid or elastic foundation and rocking deformation with elastic intermediate layer
(Lukacs et al., 2019) .................................................................................................................55
Figure 3.11. a) Single CLT walls; b) Coupled CLT walls with 4-hold-downs; c) Coupled CLT walls
with 2- hold-downs (Shahnewaz et al., 2018) ............................................................................58
Figure 3.12. Cross-section of m-ply CLT panel (Shahnewaz et al., 2018) .................................59
Figure 3.13. a) Single wall for example 1; b) Coupled wall for example 1 ..................................64
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Figure 3.14. a) Single wall for example 2; b) Coupled wall for example 2 ..................................64
Figure 3.15. Example 1 - Single wall lateral resistance .............................................................67
Figure 3.16. Example 1 - Coupled wall lateral resistance ..........................................................68
Figure 3.17. Example 1 - Displacement contribution for SW......................................................69
Figure 3.18. Example 1 - Displacement contribution for CP ......................................................69
Figure 3.19. Example 2 - Single wall lateral resistance .............................................................70
Figure 3.20. Example 2 - Coupled wall lateral resistance ..........................................................71
Figure 3.21. Example 2 - Displacement contribution for SW......................................................72
Figure 3.22. Example 2 - Displacement contribution for CP ......................................................72
Figure 3.23. Curves from analytical results ...............................................................................74
Figure 4.1. CLT shear wall test specimens: single walls with aspect ratios of a-b) 2.5 and c) 3.5;
couped walls with aspect ratios of d-e) 2.5 and f-g) 3.5 [dimensions are in mm]. Note: retrieved
from the under-review publication "Experimental parameter study on single-story nailed CLT
shear walls by Md Shahnewaz, Carla Dickof, Thomas Tannert"................................................78
Figure 4.2. a) CLT shear wall test setup; b) Positioning of sensors. Note: retrieved from the underreview publication "Experimental parameter study on single-story nailed CLT shear walls by Md
Shahnewaz, Carla Dickof, Thomas Tannert" .............................................................................81
Figure 4.3. EEEP procedure .....................................................................................................82
Figure 4.4. Strength comparison among the methods and test data for SW1 ............................87
Figure 4.5. Strength comparison among the methods and test data for CP1.............................87
Figure 4.6. Comparison against test data and shear-uplift interactions .....................................89
Figure 4.7. Comparison against test data and analytical results for Method A ...........................92

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Figure 4.8. Comparison against test data and analytical results for Method B ...........................92
Figure 4.9. Comparison against test data and analytical results for Method C ..........................93
Figure 4.10. Summary of all shear walls for

over

..........................................................94

Figure 4.11. Displacement comparison among the analytical and test results for SW1 .............97
Figure 4.12. Displacement comparison among the analytical and test results for CP1 ..............98
Figure 4.13. Comparison against test data and analytical results for Method A .......................101
Figure 4.14. Comparison against test data and analytical results for Method B .......................102
Figure 4.15. Comparison against test data and analytical results for Method C.......................102
Figure 4.16. Summary of the ratio between backbone curves and analytical results ...............104
Figure 4.17. Curves from monotonic test and analytical methods for CP1...............................107
Figure 4.18. Envelope curves from cyclic tests and analytical results for CP5 .........................107
Figure 4.19. Summary of the ratio between maximum experimental force and analytical results
...............................................................................................................................................111
Figure 4.20. The ratio of the experimental vertical joint yield force to the analytical predictions
...............................................................................................................................................113
Figure 4.21. The ratio of the experimental hold-down yield force to the analytical predictions .113
Figure A.1. Strength comparison among the methods and test data for SW2 .........................138
Figure A.2. Strength comparison among the methods and test data for SW3 .........................138
Figure A.3. Strength comparison among the methods and test data for SW4 .........................139
Figure A.4. Strength comparison among the methods and test data for SW5 .........................139
Figure A.5. Strength comparison among the methods and test data for SW6 .........................140

x

Figure A.6. Strength comparison among the methods and test data for SW7 .........................140
Figure A.7. Strength comparison among the methods and test data for SW8 .........................141
Figure A.8. Strength comparison among the methods and test data for CP2 ..........................141
Figure A.9. Strength comparison among the methods and test data for CP3 ..........................142
Figure A.10. Strength comparison among the methods and test data for CP4 ........................142
Figure A.11. Strength comparison among the methods and test data for CP5 ........................143
Figure A.12. Strength comparison among the methods and test data for CP6 ........................143
Figure A.13. Strength comparison among the methods and test data for CP7 ........................144
Figure A.14. Strength comparison among the methods and test data for CP8 ........................144
Figure A.15. Strength comparison among the methods and test data for CP9 ........................145
Figure A.16. Strength comparison among the methods and test data for CP10 ......................145
Figure A.17. Strength comparison among the methods and test data for CP11 ......................146
Figure A.18. Strength comparison among the methods and test data for CP12 ......................146
Figure A.19. Strength comparison among the methods and test data for CP13 ......................147
Figure A.20. Strength comparison among the methods and test data for CP14 ......................147
Figure A.21. Strength comparison among the methods and test data for CP15 ......................148
Figure A.22. Strength comparison among the methods and test data for CP16 ......................148
Figure A.23. Strength comparison among the methods and test data for CP17 ......................149
Figure A.24. Strength comparison among the methods and test data for CP18 ......................149
Figure A.25. Strength comparison among the methods and test data for CP19 ......................150
Figure B.1. Displacement comparison among the methods and test data for SW2 .................153

xi

Figure B.2. Displacement comparison among the methods and test data for SW3 .................153
Figure B.3. Displacement comparison among the methods and test data for SW4 .................154
Figure B.4. Displacement comparison among the methods and test data for SW5 .................154
Figure B.5. Displacement comparison among the methods and test data for SW6 .................155
Figure B.6. Displacement comparison among the methods and test data for SW7 .................155
Figure B.7. Displacement comparison among the methods and test data for SW8 .................156
Figure B.8. Displacement comparison among the methods and test data for CP2 ..................156
Figure B.9. Displacement comparison among the methods and test data for CP3 ..................157
Figure B.10. Displacement comparison among the methods and test data for CP4 ................157
Figure B.11. Displacement comparison among the methods and test data for CP5 ................158
Figure B.12. Displacement comparison among the methods and test data for CP6 ................158
Figure B.13. Displacement comparison among the methods and test data for CP7 ................159
Figure B.14. Displacement comparison among the methods and test data for CP8 ................159
Figure B.15. Displacement comparison among the methods and test data for CP09 ..............160
Figure B.16. Displacement comparison among the methods and test data for CP10 ..............160
Figure B.17. Displacement comparison among the methods and test data for CP11 ..............161
Figure B.18. Displacement comparison among the methods and test data for CP12 ..............161
Figure B.19. Displacement comparison among the methods and test data for CP13 ..............162
Figure B.20. Displacement comparison among the methods and test data for CP14 ..............162
Figure B.21. Displacement comparison among the methods and test data for CP15 ..............163
Figure B.22. Displacement comparison among the methods and test data for CP16 ..............163

xii

Figure B.23. Displacement comparison among the methods and test data for CP17 ..............164
Figure B.24. Displacement comparison among the methods and test data for CP18 ..............164
Figure B.25. Displacement comparison among the methods and test data for CP19 ..............165
Figure C.1. Curves from monotonic test and analytical methods for CP2 ................................170
Figure C.2. Envelope curves from cyclic tests and analytical results for CP3 ..........................170
Figure C.3. Envelope curves from cyclic tests and analytical results for CP4 ..........................171
Figure C.4. Envelope curves from cyclic tests and analytical results for CP6 ..........................171
Figure C.5. Envelope curves from cyclic tests and analytical results for CP7 ..........................172
Figure C.6. Envelope curves from cyclic tests and analytical results for CP8 ..........................172
Figure C.7. Envelope curves from cyclic tests and analytical results for CP9 ..........................173
Figure C.8. Envelope curves from cyclic tests and analytical results for CP10 ........................173
Figure C.9. Envelope curves from cyclic tests and analytical results for CP11 ........................174
Figure C.10. Curves from monotonic test and analytical methods for CP12 ............................174
Figure C.11. Envelope curves from cyclic tests and analytical results for CP13 ......................175
Figure C.12. Envelope curves from cyclic tests and analytical results for CP14 ......................175
Figure C.13. Envelope curves from cyclic tests and analytical results for CP15 ......................176
Figure C.14. Curves from monotonic test and analytical methods for CP16 ............................176
Figure C.15. Envelope curves from cyclic tests and analytical results for CP17 ......................177
Figure C.16. Envelope curves from cyclic tests and analytical results for CP18 ......................177
Figure C.17. Envelope curves from cyclic tests and analytical results for CP19 ......................178

xiii

List of Tables
Table 3.1. Proposed equations for strength assessment (Casagrande et al. 2017) ...................42
Table 3.2. Equations for resistance of CLT shear walls of Method B .........................................45
Table 3.3. Elastic CP to plastic SW, CPEL-SWPL design equations (Nolet et al., 2019) ...........47
Table 3.4. Equations for SW and CP for the Masroor's method.................................................49
Table 3.5. Equations for the inelastic approach .........................................................................50
Table 3.6. Comparison among the selected strength and stiffness models ...............................63
Table 3.7. Properties of the CLT shear walls .............................................................................65
Table 3.8. Example 1 - Summary of the lateral resistance ........................................................67
Table 3.9. Example 1 - Summary of the displacement contribution ...........................................68
Table 3.10. Example 2 - Summary of the lateral resistance.......................................................70
Table 3.11. Example 2 - Summary of the displacement contribution .........................................71
Table 3.12. Summary of inelastic assessment for academic examples .....................................73
Table 4.1. CLT shear wall specimen description. Note: retrieved from the under-review publication
"Experimental parameter study on single-story nailed CLT shear walls by Md Shahnewaz, Carla
Dickof, Thomas Tannert"...........................................................................................................80
Table 4.2. Connector test results. Note: retrieved from the under-review publication "Experimental
parameter study on single-story nailed CLT shear walls by Md Shahnewaz, Carla Dickof, Thomas
Tannert" ....................................................................................................................................81
Table 4.3. Main results of CLT shear wall tests. Note: retrieved from the under-review publication
"Experimental parameter study on single-story nailed CLT shear walls by Md Shahnewaz, Carla
Dickof, Thomas Tannert"...........................................................................................................83

xiv

Table 4.4. Connection model input values.................................................................................84
Table A.1. Main results of analytical methods .........................................................................136
Table A.2. Shear-uplift interaction x test data ..........................................................................137
Table B.1. Elastic displacement results for studied methods ...................................................151
Table B.2. Comparison of test data, EEEP, and analytical results ...........................................152
Table C.1. Summary of the inelastic assessment for interest points for coupled walls in Method C
...............................................................................................................................................166
Table C.2. Summary of the inelastic assessment for interest points for coupled walls in Method D
...............................................................................................................................................167
Table C.3. Comparison between the experimental and analytical results for Method C...........168
Table C.4. Comparison between the experimental and analytical results for Method D...........169

xv

List of Abbreviations
AB - Angle Brackets
ANSI - American National Standards Institute
APA - Engineered Wood Association
ASCE - American Society of Civil Engineers
ASTM - American Society for Testing and Materials
CLT - Cross-Laminated Timber
CNR - National Research Council
CP - Coupled Wall
CSA - Canadian Standards Association
CWC - Canadian Wood Council
DLT - Dowel-Laminated Timber
EEEP - Equivalent Energy Elastic-Plastic Bilinear Idealization Method
ETA - European Technical Approvals
EWP - Engineered Wood Products
FEA - Finite Element Analysis
FEMA - Federal Emergency Management Agency
GLT - Glue-Laminated Timber
HD - Hold-Downs
IBC - International Building Code
IPST - Internal Perforated Steel Plate

xvi

IN - Intermediate Wall Behaviour
LDF - Low-Density Fiberboard
LLRS - Lateral Load Resisting System
LSL - Laminated Strand Lumber
LVL - Laminated Veneer Lumber
MC - Moisture Content
MDF - Medium Density Fiberboard
NBCC - National Building Code of Canada
NDS - National Design Specification for Wood Construction
NHERI - Natural Hazards Engineering Research Infrastructure
NIED - National Institute for Earth Science and Disaster Prevention
NLT - Nail-Laminated Timber
OSB - Oriented Strand Board
PSL - Parallel Strand Lumber
SDD - Self-Drilling Dowels
STS - Self-Tapping Screws
SW - Single Wall
TP - Triple Panel
UNBC - University of Northern British Columbia
WIRL - UNBC Wood Innovation and Research Laboratory

xvii

List of Symbols
effective shear area
gross shear area
width of the timber board
the total thickness of the m-ply CLT panel
total width of the multi-panel CLT shear wall
panel width
resultant compression force
edge distance
ductility
distance from the edge of the panel to

connector

maximum positive displacement
minimum positive displacement
ultimate displacement
yield displacement
,

yield displacement from the EEEP curve

,

yield displacement from backbone curve
elastic modulus parallel to the grain
elastic modulus perpendicular to the grain
effective bending stiffness

, ,

internal force in each fastener in the vertical joints used for joining panel j
rocking resistance from test data
rocking resistance from analytical methods
compressive strength of timber
maximum positive load
minimum positive load
activation force
load-carrying capacity by rocking
load-carrying capacity by sliding

xviii

horizontal force, i.e., shear wall capacity
yield load
ultimate load
, ∗

value of transitional force in the plastic state between kinematic mode ∗ and
∗ +1

effective shear modulus
equivalent shear modulus of the CLT panel
shear modulus perpendicular to the grain
∥

shear modulus parallel to the grain

ℎ

panel height

∗

transition panel
elastic stiffness at service
ultimate stiffness
dimensionless hold-down tensile stiffness

,

modified stiffness of angle bracket
contribution of the connections’ stiffness in the rotation of panels

,

elastic stiffness of angle bracket in the horizontal direction

,

elastic stiffness of angle bracket in the vertical direction

,

elastic stiffness of hold-down in the horizontal direction

,

elastic stiffness of hold-down in the vertical direction

,

equivalent hold-down tensile stiffness

,

equivalent wall lateral stiffness

,

modified stiffness of hold-down

,

contribution of the connections’ stiffness in the uplift direction

,

contribution of the connections’ stiffness in the uplift of panels at point
vertical contribution of hold-down and angle brackets
elastic stiffness of a fastener in the vertical joint
stiffness of wall-to-wall shear connectors
number of panels in the shear wall
number of angle brackets used in the length of each panel

xix

factored resistance of the vertical joint
number of fasteners per vertical joint
uniformly distributed load applied on the top of the wall
dimensionless uniform vertical load
,

yield strength of angle brackets in the horizontal direction

,

yield strength of angle brackets in the vertical direction
yield strength of fasteners in the vertical joint
ductility reduction factor

,

yield strength of hold-down in the horizontal direction

,

yield strength of hold-down in the vertical direction
overstrength reduction factor
inelastic lateral capacity of the shear wall at the point of interest

, ∗
,

elastic strength related to the vertical joint in kinematic mode ∗
plastic strength of the wall

, ,,

horizontal force in the

, ,,

uplift force in the

angle bracket in the panel j

angle bracket in the panel j

width of the vertical lamellas
,

horizontal force in the hold-down

,

uplift force in the hold-downs

,

tensile force in each bracket

,

increase in the uplift force
panel thickness
thickness of the timber board
lateral displacement due to bending
elongation of the

connector

vertical displacement of panel j at the rotation point
lateral displacement at the top of the wall due to the rocking
lateral displacement due to shear
lateral displacement due to sliding

xx

total lateral displacement of shear wall
vertical displacement due to rocking
position of the neutral axis
∝

coefficient incorporating the effect of multiple angle brackets
coefficient incorporating the effect of compression zone in the panels

∆

lateral displacement at the point of interest

∆

displacement achieved at elastic strength

∆ ,
∆

, ∗

value of transitional displacement in the plastic state between kinematic
mode ∗ and ∗ +1
displacement achieved at plastic strength
rotation angle of CLT shear wall element
friction coefficient
angle bracket’s vertical stiffness ratio

xxi

Acknowledgments
First, I would like to express my gratitude to my supervisor Dr. Thomas Tannert. I am
grateful for the opportunity to work under his outstanding mentorship in such a strong group of
graduate students in an interdisciplinary setting. Thank you for sharing the experience,
knowledge, and positive support to conduct my research and accomplish my career goals.
Likewise, I would like to thank the members of my supervisory committee: Dr. Yuxin Pan
and Dr. Md. Shahnewaz for their insightful comments, as well as Dr. Md Shahnewaz for providing
all the EEEP analyses and calculations on the nailed CLT shear walls and connector test results.
I would like to thank the UNBC technicians Michael Billups and Ryan Stern and undergraduate
research assistant Anthony Bilodeau for their work during the experimental testing. Furthermore,
I am deeply grateful to the University of Northern British Columbia for providing a professional
environment for such a life-changing experience with all the resources needed and all faculty and
staff helping me with my inquiries during my graduate studies. Special thanks to the Mitacs
Globalink Graduate Fellowship and British Columbia Forest Innovation Investment for funding my
studies and research project.
I would like to thank God, who has granted me countless blessings, knowledge, and
opportunities in my life’s journey so far. Special thanks to my wife, parents, and family for their
unconditional love, support, encouragement, for always believing in my potential since the
beginning of my studies, and for their unwavering and tireless support in every path I take to
achieve my educational pursuits and dreams.

xxii

Chapter 1: Introduction
1.1. Motivation
Tall wood structures are on the rise, a phenomenon named the renaissance of wood
construction (Horx-Strathern et al., 2017). The renewed appreciation for wood is driven by the
emphasis on using renewable and sustainable resources in the construction industry. Novel
structural components require the use of engineered wood-based products, such as mass-timber
panels, which can provide better mechanical properties, better shape flexibility, dimensional
stability, and better fire resistance than solid wood. Consequently, mass-timber in general and
cross-laminated timber (CLT) is increasingly used in construction, particularly in tall structures.
CLT has a laminar orthogonal structure, which allows it to sustain loads in and out of the plane
(Brandner et al., 2016) and be used for floor systems, diaphragms, roof systems, and shear walls
(Karacabeyli & Gagnon, 2019).
With increasing building height, the demands on the lateral load resisting system (LLRS)
increase. Shear walls are a common LLRS in timber buildings; CLT is increasingly being applied
in shear wall applications. While the Canadian Standard for Engineering Design in Wood (CSAO86) provides generic design guidance for CLT shear walls, there are no universally recognized
analytical models that can effectively predict the strength and stiffness of CLT shear walls.
Comparisons of existing analytical models versus test findings are required.
1.2. Objectives
The primary objective of this thesis is to evaluate existing analytical CLT shear wall design
approaches and compare them against experimental test results. The specific objectives are to:
• compare existing analytical approaches to estimate strength and stiffness for CLT shear walls;
• identify the suitable analytical methods by comparing their predictions to experimental data.

1

1.3. Thesis Overview
Chapter 2 provides a literature review of current research on CLT shear walls. Chapter 3
compares the existing analytical models for CLT shear walls and includes an academic example
for better comparison. Chapter 4 summarizes previous UNBC nailed shear wall test results and
compares the chosen analytical models against the test data to comprehend CLT shear wall
behaviour better. Chapter 5 summarizes the findings from this research and proposes future work.
1.4. Scope and Limitations
This research focuses on the structural performance of CLT shear walls as LLRS,
specifically, their lateral capacity and anticipated displacements, based on the connectors'
stiffness, strength, and ductility behaviour. The scope of the study includes elastic and inelastic
behaviour of single and multi-panel CLT shear walls, as proposed by the majority of analytical
methods. However, the impact of compression zones, frictional effects, and the biaxial behaviour
of fasteners as part of the shear wall's resistance is not considered in all studied methodologies.
The research investigates previously proposed analytical approaches by comparing their
prediction to experimental test results. The research does not include numerical examination,
such as finite element modelling. The role of connections between the upper floors and the CLT
shear wall, presence of openings, redundancy effect of perpendicular walls or floor underneath,
and CLT panels moisture content is out of this thesis's scope. Fire design, acoustics, other
building physics considerations, cost analyses, and constructability are out of the scope of this
research.

2

Chapter 2: Literature Review
2.1. Construction Industry’s Environmental Impacts
Environmental concerns demand the use of sustainable building practices (Smith and
Coull, 1991). The worldwide urban population has increased steadily over the last decades, from
just over 2.5 billion in 1990 to just under 4 billion in 2015. By 2030, it is expected that 60% of the
world's population will be living in urban areas. Additionally, around 1.6 billion people are expected
to demand suitable and affordable housing by 2025. To address this need following today's typical
building practices, concrete's massive carbon footprint would increase (WCR UN-Habitat, 2016).
These environmental concerns require the use of more environmentally friendly and renewable
building materials, such as timber, to achieve a smaller carbon footprint (Wood Handbook, 2010).
Costs of embodied energy and building sustainability also must be considered (Green and
Karsh, 2012). More carbon is stored in timber than is emitted during the processes of harvesting,
manufacturing, transportation, and installation - making timber structures a viable alternative
(Chadwick et al., 2014). Trees store CO2 through their development and use it for energy
generation (Green and Taggart, 2017). Further to that, the manufacturing and processing of wood
construction components consume fewer resources than concrete or steel (Hossain, 2019). The
thermal insulation efficiency of the building envelope is also a noteworthy point, since wood is a
favorable material for insulation because of its low heat conductivity.
A comparison with sheet metal and concrete houses in environmental metrics revealed
that a wood frame house had lower environmental impacts for five of the six main factors:
embodied energy, global warming potential, air toxicity, water toxicity, weighted resource usage,
and solid waste (CWC, 2004). Construction costs for four different types of commercial buildings
were compared using timber and traditional materials. The building types were a seven-storey
office, an eight-storey apartment, a two-storey aged care facility and a single storey industrial

3

shed. It was found that timber construction was cheaper in all four cases (Dunn, 2015). Wood
building can be cost-effective due to lower on-site labour rates (Kremer & Symmons, 2015). In
addition, many elements of wood construction are prefabricated, and on-site construction time is
also reduced compared to concrete construction.
2.2. Wood as a Structural Material
2.2.1. Solid wood
Wood as a construction material has a lower weight-to-strength ratio than steel and
concrete, hence timber has a higher structural efficiency in terms of the load carried per unit
weight (Gijzen, 2017). Wood is an anisotropic material, with varying mechanical properties
depending on grain orientation (Green and Taggart, 2017), meaning its mechanical properties are
commonly measured in two directions: parallel to the grain and perpendicular to the grain. The
strength properties and stiffness of wood are highly distinct for these directions: high strength and
stiffness parallel to grain, low strength and stiffness perpendicular to grain, as well as low shear
and tension strengths perpendicular to the grain (Green, 2001).
Wood is a hygroscopic material, which means that its properties are highly dependent on
moisture content (MC), and exposure to different environmental conditions will have a significant
impact on its applications. Below the fibre saturation point, the lower the MC, the greater the
mechanical properties of wood, in such a way that if maximum strength is required, it should have
a MC of about 5% (Carll and Wiedenhoeft, 2009). In other words, fewer voids of water will be
present and more material to withstand the loads will exist. Wood is a combustible material and
its behaviour during a fire can be predicted quite reasonably, and the necessary measurements
and cross-sections to maintain a certain level of fire resistance can be determined. The use of
non-flammable surface layers allows for the development of low-flammability structures
(encapsulated mass timber construction), as well as the use of fire-retardant-treated wood.

4

The fundamental challenges of traditional timber construction are its available size,
dimensional stability, combustibility, highly variable properties, and the fact that wood can decay.
As a result, engineered mass-timber products are common in construction to meet new demands
and mitigate these shortcomings. In addition to the benefits of standard wood systems, the
mechanical properties and strength of mass-timber products are improved, as natural defects
such as knots are minimized.
2.2.2. Engineered Wood Products and Mass-Timber
Mass-timber construction uses engineered wood products composed of large, solid wood
panels, columns, or beams that are designed for load-bearing walls, floors, and roofs. The
irregular behaviour of wood is minimized, and technological processing reduces the mechanical
drawbacks of wood. This processing allows for the development of linear elements of virtually any
cross-section and length that can be used as beams or columns, regardless of the size of the
lumber supplied. In other words, large trees harvested from old-growth forests are not required to
produce beams and panels for large-scale applications. This innovative manufacturing approach
improves not only the structural stability and strength of engineered wood products, but also their
resistance to agents like fungi and insects (APA, 2010). Another important benefit to note is the
improved dimensional stability of the cross section when compared to solid wood.
To produce a cross-grain pattern, thin layers, wood strands, or wood fibers are bonded
together to provide strength and stability to the panel, preventing it from shrinking and swelling.
This reduces the likelihood of wood splitting when nailed at the edges and ensures that the panel
has strength and stability in all directions (Youngquist, 1999). A variety of derived wood products
is made by joining strands, particles, fibers, veneers, or boards of wood. For instance, the
engineered wood products in Figure 2.1 would be strong structural members without relying on
the old growth-dependent solid-sawn timber (e.g., Glued Laminated Timber (GLT), Parallel Strand
Lumber (PSL), Laminated Strand Lumber (LSL), and Laminated Veneer Lumber (LVL)). They are

5

products that can be used for floors, roofs, wall panels, and sheathing because their mechanical
properties are homogenous and predictable.

Figure 2.1. Engineered Wood Products a) Glulam; b) PSL; c) LSL; d) LVL (Green and Taggart, 2017)

2.2.3. Cross-Laminated Timber (CLT)
CLT, developed in the European Alps in the 1990s (Mohammad et al., 2012), is a
laminated material frequently made up of an odd number of layers, using wood boards (lamellas)
glued together orthogonally, as shown in Figure 2.2a. CLT is a dimensionally rigid panel with high
stability and strength in both directions. CLT panels provide plentiful advantages when compared
to traditional timber framing materials, offering alternatives to the usage of light-frame and postand-beam construction (Gijzen, 2017). The width of the panels typically ranges up to 3.0 m, the
panels may be up to 18 m long and 400 mm thick. The dimensions of the panels manufactured
may be limited by transportation (Karacabeyli & Gagnon, 2019). The orientation of the outermost
laminations dictates the major and minor strength axes; different numbers of layers are used as
exemplified in Figure 2.2 b).

Apart from its advantageous thermal, acoustic and fire performance, CLT is manufactured
with a high level of prefabrication, and requires only light cranes for erection (Karacabeyli &
Gagnon 2019). Furthermore, it exhibits high axial load capacity for bearing walls due to large
bearing surface area, as well as enhanced connection strength owing to the increased splitting

6

resistance (Gijzen, 2017). CLT is a good material for various construction applications due to its
dimensional stability, high in- and out-of-plane strength and stiffness properties (Hossain, 2019).
Consequently, CLT panels can be used as floors or roofs, in addition to shear walls in multi-storey,
and can compete with concrete slabs when it comes to floor systems.

Figure 2.2. a) CLT layup (Breneman, 2016); b) Major (lengthwise) and minor (widthwise) axes direction
and orientation of the outer fibers (Karacabeyli & Gagnon, 2019)

2.2.4. Timber Connections
A structure can be described as an assembly of members linked by its joints (McLain,
1998); in timber engineering, the joints are usually the most important details. The performance
of the joints will typically affect the structure's strength - their stiffness will have a substantial
impact on its overall behaviour, and component sizes will often be defined by the connectors
rather than the strength specifications of the material itself.
Mechanical fasteners are the most popular type of connector categories used in wood
connections, and there are two types: metal dowel type fasteners, such as nails, screws, dowels
and bolts (shown in Figure 2.3), where the load is distributed by dowel action, and bearing-type
connections, e.g. punched metal plate, shear plates, and split-rings. Since metal dowel type
fasteners are efficient at distributing loads while also being reasonably easy and economical to

7

install, wood members joined using dowel-type fasteners are the most popular mechanical
connection type (Porteous and Kermani, 2013). Given high ductility properties, dowel-type
fasteners are also well suited as energy-dissipative connections, and are often employed to resist
lateral loads, as discussed in section 2.4.

Figure 2.3. Typical timber connections: a) Nails; b) Screws; c) Bolts; d) Self-Tapping Screws; e) SelfDrilling Dowels; f) Nail plate (proHolz, 2003)

Dowel-type fasteners such as nails, screws, and bolts can be loaded in both shear and
withdrawal. Screws exhibit withdrawal capacity, with substantial displacements under loading
(Schneider et al., 2012). When the diameter is greater than 6 mm, holes should be predrilled to
avoid wood splitting and full-threaded screws may be used to improve their strength (proHolz,
2003). Bolts are normally loaded in shear due to their greater diameter compared to other types
of fasteners. The most common and current state-of-the-art steel fasteners are self-tappingscrews (STS) (proHolz, 2003). STS, as the name implies, have the capacity to tap threads into
the material (MTC, 2017). The self-tapping tip allows for easy installation and is designed to
minimize wood splitting force and drive-in torque during installation.

8

2.3. Lateral Load Resisting Systems
2.3.1. Lateral Loads
The loads that a structure can be subjected to are primarily distinguished as gravity and
lateral loads. The gravity loads are predominantly introduced by the weight of the structure, snow
loads, and by occupancy loads, whereas winds and earthquakes may introduce lateral loads.
Unlike gravity loads, which act downward, lateral loads are imposed parallel to the ground, acting
horizontally or even generating an uplift effect. Lateral loads become progressively important
when buildings increase in height.
The building's envelope and the surroundings can be used to estimate wind loads, and
earthquakes can occur either near the edges of the oceanic and continental plates or along faults,
which are cracks in the earth where the ground can unpredictably move in distinct directions at
any time (Wald, 2002). Notably, there are certain areas across the globe with high seismic activity,
such as British Columbia (Natural Resources Canada, 2019).
The weight of the structure determines the magnitude of the earthquake load, and as wood
structures are typically lighter than other building materials, this results in lower earthquake loads
and lower foundation demands (Zhang, 2017). On the other hand, flexible structures experience
larger relative horizontal displacements, which can cause damage to both structural and nonstructural building components. Due to the lack of ductility in seismic design, lack of weight against
overturning forces induced by lateral loads, and possibly lack of stiffness in wind design, a variety
of proposed hybrid timber buildings have been considered. Compared to steel and concrete, wood
structures are more susceptible to wind-induced deflections. When subjected to significant
earthquakes, wood constructions rely exclusively on their connections to provide ductility and
absorb energy (Karacabeyli & Gagnon, 2019).

9

2.3.2. Overview of Lateral Load Resisting Systems
The Lateral Load Resisting System (LLRS) of a structure withstands lateral loads and
transfers them to the foundation. Equally, LLRS must provide stiffness to control lateral drifts
(Smith and Coull, 1991). The design of LLRS with adequate stiffness, strength, and ductility to
handle significant wind and seismic loads is one of the primary challenges for tall wood structures.
Horizontal floor structures and vertical elements are denoted as diaphragms and shear walls,
respectively. A floor diaphragm and two types of walls can be seen in Figure 2.4, one of which is
a lateral wall subject to wind loading, such as a façade, and the other is a shear wall subject to
shear forces. The illustration intends to facilitate the understanding of the load path between the
structural elements. The diaphragm, which behaves as a deep beam, presents tension and
compression at its edges, which distributes the lateral loads to the shear wall, and subsequently
to the foundation. The performance of the CLT shear walls has an equivalent behaviour to those
aforementioned, being the core of this study, and it is described in the following section.

Figure 2.4. Different structural responses of lateral loading (Vessby, 2008)

A variety of LLRS may be used to withstand lateral loads (e.g., moment-resisting frame,
braced moment frame, light frame shear walls, CLT shear walls, and hybrid systems (Chen and
Chui, 2017), see Figure 2.5. Moment resisting frames are made up of a series of beams and
columns, as well as rigid connections. The construction is extremely ductile in this system, and
the open bays allow for modular configuration and open space in the architectural design. Moment
frames, on the other hand, impose greater member cross-sections and could increase the building

10

cost (Chok, 2004). In a braced frame system, beams are attached to a column via hinge links,
and the flexural tension of the beams is not included in the transmission of lateral forces. Instead,
diagonal members and bracing are used to provide lateral resistance and stabilization. The
bracing mechanism converts lateral loads to axial loads in diagonal members, which is more
efficient than moment frames (Chok, 2004). The most significant disadvantage of a braced
structure is that it is incompatible with certain architectural designs.

Figure 2.5. Lateral Load Resisting Systems for timber, steel, and concrete buildings (CCPIA, 2021)

Light-frame wood shear walls are used predominantly in low-rise residential and
commercial buildings in North America. They are typically sheathed with plywood or Oriented
strand board (OSB), nailed to the framing (Hassanzadehshirazi, 2012). Anchor bolts connect the
shear wall to the floor below or to the foundation, and hold-downs are often installed adjacent to
studs or at the corner of wall panels. Anchor bolts are used to connect structural and nonstructural elements to concrete. These bolts transfer tension forces and shear forces between the
elements. On the other hand, hold-downs provide uplift resistance against the overturning
moment imposed on the wall due to lateral loads. This culminates in an effective assembly with
sufficient stiffness and strength to withstand lateral and uplift forces. Because it incorporates the
nails yielding and some limited crushing in the wood, failure in these joints provides ductility to
the building (Bagheri and Doudak, 2020). Non-engineered wood constructions were shown to
have far more damage than engineered wood structures (CUREE, 1998; Hall, 2000; Hall et al.,

11

1996). Improper construction techniques, such as missing hold-downs, a lack of wall-to-wall
straps, insufficient tie-down devices, incorrect nailing, thin walls, and poor-quality control, were
attributed to the damages (Lam et al., 2002).
2.4. Tall and Hybrid Wood Buildings
Recently, timber mid-rise buildings have been constructed worldwide enabled by
engineered wood products. The behaviour of these structures under seismic events has been
investigated, and it has been demonstrated that CLT structures associated with ductile connectors
have good structural efficiency (Popovski et al., 2010).
Many structures demonstrate the sophistication and variety of multi-storey wood
construction, as illustrated in Figure 2.6. In London, the Stadthaus is a 9-storey residential building
constructed in 2007. It is the world's first high-density housing structure made entirely of
prefabricated CLT panels, using platform-type construction. The Wood Innovation and Design
Centre in Prince George, Canada, completed in 2014, consists entirely of wood products. The
slabs and vertical shear walls surrounding the staircase and elevator are made of CLT and LVL
panels. The structure is balloon-framed, and stands at a height of 29.9 meters.
Tall timber structures pose several obstacles: they are commonly more flexible than steel
and concrete structures. Timber hybrid systems are a potential solution to this challenge, such as
Brock Commons at UBC Vancouver, built in 2017, which incorporates a concrete core that acts
as the LLRS with timber carrying all the vertical loads (Poirier et. al, 2016). Using concrete cores
as an LLRS around the elevator or stair shaft may provide a non-combustible barrier in this area
of the building in the event of a fire (Karacabeyli & Gagnon, 2019). With a height of 53 meters and
18 stories, this high-rise structure is Canada's tallest mass-timber structure. There are many other
examples around the world; and many other under development.

12

Figure 2.6. a) The Stadthaus (Hurst, 2020); b) The Wood Innovation and Design Centre (MGA, 2014); c)
Brock Commons (Thomas, 2017)

2.5. Cross-Laminated Timber Shear Walls
2.5.1. Overview
CLT panels are well suited as shear walls in multi-storey buildings because they can carry
lateral loads to the foundation (Lukacs et al., 2019). Considerable research has been conducted
on CLT LLRS as a reflection of its growing use. During in-plane loading, CLT shear walls have
rigid body behaviour, and all deformation occurs in connections which also determine the strength
of the shear walls. Non-dissipative connections should maintain elastic and dissipative
connections should have appropriate ductility. The strength of the panels ought to be larger than
the dissipative connection's ultimate resistance (Karacabeyli & Gagnon, 2019).
Platform-type and balloon-type are the two methods for constructing CLT structures.
Extended CLT walls are erected around the height of the building in balloon-type construction,
and the floor structures of each storey are tied to it. Conversely, the platform-type construction
uses the floor system of each storey as the foundation for the wall system, resulting in a significant
number of walls in the LLRS. The performance of CLT shear wall systems using the platform-type

13

method is the subject of plentiful research (Karacabeyli & Gagnon, 2019). An illustration of single
and coupled CLT shear walls and its main connections is shown in Figure 2.7 a) and b).

Figure 2.7. CLT shear wall: a) single panel and b) coupled panel (Shahnewaz et al. 2019), and c) CLT
connections (i) wall-to-wall and floor-to-floor; (ii) wall-to-floor; (iii) wall to foundation (Brandner et al. 2016)

2.5.2. Connections in CLT Shear Walls
The degree to which a material can withstand plastic deformation under tensile stress
before failure is known as ductility. Low ductility implies that a material is brittle and will fracture
before deforming much under a tensile load, whereas high ductility denotes a material that will
deform before collapsing. In ductile failure, the material deforms, elongates and decreases in
cross section before fracture. By contrast, brittle materials fail suddenly, without any notice. A
ductile concept enables the design of the structure to go deeper into the system's inelastic zone,
allowing the structure to withstand seismic loads more cost effectively. CLT panels have almost
no ductility, making the structural behaviour dependent on the connections (Pei et al., 2016).
Hence, ductility is critical at both the connection and system levels. The parallel panel-to-panel
link is useful for a variety of reasons. Wall-to-wall or floor-to-floor connection, the wall-tofoundation connection, and the wall-to-floor connection are the three types of connections in CLT
shear walls; see Figure 2.7 c).
Relatively stiff vertical joints with high yield strength are typically used to increase the wall’s
lateral stiffness and ensure a monolithic behaviour. This approach is usually adopted in low

14

seismic areas or where wind governs the design intentions. However, panels with low aspect
ratios or panels connected together to behave as the monolithic wall may not exhibit sufficient
ductility (Gavric et al. 2013). When a higher wall ductility is required, e.g., in high seismic regions,
vertical joints are typically designed to yield and dissipate energy.
Depending on loads, mounting possibilities, and aesthetic requirements, different joints
may be used. In combination with nails or screws, LVL or plywood splines can be placed on its
surface or inserted into the CLT panels on one or both sides. For instance, no additional materials
are needed in half-lap or butt joints, and STS are the chosen type of fastener where CLT panels
are joined by half-lapped joints or butt joints, see Figure 2.8 a) and c). Splines can be configured
in a variety of ways, internal, on surface, and double spline are all examples of types of splines,
where doubled shear planes through the connectors is possible using an internal spline. Surface
splines have a disadvantage when it comes to one of CLT's most prized characteristics, aesthetics
(Falk, 2020). Since CLT is a product that builders like to exhibit in a construction, the architectural
design of the connection must be careful defined. Internal connections have the appearance of a
clean association, which is why architects typically like them. The half-lap joint is another typical
form of parallel panel-to-panel connection in Figure 2.8 a).

Figure 2.8. a) Half-Lap joint; b) Spline joint, c) Butt joint (MTC, 2019)

Hossain et al. (2016) used self-tapping screws to examine the performance of a 3-ply CLT
panel-to-panel connection under pure shear loads. Half-lap, surface spline, and butt joints were
the three types of connections that were examined. At each shear plane, the fasteners were
placed in alternate orientations, with half of the STS in tension and the other half in compression.

15

The study revealed that the withdrawal resistance of individual self-tapping screws may be used
to estimate the connection capacity conservatively. For quasi-static monotonic and reversed
cyclic tests, STS placed in double inclination had good and moderate ductility classifications.
Conventionally, L-shaped steel anchorages have been used as hold-downs at the corner
of CLT shear walls to prevent uplifting. The vertical segment is fixed to the walls with nails, while
the horizontal side is attached to the foundation with an anchorage bolt. Angle brackets are used
to join walls and floors; the major purpose of angle brackets, according to Pozza et al. (2018), is
to handle shear forces, even though certain angle brackets can carry both horizontal and vertical
loads. In a platform-type structure, the connections and CLT panels are the two main components
of CLT shear walls (see Figure 2.9). Angle brackets and hold-downs are used to link the CLT
shear walls to the foundation, the concrete podium, or the CLT slab below, using metal fasteners
Shahnewaz et al. 2019). The connections, their stiffness, and their arrangements will dictate the
kinematic motions that CLT walls will experience, another important section of this thesis.

Figure 2.9. Hold-down and shear angle bracket connected to a CLT wall and a concrete floor, showing
the load-carrying direction (SIMPSON Strong-Tie, 2019)

2.5.3. CLT Shear Wall Kinematic Motions
Because of the high in-plane stiffness of CLT panels, rigid body behaviour is commonly
assumed, with shear and bending deformations within the panel being deemed minor in

16

comparison to those observed in mechanical anchors (Casagrande et al., 2016). CLT shear walls
can undergo four kinds of kinematic motions under lateral loading, sliding (rigid body translation),
rocking (rigid body rotation), shear (deformation of the CLT panel) and bending (deformation of
the CLT panel), see Figure 2.10 and Eq. (2.1). The CSA O86-19 provisions restrict the allowed
kinematic motion only to rocking to dissipate energy (Shahnewaz et al. 2019).

Figure 2.10. a) Bending deformation; b) Shear deformation; c) Sliding Deformation; d) Rocking
Deformation (Lukacs et al., 2019)

=

+

+

+

(2.1)

where:
= lateral displacement due to sliding
= lateral displacement due to rocking
= lateral displacement due to shear
= lateral displacement due to bending
The type of connections, their stiffness, and their configurations determine the sliding and
rocking deformations, while the shear and bending deformations are influenced by the different
properties of the CLT product (Flatscher, 2017). As a result, the shear and bending deformations
are often attributed to CLT. Larger vertical loads on CLT walls and a higher height-to-length aspect
ratio of CLT wall segments might enhance the rocking mode. According to Gavric et al. (2015),
these variables also contribute to the self-centering tendency of CLT panels after unloading.

17

CLT is stiffer and does not go through in-plane shear deformation like the racking motion
in light-frame wood shear walls, but rather a rocking deformation. In other words, given the high
rigidity of CLT walls, contrary to light-frame wood shear walls, deformation of CLT panels in shear
walls is small under in-plane lateral loadings, therefore all deformation and energy dissipation
capacity must be established by their connections (Popovski et. al, 2010 and 2012).
Rocking behaviour is most common when a wall is made up of many segments with a
relatively high (usually between 2:1 and 4:1) segment height-to-width aspect ratio (Nolet et al.,
2019), whereas sliding deformation in the angle brackets is most common in CLT panels with a
low aspect ratio (Deng et al., 2019). The contribution of in-plane panel shear and bending
deformation is significantly lower in most shear wall configurations than the deformations caused
by sliding and rocking, which are regulated by steel connections that generally have a much softer
behaviour (Wallner-Novak et al., 2013; Hummel, 2016; Vogt et al., 2014, Flatscher 2017). A
complete lateral deflection occurs when the shear wall is subjected to a lateral force on the top of
the CLT wall (Henriksson, 2019). In Figure 2.11, along with Eq. (2.2), it is shown how to calculate
the lateral displacement induced by a rocking motion using the small-angle approximation.

Figure 2.11. Lateral deflection due to rocking (Henriksson and Rosenberg, 2019)

18

= ℎ.

= ℎ.

(2.2)

where:
= lateral displacement due to rocking
= vertical displacement due to rocking
= rotation angle of CLT shear wall element
According to Casagrande et al. (2017), three kinematic behaviours may be identified
based on the mechanical properties of connections and the applied loads: i) coupled-wall (CP),
where each panel has one centre of rotation; ii) single-wall (SW), where the whole wall has only
one global point of contact, and iii) intermediate behaviour (IN), which is a specific situation when
only few panels are in contact with the ground, as shown in Figure 2.12. The rocking behaviour
was found to have higher ductility and ability to dissipate energy in the panel-to-panel connection,
but lower stiffness and strength have been observed compared to single walls (Gavric et al.,
2015). Thereby, verifying the previous research that developed and spread CLT shear walls is
vital for further understanding and grasp its nuances.

Figure 2.12. Different types of rocking behaviours (a) Coupled-Wall Behaviour; (b) Intermediate
Behaviour; (c) Single-Wall Behaviour (Nolet et al., 2019)

2.5.4. Previous Research on CLT Shear Walls
The SOFIE project (Ceccotti et al. 2006) was the broadest endeavour to study the
behaviour of CLT buildings, including building physics, fire, durability, and earthquake resistance.
The project's goal was to undertake experimental testing on full-scale CLT structures that were

19

subjected to earthquake loading using a shaking table, see Figure 2.13 a). Connection system
configurations, including the types and numbers of fasteners, were found to have a significant
impact on the behaviour of CLT walls. According to the findings, the connections dissipated
energy, as well as governed the design, whereas the CLT panels virtually worked as rigid bodies
with high stiffness load-deformation curves.
Popovski et al. (2010) conducted a series of monotonic and cyclic experiments to explore
the seismic performance of CLT shear walls, using three distinct aspect ratio configurations and
four different types of angle brackets. Different fasteners were used in the connecting systems to
comprehend how they affected the lateral resistance of the walls. It was discovered that CLT walls
with steel brackets were sufficient, using hold-downs at both ends of the wall enhanced the
efficiency considerably, and shear walls having a larger aspect ratio could carry more load. The
step joints on the two CLT panel configurations allowed for a greater contribution of the walls to
the shear wall system's deformation, resulting in larger deformations.
Popovski and Karacabeyli (2012) investigated CLT shear walls with the primary goal of
determining the structural parameters of typical CLT shear walls, known as ductility factors.
Aspect ratios of panels, connection types, and opening patterns were among the factors
evaluated. According to the findings, the rigidity of the walls increased as the vertical loads
increased. The authors proposed

and

factors of 2.0 and 1.5, respectively, based on the test

findings. It was also determined that employing nails in discrete hold-downs would improve
seismic performance by increasing the system's ductility.
Gavric et al. (2013) used cyclic loading on CLT walls to determine their energy dissipation
characteristics. Coupled wall behaviour was shown to have lower elastic stiffness and strength
capacity than single wall behaviour. This behaviour, on the other hand, demonstrated greater
displacement capacity and ductility. The major sources of wall displacement were discovered to
be sliding and rocking motions. Rocking behaviour was recommended since the walls present

20

self-centering behaviour. According to the findings, hold-downs at the edges and a vertical load
on the top of the wall were used to limit the displacement, and the hold-downs should be employed
as part of the energy dissipative joints while the angle bracket is still in the elastic range.
Sustersic et al. (2015) examined the seismic performance of a four-storey CLT structure.
They created an FEA model of the building in SAP2000 (Computers and Structures Inc. 2013)
and undertook nonlinear dynamic studies on it. Smaller wall segments joined by vertical
connections dissipated more energy and have improved seismic performance.
Using cyclic testing, many SW and CP CLT wall configurations were examined by Gavric
et al. (2015). All critical design parameters were evaluated, including stiffness, strength, ductility,
strength impairment, and comparable damping ratios. While in-plane deformations of CLT panels
were negligible, local connector failure was observed. The positive impact of the vertical load was
also shown to be considerable. The number of screws used in vertical connections between
adjacent wall panels also influenced the kinematic behaviour of CLT walls. Finally, their findings
suggest that simpler models which ignore the shear capacity of hold-downs and the tension
capacity of angle brackets considerably underestimate the resistance and displacement capacity.
Yasumura et al. (2015) studied a low-rise two-storey CLT structure under reverse cyclic
loading. The building had two types of walls with openings and the capacity of the structures was
found to be up to 80% greater than the design load, according to the test findings. The larger
wall's stiffness was reported to be more than double that of the short wall. The elastic design
process produced a conservative design. Consequently, nonlinear FEA might be a valuable
technique for maximizing CLT structure design.
Popovski and Gavric (2016) tested a two-storey CLT structure at full size with the goal of
determining its behaviour under quasi-static and cyclic loading, as shown in Figure 2.13b. The
number of screws used in perpendicular wall-to-wall connections was said to have no significant
influence on total resistance, although it did result in an increase in lateral displacement. The

21

number and kind of fasteners, as well as the aspect ratio of panels, were discovered to influence
the behaviour and manner of deformation of CLT walls. This finding has repercussions for several
of the assumptions made during the development of the analytical model in their current study.
Latour and Rizzano (2017) studied the seismic behaviour of CLT structures with both
traditional and novel connections such as the "XL-Stub" under monotonic and cyclic
circumstances. When compared to typical hold-downs, the connections exhibited a greater
energy dissipation and displacement capability. Reynolds et al. (2017) and Amini et al. (2018)
tested CLT shear walls and found that the failure of the systems occurred at the connections, with
negligible in-plane deformations of the CLT wall panels. Reynolds et al. (2017) determined that
rigid-body movement of the panels controlled the movement of the whole shear wall under
ultimate loading, and that the screwed half lap connection was successful in allowing the two
panels to behave compositely. The most accurate design approach for the maximum load system
that the wall can withstand implies that the panel rotates around the wall's compression edge.
This approach, however, presupposes the unreasonable assumption that compression is
transferred at a single point.
Using the FEMA P-695 method, Amini et al. (2018) proposed a procedure for determining
seismic design parameters for CLT shear wall systems. FEMA P-695 is a procedure for estimating
global seismic performance factors such as the response modification coefficient, system
overstrength factor, and deflection amplification factor. The methodology is intended to set
minimum acceptable design criteria for code-approved seismic-force-resisting systems.
Connectors behaved as predicted, with the nonlinear behaviour concentrated in the connections.
Gravity load tests on the walls revealed that when the gravity force increases, both stiffness and
strength increase. 4:1 aspect ratio had substantially less stiffness but more deformation capacity
than 2:1 aspect ratio due to the panel's principally kinematic motion being rocking rather than a
combination of rocking and sliding mechanisms.

22

The Natural Hazards Engineering Research Infrastructure (NHERI) conducted two-storey
mass-timber shaking table experiments to better understand the LLRS behaviour of various
distinct CLT shear wall configurations (van de Lindt et al., 2019), as shown in Figure 2.13 c). The
gravity system of the structure in these tests was made up of glulam beams and columns, as well
as CLT diaphragms for the floor and roof. Shear walls of various types, including non-load bearing
and load bearing, were examined. The shaking table was used to evaluate a range of CLT shear
wall systems, as well as to recreate multiple earthquake ground movements of differing intensity.
The findings suggest that it is feasible to combine a CLT rocking-wall system with a heavy-timber
gravity system to obtain a robust performance during repeated earthquakes.

Figure 2.13. a) SOFIE project (Ceccotti et al., 2013); b) CLT house before loading (Popovski and Gavric,
2016); c) NHERI Shake Table (Pei et al., 2019)

2.5.5. Analytical Models for CLT Shear Walls
CLT shear walls are designed by determining their load-carrying capacities and stiffness.
The multiple contributions of the shear wall deformation are used to develop analytical techniques.
Equilibrium equations based on wall geometry, external loading, and connection characteristics
are used to assess the load-carrying capacity and stiffness of CLT shear walls. Understanding
the mechanical properties of CLT panels is necessary for the design of CLT shear walls.

23

Shahnewaz et al. (2017) provided an analytical formulation for a single-panel CLT shear wall that
takes into consideration the bi-directional behaviour of shear connection.
Casagrande et al. (2017) studied the kinematic models of multi-panel CLT shear walls
under lateral loading. The minimum potential energy principle, described as a relation of the
stiffness of the hold-down and wall-to-wall joints were used to derive analytical equations of elastic
stiffness and load bearing capacity. It was reported that the stiffness of the hold-down and vertical
joints affects the deformation process of CLT panels. The multi-panel CLT wall system rocks
because the wall-to-wall connections are less stiff than the hold-down system when relatively rigid
hold-down was used. The vertical load and the number of CLT panels function as effective
parameters on the kinematics of multi-panel CLT walls when the CLT panels are provided with
flexible hold-downs, where panels exhibit progressively increasing uplift (Casagrande et al. 2017).
Lukacs et al. (2019) analyzed and compared various existing methods for determining the
load-carrying capacity and stiffness of CLT shear walls. Most approaches employed the static
equilibrium equation to build analytical processes, whereas CLT walls were handled as rigid
panels, and the deformation of the CLT wall system was mostly reliant on the characteristics of
the connections. Angle brackets and hold-downs, which only resist sliding and uplifting, were
taken into consideration in all approaches.
Shahnewaz et al. (2019) investigated the lateral resistance of CLT shear walls for various
connection configurations using CLT shear walls with platform-type construction, being the major
interest of the analytical formulation. On single and coupled CLT panels, the connection system
was studied where the aspect ratio of CLT shear walls was used to calculate the ratio of sliding
to rocking deformation for each arrangement. Shahnewaz et al. (2019) compared the analytical
findings produced from the theoretical formulations to the prior experimental results, and similar
studies will be conducted in this thesis. The state-of-the-art of analytical methods associated to
strength and stiffness of CLT shear walls under lateral loading is presented in Chapter 3.

24

2.6. Design Provisions for CLT Shear Walls
2.6.1. Design Provisions in Canada
The objective-based National Building Code of Canada (NBCC 2015) defines and
regulates the structural design of buildings in Canada. Each performance criterion is linked to a
target, and code compliance is achievable through acceptable solutions and feasible "alternative
solutions". These "alternative solutions" encompass materials or designs that differ from
acceptable solutions but must meet the same minimum performance standards as the applicable
approved solution (Tannert, 2019). Applying force-reduction factors

and

for ductility and

over-strength, respectively, reduces design force levels from the elastic level. The NBCC provides
values for these two R factors for various types of seismic LLRS.
In 2014, CSA O86 Clause 8 had been reserved for design specifications that would cover
CLT manufactured in compliance with the ANSI/APA PRG 320 standard (CSA 2014). A
supplement to CSA-O86 was issued two years later in 2016, including design provisions for CLT
components and connections (CSA 2016). For the design of CLT LLRS, a new Clause 11.9
“Design of CLT shear walls and diaphragms” was created. These provisions are restricted to
platform-type constructions not exceeding 30 m in height in low seismic zones and 20 m in high
seismic zones (i.e., balloon framing is omitted). The shear resistance of CLT shear walls and
diaphragms is regulated by their boundary connections, where each panel is assumed to operate
as a rigid body. Within these limitations and aspect ratio requirements,

and

as 2 and 1.5, respectively. Any other alternative should be taken as

= 1.3.

.

can be taken

The energy dissipative connections must also be designed in such a manner that: i) yield
mode governs, ii) at least moderate ductility at the connection level is established, and iii)
adequate deformation capacity is provided so that the CLT panels can develop their anticipated
kinematic motion. Sliding, as well as simultaneous rocking and sliding, should be avoided and

25

can no longer be used to account for energy dissipation, with values between 2:1 and 4:1 limiting
the aspect ratio of all CLT shear wall segments considered part of the LLRS. Previously, discrete
hold-downs could be designed as a dissipative connection, but the new standard demands that
they be designed as a non-dissipative connection. Additionally, the resistance of connections
between the shear walls and the foundation or floor, as well as connections between individual
panels, should be used to determine the governing lateral resistance of CLT shear walls.
CSA O86 includes comprehensive guidelines for the capacity design of CLT platformframed buildings. Capacity design techniques allow designing a structure that can withstand
deformations under earthquake loading, thereby absorbing seismic input energy and giving an
economical design. This approach assures that selected ductile components experience all
inelastic deformations, while brittle components are engineered and overdesigned to remain
intact. The only dissipative components of CLT shear wall systems should be vertical joints
between walls and shear connections of shear walls to foundation and shear walls to floors
underneath. As a result, hold-downs must prevent inelastic deformation. According to capacitybased design, all non-dissipative connections, as well as the CLT panels are intended to remain
elastic under the force and displacement demands that are created when energy-dissipative
connections reach the 95th percentile of their ultimate resistance or target displacement.
Nonetheless, CSA O86 does not yet specify any precise techniques for estimating LLRS
resistance or even how to facilitate the intended kinematic mode in the presence of vertical loads,
particularly for multi-panel CLT walls, where the overall behaviour may be a consequence of
connection behaviour. Finally, according to CSA O86, deflections of CLT shear walls shall be
calculated using recognized mechanics techniques that must account for panel sliding, rocking,
and support deformation. However, there is no particular advice on this challenge other than that
the calculations must account for shear wall and connection deformations, whereas CLT panels
can be considered as rigid bodies.

26

2.6.2. Design Provisions in the United States
In the United States, seismic design is done using one of many techniques, including the
Equivalent Lateral Force Procedure (ELFP) defined in ASCE 7 (ASCE 7-16 2016). The creation
of a CLT chapter in the 2015 version of the National Design Specification for Wood Construction
(NDS) and acceptance of CLT in the 2015 International Building Code were encouraged by the
ANSI/APA PRG320 (ANSI 2017) standard for performance-rated cross-laminated wood. Unlike
traditional wood-frame shear wall and diaphragm systems, the design shear strength of CLT
shear walls and diaphragms is determined directly based on engineering mechanics principles,
using provisions of the National Design Specification for Wood Construction for connection design
and CLT panel design. Deflection estimates are based on principles of engineering mechanics or
derived from testing should account for all sources of deflection including panel bending, panel
and/or connector shear, and fastener deformation.
The International Building Code (IBC 2015) enabled CLT to be used in Type IV (heavy
timber) construction when the following conditions are satisfied: i) CLT may be used in exterior
wall assemblies with a fire rating of two hours or less if it is covered by fire retardant treated wood
sheathing of at least 15/32 inch thickness, gypsum board of at least 0.5 inch thickness, or a noncombustible material. The walls must have a minimum thickness of 6 inches; ii) floors made of
CLT must be at least 4 inches thick and continuous from support to support; iii) roofs made of
CLT must not have any concealed spaces. Roofs made of CLT must be at least 3 inches thick
and continuous from support to support.
The recently published 2021 IBC contains provisions to certify mass timber construction
under the IBC Type IV, surpassing the NBCC provisions regarding maximum building height,
building area, occupancy groups, and interior exposed timber. The 2021 IBC included three new
building types based on these proposals: Type IV-A, IV-B, and IV-C - allowing the use of mass
timber products or non-combustible materials. These new building types are based on the

27

previous heavy timber construction type (renamed Type IV-HT) but with superior fire resistance
ratings and non-combustible protective levels. The code established provisions for mass timber
buildings up to 18 storeys of Type IV-A construction for business and residential occupancies.
The proposals resulted in a complete set of code revisions for mass timber buildings in the IBC,
designed using a rational performance-based methodology.
Although the code incorporates lateral timber systems, there are significant restrictions.
Wood frame plywood shear walls are practically the only allowable timber lateral system in the
IBC and ASCE 7-16. In addition, CLT shear walls are still not included in either the 2021 IBC or
the ASCE 7-16. CLT lateral systems are currently only addressed in the NDS Special Design
Provisions for Wind and Seismic (SDPWS) for 2021. Although provisions have been proposed for
incorporation into ASCE 7-22, the existing version of ASCE 7, ASCE 7-16, does not incorporate
CLT shear walls or diaphragms.
2.6.3. Design Provisions in Europe
EC8 (EN1995 2004) provides seismic design provisions for Europe; it accounts for a
structure's energy dissipation capacity by dividing the seismic forces obtained from a linear static
or modal analysis by the "behaviour factor", , corresponding to a ductility class, which accounts
for the structure's non-linear response. Given the currently limited design assistance for CLT,
suppliers certify their products through European Technical Approval (ETA). Except for the
product regulation, there are no design rules for CLT buildings, despite the fact that CLT was
created in Europe more than 20 years ago. However, CLT will be included in the upcoming
Eurocode 8 (Follesa et al. 2015; Follesa et al. 2018).
The present concept is to classify CLT structures as dissipative structures with two
behaviour factor

values for medium and high ductility classes. Structures built of monolithic CLT

wall elements will be distinguished from buildings comprised of ‘segmented' CLT walls consisting

28

of numerous panels linked by mechanical fasteners such as STS. It is worth noting that there will
be no restriction on the number of stories that can be constructed.
The structure is to be assembled following a capacity-based methodology, with certain
parts intended for energy absorption and others given with overstrength to remain elastic. The
following parts should be built with overstrength: i) CLT panels, ii) joints between floor panels, iii)
joints between floors and walls below and (iv) joints between perpendicular walls. The shear joints
between walls and the floor below them, as well as between walls and the foundation, and the
hold-downs installed at wall ends and at wall openings, are all designed to dissipate energy.
Moreover, within the segmented shear walls, the vertical connections between successive wall
panels should be considered dissipative (Follesa et al. 2015). Despite broad consensus that
employing the capacity-based design principle is required to ensure global behaviour involving
ductile failure mechanisms, the applicability of such an approach has been affected by a lack of
a clear analytical approach in contemporary international codes (e.g., Eurocode 8 and CSA O86).
2.6.4. Recent Proposal for Capacity-Based Design of CLT Shear Walls
A recent proposal by Casagrande et al. (2021) provides a methodology for a yielding
hierarchy between dissipative and non-dissipative connections. The suggested capacity-based
design approach is based on three ductility classes. Furthermore, three different over-strength
factors are defined:

, to protect non-dissipative components when dissipative connections

yield; an over-strength factor;

, to ensure a sequence of yielding amongst dissipative

connections; and an over-strength factor;

, to protect shear-connections and limit sliding. The

authors suggest that the previous strict condition of 95th percentile may not be necessary for
establishing the yielding sequence between dissipative connections. For that reason, they
recommended that only non-dissipative components should meet the 95th percentile criterion.

29

The Level 1 of the ductility class is assigned to CLT structures consisting of either singleor multi-panel shear walls that are meant to act elastically and do not require the dissipative
components to be defined, in other words, all elements are designed not to yield. Shear walls with
a single-panel or multiple panels that exhibit predominantly SW rocking are classified as Level 2,
with hold-downs assumed to be the primary dissipative element, though in the case of multi-panel
shear walls, vertical joints may be assumed to act as either a dissipative or non-dissipative
component. A Level 3 of ductility class occurs when connections dissipate energy predominantly
through fastener yielding, and the kinematic behaviour of the wall is CP rocking. Imposing a
requirement that hold-down yields after the vertical joints have already yielded guarantees that
CP, rather than SW, rocking behaviour is achieved, either Level 2 and 3 demand the over-design
of components with restricted ductility, i.e., shear connections (Casagrande et al., 2021).
2.7. Summary of Literature Review
Timber is a suitable building material with a low environmental impact. CLT is a prominent
option among the many mass-timber products, as it can compete with concrete when it comes to
floor systems applications, because of two-way strength and its dimensional stability. In shear
wall applications, CLT panels cannot dissipate energy during earthquakes, requiring further
understanding of its connections and analytical approaches to predict their behaviour.
While hold-downs prevent uplifting, angle brackets may be activated with both sliding and
rocking of CLT walls. Ignoring the shear capacity of hold-downs and the tension capacity of angle
brackets noticeably underestimates the resistance and displacement capacity of the system. For
CLT shear walls, vertical joints are also supposed to be the primary energy dissipation system
where yielding is expected to occur. Multi-panel shear walls demonstrate better ductility and
energy dissipation capacity. The panels with a greater aspect ratio have much less stiffness but
significantly more deformation capacity. This is attributable to its kinematic motion, which is mostly
rocking rather than a combination of rocking and sliding mechanisms.

30

While accurate determination of the in-plane stiffness of CLT wall panels is essential for
designing a CLT structure subjected to lateral loads, no universally acknowledged criteria exists
at this time. CSA O86 provides design provisions for CLT shear walls in platform-type structures.
For a reliable design of CLT structures, it is critical to understand and quantify the actual behaviour
of CLT walls under lateral loads, i.e., their stiffness and strength. Nevertheless, CSA-O86 does
not yet give any specific procedures for this purpose, nor how to facilitate the intended kinematic
mode, particularly for multi-panel walls where the behaviour is a function of connection behaviour.
As a result, comparing current approaches for estimating the resistance and stiffness of
CLT shear walls assemblies would assist engineers and practitioners in designing CLT platformtype structures effectively. By comparing existing analytical methods to experimental data, the
current study aims to make a practical contribution to this crucial research gap.

31

Chapter 3: Analytical Methods for CLT Shear Wall Design
3.1. Strength Assessment Methods
3.1.1. Overview
This section provides an overview of the analytical approaches to estimate the strength of
CLT shear walls. Selected models will be discussed in detail in the next subsections.
Schickhofer et al. (2010) incorporated a triangular compression and tension zone. The
length of the compression zone, the maximum compressive force at the panel corner, and the
load in the tensile bracing are the three unknowns in the problem. There are two ways to find the
unknowns: one assumes that the tensile bracing achieves its ultimate elastic capacity, while the
other assumes that the corner of the panel reaches its ultimate compressive capacity.
Pei et al. (2012) analyses the tensile strength of all connections presented in the shear
wall. This approach is likely to be more accurate in predicting wall capacity because it considers
the axial stiffness of all connections, which corresponds to the realistic behaviour of angle
brackets that function in both directions. The elongation of the connector also shows a better
manner to evaluate the distribution of forces compared to other methods, where the elongation
itself attracts the load depending on the stiffness of the connection.
Tomasi (2013) and Wallner-Novak et al. (2013) addressed the effect of compression
zones calculating the position of the neutral axis to reach the equilibrium. Due to friction
considerations, Wallner-Novak et al. (2013) also tends to estimate a higher shear capacity, as
well as reduction of the vertical load and proposing a different length of the compression zone.
Gavric and Popovski (2014) proposed an iterative methodology to evaluate CLT shear walls for
multiple design models and applying the shear-uplift interaction, utilizing vertical joints and
anchored to the floor using hold-downs and angle brackets.

32

Tomasi (2013) and Wallner-Novak et al. (2013) included an internal lever arm between
the tensile bracing and the compression zone, the length of which is determined by the size of
the compression zone. Only the connector furthest from the point of rotation is deemed to resist
rotation, whereas the angle brackets only resist sliding. The practicality of these approaches
allows for a rapid examination of the lateral strength of a CLT shear wall. Pei et al. (2012) and
Gavric and Popovski (2014) take the vertical capacity of the shear connections into account. The
vertical strength of angle brackets must be determined, which might be difficult to accomplish in
some situations since these connections are generally employed primarily to prevent sliding.
Reynolds et al. (2017) use an approach similar to Pei et al. (2012); however, a triangular
tensile capacity distribution with the incorporation of a compressive zone is added. The lateral
load-carrying capacity is determined by the overturning resistance of connections that are not
required to resist sliding, implying that the vertical capacity of some angle brackets is utilized to
resist overturning. Only the angle brackets outside of the tensile zone are used to restrict the wall
from sliding and the number of overturning-resistant connections has been expanded to include
all connectors outside of the compression zone.
Tamagnone et al. (2018) offered a sectional design approach limited to single monolithic
CLT walls. Casagrande et al. (2017) established an analytical technique for multi-panel CLT shear
walls based on the minimum potential energy method, which encompasses the impact of vertical
joints and uplift in the hold-downs. Shahnewaz et al. (2019) proposed the in-plane resistance for
both single and coupled walls for different positioning of the brackets. Nolet et al. (2019)
developed a more complete approach for multi-panel CLT shear walls, accounting for the bi-linear
elastic-perfectly plastic properties of hold-downs in uplift and in the vertical joints. Masroor et al.
(2020) developed an elastic-plastic analytical approach for multi-panel CLT shear walls. The
model considers the hold-downs and angle brackets' bi-axial influence, as well as the impact of
the compression zone in the panels.

33

3.1.2. Pei et al. (2012)
Pei et al. (2012) interpret the rotation of a CLT panel as a rigid body rotation around its
corner (Figure 3.1). This kinematic model may be used for connections utilized to resist panel
sliding and uplift/rocking. This approach takes into consideration the resistance of each connector
as a function of its position and the wall geometry. The method assumes: i) the wall exhibits inplane rigid body behaviour; ii) when loaded from the side, the wall rotates about its corner with
lateral displacement so

=

; iii) there is no lateral sliding of the wall; iv) a vertical force can

act at the wall's centre; v) the connections are deformed according to the panel's rotation.
The elongation and stiffness/strength of the connection are taken into account while
determining the lateral force. The tensile strength of the connection is related to its distance from
the panel edge. The connection displacement is distributed in a triangular distribution. The furthest
connection (the right hold-down) is assumed to have reached its elastic tensile strength. The
remaining connections will be extended in a triangle distribution, and their tensile force
proportional to their distance

from the rotating point,

,

will be

in this thesis.

Figure 3.1. Shear wall layout for Pei et al. (2012) method (Lukacs et al., 2019).

34

The calculating steps are: i) compute the connector's tensile strength
point of rotation; ii) compute the hold-down's elongation
capacity

,

of the distant

based on its vertical stiffness

, ; iii) using a triangular distribution, compute the elongation

and

of each connection; iv)

using the stiffness of each connection, compute the tensile forces; v) compute the total lateral
load in terms of total rocking resistance
∑

, Eq. (3.1).

, .

=

+

.
2

(3.1)

.

ℎ

3.1.3. Tomasi (2013)
Tomasi (2013) replaced the nonlinear stress distribution for wood in the compression zone
with a rectangular stress block (Figure 3.2). The size of the “stress block” is specified as 0.8x,
from which a resultant compression force C, in Eq. (3.2), is computed based on the compression
resistance parallel to the grain

and the width of the vertical lamellas

calculated via equilibrium using the hold-down's tensile capacity

in Figure 3.2 is the hold-downs tensile capacity

. +
0.8. .

,

, with 0 <

=

, .

. It is worth

, .

(3.2)

= 0.8. . .

=

is

, , see Eq. (3.3). The connector

edge distance is denoted as . The sliding resistance is calculated by
mentioning that

. The neutral axis

≥

2

(3.3)

The foundation is assumed rigid compared to the CLT shear wall. The total lateral force
on the wall is then computed using the expression in Eq. (3.2) for the resulting compressive force
and the expression in Eq. (3.3) for the neutral position , determined by rotation equilibrium in
the centre of the panel, yielding the Eq. (3.4) and (3.5).

35

−

.ℎ +

,

=

2

,

−

2
+

−

+

2

. +

,

− 0.4.

2

−

= 0

( . +
2. .

(3.4)

, )

(3.5)

ℎ

Figure 3.2. Description of the “stress block” method (Lukacs et al., 2019)

3.1.4. Wallner-Novak et al. (2013)
Wallner-Novak et al. (2013) suggested a similar concept to that presented by Tomasi
(2013) with a different compression zone length

equivalent to 1/4 of the wall width (Figure 3.3)

and a 10% decreased effect of the vertical load

due to the partial safety factor for permanent

loads. Eq. (3.7) comes from rotational equilibrium. Friction is accounted for with a friction
coefficient of 0.4 of the vertical load to the sliding resistance of the shear wall Eq. (3.6) in contrast
to the general sliding resistance
The connector edge distance

computed as the sum of the resistance of the angle brackets.
states as same as .

36

Figure 3.3. Shear wall layout for Wallner-Novak et al. (2013) method (Lukacs et al., 2019)

=

=

+ . (0.9. ).

(3.6)

0.9. .
3
. 4. −
2
ℎ

(3.7)

,

,

+

3.1.5. Gavric and Popovski (2014)
The majority of methods predating the work by Gavric and Popovski (2014) assumed that
the lateral resistance of a CLT wall is the sum of the shear resistances of all bottom connections.
Although this approach is straightforward, it ignores the fact that the kinematic behaviour of CLT
walls under lateral loads is a combination of rocking and sliding of the entire panel or, in the case
of multi-panel walls, comes from each individual wall segment. Therefore, connections at the
bottom of the wall are subjected to a combination of shear and uplift loads, see Figure 3.4a. An
unreduced factored lateral resistance is computed and then iteratively decreased to reach the
“real” lateral load

until the interaction (circular or triangular) of shear and tension forces in angle

brackets is below its limit, see Figure 3.4d and Eq. (3.8):

37

,
,

Where

,

+

,

(3.8)

≤1

,

is the horizontal force in the bracket,

,

is the vertical force in the bracket and

is the factored lateral resistance of the angle bracket. Connection behaviour was assumed to
be linear elastic since models deal with forces that are at or below the calculated resistance
values. Factored resistance of CLT walls under lateral loads was regarded to be accomplished
when the first bracket or hold-down at the bottom reaches its factored resistance, while the vertical
joints have already reached their factored resistance. The friction forces in the wall to floor and
foundation were neglected. Each shear bracket was also expected to take an equal share of the
total shear force applied to the wall. On the other hand, it was assumed that each uplift connector
contributes with a triangular distribution of the total uplift force, based on its position in the wall
relative to the point of rocking and the proportion of connection stiffness ratios; see Figure 3.4a.

Figure 3.4. a) Analytical models used for determining the lateral resistance of CLT shear walls; b)
Distribution of reaction forces in a coupled CLT wall; c) Iterative procedure; d) Circular shear-uplift
interaction (Gavric and Popovski, 2014)

Connector factored resistance values (

for hold-downs and

for brackets) were

determined by multiplying the factored lateral resistance of one fastener (nail or screw) by the
38

number of fasteners utilized in one connector. The number of nails in hold-downs and brackets
must be chosen so that yielding occurs in the nails rather than the connections. Experiments with
CLT metal connections (Gavric et al., 2015) showed that an equivalent amount of load may be
transmitted in both the tension and shear. Consequently, in the kinematic analytical models
,

,

=

, equivalent strength characteristics of brackets in uplift and shear directions were assumed.

Hold-downs are assumed to have no shear resistance, thus
of the right hold-vertical down's response may be ignored
of the vertical joint is

,
,

=

= 0 and the contribution

,

= 0. The total factored resistance

. To calculate the lateral resistance, see Eq. (3.9), following steps are

required: i) determine the sliding resistance
min; iv) assume a lower

; ii) determine the rocking resistance

resistance; v) determine the decreased

,

and

; iii) specify

, ; vi) iterate until

the interaction of shear and tension in the most loaded angle bracket is ≤ 1.
=
= min

.
=
+
4. ℎ

, .
ℎ

+

,

ℎ.

.

,

+

+

+

+

(3.9)
2. ℎ

3.1.6. Casagrande et al. (2017)
Casagrande et al. (2017) proposed an analytic concept based on rigid body rotation and
static equilibrium between internal forces and the overturning moment to estimate the loadcarrying capacity of SW CLT panels. The force in the hold-down attributable to a lateral and
vertical load is computed, with the point of rotation assumed to be at right-bottom corner. The
suggested model in this study is restricted to the rocking behaviour of the wall since it overlooks
the shear-uplift interaction. Each vertical panel-to-panel joint is defined by

fasteners and elastic

springs of stiffness

, .

, and its equivalent hold-down tensile stiffness

The SW model's

equivalent stiffness mechanically reflected a system in which the hold-down and vertical joints
acts in series, whereas in CP they act in parallel. Based on the premise that all panels have the

39

same top horizontal displacement, they will have the same rotation , which reflects the system's
kinematic behaviour.
The SW model requires that all vertical displacements of the relative centre of rotation of
the panels,

, are positive. On the other hand, by requiring a positive vertical reaction at the

centre of rotation of each panel, it is guaranteed that the criterion for describing a CP is achieved.
Following both assumptions, it yields , described as

, /

. , defined as the dimensionless hold-

down tensile stiffness. Figure 3.5 provides all parameters for the calculations and the deformed
shape of SW and CP CLT shear walls.

a)

b)
Figure 3.5. a) Deformed shape of SW; b) Deformed shape of CP (Casagrande et al., 2017)

40

In CP, fasteners are subjected to the same vertical force,

, , , , regardless of which panel

is investigated, while the horizontal force is zero. It should be observed that in the SW behaviour,
fasteners placed in the same panel have identical internal force, as in the CP behaviour, but the
internal forces of vertical joints between different panels are not equal – the forces increase along
the panels. Independent of the value of , the CP model is always obtained in the situation where
≥ 1 (stiff hold-down). When

< 1 (relatively flexible hold-down), both models can be achieved

depending on the value of . At this point, the first panel with an absolute centre of rotation is
described as a transition panel

∗

, and an intermediate condition might occur. When

= 0, the

CP model is easily obtained by requiring that the hold-down stiffness be greater than the vertical
joint stiffness. The consistency criteria for the CP and SW are only complimentary when
and no vertical load

= 0 is applied.

When the activation force

is higher than the externally applied force, the lateral

displacement of the wall is zero. Because of the equivalent wall lateral stiffness
the force versus displacement curve is defined by a straight line when

,

is constant,

≥ 1, and the CP model

is obtained irrespective of the external force magnitude. On the other hand, for
value of

=2

< 1, raising the

would result in the activation of all kinematic models. As a result, the force versus

displacement curve in this situation is defined by a multi-linear curve with a slope of each segment
decreasing with

and a transition force concept will be required. Table 3.1 provides all equations

for SW and CP cases, where the wall's rocking capacity

for CP is equal to the minimal value

corresponding with the strength of the hold-down or the vertical joints depending of the
condition. For ∝ ∗ ,

∗

,

and

∗

values, please refer to Casagrande et al. (2017).

41

Table 3.1. Proposed equations for strength assessment (Casagrande et al. 2017)
Symbol

Elastic Single walls

Elastic Coupled walls

.
2. . ℎ

.
2. . ℎ

<

1 + .(

1

′
2
.
ℎ,1 .

(

,

.ℎ
2

. ′

, .

ℎ,1 . ℎ

− 1], = [1: ]

+(

− 1). .

′
2
ℎ,1 .

2

ℎ

ℎ

.

.

2.

− 2)
2

.

−

with = [1:

−1
.

+

,

,

.ℎ

− 2)
2

1− .

.

,

(3.

≥

− 2)

.ℎ
. . ( − 2. )
−
.
2
with = [1: − 1], = [1: ]
1

, ,,

1− .

1−

.ℎ
, .

2.

.ℎ

, .

.
′

≥ 1,

, .

+

( . )
2

ℎ

< 1,

⎧ ℎ, . ℎ,1 . + . .
⎪
2. ℎ
, .ℎ
′
⎨ .
. .
ℎ,1 .
⎪
+
⎩
.ℎ
2. ℎ

. . . ∗
ℎ, . . ∝ ∗
⎧
+
2. ℎ
ℎ. ∗ .
⎪
⎪
. . ∗
. . .∝ ∗
⎧
+
; ∗ = [1: − 1]
⎪
ℎ. ∗
2. ℎ. ∗
⎨
⎪⎨
. .
. . .∝
⎪⎪
+
; ∗=[ ]
⎩⎩
2. ℎ
ℎ. .

42

3.1.7. Shahnewaz et al. (2019)
Shahnewaz et al. (2019) made the following assumptions: angle brackets and hold-down
fasteners yield, but the steel brackets and the anchoring bolts remain elastic. The brackets can
support forces from both sliding and rocking, but the sliding resistance of hold-downs are ignored
- the shear capacity of hold-downs is just one-fifth of its tension capacity (Gavric et al., 2015). The
angle bracket is assumed to have identical sliding and rocking resistance, and group effects for
screw and nail capacity were not taken into account in this model. Friction forces were disregarded
at the interfaces wall-to-floor above and wall-to-foundation below. To allow each panel in a CP to
rock properly, the vertical connections between panels must yield before the wall-to-floor
connection, while the remaining joints are capacity protected. The sliding, rocking and combined
(shear-uplift interaction) for the angle bracket in CP scenario, is indicated in Figure 3.6.

Figure 3.6. a) Sliding for CP with angle bracket and hold-down; b) Rocking for CP with angle bracket and
2-hold-downs; c) Combined rocking-sliding for CP with angle bracket and 2-hold-downs (Shahnewaz et
al., 2019)

To avoid sliding failure, the sliding resistance of the wall must be greater than the rocking
resistance, see Eq. (3.10). The sliding and rocking reactions of the brackets,
considered to be proportional to the sliding

and rocking deformation

,

and

, , are

, which may be

computed in terms of the brackets' factored resistance and applied in the shear-uplift interaction,
presented in Eq. (3.11) - when there are hold-downs in the shear walls,

,

has to be

, .

43

(3.10)

>
,

,
,

=

=

.
.ℎ

,

(3.11)

.ℎ
1
− 2 .

,

,

denotes the sliding reaction of the brackets;

connection; and

,

denotes the brackets' resistance;

,

denotes the rocking response of each

,

denotes the hold-downs’ resistance;

is the resistance of vertical joints in coupled wall and

is the distance between each

connection and the right corner.
The ratio of sliding to rocking deformation determined using Eq. (3.11) are shown in the
Figure 3.7. The dominant kinematic behaviour of the wall transitions from rocking to sliding when
the panel aspect ratio varies, usually increasing the increment of width of the panel.

Figure 3.7. The ratio of sliding to rocking deformation for different aspect ratios with SW with angle
bracket and with angle bracket and hold-downs (Shahnewaz et al., 2019)

For SW, the rocking resistance of CLT shear walls with just angle bracket and only holddown may be calculated by summing the moments at the wall's lower right corner. The CLT shear
wall's rocking resistance is established when the first bracket (left corner) has reached its
maximum resistance. Because it has the longest lever arm, the first bracket transfers the highest
44

moment attributable to the rocking of the wall. For both SW and CP, equations for estimating inplane resistance were provided. Five distinct wall configurations were considered: i) SW with
angle bracket only; ii) SW with angle bracket and hold-down; iii) CP with angle bracket only; iv)
CP with angle bracket and 2-hold-downs; iv) CP with angle bracket and 4-hold-downs
(Shahnewaz et al., 2019). Previous study reported that SW with angle bracket and hold-downs
performed better in terms of strength and stiffness than walls without hold-downs (Shahnewaz et
al., 2018). The following table summarizes the equations for SW and CP walls for this method,
when subjected to rocking and rocking-sliding. The sliding reaction of each wall segment in the
coupled walls is denoted as

, , , if the geometric properties are equal in both panels the ratio for

the CP approaches will be the same, and

in the CP approach are the full width of the panels.

Table 3.2. Equations for resistance of CLT shear walls of Method B
Rocking

CLT walls
,

SW-AB

+ .

ℎ.
ℎ, .

SW-AB+HD

+

ℎ

1 2.
ℎ

CP-AB

Combined rocking-sliding

,

ℎ.

,

2. ℎ
+ .

ℎ, .

2. ℎ

.
+ . +
4
2

,

+

ℎ
1 2.
ℎ

−
ℎ.

,

,

+ .

−
ℎ.

,

−

,

CP-AB+2HD

1
ℎ

ℎ, .

2

+

2.

,

+ .

4

+

.
2

ℎ, .

2

+

2.

,

CP-AB+4HD

1
ℎ

ℎ, .

+

2.

,

+ .

4

+

.
2

ℎ, .

+

2.

,

2. ℎ

+ .

4

.
2
−

+ .
1
ℎ

+ .

, ,

+
1
ℎ

2. ℎ

, ,

4

+

.
2

−

+ .

, ,

4

+

.
2

45

3.1.8. Nolet et al. (2019)
An analytical approach for describing the elastic-plastic behaviour of CLT shear walls
when CP and SW are accomplished in the plastic range is described by Nolet et al. (2019). The
yielding of the vertical joints prior to the yielding of the hold-down governed CP behaviour, the
opposite is valid for SW behaviour. Due to diaphragm action, it is expected that all panels have
the same top lateral displacement. The index ∗ is used to specify the section of the wall beyond
which the panels, i.e., = [ ∗ ,
∗

], maintain contact with the ground. For CP and SW behaviours,

is equal to 1 and m, respectively, but for IN behaviour, ∗ takes values in the range [2 ,

− 1].

The mechanical properties of the hold-down and vertical joints are described by elastic-perfectly
plastic curves to simplify the analytical approach, which are classified by the elastic stiffness’s
,

and , strengths

,

and , for the hold-down and panel joints, respectively, see Figure 3.8a.

Figure 3.8. a) Idealized Multi-panel CLT shear wall notation; b) Elastic-plastic force-displacement curve
for CPEL -SWPL (Nolet et al., 2019)

CP behaviour can always be obtained as a final mode of failure if the vertical joints
connection yields before the hold-down, providing the system have substantial displacement
capacity. Likewise, if the hold-down fails before the panel joint connector, the SW behaviour is
always conceivable as a final mode of failure. Angle bracket type that can withstand tensile and
shear stresses may affect the rocking behaviour of the CLT shear wall and, as a result, the wall's

46

energy dissipation. However, the model ignores the shear uplift interaction. Depending on the
ductility of the various connections, several failure mechanisms can theoretically be achieved.
The force-displacement curve, depicted in Figure 3.8 b), illustrates the several behaviours.
When the panel joint remains elastic, wall failure is determined by hold-down failure. To achieve
the intermediate behaviour, a transition force denotes the situation in which the first panel is no
longer in contact with the ground, i.e., the first panel's response is equal to zero for
the last transitional force,

, is resisted by the wall, SW behaviour is obtained.

equivalent hold-down tensile stiffness,

, ∗
,

is the activation force,

,

. When
,

is the

stands for the elastic

strength related to the vertical joint in kinematic mode

∗

,

, is the plastic strength of the wall.

∆ , is the displacement achieved at elastic strength, ∆ ,

, ∗

, value of transitional displacement in

the plastic state between kinematic mode
strength and
∗

, ∗

∗

∗

and

+1, ∆ , displacement achieved at plastic

, value of transitional force in the plastic state between kinematic mode ∗ and

+1. Table 3.3 summarizes the equations of the interested points illustrated in Figure 3.8b.
Table 3.3. Elastic CP to plastic SW, CPEL -SWPL design equations (Nolet et al., 2019)
Point of
interest

X coordinate

Y coordinate

A

0

=

B

∆ =

C

∆ ,, =

D

∆ ,

E
F

,

=

,
,

−
/ℎ

, .

ℎ. (

,
,

+ . )
. .

,

ℎ. ,
. ℎ. ∗
+
. .
.
∗

ℎ. ,
. ℎ.
+
. .
.
ℎ. ,
. ℎ. ( − 1)
∆ =
+
. .
.
, ∗

∆ , =

,

,

=
, ∗

=

, .B

ℎ
, .B

ℎ

.
.

.
. [3.

. [3.

=

.
2. ℎ
, .

, .ℎ

ℎ

+

+

, .

=
, .

=

.

+

.

+ 2.

+
. (3. − 2)
2. ℎ
( ∗ − 1) − ∗ ( ∗ + 1)]
2. ℎ

( ∗ − 1) − ∗ ( ∗ + 1)]
2. ℎ
.
, .B
+
ℎ
2. ℎ
+ 2.

47

3.1.9. Masroor et al. (2020)
Masroor et al. (2020) proposed an elastic-plastic analytical method for multi-panel CLT
shear walls, which includes the bi-axial contribution of angle brackets and hold-down connections,
and suggest expressions in the elastic region to establish the CP and SW kinematic behaviours.
In this model, the hold-down connections are expected to withstand both uplift and shear loads
and all connectors are defined as elastic springs. The panels are assumed completely rigid.
Because of the presence of a compressive zone in the panel, experimental studies of CLT shear
walls (Histovski et al., 2017; Flatscher et al., 2015) have demonstrated that the centre of rotation
of the wall segments may not be centred at the corner of each panel. The model incorporates this
by assuming a shortened length of panel equal to . , by using

equal to unity.

Table 3.4 summarizes the equations for SW and CP walls, where by isolating the lateral
force and using the known resistance values of hold-down, angle bracket, and vertical joint, it is
possible to estimate

and

for the method in question.

indicates the vertical stiffness ratio

of the angle brackets, which is the association between the vertical stiffness of the hold-down and
the angle brackets. If the vertical contribution of the angle brackets is intended to be ignored, its
value has to be equal to zero. The overall contribution of the hold-down and angle brackets to
vertical stiffness is defined as

, which is obtained using the ∝ coefficient. The contribution of

the stiffness of the connectors in rotation is represented by

, that includes the vertical stiffness

influence of the hold-down and angle brackets, as well as the influence of the vertical joints.
When the CP behaviour is achieved, the internal forces in all fasteners employed in the
vertical joints

, ,

are equal due to equivalent displacements in the joints. It should be observed

that in the SW behaviour, fasteners placed in the same panel have identical internal force, as in
the CP behaviour, but the internal forces of vertical joints between different panels are not equal
– they present different equals for each panel.

48

Table 3.4. Equations for SW and CP for the Masroor's method
Symbol

Elastic Single walls

Elastic Coupled walls

,

,

,

,

, .(

∝

(

+ 1)

+(
.
, ,

.

, .

⎧
,

⎨
⎩

,

, .

.

.ℎ

−
)

+

)

+ 2.

,

.

.
, .

(

− 1). . .

, .(

,

, .(

+ ( − 1)

+
.( . . −

,

)

+ . .

.ℎ

,

+1

−

−

)

+ . .

+ 1)

+ ( − 1)

+(

− 1). . .

.

. (2. − 1)
2

. .

. (2. − 1)
2
. ,
+ 2. ,
, . .

, .

.

. . +

+ ( − 1)
+1
. ,
+ 2. ,
, . .

.

+1

, .

, .

+ ( − 1) .
.
.

.

,

+ 2.

,

The uplift forces in the SW case for the hold-down and angle bracket are calculated by
multiplying the corresponding displacement by the connection stiffness, where = [1:
[1:

] and

= [ ],

= [1:

− 1], =

], respectively. The criteria for ensuring CP behaviour is that the

vertical reactions at the rotation points be positive (i.e., in compression). To ensure SW behaviour,
the

≥ 0 condition must be met, where the vertical displacement at the rotation point of panel

− 1 must be positive. For further information about , refer to Masroor et al. (2020).
The elastic model is expanded to inelastic behaviour, including the bi-axial contribution of
angle bracket and hold-down. The proposed approach focuses on the CP behaviour because it
promotes rocking kinematic mode, which is a desired ultimate plastic behaviour Masroor et al.
(2020). When the vertical joints yield before the hold-down and angle bracket, the CP plastic
behaviour is achieved. The connections are supposed to act as elastic-perfectly plastic materials.

49

The parameters utilized are:

,

, ,

, ,

, , and

, , which indicate the fastener strength in

vertical joints, hold-downs in vertical and horizontal directions, and angle brackets in vertical and
horizontal directions, respectively.
To maintain the angle bracket and hold-down elastic, the shear-uplift interaction is
described in the circular domain. This verification is especially critical for the angle brackets
because when the angle bracket begin to yield, the wall is no longer capable of resisting additional
horizontal loads and then they will slide until the angle brackets fail completely. Table 3.5 provides
the equations in order to obtain the inelastic approach.

Table 3.5. Equations for the inelastic approach
Point of
interest

Inelastic Coupled walls

=

.

. (2.
2. ℎ

.

Verifications
.

− 1)
, .

, .

, .

, .

.

=

, .

.

.

=

,

+ 2.
.

,

+

. ℎ.

, ,

−
, .
ℎ

=

, , =

.

+ 2.

,

,

−

.ℎ

−
.
ℎ

+

+

.

+ 2.

−

+ ( − 1) .

, .

, .

, ,

+

,

, .

+

.

,

ℎ

+

<1

+ 2.

,

,

.

<1

+ 2.

, ,

, .

, .

, .

+

,

,

, ,

+

, ,

+∑

,

,

<1

+ 2.

,

, ,

,

,

. +

=1

+ 2.

.

1

.

.

, .

−
, .

,

.
.

,

=

,

.

, .

+
−

<1

.

+

,

. ℎ. .
.

,

,

−
, .

,

.

+

+

−
. ℎ.
. ( +∝. . )

+ ( − 1) .

+ 2.

,

.

,

+1

+1

, .

,

=

,
, , =

+

,

,

.

, .

<1

+ 2.

.

+

,

=

,

.

,

+

.
−

.

, .

,

+ 2.

,

.

,

+3− +

,

=1

50

Because there is no rotation in the panels prior to exceeding the activation force, the lateral
displacement in

is due to sliding alone.

,

=

+(

− 1). . .

is the contribution of the

connections’ stiffness in the uplift direction. The internal uplift force in the angle bracket and holddown, the increments between angle bracket, and other parameters can be found in Masroor et
al. (2020). The solution for this method is cumbersome and does not yield to straightforward
expressions. Software solutions is convenient, especially for higher number of panels
In Figure 3.9, the behaviour of the CLT shear wall in elastic and inelastic zones is depicted.
is the activation point at which the wall begins to rotate, and its corresponding lateral force,
, and displacement,

. Points

and

reflect fastener yielding in vertical joints and hold-

down, respectively. The yielding of the angle brackets is represented by the points

to

,

beginning with the last angle bracket away from the centre of rotation of each panel. Due to the
idealization made about the behaviour of the hold-down and angle bracket connections being
elastic-perfectly plastic, the model developed by Masroor et al. (2020) is not capable of predicting
the post-peak behaviour of the shear walls. As a result, the suggested model is terminated such
that the ultimate displacement corresponds to the results of the experimental investigations.

Figure 3.9. Inelastic diagram of multi-panel CLT shear walls (Masroor et al., 2020)

51

3.2. Stiffness Analytical Approaches
3.2.1. Overview
This section provides an overview of various stiffness approaches. In the following
subsections, some models will be studied in depth in order to understand their details and
compare their fundamental conventions.
Wallner-Novak et al. (2013) account for deformation from bending, shear, sliding and
rocking of the CLT shear wall. Gavric et al. (2015) account for all connections, as well as panel
bending and shear deformation. Flatscher and Schickhofer (2016) developed an iterative
displacement-based method for determining rotation, and displacements in connections for
single-panel and two-panel CLT shear walls. Shahnewaz et al. (2016) presented an analytical
model for reduced stiffness that took into consideration the panel's geometrical dimensions and
the openings. Hummel et al. (2016) investigated shear and bending deformation of the CLT panel,
and rocking and sliding of the wall panel. Casagrande et al. (2017) suggested that the angle
bracket have no effect on the rocking behaviour of the wall and the lateral displacement of multipanel CLT. Deng et al. (2019) developed a simplified mechanistic model based on an
approximation of the principle of virtual work to predict the rocking and sliding lateral response of
CLT shear walls.
Shahnewaz et al. (2020) also developed analytical equations and investigated the effect
of perpendicular CLT shear walls, which can minimize deflections by up to 45 percent due to the
redundancy effect. Mestar et al. (2021) examined at the kinematic modes in CLT shear walls with
openings, as well as the influence of various hold-down configurations on the base shear and
hold-down tensile load. The degree of coupling decreases with higher hold-down stiffness and
increases with wall segment width, according to the analytical analysis. Only one global kinematic
behaviour, consisting of walls with one centre of rotation for the whole wall, was obtained for all
studied situations with window opening.
52

3.2.2. Wallner-Novak et al. (2013)
The Wallner-Novak et al. (2013) approach takes into account the same contributions as
Hummel et al. (2016) method, with only a minor change in the determination of the shear stiffness
of the CLT panel due to a lower shear modulus. The overall displacement is computed using
panel bending and shear, as well as sliding and rocking deformation contributions:

=

.ℎ

=

The bending stiffness

.ℎ

.ℎ
.

(3.13)
(3.14)

=

=

(3.12)

3.

.

−

.
2

,

.

(3.15)

ℎ
.

,

in Eq. (3.12) is derived using Eq. (3.26), whereas the shear

stiffness in Eq. (3.13) is obtained using a 25% decrease in shear modulus:
= (0.75. ). ( . )

(3.16)

3.2.3. Gavric et al. (2015)
Gavric et al. (2015) claimed that prior approaches failed to account for the tensile
properties of angle brackets and suggested a method that accounts for all stiffness and strength
components of hold-down and angle bracket. The deformations may be computed by inserting a
vertical stiffness of angle bracket, a friction coefficient to prevent sliding, and a shape reduction
factor of 1.2 for shear deformations, as follows:

=

.ℎ
3.

(3.17)

53

=

1.2. . ℎ
.

=

− . .
. ,
.
2
+∑

.ℎ −
=

The bending stiffness

∑

, .

(3.18)
(3.19)

(3.20)

.ℎ
, .

is derived using Eq. (3.26), and the shear stiffness

computed using a shear modulus ( ) of 0.69

and an effective shear area

is

determined

with only the vertical layers as:
=
A friction coefficient

.

(3.21)

of 0.3 is employed in sliding. In rotation, the panel is rigid and rotates

around a corner of the wall. Gavric et al. (2015) also incorporate the non-linear behaviour of the
force-displacement curve in determining the stiffness properties of the connectors, implying that
the stiffness of each connection is assessed based on the actual deformation of each connector.
Three stiffness ranges were proposed for this resolution, with an initial elastic stiffness, a plastic
stiffness until maximum load, and a negative stiffness phase until connection failure.
The shear deformation varies between the approaches insignificantly. In terms of sliding
deformation, the values are equal in both approaches since they employ the same translation
principle and input parameters, but Gavric et al. (2015) incorporates a friction coefficient for it. All
methods take bending into account, even though its contribution to total shear wall deformation
is relatively small. As expected, the stiffness of the connections accounts for the preponderance
of the stiffness of the CLT shear wall. The approaches are quite similar and provide similar
outcomes. Nonetheless, the models are sensitive to the shear connections' vertical and horizontal
stiffness, which may lead to distinct results (Lukacs et al., 2019).

54

3.2.4. Hummel et al. (2016)
Hummel et al. (2016) analyze the enhanced panel flexibility caused by an elastic
foundation, where two situations for wall rocking are considered: i) a rigid foundation (e.g.,
concrete slab) and ii) an elastic foundation (e.g., timber floor between stories with an elastic
intermediate layer), shown in Figure 3.10.

Figure 3.10. Rigid or elastic foundation and rocking deformation with elastic intermediate layer (Lukacs et
al., 2019)

The individual contributions to shear wall deformation are calculated as following:

=

=

=

.ℎ

(3.22)

3.
.ℎ

(3.23)

.

(3.24)
.

,

.ℎ
.
max
−
;0
ℎ
2
( − 2. )
.
, rigid foundation
,
= ( − 2. )
⎨
ℎ
2.
⎪
.
, elastic foundation
− /3
⎩
.
⎧
⎪

(3.25)

55

Where the flexural stiffness is calculated using Eq. (3.26), and
vertical layers. The effective shear modulus,
shear area,

, where

=

, is provided in the Eq. (3.27) and the gross

is the average width of the lamellae, are used to calculate shear stiffness.

=

.

is the thickness of the

.

.
12

.

=

(3.26)

.

.

1 + 6. 0.32.

, where

= .

.

(3.27)

For the elastic foundation scenario, the layer contributes to increasing the rocking
deformation of the wall, and will have a stiffness of the elastic foundation
al. (2016) for further information on the length of the pressure zone
well as the thickness

and width

. Refer to Hummel et

and the

calculation, as

of the elastic foundation.

3.2.5. Casagrande et al. (2017)
A model for calculating the elastic horizontal displacement of a timber shear wall was
suggested by Casagrande et al. (2016). However, it does not take bending deformation into
account, because of the relatively high flexural rigidity assumption of the CLT panel in proportion
to the mechanical connections – this effect may be overlooked in most practical applications. Inplane shear deformation, rigid-body translation, rigid-body rotation and vertical load – used to
counteract the rotation of the wall – were all examined by Casagrande et al. (2017). The different
contributions to single shear wall deformation are presented as:
=

.ℎ

(3.28)
(3.29)

=

=

.ℎ
. .
.

−

.
2

,

.

ℎ

(3.30)

, .

56

The hold-down stiffness, in combination with the uniformly distributed vertical load, has a
significant impact to prevent deformations, since rigid-body rocking has the largest effect. The
shear area and shear modulus are key factors used for shear deformation, and the stiffness of
the angle bracket contributes the most to sliding deformation (Casagrande et al., 2016). Assuming
that the angle bracket has no effect on the rocking behaviour of the wall and neglecting panel
bending deformation, the lateral displacement of multi-panel CLT walls may be computed
according to Eq. (3.34). The rocking displacement is estimated by defining the equivalent lateral
stiffness of the wall

,

subtracted the horizontal displacement due to vertical load, as follows:

(3.32)

=

=

(3.31)

.ℎ
. .

=

.

, .

.ℎ =

−
,

=

+

. .ℎ
2. ,

+

(3.33)

(3.34)

When the lateral force is less than the activation force, the lateral displacement due to
rocking becomes zero, yielding the following equation (Casagrande et al., 2017).
=

+

(3.35)

3.2.6. Shahnewaz et al. (2020)
Shahnewaz et al. (2020) presented different equations to evaluate in-plane displacements
for SW and CP based on potential kinematic motions of CLT shear walls under lateral loading.
CLT shear walls resistance is determined by the type, quantity, and positioning of connections,
as well as the wall's aspect ratio. When the brackets' contributions to uplift are ignored, the inplane resistance of CLT shear walls is conservatively estimated (Shahnewaz et al., 2020).

57

Although it is provided the effect of perpendicular walls in the wall’s deflection and the effect of
openings, only SW and CP without perpendicular walls and with no openings will be discussed
(Figure 3.11), due to such analysis is out of the scope of this thesis.

Figure 3.11. a) Single CLT walls; b) Coupled CLT walls with 4-hold-downs; c) Coupled CLT walls with 2hold-downs (Shahnewaz et al., 2018)

The deflection of a single CLT shear wall, Figure 3.11 a), can be estimated using Eq.
(3.36), which is a simple closed-form equation, as a function of material and geometric properties
of CLT shear walls and the stiffness of its connectors. Because friction cannot always be
activated, the solution ignores the potential effect to resist sliding.

,

=

.ℎ
3.

+

.ℎ
+
. .

, .

+

.ℎ

−

.ℎ
2

1

(3.36)

,

The cantilever beam with a point load at the free end was considered as the boundary
condition for the bending displacement in the CLT panel. The effective bending stiffness of a CLT
panel loaded in-plane may be computed as follows (Blass and Fellmoser, 2004):
=
where the constant,

(

)

(3.37)

can be calculated using Eq. (3.38).

58

=
and

−

+ 1−

+ ⋯±

(3.38)

are the elastic moduli of elasticity in parallel and perpendicular directions,

is the whole thickness of the CLT panel. The parameters

through

are shown in Figure 3.12.

Figure 3.12. Cross-section of m-ply CLT panel (Shahnewaz et al., 2018)

For CP with 4-hold-downs, Figure 3.11 b), the hold-downs are positioned on each side of
the vertical joint. Each panel rocks independently, and both hold-downs withstand tension forces.
It should be emphasized, however, that the vertical connections must be assembled in a way to
allow each panel to rock separately. Eq. (3.39) may be used to determine the deflection of a
coupled CLT shear wall with two or more panels. The deflection at the top of each connected wall
section is considered to be equal.

,

,

=
∑

,

3. (

)
ℎ

+

+

. .
ℎ

∑

∑

is the modified stiffness of hold-down and

, , .

+
,

.
ℎ

−
, ,

.ℎ
2.

(3.39)

,

are the stiffness of wall-to-wall shear

connectors, where can be calculated as:
,

=

,

+

(3.40)

For the last case, because the tensile stiffness and resistance of the left most bracket
connector is different between panels, the deflection of coupled walls with 2-hold-downs has
distinct rocking equations for right and left panels, in Eq. (3.41).

59

,

,

=
∑

,

3. (

)

+

. .
ℎ

∑

ℎ

+

∑

+

, , .

.
ℎ

,

is the modified stiffness of angle bracket and

−
, ,

.ℎ
2. ∑

(3.41)

+
,

,

are the stiffness of wall-to-wall shear

connectors where can be calculated as:
,

=

stands for the summation of bending

,

(3.42)

+

, shear

, sliding

and rocking

stiffness of

each panel in the coupled wall:

=

, +

, +

, +

, =

3. (

)

+

ℎ

. .
ℎ

+

, , .

, +

.
ℎ

, ,

(3.43)

The equivalent shear modulus of the CLT panel, which is measured parallel to the outer lamella,
may be computed using the formula provided by Moosbrugger et al. (2006):

1+6
where

(3.44)

∥

=

∥

+

∥

( / )

is the shear modulus perpendicular to the grain,

∥ is the shear modulus parallel to the

grain and / is the board thickness-to-width ratio.
When the wall panels rotate as a single rigid body it means that the coupled shear wall
has stiff vertical joints. Then, to resist tension forces, only two hold-downs at the wall's outside
borders are sufficient. In this situation, the suggested equations for a single CLT shear wall may
be used to determine the total deflection of the coupled shear wall with 2-hold-downs.
3.2.7. Masroor et al. (2020)
Bending deformation is neglected in this approach similar to Casagrande et al. (2016).
However, for panels with very high aspect ratios and walls with openings, the contribution from
panel deformation, the panels' flexure and shear deformation may be studied independently of

60

the rocking and sliding deformations (Masroor, 2020). The shear deformation contribution of the
panels can be included into the overall lateral deformation equation that contains the lateral
displacements. The shear deformation of panel

may be obtained using the Eq. (3.45). In this

formula,

panel, which is

denotes the lateral load in the

/ , and

represents the

corresponding shear modulus. By combining the entire lateral displacement of the CLT shear wall
into the lateral displacement due to sliding and rocking, the expression in Eq. (3.46) and Eq. (3.47)
the total lateral displacement of the CLT shear wall is obtained in Eq. (3.48).

=

(3.46)
, .

.

+ 2.

+

,

(3.47)

= .ℎ
=

(3.45)

.ℎ
. . .

=

+

(3.48)

Comparisons among the analytical methods, practical situations, and test data, show that
the analytical approaches may underestimate or overestimate shear wall behaviour in different
circumstances (Lukacs et al., 2019). Hence, it is fundamental to compare the diverse scenarios.

61

3.3. Design Examples
3.3.1. Rationale for Method Selection
For elastic examinations, three approaches: Method A – Casagrande et al. (2016); Method
B – Shahnewaz et al. (2019); and Method C – Masroor et al. (2020) will be applied to academic
design examples, as well as utilized in the experimental comparisons in chapter 4. However, only
two methods: Method C – Masroor et al. (2020) and Method D – Nolet et al. (2019) will be applied
for a subsequent inelastic assessment. The reason for selecting these methods is that i) they
include formulations for both SW and CP behaviour of CLT shear walls, and ii) they differ from
each other encompassing the majority of relevant parameters. The other methods differ mainly in
estimating the lever arms of their respective compression zones.
Method A considers the minimum resistance between the hold-down and the vertical joint,
which is the most straightforward approach. Method B allows for different positioning of holddowns and considers the contribution of all brackets in the rocking resistance. Method C includes
the bi-axial effect of the connectors, the concept of compression zones, and an inelastic analysis.
In addition, all methods have strength and stiffness approaches for both SW and CP wall
behaviour, corroborating to a more detailed comparison between each other and with test results.
Lastly, Method D describes the elastic-perfectly plastic behaviour neglecting the bi-axial
behaviour of brackets, as well as the interaction between rocking and sliding.
Table 3.6 compares the properties that each method presents and their individual
distinctions in the study of CLT shear walls, as a summary of the attributes addressed by each
approach aiming to assist the design engineer to observe the most appropriate method for their
design intentions.

62

Table 3.6. Comparison among the selected strength and stiffness models
Properties

Methods
A

B

C

D

Superimposed dead load

✓

✓

✓

✓

Single walls

✓

✓

✓

✓

Coupled walls

✓

✓

✓

✓

Friction consideration









Material and geometric properties

✓

✓

✓

✓

Strength equations

✓

✓

✓

✓

Stiffness equations

✓

✓

✓

✓

Compression and tension zones





✓



Different options for the positioning of hold-down



✓





Bi-axial contribution of hold-downs and angle brackets





✓



Applicable within linear range

✓

✓

✓

✓

Applicable within nonlinear range





✓

✓

High computational effort and has kinematic conditions

✓



✓

✓

Influence of perpendicular walls, floors above, openings
and bending displacements



✓





Shear-uplift interaction



✓

✓



Limited to the rocking behaviour of hold-down

✓





✓

3.3.2. Examples
Two single and coupled wall examples will be analyzed as shown in Figure 3.13 and Figure
3.14. In Example 1, there is a superimposed dead load of 18 kN/m with a wall width of 3 m and
two 1.5 m segments. In Example 2, there is a superimposed dead load of 25 kN/m with a wall
width of 1 m to obtain a different aspect ratio in the comparison. The resistances and stiffness of
hold-downs and angle brackets were decreased to verify the impact of the connections. Example
2 also presents a reduction of the vertical joint fasteners in order to assess the impact on yield

63

strength of the vertical joint. The coefficient incorporating the effect of the compression zone in
the panels for Method C, , was considered equal to unity for shear wall calculations. Theoretical
force values were applied to the walls to verify their respective displacement, and the analysis is
undertaken until 100 mm of lateral displacement. Such values are fundamental to dictate the
ending point in the inelastic analysis, as the models are not capable of predicting the post-peak
behaviour of the shear walls due to the idealization made regarding the behaviour of the holddown and angle bracket connection being elastic-perfectly plastic. A harmonized notation of the
studied CLT shear wall is proposed in Table 3.7 to facilitate comparing the different methods for
assessing strength and stiffness.

Figure 3.13. a) Single wall for example 1; b) Coupled wall for example 1

Figure 3.14. a) Single wall for example 2; b) Coupled wall for example 2

64

Table 3.7. Properties of the CLT shear walls
Parameters

Example 1

Example 2

3 / 1.5

1

Height, ℎ [m]

3

3

Aspect ratio

1:1 / 2:1

3:1

3/1

1

4,500

3,000

[kN/m]

4,500

3,000

[kN/m]

1,500

1,000

7,000

5,000

11,500

11,500

5

5

600

600

Thickness of CLT panel, [m]

0.200

0.200

Superimposed dead load,

18

25

38.50

25

Length,

[m]

Number of angle brackets,
Stiffness of angle bracket in the horizontal direction,
Stiffness of angle bracket in the vertical direction,

,

Stiffness of hold-down in the horizontal direction,

,

Stiffness of hold-down in the vertical direction,
Modulus of elasticity parallel to grain,

,

[kN/m]

,

[kN/m]

[MPa]

Number of layers in CLT panel
Equivalent shear modulus of CLT panel,

[MPa]

[kN/m]

Yield strength of angle bracket in the horizontal direction,

,

Yield strength of angle bracket in the vertical direction,

[kN]

38.50

25

[kN]

10

6

50

30

2

3.5

Number of fasteners per vertical joint,

10

5

Number of panels in the shear wall,

2

2

500

750

,

Yield strength of hold-down in the horizontal direction,

,

Yield strength of hold-down in the vertical direction,

[kN]

Yield strength of fasteners in the vertical joint,

Elastic stiffness of a fastener in the vertical joint,

,

[kN]

[kN/m]

[kN]

Distance from edge of panel to

connector,

[m]

0.080

0.080

Distance from edge of panel to

connector,

[m]

0.790

0.500

Distance from edge of panel to

connector,

[m]

1.500

0.920

Distance from edge of panel to

connector,

[m]

2.210

-

Distance from edge of panel to

connector,

[m]

2.920

-

100

25

Assumed force for displacement methods [kN]

65

A shear wall is described by its width , height ℎ, and thickness , loaded by a lateral force
and a vertical load . The CLT elastic and shear moduli
, , and horizontal strengths

and

, ,

and

are defined. The vertical

, ,

, , are used to define the angle bracket and hold-down.

represent the shear wall load-carrying capacities in rocking and sliding, respectively. The

load-carrying capacity

of the CLT shear wall is

number of angle brackets,

=

(

;

).

=

, .

where

is the

is analyzed depending on the specified method.

CSA O86 provisions may be used to determine lateral deformation and resistance per nail.
The value of the anchorage deformation is not explicitly provided in CSA O86 for determining the
stiffness of hold-downs and angle brackets. Hold-down and angle bracket manufacturers typically
provide connector elongation information. Thus, the values of the design example were assumed
using generic and hypothetical connections to assess the differences between the methods for a
given input value.
At the ends of the shear wall, a hold-down is placed to anchor the wall to the ground, and
evenly spaced angle brackets attaching each wall panel to the floor below are expected to be
positioned throughout the length of the panel. The shear wall is composed primarily of

panels

that are held together by vertical joints. The vertical and horizontal stiffness of the hold-down, and
the stiffness of the vertical joints, are represented by the symbols
, , and

, ,

, , and

, respectively.

, , stand for horizontal and vertical stiffness values of the angle bracket, respectively.

A vertical joint between the CLT panels is composed of

fasteners, and

evenly spaced angle

brackets are considered for SW example, whereas for CP, they are located in the centre of the
panels. The results designated as “combined” means rocking-sliding reactions in the angle
bracket where the shear-uplift interaction is included (Method B). The shear-lift interaction is
considered to be not applicable for the other methods since it is not fully incorporated in their
elastic range. However, for the inelastic approach presented in Method C, the equations are
aimed to ensure that the hold-down and the angle bracket remain elastic.

66

3.3.3. Results
The results from the analytical methods are presented for both examples. The shear wall
resistance is analyzed by the smaller value between sliding and rocking. In turn, the
displacements were obtained by adding the individual kinematic motions of each wall, that is,
shear, bending, sliding and rocking. Table 3.8 and Table 3.9, and Figure 3.15 to Figure 3.18
summarize the lateral resistance and the displacement contribution from shear, bending, sliding,
and rocking for Example 1. Table 3.10, Table 3.11, and Figure 3.19 to Figure 3.22 summarize the
lateral resistance and displacements contribution for Example 2.

Table 3.8. Example 1 - Summary of the lateral resistance
Lateral resistance of SW (kN)

Lateral resistance of CP (kN)

Method
A

115.5

77.0

N/A

77.0

37.5

N/A

B

115.5

109.8

95.9

77.0

58.1

54.9

C

110.0

105.1

N/A

80.0

42.0

N/A

SW capacity [kN]

140
120

115.5

109.8

95.9

100
80

115.5

105.1 110.0

77.0

60
40
20
0

N/A

N/A

Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et
et al. 2017) et al. 2019) al. 2020)
Rocking

Sliding

Combined

Figure 3.15. Example 1 - Single wall lateral resistance

67

140

CP capacity [kN]

120
100

77.0

80
60
40

80.0

77.0
58.1

54.9

37.5

20

42.0
N/A

N/A

0

Method A
Method B Method C
(Casagrande (Shahnewaz (Masroor et
et al. 2017) et al. 2019) al. 2020)
Rocking

Sliding

Combined

Figure 3.16. Example 1 - Coupled wall lateral resistance

Method A estimates lower rocking capacity than the other studied methods, with 77 kN
and 37.5 kN for the SW and CP case, respectively. Method C presents intermediate values, with
42 kN and 105.1 kN for the SW and CP case, respectively. The result provides evidence that the
sliding resistance is relatively comparable among all the methods, with minor variations of 5% for
Method C, where it presents a reduction for SW and an increase for the CP scenario. Although
Method B presents the combined resistance as the governing case, its capacities are less
affected, only around 5 to 12% reduction are found for the single and coupled case, respectively.
Subsequently, the displacements results were calculated, as shown in Table 3.9.

Table 3.9. Example 1 - Summary of the displacement contribution
Displacement contribution of SW (mm)

Displacement contribution of CP (mm)

A

0.0

0.8

7.4

10.4

18.7

0.0

0.8

11.1

28.8

40.8

B

0.4

0.8

7.4

10.4

19.1

1.7

0.8

11.1

16.1

29.7

C

0.0

0.8

6.1

6.1

13.6

0.0

0.8

8.3

24.3

33.4

Method

68

SW displacement [mm]

25
20

18.7

19.1

15

13.6

10
5
0
Method A
Method B Method C
(Casagrande (Shahnewaz (Masroor et
et al. 2017) et al. 2020) al. 2020)
Bending

Shear

Sliding

Rocking

CP displacement [mm]

Figure 3.17. Example 1 - Displacement contribution for SW

50
40

40.8
29.7

30

33.4

20
10
0
Method A
Method B Method C
(Casagrande (Shahnewaz (Masroor et
et al. 2017) et al. 2020) al. 2020)
Bending

Shear

Sliding

Rocking

Figure 3.18. Example 1 - Displacement contribution for CP

Method A estimates a total displacement of 18.7 and 40.8 mm for the SW and CP,
respectively. Method A presented a 2% reduction in displacement due to rocking in the CP case
when compared to the 3 m SW, decreasing from 72% to 70%, whereas sliding remains very close
to 30%, reducing from 40% to 27%. Method B predicts 19.1 and 29.7 mm of total displacements,
with about 38% sliding and 55% rocking in both cases. Method C predicts an increase from 50%
of rocking to 72% in CP applications (from 13.6 to 33.4 mm). The result also highlights that shear
69

and bending remained almost constant and less than 10% of the total displacements for all
methods. In this example, the displacements almost doubled from the SW to the CP,
demonstrating a greater energy dissipation in CP.

Table 3.10. Example 2 - Summary of the lateral resistance
Lateral resistance of SW (kN)

Lateral resistance of CP (kN)

Method
A

25.0

14.2

N/A

50.0

21.9

N/A

B

25.0

15.6

15.2

50.0

28.3

27.5

C

30.0

15.7

N/A

48.0

24.3

N/A

40

SW capacity [kN]

35
30
25

30.0
25.0

20
15

25.0
15.6

14.2

15.2

15.7

10
5
0

N/A

N/A

Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2019)
2020)
Rocking

Sliding

Combined

Figure 3.19. Example 2 - Single wall lateral resistance

70

CP capacity [kN]

50

50.0

50.0

48.0

40
30

28.3

27.5

21.9

24.3

20

10
N/A

N/A

0

Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et
et al. 2017) et al. 2019)
al. 2020)
Rocking

Sliding

Combined

Figure 3.20. Example 2 - Coupled wall lateral resistance

In general, the results from example 2 follow the same trends as example 1. Method A
has a smaller rocking capacity than the other investigated methods, with conservative forces of
14.2 kN for the SW and 21.9 kN for the CP scenario. For the SW and CP cases, Method B displays
capacities of 15.6 kN and 28.3 kN, respectively. The sliding resistance is almost equal throughout
all approaches, with minor fluctuations of 5% to 20% for Method C, which unlike Example 1,
demonstrates a reduction for CP and an increase for the SW scenario. While Method B considers
combined resistance as the governing case for rocking and sliding, it has very little effect on total
capacity, with a 3% drop for the single and coupled walls. Method C had the highest capacity in
SW for this example. The displacement results were determined as shown in table 3.11.

Table 3.11. Example 2 - Summary of the displacement contribution
Displacement contribution of SW (mm)

Displacement contribution of CP (mm)

A

0.0

0.6

8.3

37.5

46.5

0.0

0.3

4.2

17.1

21.6

B

2.8

0.6

8.3

37.5

49.3

1.4

0.3

4.2

9.7

15.5

C

0.0

0.6

5.0

32.6

38.2

0.0

0.3

3.1

14.6

18.1

Method

71

SW displacement [mm]

60
49.3

46.5

50

38.2

40
30
20
10
0

Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et al.
et al. 2017)
et al. 2020)
2020)
Bending

Shear

Sliding

Rocking

Figure 3.21. Example 2 - Displacement contribution for SW

CP displacement [mm]

25

21.6

20

18.1
15.5

15
10
5
0

Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et
et al. 2017) et al. 2020)
al. 2020)

Bending

Shear

Sliding

Rocking

Figure 3.22. Example 2 - Displacement contribution for CP

The displacement results for Example 2 showed the same pattern from Example 1. For
the CP, Method A predicted the largest total displacements of 21.6 mm. Similarly, as compared
to the single wall, it revealed a 2% reduction in displacement from rocking in the CP shear walls,
moving from 82% to 80% - sliding remains very near to 20%, increasing from 17% to 20%, from
SW to CP, respectively. Method B predicted 49.3 and 15.5 mm of total displacements, with 17%

72

to 27% of sliding from SW to CP, and 76% of rocking to 62% for SW to CP, respectively. In CP
applications, Method C showed an increase in rocking from 81% to 86%, moving from 38.2 to
18.1 mm. The results also indicate that shear and bending displacements contributed for less
than 10% of total displacements for all methods in the Example 2. For the inelastic analysis, the
coupled walls of Examples 1 and 2 were compared between Method C and D. The results are
summarized in Table 3.12 and Figure 3.23.

Table 3.12. Summary of inelastic assessment for academic examples
Method

C - Masroor
et al. (2020)

D - Nolet et
al. (2019)

Example

[kN]

[kN]

[kN]

[kN]

[kN]

[mm]

[mm]

[mm]

[mm]

[mm]

1

13.5

42.0

49.5

58.8

58.8

1.1

11.5

15.3

32.8

100.0

2

8.3

24.3

25.2

30.1

30.1

1.0

17.0

18.5

48.2

100.0

1

13.5

37.5

48.5

48.5

N/A

0.0

8.0

14.3

100.0

N/A

2

8.3

21.9

24.2

24.2

N/A

0.0

14.0

18.0

100.0

N/A

The inelastic results demonstrate almost equal slopes for Method C and D for the input
data values (Figure 3.23). Moreover, Method D showed 20% lower values for peak force for both
examples, also presenting a lower area under the curve than Method C, which indicates a smaller
propensity to dissipate energy than Method C. Method C presents one more segment than
Method D, because it goes until to point three by including the angle brackets in its analysis. The
case studied in this thesis from Nolet et al. (2019) is an elastic-plastic force-displacement curve
for a kinematic path between

−

, where the yielding of the vertical joint is achieved in

CP behaviour and the final plastic behaviour is represented by a CP failure. Regarding the
maximum displacements captured by these methods, Method C presented about 20% to 40%
higher displacement compared to the vertical joint yield point in Method D. Both methods were
terminated at a 100 mm ultimate displacement in this example.
73

75

F [kN]

60
45
30
15
0
0

20

40

Example 1 - Method C
Example 2 - Method C

60
d [mm]

80

100

Example 1 - Method D
Example 2 - Method D

Figure 3.23. Curves from analytical results

3.3.4. Discussion
The results highlight the differences between the examined methods and indicate that their
diverse hypotheses lead to distinct results. For instance, Method A predicted smaller capacity
values than the other methods due to it relies on the resistance of either the outermost hold-down
or the yielding of the fasteners in the vertical joint to dictate the design rocking resistance. In
contrast, the angle brackets are designed to withstand sliding exclusively. Method B considers
the contribution of all brackets in the rocking resistance, leading to higher rocking resistance
values. Method C considers the bi-axial behaviour of brackets, but the minimum resistance is
dictated by whichever connection yields first. Method D depicts the elastic-perfectly plastic
behaviour of brackets while ignoring their bi-axial behaviour.
Regarding the sliding resistance for Example 2, Method C showed smaller values for CP
shear wall and greater values for SW shear walls – the opposite occurred in Example 1. This
difference occurred since the sliding resistance is based on the hold-down and angle bracket
stiffnesses and resistances values. The sliding resistance of Method C is associated with the
74

horizontal hold-down resistance, which does not occur with the other methods. Since Method C
is the only one that considers hold-downs carrying the horizontal load, the sliding resistance may
present minor changes compared to other methods and be governed by the hold-downs.
Concerning the rocking resistance values, Method B presented higher values because it
considers a unique resistance, with a single equation accounting for the resistance of all
connections in a unified equation. The shear-uplift interaction applied for Method B is only used
in the angle bracket because these carry vertical and horizontal loads, and it does not seem to
influence the results significantly. For the CP shear walls in Method A and C, the minimum
resistance is dictated by the resistance of the vertical joint that are substantially smaller than the
hold-down capacity. On the other hand, Method C predicted greater rocking resistance than
Method A because of the contribution of the vertical connections’ stiffness,

. Both methods are

comparable except for the introduction of the bi-axial behaviour of connectors.
The strength decreases in CP behaviour for Example 1, as the resistance is highly
influenced by the width of the panel, reducing its lever arms. For Example 2, the resistance of the
wall against rocking was greater than the same single wall of 1 m width because the vertical joint
works as a spring in parallel. The sliding resistance of the shear wall must be higher than the
rocking resistance to avoid sliding failure of the shear walls and to meet the current CSA-O86
provisions. To increase the sliding resistance of the wall, a minimum number of brackets are
required for the design

>

/

, . This condition was met for both examples and all methods.

In relation to the overall displacements, Methods A and C do not consider CLT bending.
Hence their values in the SW case are lower than those predicted by Method B. As Method A
only has a hold-down in parallel with the vertical joint to accommodate horizontal displacements,
in the CP case, this method has greater rocking contributions. Furthermore, Method B in both
examples properly accounts for the reduction in stiffness due to the positioning of the connectors.
Specifically, the rocking equation for the right panels is different from the left panels since the

75

tensile stiffness and resistance of the leftmost bracket connector are different between the panels,
leading to a reduction of rocking when compared to other approaches.
In the first example, the CP case produces greater displacements from rocking, making it
appropriate to dissipate more energy than SW. The reason is associated with the use of half of
the width of the panel, which promotes rocking at the expense of sliding. The top displacement is
lower when

increases to

, . But,

to the power of two yields higher impact in the rotation

angle, leading to greater rocking contributions. Ultimately, the sliding displacements in Method C
is smaller because of the bi-axial behaviour of the hold-downs and angle brackets. For the
Example 2, the sliding displacements have decreased due to adding one more angle bracket.
The rocking contribution is reduced with the same panel width as the connectors work in parallel
with the vertical joint for CP applications.
Concerning the inelastic calculation, Method D uses the values of Method A to define the
yield of the vertical joint. Despite the proximity of the results of the nonlinear analysis for Methods
C and D (Figure 3.23), there is greater energy dissipation when the bi-axial behaviour is taken
into consideration. The resistance predicted by Method D is smaller than for Method C due to the
contribution of the angle bracket, which is essential for estimating the maximum capacity versus
experimental testing results; this impact will be further investigated in Chapter 4 with test data.
In conclusion, the primary kinematic behaviour of the wall shifts from rocking to sliding with
low panel aspect ratio. The examples confirm that utilizing higher aspect ratios trigger rocking,
meeting the CSA-O86 provisions that sliding should be avoided. It is crucial to highlight that shear
wall configurations and connection systems significantly impact the shear wall's behaviour. To
facilitate CP behaviour, it is necessary to design the vertical fasteners so that they yield prior to
the hold-downs. Finally, the rocking and combined rocking–sliding resistance formulations
provided a conservative approach but did not affect the results. Designers are encouraged to use
rocking formulae that satisfy the CSA-O86 design standards and ensure that sliding is minimized.

76

Chapter 4: Comparison of Analytical Methods and Test Results
4.1. UNBC CLT Shear Wall Test Data with Nailed Connections
Note: The nailed CLT shear wall tests and analyses presented herein were not conducted as part
of this thesis. Nevertheless, the findings are included here for comparative purposes. The test
series aimed to investigate the seismic behaviour of single and coupled nailed CLT shear wall
systems where panel aspect ratio, superimposed dead load, number of angle brackets, and
number of nails in the vertical spline connection were all considered. Green Construction through
Wood (GCWood) provided funding for the experiments carried out in association with Fast + Epp.
The presented findings are at the time of writing under peer review.1
4.1.1. Materials and Methods
CLT shear walls were tested at the UNBC Wood Innovation and Research Laboratory
(WIRL), located in Prince George, Canada. A total of 27 CLT shear walls: 8 single-panel, and 19
coupled panels were tested, specifically using 4 monotonic and 4 reversed cyclic tests on single
panels and 4 monotonic and 15 reversed tests on coupled panels. Two aspect ratios (height to
length) of the wall panels were investigated: 2.5:1 (3000 mm × 1200 mm) and 3.5:1 (3000 mm ×
850 mm) for both single and coupled panel shear walls, see Figure 4.1. On each shear wall, two
hold-downs were attached on both edges for the single panels and the two outer edges of the
coupled panels. The panels were attached to the base with either one or two angle brackets. The
coupled panels were vertically connected using plywood splines attached with two rows of eight
nails spaced on centre, with distances varied between 75 mm and 300 mm.

1: Shahnewaz, Dickof, Tannert: Experimental parameter study on single-story nailed CLT shear walls by.

77

Figure 4.1. CLT shear wall test specimens: single walls with aspect ratios of a-b) 2.5 and c) 3.5; couped
walls with aspect ratios of d-e) 2.5 and f-g) 3.5 [dimensions are in mm]. Note: schematic created by Md
Shahnewaz, replicated with permission.

The CLT panels were 191 mm thick 7-ply, strength grade 191V2 (CSA, 2019), the holddowns were HT440, and the angle brackets were TCN200, both attached with Ø 4×60 mm Anker

78

nails. The panel-to-panel vertical connections for the coupled shear walls were provided with
surface mounted 25×140 mm Douglas fir plywood splines, attached to the panel with two rows of
4Ø×60 mm Anker nails. Two levels of superimposed vertical gravity loads were applied at the top
of the wall: 20 kN/m and 30 kN/m. The CLT shear wall parameters are summarized in Table 4.1.
The quasi-static monotonic pushover tests were conducted at a rate of 10 mm/min. Tests
were stopped at failure, defined as the point where the load-carrying capacity dropped to 80% of
the maximum load. The reversed cyclic tests followed the abbreviated CUREE loading history, a
displacement-controlled loading procedure per ASTM E2126 (ASTM, 2011). The horizontal,
vertical, and relative panel displacements were recorded with LVDTs and string pots. The test
setup and a photo of the sensors positioning are shown in Figure 4.2.
The hold-downs, shear brackets, and spline joints were tested at the component level to
determine their strength and stiffness; results are presented in Table 4.2. From the reversed cyclic
tests, both the maximum positive and maximum negative values,
The corresponding deformations,

and

and

were recorded.

were the measurements at the top right

corner of the shear walls (sensor #1 in Figure 4.2). The other parameters, i.e., ultimate load ( ),
displacement at ultimate load (
(

) and ultimate stiffness (

), yield load ( ), yield displacement (

), stiffness at service

), for both connections and shear walls were computed based on

equivalent energy elastic-plastic (EEEP) curves according to ASTM E2126 (ASTM, 2011).
Although there is a positive and negative side to the cyclic tests, the data will be simplified in the
subsequent analyses and only the positive value will be used.

79

Table 4.1. CLT shear wall specimen description

Wall #

Aspect
Ratio

# of
angle
brackets

Nail spacing
[mm]

Vertical Load
[kN/m]

50%
reduction of
hold-down
nails

Loading

SW1

2.5:1

2

-

20

-

Mon

SW2

2.5:1

1

-

20

-

Mon

SW3

2.5:1

2

-

20

-

Cyc

SW4

2.5:1

1

-

20

-

Cyc

SW5

3.5:1

1

-

20

-

Mon

SW6

3.5:1

1

-

20

R

Mon

SW7

3.5:1

1

-

20

-

Cyc

SW8

3.5:1

1

-

20

R

Cyc

CW01

2.5:1

4

300

20

-

Mon

CW02

2.5:1

4

150

20

-

Mon

CW03

2.5:1

4

300

20

-

Cyc

CW04

2.5:1

4

300

30

-

Cyc

CW05

2.5:1

4

150

20

-

Cyc

CW06

2.5:1

4

150

30

-

Cyc

CW07

2.5:1

2

300

20

-

Cyc

CW08

2.5:1

2

300

30

-

Cyc

CW09

2.5:1

2

150

20

-

Cyc

CW10

2.5:1

2

150

30

-

Cyc

CW11

2.5:1

2

75

20

-

Cyc

CW12

3.5:1

2

300

20

-

Mon

CW13

3.5:1

2

300

20

-

Cyc

CW14

3.5:1

2

150

20

-

Cyc

CW15

3.5:1

2

75

20

-

Cyc

CW16

3.5:1

2

300

20

R

Mon

CW17

3.5:1

2

300

20

R

Cyc

CW18

3.5:1

2

150

20

R

Cyc

CW19

3.5:1

2

75

20

R

Cyc

80

Figure 4.2. a) CLT shear wall test setup; b) Positioning of sensors. Note: schematic created by Md
Shahnewaz, replicated with permission.

Table 4.2. Connector test results. Note: data computed by Md Shahnewaz, replicated with permission.
Test ID

[kN]

[mm]

[kN/mm]

[kN/mm]

[kN]

[mm]

[kN]

[mm]

HD-F-M

64.3

33.4

3.6

2.7

53.8

15.3

51.4

37.8

HD-F-C

62.9

31.1

3.3

2.8

54.2

16.4

50.3

36.6

HD-H-M

51.8

17.5

5.3

4.6

44.9

8.8

41.4

22.3

HD-H-C

57.7

19.6

4.7

4.4

51.7

11.1

46.2

23.9

AB-F-M

56.5

35.5

1.4

1.4

48.0

34.0

45.2

37.2

AB-F-C

51.0

34.9

1.8

1.5

44.3

25.5

40.8

37.4

AB-H-M

45.3

14.1

6.1

5.3

40.5

6.7

36.2

20.0

AB-H-C

52.5

17.0

5.3

5.1

47.4

9.1

42.0

21.1

N-8-M

42.1

23.1

11.8

6.3

36.8

3.1

33.7

32.3

N-8-C

40.5

22.4

9.0

6.3

32.4

3.7

29.4

26.0

81

The backbone curve did not exhibit a well-defined yield point. Thus, both the yield
displacements from EEEP,

, and the displacement at

along the backbone curve,

, , were

determined, see Figure 4.3.

Figure 4.3. EEEP procedure

4.1.2. Shear Wall Test Results
The test results are summarized in Table 4.3. When the hold-downs and angle brackets
were connected to the floor without washers, both coupled and single shear wall specimens
exhibited fastener yield in the angle brackets and hold-downs, failure of the spline joints in coupled
walls, and plastic deformation of the horizontal steel plates for both hold-downs and angle
brackets.

82

Table 4.3. Main results of CLT shear wall tests. Note: data computed by Md Shahnewaz, replicated with
permission.

Walls #
SW1
SW2
SW3
SW4
SW5
SW6
SW7
SW8
CW01
CW02
CW03
CW04
CW05
CW06
CW07
CW08
CW09
CW10
CW11
CW12
CW13
CW14
CW15
CW16
CW17
CW18
CW19

,

[kN]

[mm]

[kN]

[mm]

[mm]

[kN]

[mm]

41.0
33.0
38.8
34.6
24.8
23.9
22.2
26.0
73.2
74.2
65.3
69.1
75.5
70.2
50.7
54.1
57.8
61.8
73.3
35.2
26.6
34.5
51.8
37.4
40.5
38.6
60.3

110.5
103.0
91.0
90.9
140.2
70.6
120.2
69.9
110.1
108.4
94.4
89.9
116.9
63.0
59.5
88.2
62.9
62.9
62.9
114.7
62.9
63.0
85.8
83.5
86.4
62.9
90.0

33.5
27.0
32.1
28.8
20.9
21.1
19.3
21.4
62.5
63.7
54.0
60.7
65.3
58.5
40.7
46.5
50.0
52.5
60.9
28.9
23.2
28.6
41.4
32.1
34.5
35.0
49.7

27.0
30.0
30.1
28.0
44.7
30.2
46.9
29.8
30.2
20.1
21.1
21.3
18.6
13.5
14.8
17.5
13.2
11.0
16.1
26.2
13.8
8.9
11.7
20.3
25.2
26.8
21.8

64.1
59.6
58.7
60.6
90.1
50.9
85.3
42.5
66.1
53.8
52.7
58.0
51.8
44.5
39.2
47.8
43.3
44.0
39.4
68.6
43.9
41.8
42.1
45.3
47.2
35.7
41.2

32.8
26.0
31.0
28.4
19.9
19.1
18.4
19.9
58.6
59.4
52.3
56.7
60.2
53.8
37.9
43.1
45.0
50.2
58.9
28.1
21.0
27.7
38.6
29.9
31.4
32.8
45.6

119.2
111.0
109.8
93.4
173.6
114.2
141.7
92.5
141.2
127.7
116.7
126.4
132.7
127.5
84.9
108.4
120.3
89.8
73.6
130.2
145.0
116.8
96.5
125.5
95.7
116.2
99.9

4.2. Model Input Parameters
Two levels of dead loads were applied, different panel aspect ratios, and both SW and CP
cases were considered. The modulus of elasticity, , was provided by Structurlam Mass Timber
Technical Guide as 9,500 MPa. The equivalent shear modulus of the CLT panel,

, was

calculated based on Eq. (3.44). The width of the timber board, , and the thickness of the timber

83

board, , are 125 and 35 mm, respectively, resulting in an equivalent shear modulus of 415 MPa.
The coefficient incorporating the effect of the compression zone in the panels for Method C, ,
was equal to unity for shear wall calculations.
The further input values for comparing the analytical models are presented in Table 4.4.
The angle brackets are assumed to have equal sliding and rocking resistance, whereas the shear
capacity of hold-downs is considered just one-fifth of its uplift capacity (Gavric et al., 2015). The
hold-down's elastic stiffness and yield strength in the nailed tests presented below are based on
full nailing (F) and reduced nailing (R) nailing which includes the use of washers. The nail test
was calculated with a 50% reduction in nails for hold-down connections and various nail spacing
for the spline joint. The number of vertical fasteners depends on the nail spacing. The number of
fasteners in the vertical joint are 10, 20, and 40 for nail spacings of 300, 150, and 75 mm,
respectively. Table 4.4 summarized the connector input parameters. Regarding the vertical joint,
the values presented in the table refer to the properties of a fastener, being directly proportional
to the number of nails for different number of fasteners used in the vertical joint.

Table 4.4. Connection model input values
Hold-down
Test type

Angle bracket

Vertical joint

,

,

,

,

,

,

,

,

[kN/mm]

[kN/mm]

[kN]

[kN]

[kN/mm]

[kN/mm]

[kN]

[kN]

[kN/mm]

[kN]

Full

3.4

0.7

54.0

10.8

1.6

1.6

46.2

46.2

0.6

2.2

Reduced

5.0

1.0

48.3

9.7

-

-

-

-

-

-

84

4.3. Evaluation of the Elastic Strength of Nailed CLT Shear Walls
4.3.1. Results
Variables such as aspect ratio, number of brackets, reduction in nails, and dead load were
studied to assess the accuracy of the experimental data for the elastic strength assessment. The
minimum resistance between sliding and rocking for the analytical methods was compared with
the experimental yield strength values,

, from the EEEP curves. Afterward, the smaller value of

rocking and sliding was compared to the experimental value

, generating the

/

ratio. The

results are summarized in Table A.1, and illustrated in Figure 4.4 and Figure 4.5 for tests SW1
and CP1, respectively. All other shear wall tests are presented in Appendix A.
The investigated aspect ratio of the studied pairs of shear walls (SW4 & SW7, SW2 &
SW5, CP7 & CP13, CP9 & CP14, and CP11 & CP15) comprised 2.5:1 and 3.5:1 ratio (ℎ: ).
Generally, the capacity of walls with an aspect ratio of 3.5:1 was nearly 38% lower than the walls
with an aspect ratio of 2.5:1. Regarding the aspect ratio results, the SW walls showed a reduced
rocking capacity of 33% in all methods when the aspect ratio was changed from 2.5:1 to 3.5:1.
For the CP walls, there was a reduction of 35%, 33%, and 35% for Methods A, B, and C,
respectively. The sliding resistance values were constant between all the shear walls. There was
an increase in the rocking resistance of the SW shear walls for Methods B and C in relation to
Method A: 27% and 21%, respectively. The increase concerning CP was different, showing
increases for Methods B and C in relation to Method A, of approximately 90% and 5%,
respectively.
Typically, gravity loads increased the rocking capacity in all the studied walls (CP3 & CP4,
CP5 & CP6, CP7 & CP8, and CP9 & CP10), and the methods properly predicted this behaviour.
The results point to an increase in rocking resistance when the superimposed dead load changed
from 20 kN/m to 30 kN/m, by approximately 18%, 8%, and 17% for Methods A, B, and C,

85

respectively, while sliding remained constant. The rocking resistance increased from Methods B
and C in relation to Method A by approximately 110% and 6%, respectively.
The wall-to-floor angle bracket varied between two to four and one to two for the coupled
and single walls. The studied pairs of shear walls comprised of SW1 & SW2, SW3 & SW4, CP3
& CP7, CP5 & CP9, CP4 & CP8, and CP6 & CP10. A higher number of angle brackets results in
higher wall capacity. Concerning the number of brackets, there was a reduction in resistance due
to sliding in the single shear walls applications by around 50%, 50%, and 35% for Methods A, B,
and C, respectively, when the number of angle brackets changed from two to one. The reductions
in resistance remained consistent with the previous values for Methods A and B regarding the CP
shear walls. However, for Method C, the reductions were around 40%. The rocking resistance
showed reductions of 17% for Method B and 5% for Method C for all shear walls - Method A
exhibited constant rocking values resistance.
Regarding the reduction in hold-down nails, several shear walls were tested with an aspect
ratio of 3.5:1 (SW5 & SW6, SW7 & SW8, CP12 & CP16, CP13 & CP17, CP14 & CP18, and CP15
& CP19) to facilitate the yielding in hold-downs nails, which is a desirable failure mechanism to
allow rocking of the wall panels. The number of nails was reduced by 50% in the hold-downs, and
other parameters were fixed to study only the influence of the nails on the shear walls. The
reduction in the number of nails indicated constant sliding resistances for Methods A and B for
both SW and CP cases - Method C showed a drop for single and coupled walls by approximately
30%, respectively. The rocking resistance for SW applications showed reductions of 9%, 7%, and
12% for Methods A, B, and C, respectively. Regarding the rocking resistance of CP shear walls,
there was an increase of 8% for Method A, 7% for Method C, and a 5% reduction for Method B.

86

SW capacity [kN]

100
90
80
70
60
50
40
30
20
10
0

92.3

92.3
71.7

36.1

32.0

23.8

Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et al.
et al. 2017)
et al. 2019)
2020)

Rocking

Sliding

Test data

Figure 4.4. Strength comparison among the methods and test data for SW1

200

184.6

184.6

CP capacity [kN]

175
150
121.8

125
100
75

50
25

60.4
25.2

22.8

0
Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et
et al. 2017) et al. 2019)
al. 2020)
Rocking

Sliding

Test data

Figure 4.5. Strength comparison among the methods and test data for CP1

87

4.3.2. Shear-uplift Interaction
The lateral load was calculated using a shear-uplift interaction formula (circular or linear
domain) for Method B to consider sliding and rocking acting simultaneously in the angle brackets.
The resistance of the CLT shear walls could be lower than the resistance of only sliding and
rocking evaluated separately, as both the sliding and rocking resistances are a function of the
resistance of the angle bracket,

,

=

, , which is measured in a uniaxial direction, in shear or

tension. Therefore, the capacity of the left bracket under combined rocking–sliding reaches a
value lower than its ultimate uniaxial resistance.

,

comprises the combined rocking and

sliding force calculated using a quadratic interaction as per Eq. (3.8).
interaction.

,

applies a linear

comprises the rocking resistance of the shear walls, which were the critical values

between sliding and rocking of each shear wall. A comparison between the linear and circular
domain of the shear-uplift interaction formula, aiming to verify which approach provides better
compliance against the test data, is provided in Table A.2.
The results, illustrated in Figure 4.6, indicate a reduction of 2 to 12% of the resistance
when considering the combined effects of rocking and sliding. The higher number of angle
brackets leveraged a more substantial decrease in resistance for coupled walls CP1 to CP6 –
ranging from 10% to 12%. This reduction increases the sliding force, leading to a more significant
reduction in the combined resistance as per Table 3.2. The circular domain usually brings the
closest value compared to the test data. Overall, the shear-uplift interaction applied for Method B
does not seem to influence the results outstandingly. The shear-uplift requires iterations, which is
not desirable for design purposes. It is verified that it is not efficient to make the interactions given
the small variation of the results - with values below 15% of the overall capacity from Method B.
Using the shear wall capacity value instead of applying the shear-uplift interactions to the nailed
CLT shear walls is advisable.

88

1.4
1.2

Fy / Force

1.0
0.8
0.6
0.4
0.2

SW1
SW2
SW3
SW4
SW5
SW6
SW7
SW8
CP1
CP2
CP3
CP4
CP5
CP6
CP7
CP8
CP9
CP10
CP11
CP12
CP13
CP14
CP15
CP16
CP17
CP18
CP19

0.0
Shear wall capacity
Combined rocking-sliding (linear domain)
Combined rocking-sliding (circular domain)

Figure 4.6. Comparison against test data and shear-uplift interactions

4.3.3. Discussion
Verifying the analytical methods that predict elastic resistance is fundamental for projects
located in areas where the elastic strength governs the design. This could assist practicing
engineers in selecting the method that best suits their intentions. Overall, the three methods
predicted similar values for SW as the hold-down is the connection that reaches the yielding point.
However, Methods A and C underestimate the actual rocking ability of the CP shear walls,
while Method B gives accurate results when compared to the test data. This is because Method
A only relies on the resistance of either the outermost hold-down or the yielding of the vertical
joint to dictate the rocking resistance while the angle brackets are designed to withstand sliding
only. Method C considers the bi-axial contribution of the connections. Still, the resistance is
dictated by whichever connection yields first - the vertical joint yields before the hold-downs for
the evaluated walls, leading to lower results than Method B. In contrast, Method B considers the
rocking contribution of all connections, leading to higher, and more accurate resistance
predictions than the other methods.

89

The impact of the aspect ratio was relatively consistent between the methods. The
reductions in rocking resistance presented almost the same values with the decrease in the width
of the walls. With the change in the panel aspect ratio from 2.5:1 to 3.5:1, the dominant kinematic
behaviour is always rocking, led by the increase in the angle of rotation of the shear walls. On the
other hand, sliding resistance values remained constant for the aspect ratio evaluation.
The dead load reduces rocking in shear walls since there is no rotation in the panels before
reaching the activation force. The activation force is defined as the lateral force at which the
gravity load is overcome, leading to the beginning of rotation in the panels. Accordingly, the
variation was relatively constant and consistent among the studied methods. Thus, it is possible
to take advantage of an increased dead load to increase the rocking resistance of the CLT shear
walls. On the other hand, the sliding resistance is not affected by relying exclusively on the number
of fasteners connected to the foundation.
The number of angle brackets directly influences the sliding resistance. The reductions
from Method C were less than 50% because the sliding equation incorporates the horizontal
rigidity of the hold-downs, adding stiffness to the system. Since Method C considers hold-downs
carrying the horizontal load, there is a difference in sliding resistance depending on the stiffness
and number of connectors placed along the shear wall. The rocking resistance of Method A did
not present variations between shear walls due to the number of angle brackets only influencing
the sliding resistance for this approach. For Method B, as all connections contribute to rocking,
there was a higher rocking reduction than other methods. Finally, SW rocking resistance for both
Method A and C are governed by the hold-down, and it is higher in Method C than in Method A
because the bi-axial behaviour leads to a higher stiffness contribution in the vertical direction,

.

Regarding the nail reduction, the analytical methods presented values closer to the
experimental values obtained with full nailing because the nail reduction was combined with an
increase in stiffness due to the implementation of washers. The sliding resistance is not affected

90

in Method A and B because they rely exclusively on the stiffness of the angle brackets connected
to the foundation, and the addition of washers does not impact the horizontal stiffness of the angle
brackets. In contrast, Method C considers hold-downs carrying the horizontal load, leading to a
difference in sliding resistance depending on the stiffness and number of connectors placed along
the shear wall. Due to the increased rigidity of the hold-downs with the addition of washers, more
load is attracted to the hold-downs. As a result, since the horizontal resistance of the hold-downs
is less than the angle brackets, it ends up dictating the horizontal resistance of Method C, reducing
the values of the sliding resistance. The rocking resistance of SW shear walls decreased due to
the smaller resistance associated with reduced nailing. There was a small variation in the rocking
strength of Method B compared to the other methods due to the increase in stiffness provided by
the addition of washers, which is not captured in the rocking equation – it only depends on the
geometric properties of the shear wall. In contrast, the coupled wall rocking strengths for Method
A and C are directly proportional to the parallel stiffness of the hold-downs with the vertical joint.
A summary of the experimental forces,

, and the minimum forces between sliding and

rocking for each method are presented in Figure 4.7 to Figure 4.9 – the results are based on
Table A.1 main findings where

governed the design. The averages of all the

/

ratios were

1.7, 0.9, and 1.5 for Methods A, B and C, respectively. The values range from 1.1 to 2.8, 0.7 to
1.1, and 0.9 to 2.5 for Method A, B, and C. The x-axis represents forces values obtained by the
analytical methods, whereas the y-axis corresponds to the experimental yield forces. It is evident
that Method B provides a remarkable estimate for SW and CP applications. The overall resistance
of the method can predict a value particularly close to the

from the EEEP. The rocking

resistance values almost converge to a linear curve. Method A and C propose that the governing
resistance is anticipated from the yielding of the fastener in the vertical joint, leading to smaller
values than the EEEP theoretical approach. As a result, these methods significantly
underestimate the observed experimental values, as illustrated in Figure 4.10.

91

70
60

Fy [kN]

50
40
30
20
10
0
0

10

20

30
40
Frg [kN]

50

60

SW1
SW2
SW4
SW5
SW6
SW7
SW8
CP1
CP2
CP3
CP4
CP5
CP6
CP7
CP8
CP9
CP10
CP11
CP12
CP13
CP14
CP15
CP16
CP17
70 CP18
CP19

Figure 4.7. Comparison against test data and analytical results for Method A

70
60

Fy [kN]

50
40
30
20

10
0
0

10

20

30
40
Frg [kN]

50

60

70

SW1
SW2
SW3
SW4
SW5
SW6
SW7
SW8
CP1
CP2
CP3
CP4
CP5
CP6
CP7
CP8
CP9
CP10
CP11
CP12
CP13
CP14
CP15
CP16
CP17
CP18
CP19

Figure 4.8. Comparison against test data and analytical results for Method B

92

70
60

Fy [kN]

50
40
30
20
10
0
0

10

20

30
40
Frg [kN]

50

60

70

SW1
SW2
SW3
SW4
SW5
SW6
SW7
SW8
CP1
CP2
CP3
CP4
CP5
CP6
CP7
CP8
CP9
CP10
CP11
CP12
CP13
CP14
CP15
CP16
CP17
CP18
CP19

Figure 4.9. Comparison against test data and analytical results for Method C

Figure 4.10 shows that Method B presents values relatively close to 1.0 for SW and CP,
while Methods A and C only provide adequate predictions for SW. For the coupled walls, the
yielding of the vertical fasteners dictates the design and ends up moving away from the values
proposed by the EEEP procedure. Therefore, the assumption presented by Method B that
brackets can carry forces from both sliding and rocking following a triangular load distribution,
unified in a single equation, leads to a better approximation. The moment at the lower-right corner
of the CLT shear wall with the rocking reaction was considered for the rocking resistance values.
Regarding the computational effort of the analytical methods utilized herein, it's worth
noting that Method B involves simplified equations, it estimates the rocking and sliding resistance
by using the equilibrium of forces in the x and z directions rather than minimum potential energy
and derivative concepts to establish wall capacity, rotation, displacement, and stiffness formulas.
As a result, Methods A and C present solutions that lead to more sophisticated equations. These

93

solutions are more appropriate for software development, particularly for higher numbers of
panels. Consequently, Method B provides more straightforward calculations, which is an essential
aspect for practising engineers.
Furthermore, the coupled walls with 300 mm spacing along the spline joint were facilitated
to rotate due to the lower stiffness of the vertical joint compared to the 150 mm and 75 mm walls,
where there were more fasteners attached to the vertical joint. An increase in rocking resistance
was observed between the CP7, CP9 & CP11 walls, and the same occurred with the CP17, CP18
& CP19 walls. This demonstrates that the number of fasteners in the vertical joint contributes
significantly to the rocking resistance as there is more vertical rigidity in parallel to the hold-downs
with a greater number of vertical fasteners. Lastly, the analytical results were closer to the
experimental findings when the loads were monotonic, showing that cyclic loading leads to
resistance losses due to low cycle fatigue induced in the walls.
4.0
3.5
3.0

2.0
1.5
1.0
0.5
0.0

SW1
SW2
SW3
SW4
SW5
SW6
SW7
SW8
CP1
CP2
CP3
CP4
CP5
CP6
CP7
CP8
CP9
CP10
CP11
CP12
CP13
CP14
CP15
CP16
CP17
CP18
CP19

Fy / Frg

2.5

Method A (Casagrande et al. 2017)
Method B (Shahnewaz et al. 2019)
Method C (Masroor et al. 2020)

Figure 4.10. Summary of all shear walls for

over

94

4.4. Evaluation of the Elastic Displacement of Nailed CLT Shear Walls
4.4.1. Results
The displacements from bending, shear, sliding, and rocking, were computed for the
studied methods at yield force, are presented in Table B.1.
Overall, the results from Method B showed higher total displacement values for SW shear
walls and lower values for CP applications compared to other methods. In contrast, Methods A
and C present very comparable results. The individual contributions of displacements point to a
dominant rocking behaviour of all walls, followed by sliding, bending, and shear. The total
displacement of the combined contribution of bending and shear was less than 3% for Methods
A and C. However, the shear and bending in Method B ranged from 8% to 20%.
Regarding the aspect ratio results, an increase in rocking contribution of all shear walls
was observed at approximately 15%, 10%, and 13% for Methods A, B and C, respectively. The
sliding reductions were 15%, 16%, and 13% for Methods A, B, and C. Changing the aspect ratio
from 2.5:1 to 3.5:1 increased the total displacements by between 10 to 30 mm for SW shear walls.
Despite the increase in rocking, the CP walls showed reductions of about 3 mm of the total
displacement. With the reduction of the panel width, , the displacements from bending increased
approximately by almost double for Method B, exceeding 10% of total displacements.
With respect to the imposed dead load, it can be noted that this contributes to the decrease
of rocking in all methods by approximately 3%. In the case of walls CP5 and CP6, there was a
more significant 20% reduction in total displacements. On the other hand, there was an increase
in sliding rates of 2% for all the methods. The overall displacement of the combined contribution
between bending and shear was less than 4% for Methods A and C, and 12% for Method B.
Regarding the number of brackets, there was an increase in sliding with the reduction in
the number of angle brackets, 13%, 12%, and 5% for Methods A, B, and C, respectively. For

95

Methods A, B, and C, the rocking reductions were approximately 12%, 10%, and 5%. For CP
shear walls, the overall sliding contribution exhibited an increase of 17%, 18%, and 12% for
Methods A, B, and C. Regarding the rocking reduction, the decrease was approximately 17%,
15%, and 11% for Methods A, B, and C. The individual contributions of displacements indicate a
predominant effect of rocking for single (62% and 83%) and couples walls (30% to 75%).
The results of the reduction in HD nails produced an increased sliding for SW shear walls
of 6%, 4%, and 2% for Methods A, B, and C, respectively. The rocking contribution showed a
decrease of 6%, 8%, and 2% for Methods A, B, and C. Sliding was only impacted around 2%.
The individual contributions of displacements indicate a predominant rocking behaviour, between
42% and 88% of the total displacements.
The sum of all kinematic motions was compared to the values measured in the tests at
each shear wall’s top displacement. The
from the EEEP curve and the
curve of the tests using the

,

displacement values refer to the yield displacement

refers to the displacement value extracted from the backbone

force value. The comparison is presented in Table B.2. It can be

seen that the displacement values from the EEEP curve are very conservative and do not
approach the values of the analytical methods for single shear walls. For example, for SW1 the
values were 27.0 mm, while the extrapolated value from the envelope curve,
64.1 mm, with
Conversely,
the

,

/
/

,

, , reached

ratios of 0.4, 0.4, and 0.6 for Method A, B, and C, respectively.
ratios were 1.0, 0.9, and 1.3 for Method A, B, and C. However, for CP1

,

values were 30.0 mm, while the extrapolated value for the envelope curve,

, , reached

66.1 mm. The

/

,

contrary,

,

ratios were 1.5, 2.1, and 1.8 for Method A, B, and C. The results indicate that

,

/

ratios were 0.7, 0.9, and 0.8 for Method A, B, and C, respectively. On the

single shear walls more closely follow the backbone curve displacements, whereas the coupled
shear wall values are more consistent with the EEEP values.

96

Two illustrative results for SW1 and CP01 are shown in Figure 4.11, and Figure 4.12,
based on the values from Table B.2 - the remaining walls are presented in Appendix B: Elastic
Displacement Results. The bar values represent the individual contributions of each shear wall
displacement, and the horizontal lines represent the experimental values from EEEP and the
backbone curve.
80

Displacement [mm]

70

69.1
62.4

60
48.9

50
40
30
20
10
0

Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2020)
2020)
Rocking
Shear
dy = EEEP value

Sliding
Bending
dy,c = backbone value

Figure 4.11. Displacement comparison among the analytical and test results for SW1

97

70

Displacements [mm]

60
50
40
30

44.4
31.9

37.5

20
10
0
Method A
Method B
Method C
(Casagrande (Shahnewaz et (Masroor et al.
et al. 2017)
al. 2020)
2020)
Rocking
Sliding
Shear
Bending
dy = EEEP value
dy,c = backbone value

Figure 4.12. Displacement comparison among the analytical and test results for CP1

4.4.2. Discussion
The analytical predictions were found to be in accordance with the expected individual
contribution for each kinematic motion of the tested shear walls. Nevertheless, the methods
overestimate the actual capacity of the wall to deform elastically compared to the experimental
results when evaluated using the EEEP approach. Analytical predictions become closer to the
experimental database when the single shear walls are compared against displacements from
the envelope curve. Yet, a greater proximity to the EEEP yield displacements was observed for
CP shear walls, specifically for the displacements obtained from Method B.
Generally, the total displacements for Method B were higher than the other methods for
the single walls scenario. This implies that Method B predicts larger displacements due to shear
and bending. Further, Method B predicts lower CP displacements because the tensile stiffness
and resistance of the left-most bracket are different between the right and left panels. In turn,
Method C has a higher vertical contribution,

, since all connectors are considered.

98

Consequently, there is a reduction in rocking and sliding displacements leading to a larger
discrepancy in the results when compared to Method B. Essentially, Method B stood out in all
single and couple wall cases, more closely following the backbone curve values for single shear
walls, and presenting better accuracy for coupled walls regarding the EEEP yield displacement.
For single shear walls, the EEEP yield displacements provides a more conservative
stiffness than the actual values of the backbone curve. As a result, the yield displacements from
EEEP are underestimated compared to the test curve values. For coupled walls, the stiffness of
the spline joint is overestimated by the methods, resulting in more conservative values in
reference to backbone curve displacements.
Regarding the aspect ratio, the results suggest a considerable increase in rocking with the
reduction in the width of the shear walls. With the increase in the panel aspect ratio from 2.5:1 to
3.5:1, the dominant kinematic behaviour of the wall shifts from sliding to rocking. This occurred
due to the other input parameters of the shear wall remaining constant, while the reduction of
is inversely proportional to the contribution of sliding, an essential characteristic to be considered
to meet the design intentions. In turn, Method B exhibited lower total rocking percentages
compared to the other methods because all connections contribute to avoiding rocking. In other
words, due to the lower rocking resistance in shear walls with an aspect ratio of 3.5:1, the total
displacement is increased as there is less force to oppose the rotation of the panels.
The dead load contributes positively to reducing the rocking displacement since there is
no rotation in the panels before reaching the activation force, defined as the lateral force at which
the gravity load is overcome. The reduction in total displacements between CP5 & CP6 shear
walls occurred due to the greater difference between the

forces for this specific pair of shear

walls. While the individual sliding contribution between the methods was similar, the contribution
of the bi-axial behaviour from Method C led to smaller sliding contributions compared to the other
methods. It is essential to point out that the change from 20 kN/m to 30 kN/m did not significantly

99

impact the final results of sliding and rocking, as there were only 3% reductions in rocking for all
the studied methods. Therefore, it would be more effective to vary the geometric properties of the
wall rather than increase the dead load to improve the rocking contribution of CLT shear walls.
It is worth mentioning that the walls with 300 mm nail spacing were facilitated to rotate due
to the lower stiffness of the vertical joint compared to the walls with 150 mm and 75 mm nail
spacing, where more fasteners were used. In this way, there is a reduction in rocking
displacements between the CP7, CP9 & CP11 walls, demonstrating that the number of fasteners
contributes significantly both to the reduction of rocking resistance and to facilitate its contribution
to the total displacements of the shear walls. The contributions of rocking in relation to the total
displacements were reduced by approximately 20% with a higher number of fasteners. The
predominant behaviour shifted from rocking to sliding - the same occurred between the walls
CP17, CP18 & CP19.
The change in the number of angle brackets produced an increase in sliding in the shear
walls since, with fewer angle brackets, the sliding resistance of the shear walls was reduced –
rocking was minimized accordingly. In addition, Method C presented smaller increases in sliding
than the other methods because its sliding displacement formula incorporates the horizontal
contribution associated with the stiffness of the hold-downs, being the only method to reduce
sliding due to the horizontal stiffness of all connectors attached to the foundation. The CP shear
walls presented a more significant reduction than the SW shear walls because the number of
angle brackets was twice the number of the SW cases.
Concerning the hold-down nails, the increase in stiffness due to the use of washers led to
a reduction in displacements due to rocking - demonstrating that the implementation of washers
adds rigidity, which is inversely proportional to the rocking displacements. The coupled walls
rocking strengths for Method A and C are directly proportional to the parallel stiffness of the hold-

100

downs with the vertical joint. With the increase in rigidity associated with washers, there were
increases in rocking for such methods, reducing the rocking displacements contributions.
The ratio of sliding to rocking kinematic motion depends on several factors during the
seismic response of CLT shear walls, including the uplift versus sliding resistance of the
connections and the aspect ratio of the wall. Rocking is generally more effective for a seismic
response since it may dissipate more energy and result in less residual displacement.
The summary of the overall comparison between experimental and analytical is presented
below in Figure 4.13 to Figure 4.16. The x-axis comprises the total displacement at the top of the
shear walls. By contrast, the y-axis represents the corresponding displacements associated with
the EEEP yield displacements from Table B.2. The values of the EEEP yield displacements
present values much lower than the values predicted by the analytical methods. Consequently, it
is noted that the methods overestimated the elastic displacements of nailed CLT shear walls.
90
80
70

dy [mm]

60
50
40
30
20
10
0
0

10

20

30

40
50
vt,an [mm]

60

70

80

90

SW1
SW2
SW3
SW4
SW5
SW6
SW7
SW8
CP1
CP2
CP4
CP3
CP5
CP6
CP7
CP8
CP9
CP10
CP11
CP12
CP13
CP14
CP15
CP16
CP17
CP18
CP19

Figure 4.13. Comparison against test data and analytical results for Method A

101

90
80
70

dy [mm]

60
50
40
30
20
10
0
0

10

20

30

40
50
vt,an [mm]

60

70

80

90

SW1
SW2
SW3
SW4
SW5
SW6
SW7
SW8
CP1
CP2
CP3
CP4
CP5
CP6
CP7
CP8
CP9
CP10
CP11
CP12
CP13
CP14
CP15
CP16
CP17
CP18
CP19

Figure 4.14. Comparison against test data and analytical results for Method B

90
80
70

dy [mm]

60

50
40
30
20
10
0
0

10

20

30

40
50
vt,an [mm]

60

70

80

90

SW1
SW2
SW3
SW4
SW5
SW6
SW7
SW8
CP1
CP2
CP3
CP4
CP5
CP6
CP7
CP8
CP9
CP10
CP11
CP12
CP13
CP14
CP15
CP16
CP17
CP18
CP19

Figure 4.15. Comparison against test data and analytical results for Method C

102

It can be observed that none of the methods predicts effectively the elastic displacements.
However, considering all connections contributing to the rocking displacements in Method B led
to a closer approximation. In practice, all connections carry uplift forces and contribute to resisting
rocking in the panels, highlighting the importance of considering all their contributions. The
displacement results from Method A suggest better results for the elastic displacement analysis
than the other methods for single shear walls. It is possible to notice that for the SW shear walls,
the values from the backbone curve presented more consistent results when compared to the
predictions of the analytical methods. However, the results of the CP shear walls point to greater
proximity to the yield displacements of the EEEP procedure, specifically to the values obtained
from Method B. Although neither of the methods realistically represents the results obtained from
test data, based on all of the shear walls, Method B presents a better approximation with EEEP
yield displacements and from the backbone values, with ratios closer to 1.0 (Figure 4.16). The
averages of all the

/

,

ratios were 0.5, 0.6, and 0.6 for Methods A, B and C, respectively.

The values range from 0.3 to 0.8, 0.4 to 1.0, and 0.4 to 1.0 for Method A, B, and C.
Because of the high flexural stiffness of the CLT material compared to the stiffness of the
connectors, the contribution of bending deformations to the overall deformation of the shear wall
is low. In particular, the combined bending and shear deformations are significantly smaller than
the connection-based deformations for Method A and C, specifically sliding and rocking.
Nevertheless, the results indicate that shear and bending for Method B contributes up to 20% of
the total displacements and should be neglected, as it could lead to overestimation of the actual
displacements of the CLT panels – the width of the panel highly increases the bending
displacements since the other parameters were constant.
It is worth mentioning that, when the values of the backbone curve are compared to the
overall displacements, a more accurate estimate is obtained for SW shear walls. Yet, the results
of the CP shear walls point to greater proximity to the yield displacements of the EEEP procedure.

103

The analysis demonstrates the limitations of the elastic approaches. Hence, further investigation
is necessary to assess the non-linear behaviour of the CLT shear walls.
1.2
1.0

dy / vt,an

0.8
0.6
0.4
0.2

SW1
SW2
SW3
SW4
SW5
SW6
SW7
SW8
CP1
CP2
CP3
CP4
CP5
CP6
CP7
CP8
CP9
CP10
CP11
CP12
CP13
CP14
CP15
CP16
CP17
CP18
CP19

0.0

Method A (Casagrande et al. 2017)
Method B (Shahnewaz et al. 2020)
Method C (Masroor et al. 2020)
Figure 4.16. Summary of the ratio between backbone curves and analytical results

4.5. Inelastic Response of Nailed Multi-panel CLT Shear Walls
4.5.1. Results
An inelastic evaluation was completed using Method C – (Masroor et al., 2020) and
Method D – (Nolet et al., 2019). Method C includes the bi-axial behaviour of brackets. The CP
plastic behaviour is achieved when the vertical joints yield before the hold-downs and angle
brackets, where the connections are intended to function as elastic-perfectly plastic materials.
The tests achieved this behaviour: the hold-downs and angle brackets demonstrated fastener
yielding and the failure of the spline joints in coupled walls with plastic deformation of the
horizontal steel plates. Because of the uncertainty related to the contribution of sliding and rocking

104

after the yielding of all connections, the equation for the ultimate displacement is not established
for Method C. The suggested models are terminated such that the ultimate displacement
corresponds to the results of the experimental investigations.
Nolet et al. (2019) presented an elastic-plastic force-displacement curve for a kinematic
path between

−

where the yielding of the vertical joint is achieved in CP behaviour,

and a CP failure represents the final plastic behaviour - this case presents a reasonable
hypothesis based on experimental observations of nailed CLT shear walls. The method described
for this case is for connections with enough ductility to achieve the final behaviour, i.e., leading to
failure mechanisms II (vertical joint failure) or III (hold-down failure) as per Nolet et al. (2019).
Table C.1 and Table C.2 present the force and displacements obtained from the methods
for the inelastic assessment.

is the activation point at which the wall starts to rotate, that is,

when the gravity load is overcome, and its corresponding lateral force and displacement,
, respectively. Points
respectively. The points

and
to

, and

reflect fastener yielding in vertical joints and hold-downs,
, represent the yielding of the angle brackets starting with the

last angle bracket away from the centre of rotation of each panel.
Table C.1 and Table C.2 show reductions in the maximum force predicted by the two
methods for different aspect ratios (CP7 & CP13, CP9 & CP14, and CP11 & CP15). The results
were approximately 26% and 32% for Methods C and D, respectively. It is worth mentioning that
the maximum forces refer to the yield values of the last angle bracket and hold-down for Methods
C and D. Regarding the maximum displacements obtained, there was an increase of 45% and
42% for Method C and D, respectively, when the aspect ratio was changed from 2.5:1 to 3.5:1.
The dead load results (CP3 & CP4, CP5 & CP6, CP7 & CP8, CP9 & CP10) showed a 6%
and 11% increase for Methods C and D regarding the force values. The maximum displacements
predicted by Method D remained constant, while Method C exhibited a 1% reduction when the

105

dead load was increased from 20 to 30 kN/m. Regarding the number of brackets (CP3 & CP7,
CP5 & CP9, CP4 & CP8, and CP6 & CP10), Method D presented constant force and
displacements values when the number of angle brackets was changed from two to one.
However, Method C showed 26% and 33% reductions for the maximum forces and displacements
values, respectively.
Regarding the reduction in HD nails (CP12 & CP16, CP13 & CP17, CP14 & CP18, and
CP15 & CP19), the analytical predictions showed reductions of 6% for the maximum force values.
The maximum displacements presented a 38% reduction for Method D and almost no variations
for Method C. The maximum forces of the methods were affected by changing the vertical joint
spacings and varying the number of fasteners from 10 to 40 nails. There was a 35% and 65%
increase in maximum forces captured by Method C and D. Maximum displacements experienced
15% and 13% reductions for Method C and D when spacings changed from 300 mm to 75 mm.
Force versus displacement curves, comparing the experimental results and the model
predictions, are presented in Figure 4.17 for the monotonic loading. For the cyclic tests, the
envelope curves were used. The methods were evaluated up to the last displacement of the
backbone curve of the shear walls. The curves were produced excluding the effects of cycles and
connecting the start of the unloading curves and the ends of reloading curves. The results
obtained for Method C and D are illustrated and compared with the load-deformation curves for
validation where the test data occasionally intersect with the proposed methods.
Each graph shows only one shear walls to ensure legibility so the reader can interpret the
results appropriately, as many shear walls have extremely similar results (e.g., CP1 & CP3, and
CP2 & CP5). The results indicate outstanding approximations against the monotonic curves for
Method C. On the other hand, Method D presented more conservative results, which are almost
two times smaller than the experimental values.

106

90
80
70

F [kN]

60
50
40
30
20
10
0
0

10

20

30

40

50

60

70 80
d [mm]

CP1-2.5-4-300-20-M Test Data
CP1 Method D (Nolet et al. 2019)

90

100 110 120 130 140 150

CP1 Method C (Masroor et al. 2020)

Figure 4.17. Curves from monotonic test and analytical methods for CP1

90
80
70

F [kN]

60
50

40
30
20
10
0
0

10

20

30

40

50

60

CP5-2.5-4-150-20-C Envelope curve
CP5 Method D (Nolet et al. 2019)

70 80
d [mm]

90

100 110 120 130 140 150

CP5 Method C (Masroor et al. 2020)

Figure 4.18. Envelope curves from cyclic tests and analytical results for CP5

107

Subsequently, the maximum experimental force was compared with the maximum values
of the analytical methods. Table C.3 and Table C.4 compare the experimental and analytical ratios
for each of the proposed methods. The ratio of peak forces,

,

/

,

, obtained from the

maximum experimental and the maximum analytical predictions are used to assess the accuracy
of the findings. A comparison with the yield points was also performed for the studied methods.
The experimental load over its corresponding value of the multi-linear analytical curves provides
the

,

/

,

ratio. The experimental values were compared with the yield forces predicted by

the methods in the interest points. Points 1, 2 and 3 refer to the yield of the vertical joint, holddown, and angle bracket, respectively.
The results indicate values of

,

/

,

remarkably close to 1.0 for Method C, with

values ranging from 0.7 to 1.2 for the nailed shear walls. By contrast, Method D did not show the
same efficiency as Method C concerning maximum force values, resulting in more conservative
results. Regarding the yielding forces ratios, the results were relatively consistent and near
between the methods. Nonetheless, the yield points of the connections tend to be closer to 1.0 in
the Method C values.
4.5.2. Discussion
Considering that the elastic analysis of the proposed models presented overdesigned
displacements, validating the nonlinear methods is fundamental for designing seismic areas
where the shear walls are likely to undergo plastic deformation and dissipate energy. The results
previously point out that Method C is in greater proximity to the experimental values. Nonetheless,
it is vital to compare the predictions that suggest Method C rather than Method D and the reasons
for data discrepancies in certain shear walls.
The comparison between the forces in shear walls under different dead loads presented
an increase in the maximum forces because the activation force at the start of rotation is directly

108

proportional to the value of the dead load, leading to an increase in the value of

for both

methods. The 30 kN/m superimposed dead load does not affect the Method D displacements.
The dead load impacts the yield forces; however, the displacements only depend on the stiffness
and strength of the vertical joint and hold-down and the wall aspect ratio. The final strength of
Method C showed minor increases due to the value of the vertical contribution of the connectors
incorporating the bi-axial effect of the hold-down and angle brackets, incorporating more stiffness
to the system. On the other hand, the displacements presented constant values.
Regarding the number of brackets, the resistance does not change for Method D as the
angle brackets do not participate in the yielding hierarchy and its calculation. For Method C, the
increase in the number of angle brackets led to an increase in the sliding resistive force, reducing
displacements. In addition, the maximum rocking resistance was reduced by 25% when the
number of angle brackets was changed from 4 to 2, as the vertical stiffness of angle brackets
directly contributed to the increase in the resisting force.
Considering the reduction in HD nails, the decrease in the number of nails produced no
significant changes in either method – reductions of only 5% of the maximum force due to the
decrease in the resistance of the hold-downs. However, the plastic displacements from the holddowns of Method D presented reductions of nearly 40% due to the increased rigidity of the holddowns from the addition of washers. In contrast, Method C presented almost constant results.
Concerning the number of nails used in the vertical joint, 300 mm of spacing facilitated the rocking
behaviour since the resistance was less than the other cases, as there was less vertical rigidity in
the system. Consequently, tighter spacing contributes to reducing the ductility of shear walls,
reducing their maximum displacements and improving the maximum force experienced by the
shear walls.
Concerning the monotonic curves (Figure 4.17), the coupled shear walls did not reach
their theoretical displacement in P4 and P3, as the test data dictated the ultimate displacement.

109

The shear walls would have reached these points if the nails had sufficient ductility in the
connections. However, the vertical joint failed first, as stated by the test data. According to Nolet
et al. (2019), the vertical and horizontal non-interaction of the connections led to a reduction in
the shear wall's dissipation energy and smaller peak load values than Method C. It can be seen
in Figure 4.17 that the method idealized by Masroor et al. (2020) has a reasonable fit compared
to the test data, particularly when it comes to peak load.
Due to the idealization of the experimental curves, it is cumbersome to compare the initial
stiffness and yield points directly. Nevertheless, the general shape of the curves was coherent
and correlated reasonably well. The initial higher elastic stiffness can be explained by the positive
contribution of the vertical load in the shear walls. The positive influence of the superimposed
dead load is lost when the lateral force is enough to produce rotation in the CLT panels. As a
result, the vertical joint and hold-down are activated, and the shear wall rigidity is reduced. Until
the shear wall reaches the yielding of the vertical joint, Method D presented stiffer results than
Method C. The model ignores the sliding behaviour of the panels, considering only the
contribution from rocking. In addition, Method D considers the displacement of the shear walls to
be zero until the activation force. As a result, the stiffness is overestimated, resulting in lesser
displacement than predicted by Method C and compared to the envelope curve.
Even though the envelope curves from the cyclic tests exhibited a good approximation
compared to the test data, they were not as effective as those from the monotonic test. In cyclic
tests, the deformation capacities were dropped due to low cyclic fatigue, reducing the ultimate
force-displacement capabilities. Although, if there were sufficient ductility in the connections, it
would be possible to reach a final theoretical value - always more prominent than the limit of the
experimental curves. Several shear walls had the same results because they only differ in the
type of loading experienced by the shear walls. Therefore, their theoretical values resulting from

110

each method are the same for the comparison. For instance, the shear walls CP1 & CP3, where
only the monotonic and cyclic loading varied.
Regarding the ratio between experimental and analytical predictions, the result strongly
implies that Method C presented expressively similar results when compared with the maximum
experimental force values from

,

/

,

ratio, with values between 0.7 and 1.2 (Figure 4.19).

In this way, it is possible to affirm that the maximum point provided with the yield of the last
connector in the yielding hierarchy presents an outstanding theoretical estimate of the actual
capacity of the studied CLT shear walls. The results of Method D were not as linear as those of
Method C, since the bi-axial behaviour of the connectors linked to the foundation and the
consideration of angle brackets in the yielding hierarchy are more representative of the actual
behaviour experienced by the walls when loading is applied.

2.0
1.8

1.4
1.2
1.0
0.8
0.6
0.4
0.2

Method C (Masroor et al. 2020)

CP19

CP18

CP17

CP16

CP15

CP14

CP13

CP12

CP11

CP10

CP9

CP8

CP7

CP6

CP5

CP4

CP3

CP2

0.0

CP1

Fmax,ex / Fmax,an

1.6

Method D (Nolet et al. 2019)

Figure 4.19. Summary of the ratio between maximum experimental force and analytical results

111

The monotonic tests were closer to the experimental values for Method C, with minor
fluctuations compared to the cyclic tests. Furthermore, when the spacing between the vertical
joints decreases and the loading type changes from monotonic to cyclic, the ratio for shear walls
CP7, CP9 & CP11 moves away from the 1.0 ratio (Figure 4.19). One of the reasons is the low
cycle fatigue induced in the walls reduces the ultimate force-displacement capabilities and the
different spacing utilized. Method D indicates that the ratio between a maximum force from test
and analytical results has more disparity because of the absence of angle brackets and the
consideration of just the hold-down and vertical joint yield points, resulting in a more conservative
evaluation and leading to underestimation regarding the maximum force that the shear walls can
undertake.
Comparing the analytical and experimental yield force of the vertical joint and the holddowns suggests overestimation for Method D compared to the observed value from the envelope
curve. By contrast, Method C consistently predicted the lab results with ratios closer to 1.0. Figure
4.20 and Figure 4.21 present the ratio of the experimental and analytical prediction based on
Table C.3 and Table C.4. Points
downs, respectively. The points

and

reflect fastener yielding in vertical joints and hold-

, represent the yielding of the angle brackets starting with the

last angle bracket away from the centre of rotation of each panel. However, only Method C
incorporates the angle bracket in the equations. Furthermore, only the ratios of CP1 to CP6 could
be estimated since the experimental curves did not achieve the theoretical values for the other
coupled walls.

112

1.2

RP1,ex / RP1,an

1.0
0.8
0.6
0.4
0.2

Method C (Masroor et al. 2020)

CP19

CP18

CP17

CP16

CP15

CP14

CP13

CP12

CP11

CP10

CP9

CP8

CP7

CP6

CP5

CP4

CP3

CP2

CP1

0.0

Method D (Nolet et al. 2020)

Figure 4.20. The ratio of the experimental vertical joint yield force to the analytical predictions

1.4

1.0
0.8
0.6
0.4
0.2

Method C (Masroor et al. 2020)

CP19

CP18

CP17

CP16

CP15

CP14

CP13

CP12

CP11

CP10

CP9

CP8

CP7

CP6

CP5

CP4

CP3

CP2

0.0

CP1

RP2,ex / RP2,an

1.2

Method D (Nolet et al. 2020)

Figure 4.21. The ratio of the experimental hold-down yield force to the analytical predictions

113

Due to the idealization of the experimental curves, it is cumbersome to compare the initial
stiffness and yield points directly. Thus, the data were compared at the interest points where the
methods predicted the yielding of the connections. In summary, Method D provides good
approximations; however, since Method C includes the bi-axial behaviour of connections and
includes the angle brackets in the analyses, it improves the evaluation leading to nearly exact
results. It is worth noting that Method C proposes a suitable approach to estimating both the
displacements and yield forces of nailed shear walls by providing an outstanding estimate. An
appropriate correlation is observed in terms of the general shape of the curves and between the
maximum lateral resistances of the shear walls when the proposed model is compared to the test
results. Therefore, this research validated that Method C would be the best option to properly
design shear walls where yielding of the connectors is required.

114

Chapter 5: Conclusions
5.1. Summary
The objective of this research was to evaluate existing analytical approaches to estimate
the strength and stiffness of CLT shear walls: firstly, on two academic design examples and
secondly to the experimental results of nailed CLT shear wall tests. The research established that
the wall behaviour is highly dependent on the panel aspect ratio, the reduction in the number of
nails in hold-downs, and the superimposed dead load.
Four methods were considered: Method A (Casagrande et al. 2017), considers the
minimum strength value of the hold-down and the vertical fasteners; Method B (Shahnewaz et al.
2019), which accounts for the rocking resistance of all connectors; Method C (Masroor et al. 2020)
which accounts for the bi-axial behaviour of connectors; and Method D (Nolet et al. 2019) which
describes the elastic-perfectly plastic behaviour of CLT shear walls while neglecting the bi-axial
behaviour of brackets. These methods stand out for presenting both SW and CP formulations for
both linear and nonlinear behaviour of CLT shear walls, which is the current state-of-the-art. Other
methods offer similar approaches; many of the differences are between the lever arms of the
compression zone, leading to minor comparisons.
The investigations from the academic design example led to the following conclusions:
•

Method C predicts greater resistance than Method A because increasing the contribution of
the vertical stiffness,

, increases the resistive strength. Both methods are comparable

except for the introduction of the bi-axial approach. Since Method C considers the hold-down
carrying a horizontal load, there will be a difference in sliding resistance depending on the
stiffness, the number of brackets, and yield strength properties.
•

Method B predicts the smallest displacement as it accounts for the reduction in stiffness due
to connector positioning. Specifically, the rocking equation for the right panels is different from

115

the left panels since the tensile stiffness and resistance of the left-most bracket connectors
are different from the left panels with hold-downs, leading to a reduction of rocking.
•

Methods A and C do not consider bending displacements; hence, their values in the SW case
are lower than Method B. As Method A only has a hold-down in parallel with the vertical joint
to accommodate horizontal displacements, in the CP case, such method has greater rocking
contributions when compared to the contribution of all brackets in the rocking resistance
(Method B), and with the bi-axial approach (Method C).

The investigation of the nailed CLT shear walls in the elastic and inelastic range led to the
following conclusions:
•

Methods B are efficient for determining the elastic resistance of CLT shear walls. In addition,
Method B stood out for the accuracy of the results for single and coupled wall applications,
being a viable solution for elastic applications.

•

With the change in the panel aspect ratio from 2.5:1 to 3.5:1, the dominant kinematic
behaviour of the wall shifts from sliding to rocking, led by the increase in the angle of rotation
of the shear walls.

•

The combined rocking-sliding interaction embedded in Method B does not seem to impact the
results for higher aspect ratios where rocking is the dominant kinematic motion. Minor
variations of the results were found with values below 15% of the overall capacity from Method
B. The shear-uplift interactions for the circular domain require iterations, which is not desirable
for design purposes; nevertheless, with the reduction in the panel aspect ratio, the dominant
kinematic behaviour of the wall shifts from rocking to sliding. As a result, it is recommended
that the combined rocking-sliding behaviour to estimate the resistance of CLT shear walls is
used rather than using the individual kinematic behaviours.

116

•

The coupled walls with 300 mm nail spacing were facilitated to rotate due to the lower stiffness
of the vertical joint compared to the walls with 150 mm and 75 mm spacing where there were
more fasteners attached to the vertical joint. This demonstrates that the number of fasteners
contributes significantly both to reducing rocking resistance and facilitating its contribution to
the total displacements of the shear walls.

•

The increase in stiffness due to the use of washers led to a reduction in displacements due to
rocking - demonstrating that the implementation of washers adds rigidity to the system, which
is inversely proportional to the rocking displacements. In addition, the coupled wall rocking
strengths for Method A and C are directly proportional to the parallel stiffness of the holddowns with the vertical joint. With the increase in rigidity associated with washers, there were
increases in rocking resistances for such methods.

•

While Method B provided remarkable yield strength values, it does not have the same
accuracy for shear wall yield displacement. When the values of the backbone curve are
compared to the overall displacements, a more accurate estimate is obtained for SW shear
walls. Yet, the results of the CP shear walls point to greater proximity to the yield
displacements of the EEEP procedure, specifically to the values obtained from Method B,
demonstrating the limitations of elastic analysis among the methods and test data. Although
Method B provided good results for the elastic strength, it does not offer any inelastic
equations, and it overestimates the rocking resistance since it neglects the bi-axial behaviour
of all the connections and overlooks the stiffness that could counteract the lateral force.

•

The effective bending stiffness of a CLT panel loaded in-plane significantly impacts the
bending displacements. The assessment embedded in Method B underestimates the bending
stiffness of the CLT shear walls leading to higher bending displacements than the other
approaches presented in the literature review. For instance, if the bending stiffness had been
calculated by considering only the thickness of the vertical layers as proposed by Gavric et al.

117

(2015), the total contribution for bending displacements would have been minimized.
However, it is worth mentioning that higher panels with smaller widths would promote bending
displacements, and their contribution should not be neglected in the design.
•

Until the shear wall reaches the yielding of the vertical joint, Method D presented stiffer results
than Method C. The model ignores the sliding behaviour of the panels, considering only the
contribution from rocking. In addition, Method D considers the displacement of the shear walls
to be zero until the activation force. As a result, the initial stiffness is overestimated, resulting
in lesser displacement than predicted by Method C and compared to the envelope curve.

•

Not considering the angle brackets in the yield hierarchy analysis and considering just the
hold-down and vertical joint yield points from the inelastic assessment from Nolet et al. (2019)
results in a more conservative evaluation, leading to underestimation in the maximum force
undertaken by the nailed CLT shear wall.

•

When compared to test data, the inelastic method by Masroor et al. (2020), has an excellent
fit with the shape of the test curves, particularly when it comes to peak load. Therefore, the
biaxial behaviour leads to almost no underestimation, closely resembling the test results being
a viable option for inelastic scenarios, where seismic design governs the design intentions.

•

Method B - Shahnewaz et al. (2019), is recommended for elastic applications of nailed CLT
shear walls. Method C - Masroor et al. (2020), is recommended for inelastic design. For the
elastic design of CLT shear walls, the EEEP procedure overestimates the actual yield force,
leading to underestimated values for Method A and C. However, when Method C is compared
to the values of the backbone curve, good approximations are observed. Thus, the definition
of the yield point significantly impacts which method is deemed appropriate since the EEEP
procedure often tends to overestimate the yield force value.

118

•

Regarding the computational effort, Method B involves simplified equations; it estimates the
rocking and sliding resistance using the equilibrium of forces in the x and z directions rather
than minimum potential energy and derivative concepts to establish wall capacity, rotation,
displacement, and stiffness formulas. As a result, Methods A and C present solutions that
lead to more sophisticated equations and sometimes to matrix development that could lead
to cumbersome solutions. Even coding and programming would be recommended. These
solutions are more appropriate for software development, particularly for higher numbers of
panels. In addition, Method A and C do not consider the effect of lever arms on the overall
rocking resistance. Consequently, Method B provides more straightforward calculations,
which is essential for practising engineers.

5.2. Future Research
It is recommended that further investigation be done to enhance the understanding of CLT shear
walls on the following aspects:
•

More studies are required on the impact of spacing in the vertical joint to validate their elastic
and inelastic effectiveness in the existing analytical method and to compare the screwed and
internal perforated steel plates in the UNBC database.

•

Further investigation into the prediction of post-peak behaviour of the shear walls and its
ultimate and failure displacement to overcome the idealization made regarding the behaviour
of the hold-down and angle bracket connection being elastic-perfectly plastic for Method C.

•

Further research is required to predict CLT shear walls' capacity to withstand seismic loads
from a dynamic point of view aiming to complement the predictions of the analytical methods
discussed herein.

119

•

Assessment of innovative and novel connection solutions with higher capacity and ductility
should be explored as an input in the methods (e.g., hyperelastic hold-downs, slip-friction
devices, and internal perforated steel plates).

•

The role of connections between the upper floors and the CLT shear wall, the presence of
openings, and the redundancy of perpendicular walls or floor underneath are essential topics
that need further investigation.

•

Building codes are increasingly incorporating capacity-based design principles. Thereby,
future research should expand the findings in this thesis to support the establishment of
performance-based CLT platform buildings and leverage the yielding hierarchy between
dissipative and non-dissipative connections.

120

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135

Appendix A: Elastic Strength Results
Table A.1. Main results of analytical methods
Method A

Shear
wall

[kN]

SW1

33.0

SW2

[kN]

Method B
/

92.3

[kN]
23.8

1.4

27.0

46.2

23.8

SW3

32.0

92.3

SW4

29.0

SW5

[kN]

Method C
/

92.3

[kN]
36.1

0.9

1.1

46.2

30.2

23.8

1.3

92.3

46.2

23.8

1.2

21.0

46.2

15.9

SW6

21.0

46.2

SW7

19.0

SW8

[kN]

/

71.7

[kN]
32.0

1.0

0.9

46.6

28.9

0.9

36.1

0.9

71.7

32.0

1.0

46.2

30.2

1.0

46.6

28.9

1.0

1.3

46.2

20.1

1.0

46.6

19.5

1.1

14.5

1.4

46.2

18.6

1.1

34.8

17.2

1.2

46.2

15.9

1.2

46.2

20.1

0.9

46.6

19.5

1.0

21.0

46.2

14.5

1.4

46.2

18.6

1.1

34.8

17.2

1.2

CP1

63.0

184.6

22.8

2.8

184.6

60.4

1.0

121.8

25.2

2.5

CP2

64.0

184.6

31.5

2.0

184.6

69.0

0.9

121.8

33.9

1.9

CP3

54.0

184.6

22.8

2.4

184.6

60.4

0.9

121.8

25.2

2.1

CP4

61.0

184.6

27.6

2.2

184.6

65.2

0.9

121.8

30.0

2.0

CP5

65.0

184.6

31.5

2.1

184.6

69.0

0.9

121.8

33.9

1.9

CP6

57.0

184.6

36.3

1.6

184.6

73.8

0.8

121.8

38.7

1.5

CP7

41.0

92.3

22.8

1.8

92.3

49.1

0.8

71.7

23.9

1.7

CP8

46.0

92.3

27.6

1.7

92.3

53.9

0.9

71.7

28.7

1.6

CP9

50.0

92.3

31.5

1.6

92.3

57.7

0.9

71.7

32.6

1.5

CP10

52.0

92.3

36.3

1.4

92.3

62.5

0.8

71.7

37.4

1.4

CP11

61.0

92.3

48.8

1.3

92.3

75.0

0.8

71.7

49.9

1.2

CP12

29.0

92.3

14.2

2.0

92.3

32.8

0.9

71.7

14.9

1.9

CP13

23.0

92.3

14.2

1.6

92.3

32.8

0.7

71.7

14.9

1.5

CP14

29.0

92.3

20.3

1.4

92.3

38.9

0.7

71.7

21.1

1.4

CP15

41.0

92.3

32.6

1.3

92.3

51.2

0.8

71.7

33.3

1.2

CP16

32.0

92.3

15.7

2.0

92.3

31.2

1.0

50.2

16.4

1.9

CP17

35.0

92.3

15.7

2.2

92.3

31.2

1.1

50.2

16.4

2.1

CP18

35.0

92.3

21.8

1.6

92.3

37.3

0.9

50.2

22.5

1.6

CP19

50.0

92.3

34.0

1.5

92.3

49.5

1.0

50.2

34.8

1.4

136

Table A.2. Shear-uplift interaction x test data
Shear
wall

[kN]

[kN]

[kN]

[kN]

SW1

33.0

36.1

34.3

34.0

SW2

27.0

30.2

28.8

SW3

32.0

36.1

SW4

29.0

SW5

,

,

/
,

,

0.9

1.0

1.0

28.3

0.9

0.9

1.0

34.3

34.0

0.9

0.9

0.9

30.2

28.8

28.3

1.0

1.0

1.0

21.0

20.1

19.6

19.5

1.0

1.1

1.1

SW6

21.0

18.6

17.9

17.7

1.1

1.2

1.2

SW7

19.0

20.1

19.6

19.5

0.9

1.0

1.0

SW8

21.0

18.6

17.9

17.7

1.1

1.2

1.2

CP1

63.0

60.4

53.5

53.0

1.0

1.2

1.2

CP2

64.0

69.0

62.2

61.7

0.9

1.0

1.0

CP3

54.0

60.4

53.5

53.0

0.9

1.0

1.0

CP4

61.0

65.2

58.1

57.5

0.9

1.1

1.1

CP5

65.0

69.0

62.2

61.7

0.9

1.0

1.1

CP6

57.0

73.8

66.8

66.3

0.8

0.9

0.9

CP7

41.0

49.1

46.3

45.4

0.8

0.9

0.9

CP8

46.0

53.9

50.9

49.9

0.9

0.9

0.9

CP9

50.0

57.7

55.0

54.2

0.9

0.9

0.9

CP10

52.0

62.5

59.7

58.8

0.8

0.9

0.9

CP11

61.0

75.0

72.4

71.6

0.8

0.8

0.9

CP12

29.0

32.8

31.7

31.5

0.9

0.9

0.9

CP13

23.0

32.8

31.7

31.5

0.7

0.7

0.7

CP14

29.0

38.9

37.8

37.6

0.7

0.8

0.8

CP15

41.0

51.2

50.1

49.9

0.8

0.8

0.8

CP16

32.0

31.2

29.7

29.3

1.0

1.1

1.1

CP17

35.0

31.2

29.7

29.3

1.1

1.2

1.2

CP18

35.0

37.3

35.8

35.5

0.9

1.0

1.0

CP19

50.0

49.5

48.1

47.8

1.0

1.0

1.0

137

SW capacity [kN]

50

46.2

46.6

46.2

40
30.2

30

28.9

23.8

20
10
0
Method A
(Casagrande et
al. 2017)
Rocking

Method B
(Shahnewaz et
al. 2019)
Sliding

Method C
(Masroor et al.
2020)
Test data

Figure A.1. Strength comparison among the methods and test data for SW2

100

92.3

92.3

90

SW capacity [kN]

80

71.7

70
60

50
36.1

40
30

32.0

23.8

20
10
0
Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2019)
2020)

Rocking

Sliding

Test data

Figure A.2. Strength comparison among the methods and test data for SW3

138

50

46.2

46.6

46.2

SW capacity [kN]

40
30

30.2

28.9

23.8

20

10
0
Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2019)
2020)
Rocking

Sliding

Test data

Figure A.3. Strength comparison among the methods and test data for SW4

50

46.2

46.2

46.6

SW capacity [kN]

40
30
20

20.1

19.5

15.9

10
0
Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2019)
2020)
Rocking

Sliding

Test data

Figure A.4. Strength comparison among the methods and test data for SW5

139

60

SW capacity [kN]

50

46.2

46.2

40

34.8

30
18.6

20

14.5

17.2

10
0
Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2019)
2020)
Rocking

Sliding

Test data

Figure A.5. Strength comparison among the methods and test data for SW6

50

46.2

46.2

46.6

SW capacity [kN]

40
30
20

20.1

19.5

15.9

10
0
Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2019)
2020)

Rocking

Sliding

Test data

Figure A.6. Strength comparison among the methods and test data for SW7

140

60

SW capacity [kN]

50

46.2

46.2

40

34.8

30
20

18.6
14.5

17.2

10
0
Method A
Method B
Method C
(Casagrande (Shahnewaz et (Masroor et al.
et al. 2017)
al. 2019)
2020)
Rocking

Sliding

Test data

Figure A.7. Strength comparison among the methods and test data for SW8

200

184.6

184.6

175
CP capacity [kN]

150
121.8

125
100
69.0

75
50

33.9

31.5

25
0
Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et al.
et al. 2017) et al. 2019)
2020)
Rocking

Sliding

Test data

Figure A.8. Strength comparison among the methods and test data for CP2

141

200

184.6

184.6

175

CP capacity [kN]

150
121.8

125
100
75

60.4

50

25.2

22.8

25
0

Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et al.
et al. 2017) et al. 2019)
2020)
Rocking

Sliding

Test data

Figure A.9. Strength comparison among the methods and test data for CP3

200

184.6

184.6

175

CP capacity [kN]

150
121.8

125
100
65.2

75
50

30.0

27.6

25
0
Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et
et al. 2017) et al. 2019)
al. 2020)
Rocking

Sliding

Test data

Figure A.10. Strength comparison among the methods and test data for CP4

142

200

184.6

184.6

175

CP capacity [kN]

150
121.8

125

100
69.0

75
50

31.5

33.9

25
0
Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et al.
et al. 2017) et al. 2019)
2020)
Rocking

Sliding

Test data

Figure A.11. Strength comparison among the methods and test data for CP5

200

184.6

184.6

175

CP capacity [kN]

150
121.8

125
100

73.8

75
50

38.7

36.3

25
0
Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et
et al. 2017) et al. 2019) al. 2020)
Rocking

Sliding

Test data

Figure A.12. Strength comparison among the methods and test data for CP6

143

100

92.3

92.3

CP capacity [kN]

80

71.7

60

49.1

40
23.9

22.8
20
0

Method A
Method B Method C
(Casagrande (Shahnewaz (Masroor et
et al. 2017) et al. 2019) al. 2020)

Rocking

Sliding

Test data

Figure A.13. Strength comparison among the methods and test data for CP7

100

92.3

92.3

CP capacity [kN]

80

71.7

60

40

53.9

28.7

27.6

20
0
Method A
Method B Method C
(Casagrande (Shahnewaz (Masroor et
et al. 2017) et al. 2019) al. 2020)
Rocking

Sliding

Test data

Figure A.14. Strength comparison among the methods and test data for CP8

144

100

92.3

92.3

CP capacity [kN]

80

71.7
57.7

60
40

32.6

31.5

20
0
Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et
et al. 2017) et al. 2019)
al. 2020)
Rocking

Sliding

Test data

Figure A.15. Strength comparison among the methods and test data for CP9

100

92.3

92.3

CP capacity [kN]

80

71.7
62.5

60
40

37.4

36.3

20
0
Method A
Method B Method C
(Casagrande (Shahnewaz (Masroor et
et al. 2017) et al. 2019) al. 2020)
Rocking

Sliding

Test data

Figure A.16. Strength comparison among the methods and test data for CP10

145

100

92.3

92.3
75.0

CP capacity [kN]

80
60

71.7

49.9

48.8

40
20
0
Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et
et al. 2017) et al. 2019) al. 2020)

Rocking

Sliding

Test data

Figure A.17. Strength comparison among the methods and test data for CP11

100

92.3

92.3

CP capacity [kN]

80

71.7

60
40
20

32.8
14.9

14.2

0
Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et al.
et al. 2017) et al. 2019)
2020)
Rocking

Sliding

Test data

Figure A.18. Strength comparison among the methods and test data for CP12

146

100

92.3

92.3

CP capacity [kN]

80

71.7

60
40

32.8

20

14.9

14.2

0
Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2019)
2020)
Rocking

Sliding

Test data

Figure A.19. Strength comparison among the methods and test data for CP13

100

92.3

92.3

CP capacity [kN]

80

71.7

60
38.9

40

20

21.1

20.3

0
Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et al.
et al. 2017)
et al. 2019)
2020)
Rocking

Sliding

Test data

Figure A.20. Strength comparison among the methods and test data for CP14

147

100

92.3

92.3

CP capacity [kN]

80

71.7

60
40

51.2
33.3

32.6

20
0
Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et al.
et al. 2017)
et al. 2019)
2020)
Rocking

Sliding

Test data

Figure A.21. Strength comparison among the methods and test data for CP15

100

92.3

92.3

CP capacity [kN]

80
60

50.2

40
20

31.2
16.4

15.7

0
Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et
et al. 2017) et al. 2019)
al. 2020)
Rocking

Sliding

Test data

Figure A.22. Strength comparison among the methods and test data for CP16

148

100

92.3

92.3

CP capacity [kN]

80
60

50.2

40
20

31.2
16.4

15.7

0
Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2019)
2020)
Rocking

Sliding

Test data

Figure A.23. Strength comparison among the methods and test data for CP17

100

92.3

92.3

CP capacity [kN]

80
60

50.2
37.3

40

22.5

21.8
20
0

Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2019)
2020)
Rocking

Sliding

Test data

Figure A.24. Strength comparison among the methods and test data for CP18

149

100

92.3

92.3

CP capacity [kN]

80
60
40

50.2

49.5
34.8

34.0

20
0
Method A
Method B
Method C
(Casagrande (Shahnewaz et (Masroor et al.
et al. 2017)
al. 2019)
2020)
Rocking

Sliding

Test data

Figure A.25. Strength comparison among the methods and test data for CP19

150

Appendix B: Elastic Displacement Results
Table B.1. Elastic displacement results for studied methods
Method A

Method B

Method C

Shear wall
[mm]

[mm]

[mm]

[mm]

[mm]

[mm]

10.3

[mm]
51.1

[mm]

[mm]

[mm]

10.3

[mm]
51.1

0.0

1.0

7.2

[mm]
40.6

SW1

0.0

1.0

6.6

1.0

SW2

0.0

0.8

16.9

40.2

5.4

0.8

16.9

40.2

0.0

0.8

9.1

36.0

SW3

0.0

1.0

10.0

49.3

6.4

1.0

10.0

49.3

0.0

1.0

7.0

39.2

SW4

0.0

0.9

18.1

43.8

5.8

0.9

18.1

43.8

0.0

0.9

9.7

39.3

SW5

0.0

0.9

13.1

67.1

11.9

0.9

13.1

67.1

0.0

0.9

7.0

60.2

SW6

0.0

0.9

13.1

46.3

11.9

0.9

13.1

46.3

0.0

0.9

5.8

42.9

SW7

0.0

0.8

11.9

59.9

10.7

0.8

11.9

59.9

0.0

0.8

6.4

53.7

SW8

0.0

0.9

13.1

46.3

11.9

0.9

13.1

46.3

0.0

0.9

5.8

42.9

CP1

0.0

1.0

9.8

33.5

2.6

1.0

9.8

18.5

0.0

1.0

8.1

28.5

CP2

0.0

1.0

10.0

20.7

2.6

1.0

10.0

10.9

0.0

1.0

8.2

18.7

CP3

0.0

0.8

8.4

27.9

2.2

0.8

8.4

15.4

0.0

0.8

6.9

23.7

CP4

0.0

1.0

9.5

29.3

2.5

1.0

9.5

16.1

0.0

1.0

7.8

24.8

CP5

0.0

1.0

10.2

21.0

2.7

1.0

10.2

11.1

0.0

1.0

8.4

19.0

CP6

0.0

0.9

8.9

16.2

2.3

0.9

8.9

8.6

0.0

0.9

7.3

14.6

CP7

0.0

0.6

12.8

19.7

1.7

0.6

12.8

10.9

0.0

0.6

9.0

18.3

CP8

0.0

0.7

14.4

19.8

1.9

0.7

14.4

10.9

0.0

0.7

10.0

18.4

CP9

0.0

0.8

15.6

15.3

2.1

0.8

15.6

8.1

0.0

0.8

10.9

14.6

CP10

0.0

0.8

16.3

14.3

2.1

0.8

16.3

7.6

0.0

0.8

11.4

13.6

CP11

0.0

1.0

19.1

10.9

2.5

1.0

19.1

5.6

0.0

1.0

13.3

10.6

CP12

0.0

0.6

9.1

30.3

3.3

0.6

9.1

16.7

0.0

0.6

6.3

28.0

CP13

0.0

0.5

7.2

22.8

2.7

0.5

7.2

12.5

0.0

0.5

5.0

21.1

CP14

0.0

0.6

9.1

18.3

3.3

0.6

9.1

9.7

0.0

0.6

6.3

17.5

CP15

0.0

0.9

12.8

15.3

4.7

0.9

12.8

7.9

0.0

0.9

9.0

14.9

CP16

0.0

0.7

10.0

29.4

3.7

0.7

10.0

17.2

0.0

0.7

6.2

27.5

CP17

0.0

0.8

10.9

32.7

4.0

0.8

10.9

19.1

0.0

0.8

6.7

30.6

CP18

0.0

0.8

10.9

20.9

4.0

0.8

10.9

11.5

0.0

0.8

6.7

20.0

CP19

0.0

1.1

15.6

18.2

5.8

1.1

15.6

9.6

0.0

1.1

9.6

17.7

151

Table B.2. Comparison of test data, EEEP, and analytical results
Method A
Shear walls

Method B

,

[mm]

[mm]

,

[mm]

,

/

/

,

,

,

[mm]

Method C
,

/

/

,

,

,

[mm]

,

/

/

,

,

SW1

27.0

64.1

62.4

0.4

1.0

69.1

0.4

0.9

48.9

0.6

1.3

SW2

30.0

59.6

57.9

0.5

1.0

63.4

0.5

0.9

45.9

0.7

1.3

SW3

30.0

58.7

60.3

0.5

1.0

66.7

0.4

0.9

47.2

0.6

1.2

SW4

30.0

60.6

62.9

0.5

1.0

68.7

0.4

0.9

49.9

0.6

1.2

SW5

45.0

90.1

81.2

0.6

1.1

93.1

0.5

1.0

68.1

0.7

1.3

SW6

30.0

50.9

60.4

0.5

0.8

72.2

0.4

0.7

49.7

0.6

1.0

SW7

47.0

85.3

72.6

0.6

1.2

83.4

0.6

1.0

60.9

0.8

1.4

SW8

30.0

42.5

60.4

0.5

0.7

72.2

0.4

0.6

49.7

0.6

0.9

CP1

30.0

66.1

44.4

0.7

1.5

31.9

0.9

2.1

37.5

0.8

1.8

CP2

20.0

53.8

31.7

0.6

1.7

24.6

0.8

2.2

27.9

0.7

1.9

CP3

21.0

52.7

37.2

0.6

1.4

26.9

0.8

2.0

31.5

0.7

1.7

CP4

21.0

58.0

39.8

0.5

1.5

29.1

0.7

2.0

33.6

0.6

1.7

CP5

19.0

51.8

32.2

0.6

1.6

25.0

0.8

2.1

28.4

0.7

1.8

CP6

16.0

44.5

26.0

0.6

1.7

20.7

0.8

2.1

22.8

0.7

1.9

CP7

15.0

39.2

33.2

0.5

1.2

26.0

0.6

1.5

27.9

0.5

1.4

CP8

17.0

47.8

34.9

0.5

1.4

27.9

0.6

1.7

29.1

0.6

1.6

CP9

13.0

43.3

31.8

0.4

1.4

26.6

0.5

1.6

26.3

0.5

1.6

CP10

11.0

44.0

31.4

0.4

1.4

26.8

0.4

1.6

25.8

0.4

1.7

CP11

16.0

39.4

30.9

0.5

1.3

28.2

0.6

1.4

24.9

0.6

1.6

CP12

26.0

68.6

40.0

0.7

1.7

29.7

0.9

2.3

35.0

0.7

2.0

CP13

14.0

43.9

30.5

0.5

1.4

22.9

0.6

1.9

26.6

0.5

1.7

CP14

9.0

41.8

28.0

0.3

1.5

22.8

0.4

1.8

24.4

0.4

1.7

CP15

12.0

42.1

29.0

0.4

1.5

26.4

0.5

1.6

24.8

0.5

1.7

CP16

20.0

45.3

40.2

0.5

1.1

31.6

0.6

1.4

34.4

0.6

1.3

CP17

25.0

47.2

44.4

0.6

1.1

34.9

0.7

1.4

38.1

0.7

1.2

CP18

27.0

35.7

32.6

0.8

1.1

27.3

1.0

1.3

27.5

1.0

1.3

CP19

22.0

41.2

34.9

0.6

1.2

32.1

0.7

1.3

28.4

0.8

1.4

152

Displacement [mm]

70
60

57.9

63.4

50

45.9

40
30
20
10
0
Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2020)
2020)
Rocking
Shear
dy = EEEP value

Sliding
Bending
dy,c = backbone value

Figure B.1. Displacement comparison among the methods and test data for SW2

80

Displacement [mm]

70
60

66.7
60.3
47.2

50
40
30
20
10
0

Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2020)
2020)
Rocking
Shear
dy = EEEP value

Sliding
Bending
dy,c = backbone value

Figure B.2. Displacement comparison among the methods and test data for SW3

153

80

Displacement [mm]

70
60

68.7
62.9

49.9

50
40
30
20
10
0

Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2020)
2020)
Rocking
Shear
dy = EEEP value

Sliding
Bending
dy,c = backbone value

Figure B.3. Displacement comparison among the methods and test data for SW4

Displacement [mm]

100
80

93.1
81.2
68.1

60

40
20
0
Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2020)
2020)
Rocking
Shear
dy = EEEP value

Sliding
Bending
dy,c = backbone value

Figure B.4. Displacement comparison among the methods and test data for SW5

154

80

72.2

Displacement [mm]

70
60

60.4
49.7

50
40
30
20
10
0

Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2020)
2020)
Rocking
Sliding
Shear
Bending
dy = EEEP value
dy,c = backbone value
Figure B.5. Displacement comparison among the methods and test data for SW6

90

Displacement [mm]

80

83.4
72.6

70

60.9

60

50
40
30
20
10
0
Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2020)
2020)
Rocking
Shear
dy = EEEP value

Sliding
Bending
dy,c = backbone value

Figure B.6. Displacement comparison among the methods and test data for SW7

155

80

72.2

Displacement [mm]

70
60.4

60

49.7

50
40
30
20
10
0

Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2020)
2020)
Rocking
Sliding
Shear
Bending
dy = EEEP value
dy,c = backbone value
Figure B.7. Displacement comparison among the methods and test data for SW8

60

Displacement [mm]

50
40
31.7
30

24.6

27.9

20

10
0
Method A
Method B
Method C
(Casagrande (Shahnewaz et (Masroor et al.
et al. 2017)
al. 2020)
2020)
Rocking
Shear
dy = EEEP value

Sliding
Bending
dy,c = backbone value

Figure B.8. Displacement comparison among the methods and test data for CP2

156

60

Displacement [mm]

50
40

37.2
26.9

30

31.5

20
10
0
Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2020)
2020)
Rocking
Shear
dy = EEEP value

Sliding
Bending
dy,c = backbone value

Figure B.9. Displacement comparison among the methods and test data for CP3

Displacement [mm]

70
60
50
40

39.8
29.1

30

33.6

20
10
0
Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2020)
2020)
Rocking
Shear
dy = EEEP value

Sliding
Bending
dy,c = backbone value

Figure B.10. Displacement comparison among the methods and test data for CP4

157

Displacement [mm]

60
50
40

32.2

30

25.0

28.4

20

10
0
Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et al.
et al. 2017)
et al. 2020)
2020)
Rocking
Sliding
Shear
Bending
dy = EEEP value
dy,c = backbone value
Figure B.11. Displacement comparison among the methods and test data for CP5

Displacement [mm]

50

40
30
20

26.0
20.7

22.8

10
0
Method A
Method B
Method C
(Casagrande (Shahnewaz et (Masroor et al.
et al. 2017)
al. 2020)
2020)
Rocking
Sliding
Shear
Bending
dy = EEEP value
dy,c = backbone value
Figure B.12. Displacement comparison among the methods and test data for CP6

158

Displacement [mm]

50
40
33.2
30

26.0

27.9

20
10
0
Method A
Method B
Method C
(Casagrande (Shahnewaz et (Masroor et al.
et al. 2017)
al. 2020)
2020)
Rocking
Sliding
Shear
Bending
dy = EEEP value
dy,c = backbone value

Figure B.13. Displacement comparison among the methods and test data for CP7

60

Displacement [mm]

50
40
30

34.9
27.9

29.1

20
10
0

Method A
Method B
Method C
(Casagrande (Shahnewaz et (Masroor et al.
et al. 2017)
al. 2020)
2020)
Rocking
Sliding
Shear
Bending
dy = EEEP value
dy,c = backbone value
Figure B.14. Displacement comparison among the methods and test data for CP8

159

Displacement [mm]

50
40
31.8
30

26.6

26.3

20
10
0
Method A
Method B
Method C
(Casagrande (Shahnewaz (Masroor et al.
et al. 2017)
et al. 2020)
2020)
Rocking
Sliding
Shear
Bending
dy = EEEP value
dy,c = backbone value

Figure B.15. Displacement comparison among the methods and test data for CP09

Displacement [mm]

50
40
30

31.4
26.8

25.8

20
10
0
Method A
Method B
Method C
(Casagrande (Shahnewaz et(Masroor et al.
et al. 2017)
al. 2020)
2020)
Rocking
Sliding
Shear
Bending
dy = EEEP value
dy,c = backbone value

Figure B.16. Displacement comparison among the methods and test data for CP10

160

Displacement [mm]

50
40
30.9
30

28.2

24.9

20
10
0
Method A
Method B
Method C
(Casagrande (Shahnewaz et (Masroor et al.
et al. 2017)
al. 2020)
2020)
Rocking
Sliding
Shear
Bending
dy = EEEP value
dy,c = backbone value

Figure B.17. Displacement comparison among the methods and test data for CP11

80

Displacement [mm]

70
60
50
40

40.0

35.0
29.7

30
20
10
0

Method A
Method B
Method C
(Casagrande (Shahnewaz et (Masroor et al.
et al. 2017)
al. 2020)
2020)
Rocking
Shear
dy = EEEP value

Sliding
Bending
dy,c = backbone value

Figure B.18. Displacement comparison among the methods and test data for CP12

161

50

Displacement [mm]

40
30

30.5
26.6
22.9

20
10
0
Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2020)
2020)
Rocking
Sliding
Shear
Bending
dy = EEEP value
dy,c = backbone value

Figure B.19. Displacement comparison among the methods and test data for CP13

50

Displacement [mm]

40
30

28.0
22.8

24.4

20
10
0
Method A
Method B
Method C
(Casagrande (Shahnewaz et (Masroor et al.
et al. 2017)
al. 2020)
2020)
Rocking
Sliding
Shear
Bending
dy = EEEP value
dy,c = backbone value

Figure B.20. Displacement comparison among the methods and test data for CP14

162

50

Displacement [mm]

40
30

29.0

26.4

24.8

20
10
0
Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2020)
2020)
Rocking
Shear
dy = EEEP value

Sliding
Bending
dy,c = backbone value

Figure B.21. Displacement comparison among the methods and test data for CP15

50

Displacement [mm]

40

40.2
31.6

34.4

30
20
10

0
Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2020)
2020)
Rocking
Shear
dy = EEEP value

Sliding
Bending
dy,c = backbone value

Figure B.22. Displacement comparison among the methods and test data for CP16

163

Displacement [mm]

50

44.4

40

38.1
34.9

30
20
10

0
Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2020)
2020)
Rocking
Shear
dy = EEEP value

Sliding
Bending
dy,c = backbone value

Figure B.23. Displacement comparison among the methods and test data for CP17

40

Displacement [mm]

32.6
30

27.3

27.5

20

10

0
Method A
Method B
Method C
(Casagrande et (Shahnewaz et (Masroor et al.
al. 2017)
al. 2020)
2020)
Rocking
Sliding
Shear
Bending
dy = EEEP value
dy,c = backbone value
Figure B.24. Displacement comparison among the methods and test data for CP18

164

45

Displacement [mm]

40
35
30

34.9

32.1
28.4

25
20
15
10
5
0
Method A
Method B
Method C
(Casagrande (Shahnewaz et(Masroor et al.
et al. 2017)
al. 2020)
2020)
Rocking
Sliding
Shear
Bending
dy = EEEP value
dy,c = backbone value

Figure B.25. Displacement comparison among the methods and test data for CP19

165

Appendix C: Inelastic Response of Multi-panel CLT Shear Walls
Table C.1. Summary of the inelastic assessment for interest points for coupled walls in Method C
Loading

Shear
Wall

[kN]

[kN]

[kN]

[kN]

[kN]

[mm]

[mm]

[mm]

[mm]

[mm]

CP1

9.6

25.2

48.3

67.3

73.0

1.2

11.5

42.1

111.8

212.3

CP2

9.6

33.8

56.0

75.0

80.5

1.2

12.7

41.9

111.5

210.3

CP12

4.8

14.9

28.3

37.5

N/A

1.1

15.0

56.9

203.0

N/A

CP16

4.8

16.4

24.8

35.5

N/A

0.9

14.9

34.4

204.3

N/A

CP3

9.6

25.2

48.3

67.3

73.0

1.2

11.5

42.1

111.8

212.3

CP4

14.4

30.0

52.6

71.6

77.2

1.9

12.2

42.1

111.6

211.2

CP5

9.6

33.8

56.0

75.0

80.5

1.2

12.7

41.9

111.5

210.3

CP6

14.4

38.6

60.1

79.2

84.6

1.9

13.3

41.8

111.3

209.1

CP7

9.6

23.9

40.3

52.9

N/A

2.1

13.5

41.2

143.1

N/A

CP8

14.4

28.7

44.0

56.6

N/A

3.1

14.6

40.5

142.0

N/A

CP9

9.6

32.5

47.0

59.5

N/A

2.1

15.4

39.8

141.0

N/A

CP10

14.4

37.3

50.5

63.0

N/A

3.1

16.5

38.8

139.6

N/A

CP11

9.6

49.8

59.2

71.7

N/A

2.1

19.2

35.0

135.7

N/A

CP13

4.8

14.9

28.3

37.5

N/A

1.1

15.0

56.9

203.0

N/A

CP14

4.8

21.1

33.7

42.9

N/A

1.1

16.3

56.1

201.4

N/A

CP15

4.8

33.3

44.1

53.2

N/A

1.1

19.0

53.2

197.2

N/A

CP17

4.8

16.4

24.8

35.5

N/A

0.9

14.9

34.4

204.3

N/A

CP18

4.8

22.5

29.5

40.6

N/A

0.9

16.1

33.2

203.3

N/A

CP19

4.8

34.8

39.2

50.1

N/A

0.9

18.4

28.8

200.8

N/A

Mon

Cyc

166

Table C.2. Summary of the inelastic assessment for interest points for coupled walls in Method D
Loading

Shear
Wall

[kN]

[kN]

[kN]

[kN]

[kN]

[mm]

[mm]

[mm]

[mm]

[mm]

CP1

9.6

22.8

39.8

39.8

N/A

0.0

8.3

39.1

141.0

N/A

CP2

9.6

31.5

48.5

48.5

N/A

0.0

8.3

39.1

128.0

N/A

CP12

4.8

14.2

26.2

26.2

N/A

0.0

11.7

55.2

130.0

N/A

CP16

4.8

15.6

24.6

24.6

N/A

0.0

11.7

34.1

125.0

N/A

CP3

9.6

22.8

39.8

39.8

N/A

0.0

8.3

39.1

117.0

N/A

CP4

14.4

27.6

44.6

44.6

N/A

0.0

8.3

39.1

126.0

N/A

CP5

9.6

31.5

48.5

48.5

N/A

0.0

8.3

39.1

133.0

N/A

CP6

14.4

36.3

53.3

53.3

N/A

0.0

8.3

39.1

113.0

N/A

CP7

9.6

22.8

39.8

39.8

N/A

0.0

8.3

39.1

85.0

N/A

CP8

14.4

27.6

44.6

44.6

N/A

0.0

8.3

39.1

108.0

N/A

CP9

9.6

31.5

48.5

48.5

N/A

0.0

8.3

39.1

120.0

N/A

CP10

14.4

36.3

53.3

53.3

N/A

0.0

8.3

39.1

90.0

N/A

CP11

9.6

48.7

65.8

65.8

N/A

0.0

8.3

39.1

74.0

N/A

CP13

4.8

14.2

26.2

26.2

N/A

0.0

11.7

55.2

145.0

N/A

CP14

4.8

20.3

32.4

32.4

N/A

0.0

11.7

55.2

117.0

N/A

CP15

4.8

32.5

44.6

44.6

N/A

0.0

11.7

55.2

96.0

N/A

CP17

4.8

15.6

24.6

24.6

N/A

0.0

11.7

34.1

96.0

N/A

CP18

4.8

21.8

30.7

30.7

N/A

0.0

11.7

34.1

116.0

N/A

CP19

4.8

34.0

43.0

43.0

N/A

0.0

11.7

34.1

100.0

N/A

Mon

Cyc

167

Table C.3. Comparison between the experimental and analytical results for Method C
Loading

Shear

,

,

,

,

,

Wall

[kN]

[mm]

,

,

,

,

CP1

73.0

73.0

1.0

1.0

1.0

1.1

CP2

80.5

74.0

0.9

1.0

1.0

1.0

CP12

37.5

35.0

0.9

0.9

0.9

N/A

CP16

35.5

37.0

1.0

1.1

1.1

N/A

CP3

73.0

65.3

0.9

1.1

1.0

0.9

CP4

77.2

69.1

0.9

1.1

1.0

0.9

CP5

80.5

75.5

0.9

1.0

1.0

1.0

CP6

84.6

70.2

0.8

0.9

1.0

0.7

CP7

52.9

50.7

1.0

1.1

1.1

N/A

CP8

56.6

54.1

1.0

1.0

1.0

N/A

CP9

59.5

57.8

1.0

1.1

1.0

N/A

CP10

63.0

61.8

1.0

1.1

1.0

N/A

CP11

71.7

73.3

1.0

1.0

1.0

N/A

CP13

37.5

26.6

0.7

1.1

0.9

N/A

CP14

53.2

34.5

0.6

1.0

1.0

N/A

CP15

35.5

51.8

1.5

1.0

1.0

N/A

CP17

35.5

40.5

1.1

1.1

1.2

N/A

CP18

40.6

38.6

1.0

0.7

0.9

N/A

CP19

50.1

60.3

1.2

1.0

1.1

N/A

,

Mon

Cyc

168

Table C.4. Comparison between the experimental and analytical results for Method D
Loading

Shear Wall

,

,

,

,

,
,

[kN]

[mm]

,

,

CP1

39.8

73.0

1.8

0.7

1.2

CP2

48.5

74.0

1.5

0.9

1.1

CP12

26.2

35.0

1.3

0.6

1.0

CP16

24.6

37.0

1.5

1.0

1.1

CP3

39.8

65.3

1.6

1.1

1.2

CP4

44.6

69.1

1.5

1.0

1.2

CP5

48.5

75.5

1.6

0.9

1.2

CP6

53.3

70.2

1.3

0.8

1.0

CP7

39.8

50.7

1.3

1.0

1.0

CP8

44.6

54.1

1.2

0.9

1.0

CP9

48.5

57.8

1.2

0.9

1.0

CP10

53.3

61.8

1.2

0.9

1.0

CP11

65.8

73.3

1.1

0.7

0.9

CP13

26.2

26.6

1.0

1.0

1.0

CP14

32.4

34.5

1.1

0.9

1.0

CP15

44.6

51.8

1.2

0.8

1.0

CP17

24.6

40.5

1.6

1.0

1.2

CP18

30.7

38.6

1.3

0.5

0.8

CP19

43.0

60.3

1.4

0.8

1.1

Mon

Cyc

169

90
80
70

F [kN]

60
50
40
30
20

10
0
0

10

20

30

40

50

60

CP2-2.5-4-150-20-M Test Data
CP2 Method D (Nolet et al. 2019)

70 80
d [mm]

90 100 110 120 130 140 150
CP2 Method C (Masroor et al. 2020)

Figure C.1. Curves from monotonic test and analytical methods for CP2

80
70
60

F [kN]

50
40
30
20
10
0
0

10

20

30

40

50

60

70 80 90 100 110 120 130 140 150
d [mm]
CP3-2.5-4-300-20-C Envelope curve
CP3 Method C (Masroor et al. 2020)
CP3 Method D (Nolet et al. 2019)
Figure C.2. Envelope curves from cyclic tests and analytical results for CP3

170

80
70
60

F [kN]

50
40

30
20
10
0
0

10

20

30

40

50

60

70 80
d [mm]

CP4-2.5-4-300-30-C Envelope curve
CP4 Method D (Nolet et al. 2019)

90

100 110 120 130 140 150

CP4 Method C (Masroor et al. 2020)

Figure C.3. Envelope curves from cyclic tests and analytical results for CP4

90
80
70

F [kN]

60
50
40
30
20
10
0
0

10

20

30

40

50

60

CP6-2.5-4-150-30-C Envelope curve
CP6 Method D (Nolet et al. 2019)

70 80
d [mm]

90

100 110 120 130 140 150

CP6 Method C (Masroor et al. 2020)

Figure C.4. Envelope curves from cyclic tests and analytical results for CP6

171

60
50

F [kN]

40
30
20
10
0
0

10

20

30

40

50

60

70 80 90 100 110 120 130 140 150
d [mm]
CP7-2.5-2-300-20-C Envelope curve
CP7 Method C (Masroor et al. 2020)
CP7 Method D (Nolet et al. 2019)
Figure C.5. Envelope curves from cyclic tests and analytical results for CP7

60
50

F [kN]

40
30
20
10
0

0

10

20

30

40

50

60

CP8-2.5-2-300-30-C Envelope curve
CP8 Method D (Nolet et al. 2019)

70 80
d [mm]

90

100 110 120 130 140 150

CP8 Method C (Masroor et al. 2020)

Figure C.6. Envelope curves from cyclic tests and analytical results for CP8

172

70
60

F [kN]

50
40
30
20
10
0
0

10

20

30

40

50

60

70 80
d [mm]

CP9-2.5-2-150-20-C Envelope curve
CP9 Method D (Nolet et al. 2019)

90

100 110 120 130 140 150

CP9 Method C (Masroor et al. 2020)

Figure C.7. Envelope curves from cyclic tests and analytical results for CP9

90
80
70

F [kN]

60
50
40
30
20
10
0
0

10

20

30

40

50

60

CP10-2.5-2-150-30-C Envelope curve
CP10 Method D (Nolet et al. 2019)

70 80
d [mm]

90 100 110 120 130 140 150
CP10 Method C (Masroor et al. 2020)

Figure C.8. Envelope curves from cyclic tests and analytical results for CP10

173

90
80
70

F [kN]

60
50
40
30
20
10
0
0

10

20

30

40

50

60

70 80
d [mm]

CP11-2.5-2-75-20-C Envelope curve
CP11 Method D (Nolet et al. 2019)

90

100 110 120 130 140 150

CP11 Method C (Masroor et al. 2020)

Figure C.9. Envelope curves from cyclic tests and analytical results for CP11

90
80
70

F [kN]

60
50
40
30
20
10
0
0

10

20

30

40

50

60

CP12-3.5-2-300-20-M Test Data
CP12 Method D (Nolet et al. 2019)

70 80
d [mm]

90 100 110 120 130 140 150
CP12 Method C (Masroor et al. 2020)

Figure C.10. Curves from monotonic test and analytical methods for CP12

174

90
80
70

50
40
30
20
10
0
0

10

20

30

40

50

60

70 80
d [mm]

CP13-3.5-2-300-20-C Envelope curve
CP13 Method D (Nolet et al. 2019)

90

100 110 120 130 140 150

CP13 Method C (Masroor et al. 2020)

Figure C.11. Envelope curves from cyclic tests and analytical results for CP13

90
80
70
60

F [kN]

F [kN]

60

50

40
30
20
10
0
0

10

20

30

40

50

60

70 80
d [mm]

CP14-3.5-2-150-20-C Envelope curve
CP14 Method D (Nolet et al. 2019)

90 100 110 120 130 140 150
CP14 Method C (Masroor et al. 2020)

Figure C.12. Envelope curves from cyclic tests and analytical results for CP14

175

90
80
70

F [kN]

60
50
40
30
20
10
0
0

10

20

30

40

50

60

70 80
d [mm]

CP15-3.5-2-75-20-C Envelope curve
CP15 Method D (Nolet et al. 2019)

90

100 110 120 130 140 150

CP15 Method C (Masroor et al. 2020)

Figure C.13. Envelope curves from cyclic tests and analytical results for CP15

90
80
70

F [kN]

60
50

40
30
20
10
0
0

10

20

30

40

50

60

CP16-3.5-2-300-20-R-M Test Data
CP16 Method D (Nolet et al. 2019)

70 80
d [mm]

90 100 110 120 130 140 150
CP16 Method C (Masroor et al. 2020)

Figure C.14. Curves from monotonic test and analytical methods for CP16

176

90
80
70

F [kN]

60
50
40
30
20
10
0
0

10

20

30

40

50

60

70 80 90 100 110 120 130 140 150
d [mm]
CP17-3.5-2-300-20-R-C Envelope curve
CP17 Method C (Masroor et al. 2020)
CP17 Method D (Nolet et al. 2019)
Figure C.15. Envelope curves from cyclic tests and analytical results for CP17

90
80
70

F [kN]

60
50

40
30
20
10
0
0

10

20

30

40

50

60

70 80 90 100 110 120 130 140 150
d [mm]
CP18-3.5-2-150-20-R-C Envelope curve
CP18 Method C (Masroor et al. 2020)
CP18 Method D (Nolet et al. 2019)
Figure C.16. Envelope curves from cyclic tests and analytical results for CP18

177

90

80
70
60

F [kN]

50
40
30
20
10
0
0

10

20

30

40

50

60

CP19-3.5-2-75-20-R-C Envelope curve
CP19 Method D (Nolet et al. 2019)

70 80
d [mm]

90

100 110 120 130 140 150

CP19 Method C (Masroor et al. 2020)

Figure C.17. Envelope curves from cyclic tests and analytical results for CP19

178