1. business and industrial
2. construction

DYANMIC ANALYSIS OF THE FFTT SYSTEM
by
Michael Fairhurst
B.ASc., The University of British Columbia, 2012
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF APPLIED SCIENCE
in
THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES
(Civil Engineering)
THE UNIVERSITY OF BRITISH COLUMBIA
(Vancouver)
August 2014
© Michael Fairhurst, 2014
Abstract
The advantages of using timber as the primary construction material in mid- and high-rise
buildings are undisputed. Timber is sustainable, renewable, and has a very good strength-toweight ratio, which makes it an efficient building material. However, perceived shortcomings
with respect to its ductility and system level behavior; along with lack of appropriate design
guidance currently limits the use of timber in taller structures. Overcoming these obstacles
will allow timber, and its wood product derivatives, to further expand into the multi-storey
construction sector - most likely in hybrid-type structures.
The ―Finding the Forest Through the Trees‖ (FFTT) system is an innovative timber-steel
hybrid system that may allow high-rise timber construction, even in highly seismic regions.
The FFTT system utilizes engineered timber products to resist gravity and lateral loads with
interconnecting steel members to provide the necessary ductility and predictability for
seismic demands.
For a novel hybrid system, such as the FFTT, to gain recognition, experimental data must be
gathered and supported by computational modeling and analysis in order to prove its
component- and system-level performance. This thesis presents research utilizing nonlinear
dynamic analysis of finite element (FE) models of the FFTT system, with properties
calibrated to physical component tests, to capture the response under significant wind and
seismic loads. From the results presented herein, it appears that the FFTT system can meet
the design performance requirements required for seismic loading; however, due to its
relatively low weight, may be susceptible to wind induced vibrations. All results are based on
Vancouver, BC loading as specified by 2010 the National Building Code of Canada.
ii
Preface
The methodology and results presented in Chapters 2 and 3 of this thesis were published and
presented at the World Conference on Timber Engineering (Quebec City, Quebec, 2014).
The paper included in the conference proceedings was:
―Fairhurst M., Zhang X., Tannert T., 2014. Nonlinear Dynamic Analyses of a novel TimberSteel Hybrid System. Proceedings of the 2014 World Conference on Timber Engineering,
Quebec City, Quebec, Canada.‖
I prepared the majority of the manuscript and developed the numerical models and results
presented in the paper. Tannert, T. and Zhang, X. helped to prepare and edit the manuscript
and provided invaluable guidance and discussion throughout the study.
The study described in Chapter 5 is part of a manuscript which is currently under review:
―Zhang X., Fairhurst M., Tannert T., 2014. Ductility Estimation for a Novel Timber-SteelHybrid System. Submitted and Under Review.‖
I helped to prepare and edit the manuscript and provided the three dimensional structural
numerical modeling and results for a study to support the results developed by Zhang, X. and
myself using simplified two dimensional models. Zhang, X. and Tannert, T. prepared the
majority of the manuscript. Tannert, T. provided guidance and feedback about the study and
results.
iii
Table of Contents
Abstract .................................................................................................................................... ii
Preface ..................................................................................................................................... iii
Table of Contents ................................................................................................................... iv
List of Tables ........................................................................................................................ viii
List of Figures ......................................................................................................................... ix
Acknowledgements ............................................................................................................... xv
Dedication ............................................................................................................................ xvii
Chapter 1: Introduction ........................................................................................................ 1
1.1
Tall Wood-Based Building ....................................................................................... 1
1.2
Research Needed ....................................................................................................... 2
1.3
Objectives ................................................................................................................. 2
1.4
Scope ......................................................................................................................... 3
Chapter 2: Literature Review ............................................................................................... 4
2.1
History of Tall Wood Buildings ............................................................................... 4
2.2
Future of Tall Wood Buildings ................................................................................. 8
2.2.1 Timber Hybridization.......................................................................................... 10
2.2.2 Glued Laminated Timber (Glulam) .................................................................... 14
2.2.3 Mass Timber ....................................................................................................... 15
2.2.3.1
Cross Laminated Timber (CLT) ................................................................. 16
iv
2.3
2.2.3.2
Laminated Strand Lumber (LSL)................................................................ 18
2.2.3.3
Laminated Veneer Lumber (LVL) .............................................................. 18
Previous Research Related to Modeling and Design of Tall Timber Structures .... 19
2.3.1 The FFTT System ............................................................................................... 20
2.3.2 Experimental Research on the FFTT System ..................................................... 27
2.3.3 Glulam Frame Connections ................................................................................ 30
2.3.4 Lateral Resistance of CLT Walls ........................................................................ 32
2.3.5 Seismic Force Modification Factors for CLT Buildings .................................... 35
Chapter 3: Three-dimensional Models for the FFTT System ......................................... 37
3.1
Structural Member Specifications........................................................................... 38
3.2
Glulam Columns and Beams .................................................................................. 39
3.3
Glulam Frame Connections .................................................................................... 40
3.4
CLT Shearwalls ...................................................................................................... 43
3.4.1 Orthotropic CLT Properties ................................................................................ 44
3.4.2 Composite Theory – k Method ........................................................................... 45
3.4.3 Anisotropic CLT Numerical Modeling ............................................................... 47
3.5
CLT Wall Connections ........................................................................................... 49
3.5.1 Axial springs for CLT Panel Connections .......................................................... 50
3.5.2 Rotational springs for CLT Panel Connections .................................................. 53
3.6
CLT Slabs ............................................................................................................... 54
3.7
Steel Beams ............................................................................................................. 55
3.7.1 Spring Properties for Steel Beam Models ........................................................... 57
3.7.2 Beam-Column Element Modeling ...................................................................... 60
v
3.8
Other Modeling Considerations .............................................................................. 63
3.8.1 Supports .............................................................................................................. 63
3.8.2 Gravity Loads...................................................................................................... 66
3.8.3 Mass .................................................................................................................... 68
3.8.4 Damping .............................................................................................................. 68
3.9
Summary of developed models ............................................................................... 72
Chapter 4: Non-linear Dynamic Seismic Analysis ............................................................ 75
4.1
Seismic Analysis ..................................................................................................... 75
4.1.1 Ground Motion Selection .................................................................................... 75
4.1.2 Ground Motion Scaling....................................................................................... 78
4.2
Performance Criteria ............................................................................................... 80
4.2.1 Interstorey Drifts ................................................................................................. 82
4.2.2 Plastic Rotations.................................................................................................. 84
4.3
Results of Non-linear Seismic Analyses ................................................................. 86
4.3.1 Interstorey Drift Results ...................................................................................... 87
4.3.2 Beam Plastic Rotation Results ............................................................................ 91
4.3.3 Base Shear ........................................................................................................... 94
4.4
Discussion of Seismic Analyses ............................................................................. 96
Chapter 5: Dynamic Wind Analysis ................................................................................... 97
5.1
Introduction ............................................................................................................. 97
5.2
NBCC Dynamic Procedure ..................................................................................... 98
5.2.1 External Pressure Coefficients ............................................................................ 99
5.2.2 Exposure Factor .................................................................................................. 99
vi
5.2.3 Gust Effect Factor ............................................................................................. 100
5.3
Wind Analyses ...................................................................................................... 103
5.4
Results of Wind Analyses ..................................................................................... 103
5.5
Discussion of Wind Analyses ............................................................................... 104
Chapter 6: Force Reduction Factor Study ...................................................................... 106
6.1
Seismic Force Modification Factors in the NBCC ............................................... 106
6.2
Force Reduction Factor Study for the FFTT System ............................................ 108
6.2.1 Two Dimensional Model .................................................................................. 109
6.2.2 Three Dimensional Model ................................................................................ 111
6.2.3 Ground Motion Record Selection and Scaling ................................................. 111
6.2.4 Results from the Three Dimensional Model ..................................................... 115
Chapter 7: Conclusions ..................................................................................................... 120
7.1
Summary ............................................................................................................... 120
7.2
Recommendations for Design ............................................................................... 121
7.3
Recommendations for Future Studies ................................................................... 122
Bibliography ........................................................................................................................ 123
Appendix A – FFTT Numerical Model Mode Shapes and Periods ................................ 127
vii
List of Tables
Table 1: Mass Timber Strength Properties ............................................................................. 19
Table 2: FFTT Option Summary ............................................................................................ 22
Table 3: Structural Member Specifications ............................................................................ 39
Table 4: Glulam Beam and Column Material Properties........................................................ 40
Table 5: Orthotropic Stiffness Used for Modeling ................................................................. 45
Table 6: Composition Factors for Wood Panels with Cross Layers (FPInnovations, 2012) .. 46
Table 7: CLT Shear Wall Anisotropic Material Properties .................................................... 47
Table 8: CLT Shear Wall Strength Properties ........................................................................ 47
Table 9: Composite Factors for CLT Walls ............................................................................ 48
Table 10: Orthotropic Modeling Parameters for 6 Layer CLT Wall ...................................... 48
Table 11: Orthotropic Modeling Parameters for 8 Layer CLT Wall ...................................... 48
Table 12: Design Gravity Loads ............................................................................................. 66
Table 13: Heights (Number of Stories) Modelled for each FFTT Option .............................. 73
Table 14: Ground Motion General Information...................................................................... 76
Table 15: Ground Motion Database Information.................................................................... 76
Table 16: 12 Storey Option 1 Model Beam Sections Design with RdRo = 7.5 ..................... 111
Table 17: Ground Motion Summary ..................................................................................... 114
viii
List of Figures
Figure 1: The Landing, Gastown, Vancouver (Koo, 2013) ...................................................... 5
Figure 2: Leckie Building, Yaletown, Vancouver (Koo, 2013) ............................................... 5
Figure 3: Wood Frame Structure Height by Regulation in British Columbia (Green and
Karsh, 2012) .............................................................................................................................. 6
Figure 4: Stadthaus, London (Image: Waugh Thistleton Architects) ....................................... 7
Figure 5: Wood Innovation Design Center, Prince George (jtst.gov.bc.ca) ............................. 8
Figure 6: Forte, Sydney, Australia (victoriaharbor.com.au) ..................................................... 8
Figure 7: Vasterbroplan, Stockholm (skyscrapercentral.com) ............................................... 10
Figure 8: Kanazawa M Building, Japan (Koshihara et al. 2005) ............................................ 12
Figure 9: Rendering of (a) Concrete Jointed Timber Frame System and (b) SOM’s Prototype
42 storey building (SOM 2013) .............................................................................................. 13
Figure 10: Glulam Frame System from the Center of Interactive Research on Sustainability
(CIRS), UBC (naturallywood.com) ........................................................................................ 14
Figure 11: CLT Panels (structurlam.com) .............................................................................. 17
Figure 12: Rolling Shear (Stalnaker and Harris, 1997) .......................................................... 17
Figure 13: LSL Panel (Green and Karsh, 2012) ..................................................................... 18
Figure 14: LVL Board (awc.org) ............................................................................................ 19
Figure 15: FFTT Option 2 Rendering (Green and Karsh, 2012) ............................................ 20
Figure 16: Beam-diaphragm-wall Connection (Green and Karsh, 2012) ............................... 21
Figure 17: FFTT Option 1 Structural System (Green and Karsh, 2012) ................................ 22
Figure 18: FFTT Option 1 (Green and Karsh, 2012) .............................................................. 23
Figure 19: FFTT Option 2 (Green and Karsh, 2013) .............................................................. 24
ix
Figure 20: FFTT Option 3 (Green and Karsh, 2013) .............................................................. 25
Figure 21: FFTT Option 4 (Green and Karsh, 2013) .............................................................. 26
Figure 22: Typical Beam Embedment Procedure (Bhat, 2013) .............................................. 27
Figure 23: Typical Setup and Instrumentation (Bhat, 2013) .................................................. 28
Figure 24: HSS Section Test Results (a) Beam Yielding at the Interface and (b) Wood
Crushing at Beam End (Bhat, 2013) ....................................................................................... 29
Figure 25: Sample HSS Section Hysteretic Response (Bhat, 2013) ....................................... 29
Figure 26: Beam-column Test Layout (Buchanan and Fairweather, 1993)............................ 30
Figure 27: Hysteretic Response for a Beam-Column Subassembly with Steel Beam Brackets
(Buchanan and Fairweather, 1993) ......................................................................................... 31
Figure 28: Local Bending of Steel Bracket (Buchanan and Fairweather, 1993) .................... 32
Figure 29: Brackets Types Tested (Popovski et al., 2010) ..................................................... 33
Figure 30: FPInnovation CLT Wall Test Setup (Popovski et al., 2010)................................. 33
Figure 31: Sample Hysteresis Loop From CLT Panel with ―Type A‖ Brackets (Popovski et
al., 2010) ................................................................................................................................. 34
Figure 32: Bracket Failure Mechanism (Popovski et al., 2010) ............................................. 35
Figure 33: Vancouver, BC 2% in 5 year 5% Damped Design Spectrum for Site Class C Soil
................................................................................................................................................. 38
Figure 34: Beam-column Connection Modeling Details ........................................................ 40
Figure 35: Pinching4 Material Backbone and Cyclic Behavior (Lowes et al. 2004) ............. 42
Figure 36: Pinching4 Material Calibration for Column-beam Connections ........................... 42
Figure 37: Cross Section for (a) Six Layer Wall and (b) Eight Layer Wall ........................... 44
Figure 38: CLT Shear Wall Orthogonal Axes ........................................................................ 44
x
Figure 39: Wall Spring Illustration ......................................................................................... 49
Figure 40: (a) In-plane Rocking and (b) Out-of-plane Rocking ............................................. 50
Figure 41: OpenSees Model for CLT Panel Connections ...................................................... 51
Figure 42: SAWS Material Backbone and Cyclic Behavior (Folz and Filiatrault, 2001) ...... 51
Figure 43: SAWS Material Calibration for Wall Axial Springs ............................................. 52
Figure 44: Example Wall Spring Time History Response to an Earthquake Record ............. 53
Figure 45: SAP2000 Model First Mode Shape ....................................................................... 54
Figure 46: FFTT Ductile Failure Mechanism ......................................................................... 55
Figure 47: Laterally Loaded Beam Deformed Shape and Corresponding Bending Moment
Diagram................................................................................................................................... 57
Figure 48: SAWS Material Calibration for Beam-Wall Connections .................................... 58
Figure 49: Assumed Moment-rotation Backbone Response of a Steel Beam ........................ 60
Figure 50: FFTT Failure Mechanism ...................................................................................... 63
Figure 51: Wall Boundary Conditions Including Rocking Springs ........................................ 64
Figure 52: Rocking Spring Backbone Curve .......................................................................... 66
Figure 53: Rayleigh Damping Plot ......................................................................................... 72
Figure 54: FE Model for Typical Storey of (a) Option 1, (b) Option 2, (c) Option 3, and (d)
Option 4 .................................................................................................................................. 74
Figure 55: Ground Motion Component 1 Spectra .................................................................. 77
Figure 56: Ground Motion Component 2 Spectra .................................................................. 77
Figure 57: Ground Motions Scaling Example ........................................................................ 80
Figure 58: Typical Discrete Performance Levels (ATC, 2009) .............................................. 81
xi
Figure 59: Hysteresis Loops for Beam-Column Assembly with Steel Beam Brackets
(Buchanan and Fairweather, 1993) ......................................................................................... 83
Figure 60: Moment-Rotation Results from Steel Beam-CLT Wall Test ................................ 85
Figure 61: Example 30 Storey Model Displacement subjected to the Chi-Chi, Taiwan Ground
Motion at two Orientations ..................................................................................................... 86
Figure 62: Interstorey Drift Combined Results: a) Mean Results and b) Mean Plus One
Standard Deviation results ...................................................................................................... 87
Figure 63: Interstorey Drift Results for (a) Option 1, (b) Option 2, (c) Option 3, and (d)
Option 4 Models ..................................................................................................................... 88
Figure 64: Roof Drift Combined Results: a) Mean Results and b) Mean Plus One Standard
Deviation results ..................................................................................................................... 89
Figure 65: Roof Drift Results for (a) Option 1, (b) Option 2, (c) Option 3, and (d) Option 4
Models..................................................................................................................................... 90
Figure 66: Beam Plastic Rotations Combined Results: a) Mean Results and b) Mean Plus
One Standard Deviation results .............................................................................................. 92
Figure 67: Plastic Rotation Results for (a) Option 1, (b) Option 2, (c) Option 3, and (d)
Option 4 Models ..................................................................................................................... 93
Figure 68: Base shear results from model compared to those predicted by the NBCC (NRC,
2010) for different R (RdRo) values ......................................................................................... 94
Figure 69: Base Shear Results for (a) Option 1, (b) Option 2, (c) Option 3, and (d) Option 4
Models..................................................................................................................................... 95
Figure 70: Frequency Ranges for Excitations of Structures (Holmes, 2001.) ........................ 98
xii
Figure 71: Wind Loading External Pressure Coefficients from Figure I-15 of the NBCC
(NRC, 2010)............................................................................................................................ 99
Figure 72: Gust Energy Ratio as a Function of Wave Number ............................................ 102
Figure 73: (a) Wind Loading Interstorey Drift Results and (b) with h/500 limits ................ 104
Figure 74: Ductility Factor Based on Equal Displacement Approximation ......................... 108
Figure 75: Simplified Model Illustration (Zhang et al., 2014) ............................................. 110
Figure 76: Example CDF for a 12 Storey Model Design with Different Rd Factors (Zhang et
al.) ......................................................................................................................................... 110
Figure 77: Vancouver, BC Site Hazard De-aggregation at 2 Seconds for (a) Distance and (b)
Magnitude ............................................................................................................................. 112
Figure 78: Spectral Accelerations for (a) Linearly Scaled Motions and (b) Spectrally Matched
Motions ................................................................................................................................. 114
Figure 79: Interstorey Drift Results for Matched Motions Applied in (a) Direction 1 and (b)
Direction 2 ............................................................................................................................ 116
Figure 80: Interstorey Drift Results for Matched Motions Applied in (a) Direction 1 and (b)
Direction 2 ............................................................................................................................ 116
Figure 81: Steel Beam Rotations Results for Scaled Motions Applied in (a) Direction 1 and
(b) Direction 2 ....................................................................................................................... 117
Figure 82: Steel Beam Rotations Results for Matched Motions Applied in (a) Direction 1 and
(b) Direction 2 ....................................................................................................................... 117
Figure 83: Storey Acceleration Results for Scaled Motions Applied in (a) Direction 1 and (b)
Direction 2 ............................................................................................................................ 118
xiii
Figure 84: Storey Acceleration Results for Matched Motions Applied in (a) Direction 1 and
(b) Direction 2 ....................................................................................................................... 119
xiv
Acknowledgements
First, I would like to thank my supervisor: Dr. Thomas Tannert, for giving me the
opportunity to work on this research project. His guidance and support was invaluable
throughout my research. It was a pleasure working with him.
I would also like to thank my co-supervisor: Dr. Terje Haukaas. His enthusiasm for the topic
was extremely motivating, and I appreciate his dedication to provide advice and discussion,
no matter the time or place. His commentary and questions were always valuable and
thought-provoking.
I also sincerely thank Drs. Armin Bebamzadeh and Carlos Ventura for their support and for
giving me the opportunity to work on many other extremely interesting projects outside of
my thesis work. My time at UBC would not have been nearly as rewarding without them and
the rest of the team at the Earthquake Engineering Research Facility (EERF).
I thank Dr. Kenneth Elwood for his advice and support throughout my undergrad and
graduate studies at UBC. He was always available for discussion and questions, and greatly
helped me all the way from my application to completion of my M.ASc degree.
I offer my enduring gratitude to the faculty, staff, and my fellow students and teammates at
UBC, who have inspired and motivated me and made my time at, and away from, UBC much
more enjoyable.
Special thanks to my parents: Donna, Bob, and Nancy; who always offered support and
advice throughout my years of education. And of course my siblings: Chris, Matt, and Sarah;
xv
who always believed in me. I also thank my grandparents: Ron, Doreen, Gordon, and
Dorothy; along with the rest of my family, for their unlimited encouragement and support.
I also must thank all my friends, who have continued to support me throughout all my years
of study and made my time in Vancouver much more enjoyable. I could not have made it this
far without you all.
The research funding was provided by Natural Sciences and Engineering Research Council
of Canada (NSERC) through a grant to Dr. Tannert, as part of a project within the
NEWBuildS strategic research network.
xvi
Dedication
Dedicated to AL and JA…
xvii
Chapter 1: Introduction
1.1
Tall Wood-Based Building
Throughout the early 20th century, numerous mid-rise timber structures were constructed
across Canada and North America. However, since then, area and height restriction have
been put on buildings that use combustible construction materials due to fire incidents. These
restrictions remain to this day in the National Bulking Code of Canada (NBCC) (NRC,
2010).
Recent regulatory changes, such as the introduction of light frame wood construction up to 6
stories in British Columbia (BCBC, 2012) now allow for mid-rise timber construction once
again. Additionally, engineered wood products such as glued laminated timber (glulam),
cross laminated timber (CLT), laminated veneer lumber (LVL), and others provide a more
sustainable building material compared to concrete or steel, with reliable structural
properties. These products may push the feasible height of timber structures into the high
rise-building range (8+ stories). As a consequence, mass timber is increasingly gaining
popularity in mid- and high-rise residential and commercial construction both in British
Columbia and worldwide. Studies such as Gagnon et al., 2011; Ceccotti et al., 2010;
Popovski et al., 2010; and others have shown good structural performance of CLT structures,
including good seismic performance when combined with ductile connectors.
Timber as a building material is lightweight, sustainable, and can provide efficient and
elegant structural solutions. Currently, the most promising method for utilizing timber in
mid- and high-rise construction, however, is as part of steel- or concrete-hybrid systems. This
allows the design to reap the benefits of timber as a building material while exploiting the
1
properties of steel and concrete such as their weight and ductility. Several innovative timber
hybrid systems have been already been developed including those proposed by SOM, 2013;
Professner and Mathis, 2012; and the ―Finding the Forest Through the Trees‖ (FFTT) system
proposed by Green and Karsh (2012).
1.2
Research Needed
For a novel hybrid system to gain recognition, experimental data must be gathered and
supported by computational modeling and analysis to predict its structural performance. For
hybrid high-rise timber buildings, both component and system level testing are required,
along with detailed finite element analyses (FEA) to optimize the structural details. Once this
work is done, sophisticated, nonlinear system level models must be developed and used to
predict the structural and dynamic behavior of the systems under gravity and lateral loads,
including wind and seismic induced forces. Only after completing these steps can the
performance of a proposed system be determined and proper design guidance be given.
1.3
Objectives
The first main objective of the research is to determine whether the ―Finding the Forest
Through the Trees‖ (FFTT) system (Green and Karsh, 2012) is structurally feasible, as
proposed, in a moderately seismic environment accounting for both significant seismic and
wind events. The second objective of this research is to gain a preliminary understanding of
the dynamic behavior of tall hybrid timber structures including the determination of the
governing lateral load to help provide design guidance and direction for further studies of this
type of structure.
2
Other objectives involve using the results and methodology presented herein to further
develop and refine the FFTT concept and to developed further design guidance for high-rise
timber construction in general. Furthermore, the models and framework developed in for this
study will be refined and modified as more physical and numerical test results are developed
to further study the dynamic response of the FFTT structural system.
1.4
Scope
Although there are several proposals for hybrid high-rise timber structural systems, this
research is focused on the FFTT system proposed by Green and Karsh (2012) for Vancouver,
BC. This research focused on the non-linear dynamic behavior of this system designed over
its range of proposed heights (6-30 stories) under seismic and wind loading.
3
Chapter 2: Literature Review
2.1
History of Tall Wood Buildings
The concept of tall timber buildings is not a new one – there are 19 storey pagodas built in
Japan as far back as 1400 years ago which are still standing despite being located in a highly
seismically active region (Green and Karsh, 2012). Additionally, mid-rise buildings have
been commonly built in across Canada from the 1850s up until 1940. Typical timber
buildings during that time consisted of unreinforced masonry on the exterior and heavy
timber beam and post construction in the interior. These structures were commonly built as
factories, warehouses, manufacturing plants, and other industrial buildings during the
industrial era. The buildings were built up to nine stories and up to 30m tall. Some of the
building had a total floor space of up to 312,000 ft2 (29,000 m2) (Koo, 2013). These buildings
are commonly referred to as ―brick and beam‖ buildings.
Locations such as Gastown and Yaletown in Vancouver, BC, are areas with a high
concentration of early-20th century brick and beam buildings. One example is ―The Landing‖
(Figure 1), which was constructed in 1905 in Vancouver’s Gastown as a large warehouse. It
is one of the largest brick and beam buildings with a floor space of 175,000 ft2 (16,000 m2)
(Koo, 2013). It is nine stories high and was retrofitted in 1987 to meet modern building code
requirements.
4
Figure 1: The Landing, Gastown, Vancouver (Koo, 2013)
Another example is the Leckie building, a six-storey warehouse/factory building built in
Yaletown in 1993 and renovated in 1991 (Figure 2).
Figure 2: Leckie Building, Yaletown, Vancouver (Koo, 2013)
As concrete and steel technology and design methods developed, timber construction for
taller buildings diminished in Canada and the prime use of timber for construction became
low-rise residential buildings and smaller low-rise commercial buildings. One of the main
5
reasons that tall timber construction diminished was building code regulations that limited
the height of ―combustible‖ building material structures. Timber construction was considered
unsafe for taller buildings because the wood could combust and provide additional fuel for a
fire and evacuation of the upper stories was not easily possible. Figure 3 presents a timeline
of timber structure construction and height limits in British Columbia from pre-1900 to the
present. Currently timber construction is allowed by the British Columbia Building Code
(BCBC, 2009) up to six stories provided proper fire suppression features are included.
Figure 3: Wood Frame Structure Height by Regulation in British Columbia (Green and Karsh, 2012)
Currently, tall timber buildings are making a comeback in mid- and even high-rise
construction. With modern mass timber building products (see Section 2.2.3) and fire
suppression technology, it is possible to build timber buildings well beyond the current six
storey limit in British Columbia.
The Stadthaus project in London (Figure 4) is an excellent example. The Stadthaus is a nine
storey building with a structural system constructed entirely from timber. It utilizes large
CLT walls as its structural system to resist both gravity and lateral loads. At its time of
completion in 2008, it was claimed to be the world’s tallest pure timber structure.
6
Figure 4: Stadthaus, London (Image: Waugh Thistleton Architects)
In British Columbia the tallest timber building is the recently completed Wood Innovation
Design Center (WIDC) located in downtown Prince George (Figure 5). The WIDC is 7
stories and 30 m tall with a structural system comprising CLT and LVL panels with glulam
beams and columns. The WIDC is projected to be an iconic and inspirational building that
contributes to BCs expertise and reputation as a global leader in wood construction and
design.
A 10 storey timber apartment building, called Forte, has recently been completed in Australia
as the world’s tallest timber building (Figure 6). Forte was constructed from CLT panels
which reduced carbon emissions by over 1,400 tonnes compared to conventional construction
methods (theurbandeveloper.com).
7
Figure 5: Wood Innovation Design Center, Prince George (jtst.gov.bc.ca)
Figure 6: Forte, Sydney, Australia (victoriaharbor.com.au)
2.2
Future of Tall Wood Buildings
Over the last century high-rise development has been dominated by the steel and concrete
industries. These materials are well understood and have excellent structural properties
8
including strength, stiffness, and ductility which allowed engineers and architects to
construct taller buildings then could have been imagined at the beginning of the 20th century,
even in windy and earthquake prone regions. However, these building materials are
accompanied with severe environmental consequences. Studies by the Canadian Wood
Council (CWC) estimate that using steel and concrete for buildings requires 26% and 57%
more energy, emits 34% and 81% more greenhouse gasses, releases 24% and 47% more
pollutants, and discharges 400% and 300% more water compared to using timber for similar
buildings, respectively (CWC, 2004).
According to UN Habitat, currently 50% of the world’s population lives in urban
environments – and by 2050 this number is estimated to surpass 70% (UN-Habitat, 2008).
This change will require huge developments in infrastructure and affordable high-density
housing. Building the approximately 3 million homes (UN Habitat, 2008) from steel or
concrete will have huge impacts on the environment especially in terms of greenhouse gas
emissions.
One solution is to build these homes from timber. Timber is renewable and timber actually
stores – rather than emits – carbon, since trees grow using carbon from the environment. Yet,
to build the necessary homes, large high-rise structures will be required to provide the
population density essential in large cities, which is typically the domain of steel and
concrete. However, with the recent development of mass timber products such as CLT and
LVL, it may be possible to begin constructing 30+ storey mass timber structures to provide a
more environmentally friendly solution to this global housing problem.
The previously mentioned examples demonstrate that taller wood construction is not only
possible but rapidly increasing in both in BC and around the world. The Vasterbroplan
9
(Figure 7) is another example. The Vasterbroplan is a 34 storey timber (approximately 110m)
building proposed for construction in Stockholm, Sweden. Other extreme tall wood buildings
have been proposed around the world. Examples in include the FFTT system (Green and
Karsh, 2012) and the Skidmore, Owings & Merrill (SOM) Tall Timber Research Project
(SOM, 2013).
Figure 7: Vasterbroplan, Stockholm (skyscrapercentral.com)
2.2.1
Timber Hybridization
Timber members have high strength to weight ratio compared to steel and concrete which
can result in lighter structures and subsequently lower forces during ground excitation.
Timber does have several disadvantages however; the most prominent from a structural, or
more specifically seismic, perspective is its brittle nature when loaded in tension or shear.
Under these loadings, timber will break in a very non-ductile manner, which is not ideal
10
during an intense ground motion as it does not dissipate energy and could lead to a brittle,
catastrophic failure of the structure. Due to this characteristic, the most promising approach
for using timber in mid- and high-rise construction is as part of hybrid structural systems.
Hybridization refers to combining two different materials to form a system that makes use of
the unique advantages of each material. Hybridization can occur on both a component level,
such as reinforced concrete, or on a system level. System hybridization combines two
materials at the structural level to distribute and share the loads acting on them.
Through designing hybrid structures, engineers are able to capitalize on the light weight and
environmental benefits of timber while exploiting the unique benefits of the other building
materials, such as the ductility that can be provided by steel, or the weight that can be
provided by reinforced concrete.
The Kanazawa M Building (Figure 8), constructed in 2005 in Kanazawa, Japan, provides an
example of both system and component hybridization. It is a 5 storey building with four
timber-steel composite levels supported by a reinforced concrete first floor. The building
system comprises steel-timber composite frames, concrete floors slabs and roof, plywood
walls, and stairs constructed with a steel frame. The composite frames consist of laminated
timber with built-in square steel bars. The steel bars resist load while the timber provides
restraint from buckling and increases the fire resistance of the members, providing an
efficient hybrid-type component (Koshihara et al., 2005).
System level hybridization, as used in the Kanazawa Building, may be necessary to build
taller timber buildings up to and beyond 30 stories. Two studies that exemplify this are ―The
11
Case for Tall Wood Buildings‖ (Green and Karsh, 2012), which introduced the FFTT design
concept, and the SOM Tall Timber Research Project (SOM, 2013).
Figure 8: Kanazawa M Building, Japan (Koshihara et al. 2005)
The goal of the SOM Tall Timber Research Project was to develop a mass timber structural
system for high-rise buildings – up to 42 stories in Chicago, Il. SOM proposed an innovative
system called the ―Concrete Jointed Timber Frame‖ to effectively resist the overturning and
lateral forces induced by significant wind loading. The SOM system relies on stiff mass
timber panels for the main structural elements and lateral force resisting system,
supplemented with reinforced concrete at the connecting joints. The reinforced concrete
joints provide any necessary ductility, while effectively distributing the majority of the mass
at each floor to its perimeter, where it is most useful in resisting overturning forces. The
result is an efficient system that benefits from the unique advantages of the three materials
(steel, concrete, and timber) while reducing the carbon footprint of the structure by 60 to
12
75% compared to an equivalent concrete building (SOM, 2013). Figure 9a illustrates the
Concrete Jointed Timber Frame system, and shows how the mass timber panels could be
connected through reinforced concrete joints. Figure 9b presents a rendering of the 42 storey
prototype structure considered in the report (SOM, 2013).
Although this idea is still in its proposal phase, SOM considers it to be feasible from the
standpoint of structural engineering, architecture, interior layouts, and building services.
Additional studies, however, are required to verify the performance of the structural system,
possibly requiring physical testing. The structure was designed with particular attention to its
constructability, cost, and fire protection; however, expert review and physical testing related
to its fire safety may also be required (SOM, 2013).
(a)
(b)
Figure 9: Rendering of (a) Concrete Jointed Timber Frame System and (b) SOM’s Prototype 42 storey
building (SOM 2013)
13
2.2.2
Glued Laminated Timber (Glulam)
Glulam is a structural engineered timber product manufactured by bonding a number of
layers of dimensioned timber with a durable, moisture-resistance, structural adhesive. These
members are extensively used as columns and beams in timber construction and can be
manufactured in curved or arch shapes for a wide variety of architectural designs (see Figure
10).
Glulam members optimize wood as a building material because they allow for construction
of large members from small trees, which gives them the advantage over large sawn timber
members which must be manufactured from old-growth trees. Because glulam members can
be manufactured in large sizes they can be utilized for long spans and large loads. Size is
only constrained by transportation and handling limits. Glulam can even offer greater poundfor-pound strength than steel (APA, 2010) and may be slightly more cost-effective (Sathre
and O’Connor, 2008). Glulam also performs well in fires, as it burns slowly and maintains
strength and stiffness.
Figure 10: Glulam Frame System from the Center of Interactive Research on Sustainability (CIRS), UBC
(naturallywood.com)
14
2.2.3
Mass Timber
In order to efficiently construct mid- and high-rise timber structures, traditional sawn timber
and glulam will need to be supplemented with mass timber products. Mass timber utilizes
large, solid wood panels which can range in size up to 2.4 x 20m and can be constructed up
to or greater than 400mm in thickness. The three primary mass timber products are:

Cross Laminated Timber (CLT)

Laminated Strand Lumber (LSL)

Laminated Veneer Lumber (LVL)
Mass timber construction is very different from typical light-frame construction used in
residential building, and offers significant advantages in fire, acoustic, and structural
performance as well as building scale, construction efficiency, and material stability and
reliability. Mass timber, and engineered timber products in general have a wide variety of
unique benefits. Compared to traditional sawn lumber, mass timber:
 Can be designed for specific performance objectives
 Is very versatile. A wide variety of thicknesses, sizes, and grades are available and can
be custom manufactured.
 Is engineered to maximize the strength and stiffness properties of natural wood while
limiting potential material disadvantages.
 Is dimensionally stable.
 Is reliable. Strength and stiffness characteristics can be more accurately determined than
in sawn lumber.
 Performs well in fire.
 Makes efficient use of wood since it can be made from small or defective pieces.
15
And compared to steel and concrete, mass timber:

Has very good strength and stiffness properties, especially per unit mass.

Is easy to work with and to assemble.

Is prefabricated, allowing for rapid on-site construction.

Provides very good natural acoustic and heat insulation.

Is sustainable.

Stores carbon rather than produces it.

Comes from a renewable resource.
2.2.3.1
Cross Laminated Timber (CLT)
CLT panels consist of layers of sawn lumber which are stacked in perpendicular orientations.
The wide faces of the boards are glued together with an adhesive providing a strong and stiff
bond between layers. Although timber is highly anisotropic and much stronger when loaded
parallel to its grain orientation compared with loading perpendicular to its grain, when glued
together in alternating orientations, this property is reduced and a more dimensionally stable
product is achieved. CLT panels can be produced up to 12m in length (structurlam.com) and
are extensively used in walls and floor systems where long spans are required.
In the FFTT systems, CLT panels may be utilized in the walls and slabs of the structures due
to their ability to span long distances and their in-plane stiffness and strength properties. CLT
panels are able to be manufactured thicker than LSL or LVL panels, which is a benefit for the
taller designs.
16
Figure 11: CLT Panels (structurlam.com)
One of the major drawbacks with CLT, however, is its material efficiency under axial
loading. Under axial loading, up to half of the area of a panel under load will be loaded
perpendicular to its grain (the weaker direction), which limits the overall strength of a panel.
Another drawback is related to the rolling shear strength and stiffness in the panel cross
layers. Rolling shear is the rolling of the wood fibers when loading in shear perpendicular to
the grain of the wood, as illustrated in Figure 12. Timber is much weaker and softer in rolling
shear compared to regular shear, and consequently, the shear deformation of a panel will be
greatly amplified due to the rolling shear in the cross layers of the panel. Rolling shear
stiffness is approximately one tenth of parallel-to-grain shear (Mestek et al., 2008).
Figure 12: Rolling Shear (Stalnaker and Harris, 1997)
17
2.2.3.2
Laminated Strand Lumber (LSL)
LSL is produced from strands of timber glued together orientated parallel to the length of the
member. LSL is highly consistent and has a uniform structure and predictable strength and
stiffness properties. Because it can be made from small trees and defective wood, LSL is a
sustainable building material. In the FFTT system, LSL may be specified for use as floors,
slabs or walls.
Figure 13: LSL Panel (Green and Karsh, 2012)
2.2.3.3
Laminated Veneer Lumber (LVL)
LVL is manufactured by laminating layers of wood veneers using a waterproof adhesive. The
grain of each layer is orientated in the same direction to achieve predictable behavior and
uniformity. Due to the controlled manufacturing process, LVL products are straight and
defect free. LVL may also be specified for the slabs or walls or the FFTT system.
18
Figure 14: LVL Board (awc.org)
LVL and LSL panels can be manufactured up to 20m long and have higher shear strength
than CLT. Additionally, since bearing depends on grain orientation in CLT panels, LVL and
LSL may perform better at steel beam connections than CLT panels. Table 1 summarizes
some of the key strength properties of the three mass timber products based on typical
manufacturer’s data (redbuilt.com; lpcorp.com) for LVL and LSL, and local manufacturer’s
data for CLT (structurlam.com).
Table 1: Mass Timber Strength Properties
2.3
Bending
Compression
Tension
Shear
CLT
11.8 MPa
11.5 MPa
5.5 MPa
1.5 MPa
LVL
15-21 MPa
15-21 MPa
9-12 MPa
1.5-2 MPa
LSL
12-19 MPa
11-17 MPa
9-15 MPa
1-3 MPa
Previous Research Related to Modeling and Design of Tall Timber Structures
The FFTT system is an innovative structural system recently proposed in The Case for Tall
Wood report (Green and Karsh, 2012), and little additional literature is available on the
19
system. However, the individual components of the system; such as CLT shear walls, glulam
frames, and steel beam-CLT wall connections; have been researched.
2.3.1
The FFTT System
The FFTT system, an acronym for ―Finding the Forest Through the Trees‖ is an innovative
building system designed for high-rise timber-steel composite structures using mass timber
panels connected with steel beams (Green and Karsh, 2012). This system uses engineered
timber products to resist lateral and gravity induced forces, and utilizes the ―strong-column
weak-beam‖ design methodology in that interconnecting steel beams are designed to yield
before the vertical timber elements exhibit damage or break and therewith provide energy
dissipation and ductility for seismic induced demands. The timber members provide a stiff
system that, if properly designed, stays rigid and will deflect little under wind induced loads.
A rendering of a 20 storey FFTT building is presented in Figure 15 and a beam-walldiaphragm connection is presented in Figure 16.
Figure 15: FFTT Option 2 Rendering (Green and Karsh, 2012)
20
Figure 16: Beam-diaphragm-wall Connection (Green and Karsh, 2012)
The advantage of the FFTT system is that it optimizes the unique benefits of the two
materials for an efficient and sustainable design. Timber provides a lightweight, stiff, and
sustainable building material, that not only is renewable, but stores carbon emissions rather
than producing them. This is combined with steel which can provide a reliable and ductile
failure mechanism as well as significant energy dissipation which allows the system to
perform adequately during seismic events.
Four different Options were proposed for the FFTT system (Green and Karsh, 2012), all of
which are based off of this design methodology and contain interior mass timber shearwalls
(either CLT or LVL) interconnected with steel elements. The structural system of Option 1 is
shown in Figure 17.
21
Figure 17: FFTT Option 1 Structural System (Green and Karsh, 2012)
The main lateral load resisting systems of the four FFTT options are summarized in Table 2.
Table 2: FFTT Option Summary
Option 1
Option 2
Option 3
Option 4
LRFS
Core shearwalls
Core and interior
shearwalls
Core and exterior
shearwalls
Core, interior and
exterior shearwalls
GFRS
Shearwalls and
exterior columns
Shearwalls and
exterior columns
Shearwalls
Shearwalls
Height limit
(stories)
12
20
20
30
The first option (Figure 18), for structures up to 12 stories, utilizes perimeter glulam columns
and beams as part of the gravity force resisting system (GFRS). Interior core shearwalls
provide the lateral force resisting system (LFRS).
22
Figure 18: FFTT Option 1 (Green and Karsh, 2012)
Option 2, illustrated in Figure 19, which may be viable up to 20 stories is based on the same
layout, and includes additional interior shearwalls to increase the lateral load capacity of the
system. Because these shearwalls effectively separate and compartmentalize the area within
each storey, this layout may be well suited for residential construction.
23
Figure 19: FFTT Option 2 (Green and Karsh, 2013)
Option 3 (Figure 20) uses the Option 1 plan and incorporates exterior shearwall connected
with steel beams. Similar to Option 2, it was designed for structures up to 20 stories. Because
this design provides a more open floor layout it would be well suited to a commercial or
office type building.
24
Figure 20: FFTT Option 3 (Green and Karsh, 2013)
The final design, Option 4 (Figure 21), combines the previous two designs to create an
extremely stiff, strong system that may be feasible in structures up to 30 stories.
25
Figure 21: FFTT Option 4 (Green and Karsh, 2013)
26
2.3.2
Experimental Research on the FFTT System
As part of a Master’s thesis at the University of British Columbia (UBC), Bhat (2013) tested
a variety of steel beams embedded into CLT panels as a first step towards understanding the
behavior of the FFTT system. Her tests involved static and cyclic in-plane loading of a setup
comprising a steel beam embedded into a 7 layer CLT panel. Tests were conducted, both
monotonic and cyclic, on a variety embedment lengths and embedment depths. Both a wide
flange section, with and without notches cut into the flanges at the plastic hinge zone, and a
rectangle hollow structural steel (HSS) section were tested. To build the connections, a steel
beam was embedded into slots cut into a CLT panel as shown in Figure 22, and then held in
place with lag screws.
A typical test setup is shown in Figure 23. Beams were pin-connected at two points along the
CLT panel and loaded by an actuator at one end of the cantilevered beam. Displacements
along the beam were measured by six linear variable differential transformers (LVDTs).
Figure 22: Typical Beam Embedment Procedure (Bhat, 2013)
27
Figure 23: Typical Setup and Instrumentation (Bhat, 2013)
Two sections were tested: a W150x100 wide flange section and a HSS 100x50x3.125 hollow
section. Embedment lengths and depths and bolted connections were varied between tests.
None of the sections were laterally supported and the stronger wide flange sections
consistently buckled out of plane and produced lopsided hysteresis curves under cyclic
loading. The HSS tests yielded and plastified and demonstrated much more symmetric and
predictable hysteresis curves. Yielding of the beam, followed by local crushing in the CLT
panel was observed, as shown in Figure 24. The connection was highly ductile with a
pinched hysteretic response (Figure 25).
28
(a)
(b)
Figure 24: HSS Section Test Results (a) Beam Yielding at the Interface and (b) Wood Crushing at Beam
End (Bhat, 2013)
A typical hysteretic curve for the HSS section embedded at a depth of 50.8mm for a length of
304.8mm is presented in Figure 25. The beam was loaded cyclically with the CUREE
loading protocol (Krawinkler et al., 2001) and displacements were measured at the end of the
1.8m beam where the actuator force was applied.
Figure 25: Sample HSS Section Hysteretic Response (Bhat, 2013)
29
2.3.3
Glulam Frame Connections
Buchanan and Fairweather (1993) present an overview of the seismic performance of glulam
timber frame structures. They describe a wide range of connections available for glulam
frames with particular reference to seismic loading and present test results for several new
connection types.
The arrangement used for the beam-column connection testing is presented in Figure 26. This
arrangement was designed to give a representative force and moment distribution while
under a simulated lateral load, which was applied to the top of the frame. The mid-height of
the column and mid-lengths of the beams were points of contraflexure, similar to lateral
loading in a multistorey building.
Figure 26: Beam-column Test Layout (Buchanan and Fairweather, 1993)
Test load-deflection hysteretic results for a beam-column subassembly with steel beam
brackets are shown in Figure 27.
30
Figure 27: Hysteretic Response for a Beam-Column Subassembly with Steel Beam Brackets (Buchanan
and Fairweather, 1993)
The particular test setup that produced Figure 27 was comprised of 495 x 135mm glulam
beams connected to 495 x 180mm glulam columns with steel brackets connecting the
members. The beams had steel bars epoxied into the end grain, while the columns had bars
epoxied through the joint region. All the connections were bolted together. A high degree of
ductility was observed and most of the energy absorption was accomplished through local
bending of the steel beam bracket. Local splitting of the bracket near the weld on the web
was observed, in the final load cycle, however no catastrophic failure occurred. Figure 28
shows the local bending of the steel bracket at the end of a test.
31
Figure 28: Local Bending of Steel Bracket (Buchanan and Fairweather, 1993)
2.3.4
Lateral Resistance of CLT Walls
Popovski et al. (2010) conducted a series of quasi-static tests on CLT wall panels to
investigate the behavior of the panels and their connections under lateral loads. A wide range
of configurations and connection details were considered. Single panel walls with three
different aspect ratios, multi-panel walls connected with step joints, as well as two storey
walls were all tested. Connections tested included steel brackets with annular ring nails,
spiral nails, and screws; combinations of steel brackets and hold-downs; diagonal long
screws; and custom made brackets with timber rivets. The brackets tested are shown in
Figure 29. An example test setup is presented in Figure 30.
32
Figure 29: Brackets Types Tested (Popovski et al., 2010)
(a)
(b)
Figure 30: FPInnovation CLT Wall Test Setup (Popovski et al., 2010)
33
Results showed that both nails and screws can perform adequately under seismic loading
while the use of hold-downs with nails at wall ends can further improve the performance.
Diagonally placed screws to connect the walls to the floor displayed less ductile behavior and
were not recommended. Timber rivets with custom brackets were also demonstrated to be
effective.
The hysteretic response of a single storey wall with ―Type A‖ brackets is presented in Figure
31. The brackets were connected to the CLT panels with 16 – 89mm long, 3.9mm spiral nails
and bolted to the ground. The majority of the deformation was in the connections and the
panels moved almost like rigid bodies. A very ductile failure mechanism was observed, as
shown in Figure 32, which included nail withdrawal, nail yielding, and timber yielding.
Figure 31: Sample Hysteresis Loop From CLT Panel with “Type A” Brackets (Popovski et al., 2010)
34
Figure 32: Bracket Failure Mechanism (Popovski et al., 2010)
2.3.5
Seismic Force Modification Factors for CLT Buildings
Pei et al. (2013) modelled CLT wall buildings and estimated their potential seismic force
reduction factors (Rd and Ro). These are factors that allow for a reduction in design base shear
of a structure due to its inelastic response and predicted overstrength when using an elastic
static force method, which is one of the acceptable solutions for seismic design in the NBCC
(NRC, 2010). Currently, no modification factors are listed in the NBCC for CLT wall
buildings, which means designers must either design CLT buildings to remain elastic under
seismic loading (which can be very difficult and costly in high seismic zones) or try to
generate and justify their own modification factors.
In this study, material models were developed based on the tests conducted by Popovski et al.
(2010) and then input into numerical models of multistorey low- and mid-rise CLT wall
buildings, designed using the NBCC 2010 (NRC, 2010) provisions with multiple trial
ductility factors (Rd). The models were subjected to a suite of 22 earthquake acceleration
35
time-history records, and the interstorey drift was recorded. Acceptable Rd factors were
developed through limiting interstorey drift to 2.5% (as is commonly used for life safety
performance in the NBCC 2010 (NRC, 2010) and other building codes) with an acceptable
level of confidence (80% probability of non-exceedance). Vancouver, BC was considered as
the location of these fictional buildings to provide the hazard level. The Vancouver 2% in 50
year 5% damped spectrum was used as a design spectrum. Results indicated that an Rd equal
to 2.0, with a Ro (overstrength reduction factor) equal to 1.5 would produce desirable
performance during a design level earthquake in Vancouver. These values were considered in
the design of the FFTT system options (Green and Karsh, 2012) as well.
36
Chapter 3: Three-dimensional Models for the FFTT System
A number of non-linear three-dimensional finite element models were developed in order to
analyze the four FFTT options over their range of proposed heights. These models are able to
capture both the linear and post-yielding behavior of the structures and were assessed with a
suite of bi-directional time-history earthquake records and a series of dynamic wind analyses.
All models were developed using OpenSees, the Open System for Earthquake Engineering
Simulation (McKenna et al. 2000). OpenSees is an open-source, object-orientated framework
developed for finite element applications to simulate structural and soil response of structures
to earthquakes. OpenSees offers a wide variety of one, two, and three dimensional materials
and element types, making it suitable for a wide variety of structural and geotechnical
simulations. OpenSees used input files written in Tool Command Language (Tcl) (tcl.tk), a
free scripting language commonly used for rapid prototyping, scripted applications, graphical
user interfaces and testing. Due to this open nature, OpenSees is highly programmable and
allows any user with basic Tcl programming knowledge to develop simple or sophisticated
codes and analyze models.
In order to model the proposed system, six main elements had to be considered:

Glulam columns

Glulam beams

CLT shear walls

CLT slabs

Connections between timber elements

Steel beams including connections to the other components
37
3.1
Structural Member Specifications
The models were initially designed using an equivalent static force procedure based on the
NBCC (NRC, 2010) methodology. Timber gravity resisting elements (beams and columns)
were sized based on their specified dead load, while the lateral force resisting members
(walls and steel beams) were sized to resist the forces determined from the static analyses.
The Vancouver, BC, 5% damped 2% in 50 year design spectrum for Site Class C (NRC,
2010) was used to determine the elastic base shear for the analyses (Figure 33). A Ro of 1.5
and Rd of 2.0 were considered as the force reduction factors according the preliminary results
by Pei et al. (2013) and recommendations from Green and Karsh (2012). The members were
selected based on the suite of options so that similar sections could be used in all the models.
Table 3 summarizes the members specified for the models.
Figure 33: Vancouver, BC 2% in 5 year 5% Damped Design Spectrum for Site Class C Soil
38
The main model difference between the four different options is that 6 layer CLT panels
were chosen for Options 1, 2, and 3; while 8 layer CLT panels were chosen for the shear
walls in the Option 4 models.
Table 3: Structural Member Specifications
Member
Material
Section
Glulam Beam
D. Fir 16c-E
264x484mm
Glulam Column
D. Fir 20f-EX
418x418mm
Steel Beam
Grade 350W
W250x33
CLT Wall
D. Fir
204mm (6 layers)
or 274mm (8 layers)
3.2
Glulam Columns and Beams
All FFTT systems were designed with glulam columns as part of the gravity load resisting
system. Some of the systems, such as Option 1, included exterior columns to provide
significant resistance to gravity induced loads. Whereas, other systems, such as Option 4,
utilized exterior and interior shearwalls to provide the majority of the gravity load resistance.
To avoid a brittle failure mechanism, the glulam columns must be designed to remain elastic.
Due to this requirement, it was deemed acceptable to model these timber members with
elastic elements. To ensure the validity of this assumption, the stresses from both shear forces
and combined axial and bending forces were recorded during the analyses. These stresses
were compared to the strength values of the timber material to ensure that they were below
the typical strength values of the material. The elastic beam-column elements used to model
these elements included the elastic shear and axial modulus values for a typical glulam
39
member as presented in Table 4. These values were obtained from the 2010 Canadian Wood
Design Handbook (CSA, 2009).
Similar to the glulam columns, the glulam beams were modelled with the same type of elastic
beam-column element with the same elastic material properties.
Table 4: Glulam Beam and Column Material Properties
Modeling Parameters
Strength Parameters
Material
Elastic
Modulus
Shear
Modulus
Compression
(Parallel to Grain)
Tension
(Parallel to Grain)
Shear
(Perpendicular to
Grain)
D. Fir 16c-E
12400 MPa
530 MPa
30.2 MPa
20.4 MPa
2.0 MPa
3.3
Glulam Frame Connections
The columns were modelled with two degree of freedom rotational springs at the top and
bottom of each storey. These hinges were included to model the flexibility and nonlinear
behavior of the glulam column to beam connections. The springs were included at half of the
beam depth above or below the beam-column connection node to simulate the depth of the
beam. Between the beam and each spring a rigid elastic element was included. This detail is
illustrated in Figure 34.
Figure 34: Beam-column Connection Modeling Details
40
The springs were modelled with a zero-length element which included the connection
rotational stiffness in the two rotational degrees of freedom. The springs were modelled to be
rigid axially and in torsion and shear. The nonlinear properties of these springs were not
known explicitly since this part of the FFTT system has not been sufficiently investigated. It
is known, however, that there will be some flexibility associated with these connections and
that they should not be modelled as completely rigid. To get a reasonable estimate of the
possible behavior of these connections, results presented by Buchanan and Fairweather
(1993) on tests of glulam beam-column connections with steel brackets were considered.
The test setup was presented in Figure 26 was numerically modelled in OpenSees with the
beam and columns modelled as elastic elements. The hinges were modelled as zero-length
rotational springs with material behavior defined by the Pinching4 material model (Lowes et
al., 2003), as shown in Figure 35. This model provides a uniaxial ―pinched‖ forcedeformation response with degradation under cyclic loading. Strength and stiffness
degradation occur through cyclic stiffness degradation, reloading stiffness degradation, and
strength degradation. The model was developed to simulate reinforced concrete beamcolumn joints – but can also be applicable to timber-steel connections, as seen in studies of
bracket connections of CLT shear walls (Shen et al., 2013).
In this model (ePdx, ePfx) and (eNdx, eNfx) provide the positive and negative backbone curves
for the material. The d and f parts of the names refer to displacement and force, and x is 1:4.
The factors uForceP and uForceN describe the unloading properties, while rDispP, rForceP,
rDispN, and rForceN determine the reloading properties.
41
Figure 35: Pinching4 Material Backbone and Cyclic Behavior (Lowes et al. 2004)
The material model was calibrated in an iterative process, with the resulting hysteretic
response as illustrated in Figure 36.
Figure 36: Pinching4 Material Calibration for Column-beam Connections
42
3.4
CLT Shearwalls
Any of the three mass-timber products, as introduced in Section 2.2.3, are suitable for use in
the FFTT system. For this study, however, only CLT panels were considered due to their
ability to be manufactured thicker than LVL or LSL panels. However, since LSL or LVL
exhibit similar stiffness, the conclusions of this study are still applicable to these materials.
The lateral force resisting system (LFRS) for all of the proposed FFTT layouts comprises
CLT shearwalls. All of the options include CLT shearwalls in the core, and several also
include additional interior or exterior walls to add lateral stiffness to the system. Options 3
and 4 also utilize interior and exterior shearwalls as the main gravity force resisting system.
CLT shearwalls, six layer and 204mm thick, were used in all layouts, except in the taller
Option 4 designs, where eight layer 274mm thick panels were required. Figure 37 presents
the cross section for the type CLT wall thicknesses.
The shearwalls were modelled with a grid of shell elements at each storey level. The
elements are four-noded quad elements that utilize a bilinear isoparametric formulation as
well a modified shear interpolation. The elements are formulated with thin-plate expressions
and can resist both in-plane and out-of-plane deflections (Dvorkin and Bathe, 1984).
43
(a)
(b)
Figure 37: Cross Section for (a) Six Layer Wall and (b) Eight Layer Wall
3.4.1
Orthotropic CLT Properties
Due to the orientation of timber layers in CLT panels, as well as the anisotropic nature of
timber, the wall elements had to be modelled with different properties in each orthogonal
direction shown in Figure 38.
Figure 38: CLT Shear Wall Orthogonal Axes
44
3.4.2
Composite Theory – k Method
In order to determine the orthotropic stiffness properties of the CLT walls the CLT handbook
(FPInnovations, 2012) presents a method called the ―k method‖ (Blass, 2004) which
proposes a method to calculate the effective bending stiffness of a CLT panel given its layer
geometry and material properties based on the loading configuration. Several assumptions
are made in this method, including:
1) Plane sections are assumed to remain plane, resulting in a linear stress-strain
distribution.
2) The stiffness of layers loaded perpendicular and parallel to the grain are considered.
3) Shear deformation is not taken into account.
4) Stiffness factors are based on the loading configuration.
Given these assumptions, the composition (k) factors can be calculated as illustrated in Table
6. Note that not all loading configurations are presented in this table – only the cases
particularly important for an in-plane bending shear wall. E0 and E90 refer to the elastic
moduli when considering loading parallel and perpendicular to the grain, respectively. Table
5 shows how these factors can be implemented into the orthotropic shell elements.
Table 5: Orthotropic Stiffness Used for Modeling
Loading
Effective Stiffness
Perpendicular to Plane Loading
Bending Parallel
Eo·k1
In-Plane Loading
Bending Parallel
Eo·k3
Bending Perpendicular
Eo·k4
45
Table 6: Composition Factors for Wood Panels with Cross Layers (FPInnovations, 2012)
Loading Configuration
k
46
3.4.3
Anisotropic CLT Numerical Modeling
To model the anisotropic CLT walls, an elastic orthotropic material that has been
implemented in OpenSees was utilized. This material required three elastic moduli, three
shear moduli, and three Poisson ratios, to create a material with unique properties in each
orthogonal direction. Purely elastic behavior of the CLT was assumed based on the fact that
they would be capacity designed to remain elastic while the steel beams that connected the
panels yielded.
Material properties for the CLT wall panels were based on local manufacturer’s data
(structurlam.com), values proposed by Blass and Görlacher (2004), and relationships as
observed by Stürzenbecher et al. (2010) as summarized in Table 7. E0 and G0 refer to the
elastic and shear moduli parallel to the grain of the timber laminations, respectively. E90 and
G90 refer to the elastic properties perpendicular to the grain of the timber and are assumed to
be identical for the radial or tangential direction of the grain of the laminations.
Table 7: CLT Shear Wall Anisotropic Material Properties
E0
9500 MPa
G0
950 MPa
E90
700 MPa
G90
50 MPa
The strength properties are also summarized in Table 8. All values were based on local
manufacturer’s data (structurlam.com).
Table 8: CLT Shear Wall Strength Properties
Bending
Compression
(Parallel to Grain)
Tension
(Parallel to Grain)
Shear
(Perpendicular to Grain)
11.8 MPa
11.5 MPa
5.5 MPa
1.5 MPa
47
For these two walls considered in the FFTT system, the equations and properties from Table
6 and Table 7 were utilized to calculate the composite factors as summarized in Table 9.
Table 9: Composite Factors for CLT Walls
k1
k3
k4
Six Layer Wall
0.93
0.675
0.377
Eight Layer Wall
0.95
0.758
0.295
Using these composite factors the modeling parameters for the 6 and 8 layer CLT wall were
calculated as summarized in Table 10 and Table 11, respectively.
Table 10: Orthotropic Modeling Parameters for 6 Layer CLT Wall
Direction
E (MPa)
G (MPa)
υ
1
3,590
360
0.04
2
6,400
640
0.04
3
700
70
0.40
Table 11: Orthotropic Modeling Parameters for 8 Layer CLT Wall
Direction
E (MPa)
G (MPa)
υ
1
2,800
280
0.04
2
7,200
720
0.04
3
450
45
0.40
48
3.5
CLT Wall Connections
Since CLT panels can only be constructed with a limited height, modeling one continuous
panel over the height of a high-rise building would be inappropriate. This is because, in
reality, several panels would have to be connected together over the height of the building,
and these connections add flexibility to the system that would not be accounted for using one
continuous panel in the model. Additionally, it could be possible for these connections to
yield and add nonlinearity to the system. A maximum feasible length of a panel would be
about four – 3m high stories (12m total height) (Green and Karsh, 2012). Based on this panel
length, axial and one degree of freedom rotational springs were added between adjacent wall
nodes at every fourth storey of every wall to model the connections, as shown in Figure 39.
Figure 39: Wall Spring Illustration
These springs allowed for in-plane and out-of-plane rocking of the panels at the connections
(Figure 40a and b). The springs were modelled with zero length elements containing the
material properties desired to represent the flexibility of the connections as described in the
following sections.
49
(a)
(b)
Figure 40: (a) In-plane Rocking and (b) Out-of-plane Rocking
3.5.1
Axial springs for CLT Panel Connections
In order to model the axial springs which account for in-plane wall rocking, the tests
conducted by Popovski et al. (2011) at FPInnovations were considered. The test comprised a
single storey CLT panel with steel brackets nailed into the panel and bolted to the ground.
The test setup was modelled in OpenSees, as illustrated in Figure 41, with axial springs to
represent the bracket connections. The SAWS material was used to model the behavior of the
springs (Folz and Filiatrault, 2001). This material provides a one-dimensional hysteretic
model developed as part of the CUREE Caltech project for the seismic analysis of wood
frame structures. This material model is defined by an initial tangent slope, S0; a second,
softer slope, R1*S0; and a strength degradation slope, R2*S0. A pinching slope is defined by
R4*S0 and stiffness degradation is included through two factors: ALPHA and BETA. The
general backbone curve and hysteretic properties of the SAWS material model are illustrated
in Figure 42.
50
Figure 41: OpenSees Model for CLT Panel Connections
Figure 42: SAWS Material Backbone and Cyclic Behavior (Folz and Filiatrault, 2001)
The results of the numerical model with a calibrated material compared to the test by
Popovski et al. (2011) are presented in Figure 43.
51
Figure 43: SAWS Material Calibration for Wall Axial Springs
Similar spring properties were given to the axial springs at the panel connections at every
fourth storey. However, these connections only work in tension, when the panels are pulled
apart. In compression, the panels would contact each other and form a rigid connection. To
account for different behavior in each direction, two zero-length springs were modelled in
each connection. One element contained the SAWS material properties shown in Figure 43,
and the other had bilinear axial properties, in which compression was rigid, and tension was
almost completely flexible. This means that in tension, the combined springs behave with the
SAWS material properties; while in compression; they form a rigid connection between the
adjacent panels to simulate the physical contact between the two panels.
An example response to an earthquake time history record of one of these compound spring
components is illustrated in Figure 44. This example shows the displacement time history of
a spring in the first storey of a 12 storey Option 1 model subject to the Chi-Chi, Taiwan
52
earthquake. The downwards gravity forces hold the wall down for the first 8 seconds, but
then large pulses in the ground motion cause forces which overcome the gravitational forces
and cause the wall to rock slightly – as seen by the positive displacements in the spring. This
configuration produces a slightly more flexible system than if the walls were modelled as
continuous over the height of the building.
Figure 44: Example Wall Spring Time History Response to an Earthquake Record
3.5.2
Rotational springs for CLT Panel Connections
The rotational springs were included to model out-of-plane rocking of the CLT panel
elements. This type of behavior has not been studied in depth and no test results could be
found for this type of connection. Since the panels do not resist much lateral force out-ofplane, decreasing the stiffness of this property was found to have a negligible effect on the
structure as a whole. Due to this finding, the springs were modelled as elastic and very stiff;
as a consequence, out-of-plane rocking did not occur in the model.
53
3.6
CLT Slabs
The floor slabs specified for the FFTT systems were nine layer, 309mm thick, CLT panels
with a thin concrete topping. These stiff floors were assumed to be rigid in the OpenSees
models based on modal analysis of elastic models with explicitly modelled slabs. SAP2000
(CSI, 2002) was used to create preliminary elastic models of several heights from each FFTT
system option. The models included all beam, column, wall, and slab elements. The slabs
were modelled with a grid of shell elements at each storey. A typical example of a first mode
shape for a 30 storey Option 4 model is presented in Figure 45.
Figure 45: SAP2000 Model First Mode Shape
Based on these preliminary SAP results, the effect of the slabs in the OpenSees models were
captured using rigid diaphragm constraints at each storey in lieu of a grid of two dimensional
finite elements. This approach constrained the in-plane translation of the nodes at each storey
and provided the same effect as a rigid diaphragm. Modal analyses of the OpenSees and the
SAP200 models, which included the slabs explicitly, showed equivalent dynamic behavior,
54
validating this simplification. Not only did this simplification decrease the modeling
complexity, but by limiting the number of elements in the model, also significantly decreased
the analysis time.
3.7
Steel Beams
In the FFTT system, the steel beams, which connect the shearwalls and columns, are
designed to yield before the timber elements and to deform inelastically in order to provide
energy dissipation and a ductile failure mechanism (Figure 46). Due to this requirement, the
nonlinear modeling of these beam elements was quintessential to the accuracy of the models.
Figure 46: FFTT Ductile Failure Mechanism
To accomplish the nonlinear modeling of these steel beam elements, nonlinear rotational
springs were included at each interface between a steel beam and timber element. This type
of model is widely used in nonlinear analysis and referred to as a concentrated plasticity
model, since all plasticity in a member is concentrated into one spring element at each end.
55
This type of element modeling can be compared to the modeling of a distributed plasticity
element in which plasticity is integrated over the element section and then over the length.
This approach allows for yielding to occur at any length along the element, which is more
representative of the physical behavior of a structural element. Nevertheless, concentrated
plasticity was chosen for the models for three main reasons.
First, a beam element fixed at both ends and then rotated so that it deforms in double
curvature, such as under lateral load, will have its highest moment at each end of the element,
as illustrated in Figure 47. Because of this, for a uniform section, yielding will occur at the
end points of the beam, which is where the spring elements are modelled in a concentrated
plasticity model. Due to the locations of the hinges, this type of model will be able to capture
yielding in the proper location, similar to a distributed plasticity model.
Second, because all nonlinearity is concentrated at one point in each element, the rest of the
element can be modelled as elastic. An elastic element with all of it plasticity concentrated
into springs is much faster to solve since there is no section and length integration required at
each analysis step.
Finally, and most importantly for this study, is that a member modelled with distributed
plasticity is only able to capture the plastic behavior of the member itself (based on its
sectional and material properties) - the connection behavior is not captured unless separately
modelled. In capacity designed steel-timber connections, however, the steel member will
(ideally) yield first, but once this happens, the force in the connection can still increase as the
steel begins to harden due to strain-hardening. This strength increase can lead to additional
timber crushing after the initial steel yielding. With concentrated plasticity models the total
56
behavior of the connection (steel yielding and timber crushing) can be captured with one
spring.
Figure 47: Laterally Loaded Beam Deformed Shape and Corresponding Bending Moment Diagram
3.7.1
Spring Properties for Steel Beam Models
Springs were modelled at each end of each steel beam element as previously described.
There were three main steel-timber connections that had to be considered:
1) Beam to wall (in-plane)
2) Beam to wall (out-of-plane)
3) Beam to column
The spring properties were modelled from the tests performed by Bhat (2013) as described in
Section 2.3.2. As previously noted, the HSS sections produced much more consistent results,
as the wide flanged sections had lateral stability problems and tended to buckle out-of-plane,
which affected the test results. Due to this better experimental performance, a test done on a
HSS section was used for calibration and considered in the OpenSees models, even though
wide flange sections would most likely be used in the design of a FFTT system due to their
57
superior strength. However, if the wide flange sections were restrained from out-of-plane
buckling, it is postulated that their test results would likely be similar.
The test considered for calibration comprised a HSS 100 x 50 x 3.125mm hollow rectangular
beam embedded into a 239mm seven layer CLT panel at a depth of 50.8mm for a length of
304.8mm. The 1.8m beam was loaded at its far end from the panel and the displacements
were recorded at six locations along the length of the beam and into the panel. The beam was
first loaded quasi-statically and then reversed-cyclically using the CUREE loading protocol
(Krawinkler et al., 2001).
The test setup and loading protocol was modelled with OpenSees. The HSS beam was
modelled as elastic with one rotational spring located at the interface of the connection with
the SAWS material. The resulting force-deflection plot is shown in Figure 48 along with the
test results.
Figure 48: SAWS Material Calibration for Beam-Wall Connections
58
The simulation matched very well with the test results; therefore, the same cyclic properties
were utilized for the model springs. The elastic properties (stiffness and yielding moment)
were calculated based on the properties of the chosen beams.
Additionally, several assumptions were made to extend the test results to predict the response
from other steel sections with a similar connection detail. First, the rotation at each change in
stiffness of the backbone curve was assumed to be constant for each steel section. Secondly,
the ratio of the each subsequent moment along the moment-rotation curve to the initial yield
moment was assumed to be constant. Finally, the hysteretic behavior and strength
degradation properties of each model were similar. These assumptions are summarized and
illustrated in Figure 49, where My*, M1*, M2*, and M3* represent the backbone shape from
the test results; while My, M1, M2, and M3 represent the assumed backbone shape from other
steel sections. Also the hysteretic behavior and strength degradation properties were
modelled identically. These assumptions allowed the material model calibrated to the HSS
section tests conducted by Bhat (2013) to be easily modified for the steel sections considered
in the numerical models.
59
Figure 49: Assumed Moment-rotation Backbone Response of a Steel Beam
The other two connections, the steel beam to wall (out-of-plane) and to column, were not
previously experimentally tested. Therefore, they were modelled with elastic properties based
on the selected member properties, with the same backbone behavior observed in the glulam
column-beam connections (Section 3.3). This seemed rationale because both systems have a
similar failure mechanism of steel yielding followed by local timber crushing, with a pinched
hysteresis.
3.7.2
Beam-Column Element Modeling
The steel beams were modelled as elastic beam-column elements, with rotational zero length
elements at each end. Tests conducted by Bhat (2013) showed that, if properly capacity
designed, the steel beams would consistently yield first, and therefore the elastic spring
properties depended solely on the steel section. The yielding moment of the hinges were
calculated as the yielding moment of the steel beams, and the initial stiffness was based on
60
the element and section properties of these beams. Because the beams are laterally loaded,
they will deform in double curvature (Figure 47) and thus will have a resulting stiffness of:
(
)
(1)
Where kmember is the stiffness of the total member, including the elastic beam and rotational
springs. Because both the springs and elastic beam members have an inherit elastic
flexibility, the stiffness of the complete member is equal to the stiffness of the resulting
components acting as a pair of springs in series:
(2)
( )
(
)
Where ks is the stiffness of the spring, and kbc is the stiffness of the elastic beam-column
element. In order to reduce the number of variables in the previous equation, the spring
stiffness is defined as a multiple of the beam-column stiffness:
(3)
Which leads to two expressions for the spring and beam stiffness:
(4)
and,
(
)
(5)
Where n is a factor from zero to infinity that defines the spring stiffness in terms of the beamcolumn stiffness. Any value for n will work in Equations 3-5, although, some values clearly
are not ideal. For example, n = infinity would mean that the springs are completely rigid, and
61
thus, the stiffness of the element is equal to the stiffness of the beam-column member. This is
not ideal because then the springs would have no effect on the system and the nonlinear
properties assigned to the springs would never be realized. Basically, the element would be
modelled as an elastic beam-column element, fixed at each end. The other extreme, n = 0,
would result in an ill-defined kmember and would produce a laterally unstable system. Based on
the recommendations by Ibarra and Krawinkler (2005), n = 10 was chosen.
To implement these results into the model the second moment of area of the beam element,
Ibc, is modified to:
(
)
(6)
Where Ibeam is the second moment of area for the beam section.
And the initial elastic stiffness of the spring is defined as:
(
)
(7)
By implementing these stiffness values, the stiffness of the complete member model is equal
to the appropriate stiffness of a simple elastic model, without added flexibility from the
inclusion of the spring elements.
62
3.8
3.8.1
Other Modeling Considerations
Supports
In order to avoid creating a rigid moment connection at the base, each wall could only be
modelled with a single pin support in order to achieve the desired failure mechanism as
illustrated in Figure 50.
Figure 50: FFTT Failure Mechanism
Large shear walls sitting on single pins are, however, not a realistic modeling assumption.
Thus, in order to capture to behavior of the foundation and hold-downs, a pair of springs
were modelled at each end of the wall as shown in Figure 51.
63
Figure 51: Wall Boundary Conditions Including Rocking Springs
These springs allowed the wall to resist a small moment, but would then yield to allow the
desired failure mechanism to form. The springs were capacity designed so that yielding of
the springs would occur before the wall could reach its yielding stress – effectively
guaranteeing that the assumption of the wall remaining elastic would hold true.
These springs were modelled with separate tension and compression properties. In tension, to
model the behavior of the hold-downs, the same material properties as in the wall connection
springs were utilized, since these springs were calibrated to tests performed on CLT walls
with hold downs. In compression, the effect of the foundation was simplified to an elasticperfectly-plastic (EPP) response. The yielding moment was calculated so that the yielding
stress in the wall could not develop:
( )
(8)
64
Where σmax is the maximum stress in the extreme fibers of the section, M is the moment
applied to the section, h is the length of the wall section, and I is the second moment of area
of the walls section.
Substituting the CLT yield stress for σmax and inputting the appropriate geometric section
properties gives a simple expression for the maximum moment that the wall should be able to
resist. Since the two springs produce a force couple at a distance equal to the section length
of the wall, the moment resisted by the rocking wall is:
(9)
Where fy,spring is the yielding force of the spring. Since the spring was modelled as EPP, no
further force can develop after yielding so Mmax will be the maximum moment possible.
Combining Equations 8 and 9 yields a simple result for the maximum possible yielding force
of the spring:
( 10 )
The yield stress, σmax, was taken as 11.5 MPa based on local manufacturers data
(structurlam.com) (see Table 8). The general backbone curve of this spring is shown in
Figure 52.
65
Figure 52: Rocking Spring Backbone Curve
The springs were modelled with the Pinching4 material with tension properties which were
based on the tension properties of the wall connection springs. The compression properties
were determined as explained before, with a yielding displacement, Δy, based on an assumed
1% rotation at yielding.
3.8.2
Gravity Loads
The gravity induced loading on the building prototypes was specified in the Tall Wood report
(Green and Karsh, 2012) and is summarized in Table 12.
Table 12: Design Gravity Loads
Floors
Roof
Dead Load (DL)
4.00 kPa + perimeter wall weight
3.00 kPa
Live Load (LL)
1.90 kPa
1.82 kPa
Snow Load (Ss)
-
1.80 kPa
Rain Load (Sr)
-
0.2 kPa
66
The loading combinations applied to the structures for the two types of lateral load analysis,
based on the relevant load combinations as specified in the NBCC (NRC, 2010), were:
1) 1.0DL + EQ + 0.5LL + 0.25SL
2) 1.4DL + 1.4WL + 0.5LL
3) 0.9DL + 1.4WL + 0.5SL
Where the bold terms; EQ and WL, represent the forces induced from the earthquake and
wind dynamic analyses, and the snow load SL is as defined in the NBCC (NRC, 2010) based
on Ss and Sr from Table 12.
The two wind load cases (2) and (3) were chosen to estimate the worst case for wind induced
forces and wind induced uplift, respectively. The higher mass in case (2) will cause greater
forces in the structure, while the lower weight in (3) will provide less resistance against
uplift.
The loads from Table 12 were multiplied by the total floor area of the structures to determine
the weight per storey which was then distributed as point loads on the nodes at each floor.
The forces were applied based on the assumption of a rigid slab, so that the force resisted by
a gravity force resisting element (column or shear wall) was proportional to its axial stiffness.
This way the nodes at each floor would all displace equally, as if they were rigidly connected
by a thick slab.
All analyses were conducted with P-Delta effects considered. The P-Delta effect is the
nonlinear geometric effect caused by weights moving through displacements which cause
additional moment demand at the base of a structure.
67
3.8.3
Mass
In OpenSees, mass is applied to a model separately from the weight of the structure. Weight
is applied as point or distributed loads which induce forces in the elements. Mass can be
applied at points or distributed over elements and causes inertial forces when subjected to
accelerations. In this modeling approach, the mass was applied as point loads on each node at
each floor level, similar to the weight. The mass was applied in the two horizontal directions,
but not in the vertical direction, since the ground excitations were only applied in the
horizontal directions, as is common practice in earthquake and structural engineering.
When accelerations in the structure are induced by the lateral loads, the masses at each load
will induce forces in the structure according to Newton’s Second Law of Motion. Since the
nodes at each floor are rigidly constrained in the horizontal directions, each node at each
floor level will accelerate at the same rate, causing a lateral force at the floor level that is
distributed into the lateral force resisting elements based on their respective stiffness’s.
3.8.4
Damping
Damping can be defined as the effect that reduces motions in oscillating systems and is
related to the energy absorption of the system due to the combined effect of elastic
deformations and hysteretic energy absorption during inelastic response. Although it is a
highly complex phenomenon, damping is typically applied as a factor that induces a force
that opposed the oscillation of the system that is linearly proportional to the velocity of the
system. This allows for the development of a convenient mathematic expression for the
motion of a vibrating system, and allows the derivation following second order linear
differential equation for the motion of a single degree of freedom (SDOF) system:
68
(
)
(
)
( )
( 11 )
( )
Where M, C, and K are the mass, damping, and stiffness values of the SDOF system, F(t) is a
time-dependent force induced on the system, and u is the displacement of the system at any
time. The first and second derivatives of u with respect to time define the velocity and
acceleration of the system, respectively.
Since, under a ground motion excitation, the forces applied on the system are equal to the
mass time the ground acceleration, according to Newton’s Second Law of Motion, the
equation may be rewritten as follows:
(
)
(
( )
)
(
)
( 12 )
Where ug is the ground displacement.
By dividing each term in the equation by the mass of the system, M, Equation ( 12 ) becomes:
(
)
( )(
( )
)
(
)
( 13 )
Where, ω, the circular frequency of the system, is defined as:
√
( 14 )
Then, the following relationship can be derived:
( )
( 15 )
69
Where ζ is the damping of the system, as a percent of the critical damping. Critical damping
is defined as the damping level in the system at which no oscillatory motion would occur.
This relationship holds true in the more general multi degree of freedom case, except that ω
and ζ are specific to each individual mode of vibration and the mass, stiffness, and damping
values become matrices.
The mass and stiffness of a structure are measurable, physical quantities that are typically
well defined. However, the damping in the structure is much more difficult to accurately
define. One common method to define the damping properties of a system is Rayleigh’s
Method (Chopra, 1995). Rayleigh’s method simplifies the derivation of defining a damping
matrix by noting that damping of a system is typically related to both the mass and stiffness
of the system. This can be defined mathematically as:
[ ]
[ ]
[ ]
( 16 )
Substituting this relationship into Equation ( 15 ) yields:
( 17 )
Where n can be any mode of the structure. To solve the two variables, α and β, two equations
are required which can be defined by choosing any two significant modes and their
respective circular frequencies and damping ratios. Damping ratios in the range of 1% to 5%
are typically recommended with up to 10% being possible under significant seismic demands
(Deierlein et al. 2010). Since the FFTT system has a large number of ductile steel
connections which can provide significant energy dissipation under seismic loads, and steel
70
and timber buildings are typically considered to have relatively high damping ratios, a value
of 5% was chosen as the damping ratio.
A convenient method for solving for the Rayleigh damping coefficient is described by Hall
(2006). In this method, a damping range (Δ) is defined over a range of frequencies (ω’ to
Rω’) based on the assumed behavior of the structure. The parameter ω’ is set to two thirds of
the first fundamental frequency of the structure to account for frequency change due to
nonlinear softening of the structure. Rω’ is set to the second mode of the structure, which in a
typical shear-beam type structure is about three times the first mode frequency. This results
in an R value of 4.5. Then, the range of damping can be defined as:
√
( 18 )
√
And the Rayleigh coefficients can be determined from:
( 19 )
√
( 20 )
√
The resulting damping ratio as a function of the circular frequency of the system is illustrated
in Figure 53.
71
Figure 53: Rayleigh Damping Plot
Using these relationships, the Rayleigh damping coefficients are calculated and applied to the
models based on the first circular frequency as determined through modal analysis.
In a nonlinear numerical model, the stiffness can change throughout the analysis, so the
stiffness that the β coefficient will be applied to must be specified. This is typically either the
initial (elastic) stiffness, the tangent stiffness (which changes as the stiffness of the structure
changes), or a committed stiffness matrix, which is a less common approach. The initial
stiffness matrix was chosen for this study for three reasons. First, the tangent stiffness matrix
can rapidly change, which may potentially cause convergence problems. Secondly, there is
not physical basis to a tangential stiffness proportional damping matrix. And finally, a welldefined committed stiffness matrix would be difficult to determine (Hall, 2006).
3.9
Summary of developed models
In order to assess the seismic and wind performance of the FFTT system, a total of 39 models
ranging from 6 to 30 stories were developed and analyzed. All models were developed in
72
OpenSees using a MATLAB preprocessor to write the Tcl files. Table 13 summarizes the
range of models considered. Figure 54 illustrates typical stories of the OpenSees models for
each of the four options. Initially a modal analysis was performed on each model. The results
of these analyses, including the fundamental period of each model and typical mode shapes
for each option, are presented in Appendix A.
Table 13: Heights (Number of Stories) Modelled for each FFTT Option
FFTT
Option 1
Option 2
Option 3
Option 4
No of
stories
6-12
11-20
11-20
19-30
73
(a)
(b)
(c)
(d)
Figure 54: FE Model for Typical Storey of (a) Option 1, (b) Option 2, (c) Option 3, and (d) Option 4
74
Chapter 4: Non-linear Dynamic Seismic Analysis
4.1
Seismic Analysis
The NBCC (NRC, 2010) requires that a dynamic procedure be used to analyze regular
structures taller than 60m or with a period greater than 2 seconds in either of the two primary
orthogonal directions. For seismic analyses, the majority of models were too tall to be
analyzed with an equivalent static force method, and therefore, dynamic analyses had to be
completed instead. The methods used to perform these analyses are described in the
following sections.
4.1.1
Ground Motion Selection
In order to evaluate the seismic performance of the FFTT system, nonlinear dynamic
analyses were conducted with a suite of ten ground motions as summarized in Table 14.
In their recommendations for nonlinear dynamic analysis, Deierlein et al. (2010) state that a
minimum of seven ground motions is required to determine the mean values for design,
however it may be possible with even fewer records. Seven motions is also the
recommendation in both the NBCC (NRC, 2010) and ASCE 07 (ASCE, 2013). Ten motions
were considered to give a slightly broader range of results and to help account for the
difference between the spectra of the ground motions and the design spectrum. All ground
motions were obtained from the PEER strong motion database (Chiou et al., 2008). The
ground motion database information is listed in Table 15.
75
Table 14: Ground Motion General Information
Earthquake
Source
GM
Number
M
Year
Name
Recording Station
Type
Distance
(km)
1
6.7
1994
Northridge
Beverly – Mulholland
Thrust
13.3
2
6.7
1994
Northridge
Canyon Country WLC
Thrust
26.5
3
7.1
1999
Duzce, Turkey
Bolu
Strike-slip
41.3
4
7.1
1999
Hector Mine
Hector
Strike-slip
26.5
5
6.5
1979
Imperial Valley
Delta
Strike-slip
33.7
6
7.5
1999
Kocaeli, Turkey
Duzce
Strike-slip
98.2
7
7.3
1992
Landers
Yermo Fire Station
Strike-slip
86
8
6.9
1989
Loma Prieta
Gilroy Array #3
Strike-slip
31.4
9
6.5
1987
Superstition
Hills
Poe Road
Strike-slip
11.2
10
7.6
1999
Chi-Chi, Taiwan
CHY101
Thrust
32
Table 15: Ground Motion Database Information
PEER-NGA Record Information
Recorded Motions
GM
Number
Record
No.
Component 1
Component 2
PGA
(g)
PGV
(cm/sec)
1
953
NORTHR/MUL009
NORTHR/MUL279
0.52
63
2
960
NORTHR/LOS000
NORTHR/LOS270
0.48
45
3
1602
DUZCE/BOL000
DUZCE/BOL090
0.82
62
4
1787
HECTOR/HEC000
HECTOR/HEC090
0.34
42
5
169
IMPVALL/HDLT262
IMPVALL/HDLT352
0.35
33
6
1158
KOCAELI/DZC180
KOCAELI/DZC270
0.36
59
7
900
LANDERS/YER270
LANDERS/YER360
0.24
52
8
767
LOMAP/G03000
LOMAP/G03090
0.56
45
9
725
SUPERST/B-POE270
SUPERST/B-POE360
0.45
36
10
1244
CHICHI/CHY101-E
CHICHI/CHY101-N
0.44
115
76
The ground motions were all far-field events as defined by FEMA P695 (FEMA, 2009) and
selected based on their agreement with the Vancouver 2% in 50 year 5% damped design
spectrum. The response spectra of the two components of the recorded motions, compared
with the Vancouver design spectrum, are illustrated in Figure 55 and Figure 56.
Figure 55: Ground Motion Component 1 Spectra
Figure 56: Ground Motion Component 2 Spectra
77
4.1.2
Ground Motion Scaling
Once a target (design) spectrum has been chosen and a set of motions selected, the records of
the motions still must be modified in order to appropriately reflect the hazard defined by the
target spectrum. There are many commonly used methods to modify ground motions. The
simplest would be selecting ground motion records that match the target spectrum in the
desired period range (typically, near the fundamental period of the structure). Since the
records do not need to be modified, they retain all their natural characteristics, which make
this method preferred in most cases. However, it is very difficult, if not impossible in some
cases to select appropriate unmodified records for most structures and sites due to the limited
number of records available.
Since selecting real, unscaled records is not typically feasible (especially when several
records are required), often recorded motions will be linearly scaled to reflect the hazard
defined by the target spectrum. This method retains the characteristics of the recorded motion
including spectral ratios at different periods, and is usually considered appropriate if required
scaling factors are reasonable (extreme scaling factors may distort motions outside of the
scaling range and produce unrealistic records).
Records can be scaled at a single period or scaled to an average over a range of periods,
typically to an acceleration spectrum, however scaling to other parameters is often possible
including velocity spectra, peak ground acceleration, peak ground velocity, etc. The reader is
referred to ―Selecting and Scaling Ground Earthquake Ground Motions for Performing
Response History Analysis” (NIST, 2011), specifically Chapter 3, for more information
about the state of practice for ground motion selection and scaling.
78
Other, more sophisticated methods for selecting appropriate ground motions also exist. An
example is spectral matching, which involves modifying the frequency content of a recorded
motion in either the time or frequency domain so that is matches a target spectrum at a
specific period or range of periods. However, it has been argued that this procedure may
produce unrealistic ground motion signatures and may even induce lower demands from
nonlinear analysis due to the resulting unnaturally smooth ground motion spectrum in period
range matched motions (Atkinson and Macias, 2009).
In this study, the ground motion suite was collectively scaled by a linear factor so that the
median of the geometric mean (geomean) or the motions matched the design spectral
acceleration at the fundamental period, T1, of the structure. The geomean is simply defined
as the square root of the product of the spectral accelerations of each direction:
√
(
)
(
)
( 21 )
This method was selected to maintain the natural characteristics and variability of the
motions; additionally, the geomean of most of the motions already matched reasonable well
with the Vancouver 2% in 50 year spectrum. Also, the method was simple and
computationally efficient to implement for the large number of models that each required
individual scaling factors for the motions.
An example of this scaling procedure is illustrated in Figure 57. The thick line is the
Vancouver 2% in 50 year Site Class C spectrum, while the thinner solid and dashed lines are
the median geomean of the ground motion suite, unscaled, and scaled at a period of 1 second,
respectively.
79
Figure 57: Ground Motions Scaling Example
4.2
Performance Criteria
Before the dynamic analyses were conducted, performance criteria had be developed in order
to assess the results of the analyses. Performance criteria comprise a set of standards that a
structural model must conform to in order to be classified under a certain performance level.
Typically four discrete performance levels are considered, as illustrated in Figure 58:
operational, immediate occupancy, life safety, and collapse prevention (ATC, 2009).
Operation performance, as it relates to earthquake engineering, requires that a structure be
completely operational after a significant seismic event and is typically defined by very strict
criteria, such as very small interstorey drift levels and little to no plastic deformations.
Immediate occupancy performance does not require everything in the structure to be operable
after a seismic event, but does require the structural system to be completely intact so the
structure can provide a safe area of refuge in a post-disaster situation. Life safety
80
performance allows for structural damage, yet ensures the safety of any occupants inside
must be conserved. For most regular buildings (i.e., not essential or emergency buildings and
not post-disaster areas of refuge) this is the type of performance criterion typically specified.
Finally, collapse prevention performance is considered for buildings with no permanent
occupancy and little importance, and allows for major structural damage. As long as the
gravity resisting system remains intact and the building does not collapse, collapse
prevention performance is met.
Figure 58: Typical Discrete Performance Levels (ATC, 2009)
Performance criteria, however, are much easier to describe than to explicitly or numerically
define. Often times performance levels can be difficult to distinguish and may be completely
different for different structural systems. Performance measures such as interstorey drift,
plastic deformations, strain in reinforcement, etc. may be used to define the performance of
different structural systems.
In this study, interstorey drift and steel beam plastic rotations were considered as the main
performance criteria. Roof drift and base shear were also presented. Additionally, the stress
81
state in all timber members was monitored throughout the analyses to ensure they remained
elastic; this is also a performance requirement by definition.
4.2.1
Interstorey Drifts
For most applications, differential movement between stories, or interstorey drift, is
considered as the main indicator of damage (Mayes, 1995; ATC, 2009). For this reason, the
NBCC (NRC, 2010) limits interstorey drift in regular structures to 2.5%, and considers this
appropriate to maintain the life safety of building occupants during severe seismic events.
This limit is also the value proposed in the Tall Wood report (Green and Karsh, 2012).
However, since the FFTT is not a typical building system, the usual interstorey drift limit is
not necessarily appropriate. For any type of structural system, a life safety interstorey drift
limit should be chosen to maintain the integrity of the gravity resisting system at each storey.
This is because loss of the gravity resisting system will almost definitely result in the
catastrophic collapse of a structure or storey of a structure. The lateral deformation resisting
system (LDRS) is of secondary importance in that it is only required to maintain enough
integrity to limit storey drifts to a level that protects the gravity resisting system.
In the FFTT system, the gravity resisting system comprises glulam columns and frames
interconnected with steel connections. For this study, physical tests conducted by Buchanan
and Fairweather (1993) were consider to be representative of typical glulam frame
connections, so these tests were also consulted to help determine the appropriate performance
criterion. The hysteresis loops from the test of a beam-column assembly with steel brackets
by Buchanan and Fairweather (1993) is shown in Figure 59.
82
Figure 59: Hysteresis Loops for Beam-Column Assembly with Steel Beam Brackets (Buchanan and
Fairweather, 1993)
From these test results it is noted that the assembly was able to undergo very large interstorey
drifts, however yielding occurred at about 1% interstorey drift. Since the FFTT system is
designed to rely on its steel beams for all required ductility, ideally, the glulam gravity
resisting frame should not undergo any yielding. Unexpected yielding of the glulam
perimeter frames would change the source of ductility in the system and the proposed
ductility factor would not be appropriate.
The total interstorey drift at the yielding of this type of joint in this structure is calculated by
adding the elastic displacement of the glulam column to the 1% drift from the connection.
This can be done by considering the relative stiffness of these two components. The elastic
stiffness of the joint connection, kc, obtained from Figure 59 is approximately 264,000N/rad.
The elastic stiffness of the 418x415mm glulam column, kbc, is calculated as:
( 22 )
83
(
)
Then, the total deflection, Δt is calculated as:
( 23 )
Where Δc and Δbc are the elastic deformations in the connection and column element,
respectively. Equations 21-23 can be rearranged based on the relative stiffness of the two
components:
(
(
( 24 )
)
)
Which yields an interstorey drift of 1.12*1%, or about 1.1%. This value is the interstorey
drift where the steel connections in the glulam frame are expected to yield. Thus, the
interstorey drift should be limited to 1.1%, rather than 2.5% to ensure ductility is provided
solely by the yielding of the steel beams.
4.2.2
Plastic Rotations
Another indicator of damage in a structure which is subjected to significant ground shaking is
the maximum plastic rotation observed in its header beams (ASCE, 2013). Too much plastic
rotation in these members can affect their ability to transfer shear between the walls they
connect, which in turn, affects the degree of coupling between the walls. Since coupled walls
are much stiffer than uncoupled walls, if shear transfer between coupled walls is lost,
84
coupling between the walls will be lost, and the total storey stiffness provided by the walls
will significantly decrease. Thus, beam plastic rotation is included as a criterion for structural
performance in documents such as ASCE/SEI 41-06 (ASCE, 2007).
In ASCE/SEI 41-06 (ASCE, 2007), life safety performance criteria for Class I steel sections
is defined as the plastic rotation at which strength degradation in the section begins. This
methodology was adopted for this study. To determine the degradation limit, the tests
conducted by Bhat (2013) were consulted. The moment-rotation hysteretic result from the
same test that was considered for the calibration of the OpenSees material models is
reproduced in Figure 60, modified to shown moment-rotation rather than force-displacement.
From this figure, a rotation of about 0.15 rad is observed as the capping point, at which
strength degradation commences. By subtracting an elastic rotation of about 0.1 rad, a life
safety plastic rotation for the steel beams of approximately 0.05 rad is obtained.
Figure 60: Moment-Rotation Results from Steel Beam-CLT Wall Test
85
4.3
Results of Non-linear Seismic Analyses
For each considered model and bi-directional ground motion, two analyses were run, one for
each of the two main ground motion orientations (orientation of the primary component of
the motion). The ground motions were always applied parallel to the primary axes of the
structure. Then, for each scenario (a particular height of a particular building plan option
subjected to a particular ground motion), the results were taken as the maximum of the two
ground motion orientations. Figure 61 exemplarily presents the displacement results of a 30
storey model (FFTT Option 4) subjected to the Chi-Chi, Taiwan ground motion orientated in
both directions. The orientation which produces the higher response is taken as the result for
that scenario (the solid line).
Figure 61: Example 30 Storey Model Displacement subjected to the Chi-Chi, Taiwan Ground Motion at
two Orientations
86
4.3.1
Interstorey Drift Results
For the performance-based design of structures, building codes typically specify that mean
response values may be used for design if seven or more ground motions are used in the
analysis (NRC, 2010; ASCE, 2013; Deierlein et al., 2010). Since this study considered 10
unique motions, it is reasonable to base the performance on the mean structural response
from the 10 motions. The results for the mean and mean plus one standard deviation are
combined for the suite of models in Figure 62. Additionally, the interstorey drift results for
each model for all the four FFTT system options are illustrated in Figure 63.
(a)
(b)
Figure 62: Interstorey Drift Combined Results: a) Mean Results and b) Mean Plus One Standard
Deviation results
87
(a)
(b)
(c)
(d)
Figure 63: Interstorey Drift Results for (a) Option 1, (b) Option 2, (c) Option 3, and (d) Option 4 Models
88
From the results presented in Figure 63 it can be seen that the mean results are consistantly
below the 2.5% interstorey drift limit typically considered for life safety performance as well
as the 1.1% limit chosen to prevent yielding of the glulam perimeter frame. The mean plus
one standard deviation and maximum results are all below 2.5% as well. Because the mean
results conform to the life safety drift limit, interstorey drift life safety performance is
achieved.
Figure 65 and Figure 64 illustrate the roof drift results for four combined and individual
options, respectively.
(a)
(b)
Figure 64: Roof Drift Combined Results: a) Mean Results and b) Mean Plus One Standard Deviation
results
89
(a)
(b)
(c)
(d)
Figure 65: Roof Drift Results for (a) Option 1, (b) Option 2, (c) Option 3, and (d) Option 4 Models
90
Roof drift does not necessarily predict damage in a structure; however it is correlated to the
performance of the structure and is included here as it may be useful to compare the
modelled seismic behavior of the structures. Similar to the interstorey drift results, mean roof
drift tends to decrease as the height of the structures increases, indicating that the taller
models are less affected by the effects induced by ground motions.
4.3.2
Beam Plastic Rotation Results
Figure 67 and Figure 66 present the maximum steel beam plastic rotation results for all
structural options. All results are normalized by the life safety plastic rotation, θLS, defined as
0.05 in Section 4.2.2. Since the results are normalized, any result below 1.0 meets life safety
performance, which is the case for all mean results and even all mean plus standard deviation
results. As well, very few of the maximum recorded rotations exceed this limit. These results
indicate well above adequate performance for all of the modelled structures.
91
(a)
(b)
Figure 66: Beam Plastic Rotations Combined Results: a) Mean Results and b) Mean Plus One Standard
Deviation results
92
(a)
(b)
(c)
(d)
Figure 67: Plastic Rotation Results for (a) Option 1, (b) Option 2, (c) Option 3, and (d) Option 4 Models
93
4.3.3
Base Shear
Also relevant for this study was the maximum base shear experienced by the structures under
seismic excitation. Because the models were fixed at their base, they were essentially rigid in
shear. Thus, for the design of this type of structure, it would be necessary to know the base
shear demands so the foundation and base connections can be properly designed.
Individual option base shear results are presented in Figure 69. The mean results for each
model were compiled and compared to the NBCC (NRC, 2010) base shear predicted values
for several different R factors (R = RdRo) in Figure 68.
Figure 68: Base shear results from model compared to those predicted by the NBCC (NRC, 2010) for
different R (RdRo) values
94
(a)
(b)
(c)
(d)
Figure 69: Base Shear Results for (a) Option 1, (b) Option 2, (c) Option 3, and (d) Option 4 Models
95
As previously mentioned, the structures were designed with an RdRo of 3.0 (Rd = 2.0; Ro =
1.5). All of the results are normalized by the weight of the structure, W. The computed base
shears correlate well with predictions based on the NBCC for an R factor of 3.0. Moderately
higher than predicted base shears were observed in the taller Option 4 models, that match
more closely to the R = 2.0 calculations. This difference could be for several reasons
including higher mode effects increasing the base shear force in the structure more than
anticipated. Also the taller models had stiffer LFRSs comprising many thick shear walls
which would induce large base reactions.
4.4
Discussion of Seismic Analyses
From the results presented in Chapter 4.3, it appears that the FFTT systems, as they were
designed for this study, meet the performance required under seismic loading. Interstorey
drifts were lower than required and local plastic deformations were within a reasonable range
for life safety performance. Base shears correlated well with those predicted by the NBCC
(NRC, 2010). Maximum drifts and plastic deformations tended to decrease with taller
structures, as these more flexible structures were less impacted by the seismic excitations.
This is because the taller, softer structures had lower seismic forces and consequently less
yielding in the interconnecting steel beams. However, these characteristics, which made the
taller structures less susceptible to damage induced by ground shaking, may cause
serviceability issues under high wind loads.
Previous studies, such as Reynolds et al. (2012) have indicated unacceptable dynamic
response of tall timber buildings under significant wind loading, based on human perception
of vibrations, primarily due to their light weight. The potential problematic performance of
the FFTT system under wind loads will be investigated in Chapter 5.
96
Chapter 5: Dynamic Wind Analysis
5.1
Introduction
In order to fully assess the structural feasibility of the FFTT building system, wind loading
also had to be checked to ensure serviceability requirements could be met under wind load.
To accomplish this, the NBCC (NRC, 2010) Dynamic Wind Procedure was adopted (NRC,
2010). According to the NBCC Sentence 4.1.7.2(1): the use of the Dynamic or Experimental
Procedure is required for buildings whose height is greater than 4 times their minimum
effective width, or greater than 120m, and other buildings whose properties make them
susceptible to vibration. Since the taller FFTT models are relatively flexible, especially
compared to typical reinforced concrete shearwall structures (see table A1 in Appendix A),
they were deemed as potentially susceptible to vibration under wind loading.
Typically, longer period structures, such as bridges or high-rise buildings, are more
susceptible to dynamic wind effects, while shorter buildings with shorter periods are excited
more through seismic loading, as illustrated by Figure 70. As seen previously, the period
range of the FFTT models ranges from about 1 to 3 seconds (frequencies of 1 to 0.33Hz)
which puts them in the range between maximum earthquake and wind spectral density.
Since the structures were designed and analyzed for seismic loading from Vancouver, BC,
the wind pressures were also based on Vancouver data from the NBCC (NRC, 2010). The 1
in 50 year hourly wind pressure for Vancouver is 0.48 kPa, which was considered for all the
wind analyses.
97
Figure 70: Frequency Ranges for Excitations of Structures (Holmes, 2001.)
5.2
NBCC Dynamic Procedure
The NBCC Dynamic Procedure for wind analysis (NRC, 2010) comprises a static analysis
with forces determined accounting for the dynamic effects of the loading and structure:
( 25 )
Where Pe is the pressure applied the structure, Iw is the importance factor (taken as 1.0), q is
the wind pressure (0.48kPa), and Ce, Cg, and Cp are the exposure, gust, and external pressure
coefficients.
The wind load is applied with a load factor of 1.4 to the structure with a dead load factor of
1.25 or 0.9. The governing case is used for the design or assessment of the structure.
Additionally, the wind load must be applied in both primary directions of the structure to
determining the governing wind direction.
98
5.2.1
External Pressure Coefficients
The external pressure coefficient, Cp, is based on Figure I-15 of the NBCC (NRC, 2010),
which is reproduced in Figure 71. This factor accounts for uplift on the roof of the structure
as well as suction on the side of the building opposite to the wind direction.
Figure 71: Wind Loading External Pressure Coefficients from Figure I-15 of the NBCC (NRC, 2010)
5.2.2
Exposure Factor
Because the exposure of a structure will significantly affect how wind pressure can be
applied to it, the NBCC (NRC, 2010) wind loading procedure accounts for three different
levels of exposure: A, B, and C.
Exposure B, which is defined as rough terrain, such as urban, suburban, or wooded terrain,
was chosen as the factor for these buildings. Based on this assumption, the exposure factor is
calculated as:
99
(
)
( 26 )
Where h is the height of the building in meters.
5.2.3
Gust Effect Factor
The gust effect factor is used to account for the effect of short periods of very high wind
velocities, or gusts, on the response of a structure. It is based on a general probabilistic
expression for peak wind loading, Wp:
( 27 )
Where μ is the mean wind loading, gp is the statistic peak factor of the wind loading, and σ is
the ―root mean square‖ of the wind loading effect. This is a statistical measure of the
magnitude of a varying quantity - in this case wind pressure.
By defining the gust effect factor, Cg, as:
( 28 )
The previous equation for peak wind loading can be substituted in resulting in the statistical
expression for the wind gust effect factor:
( ⁄ )
( 29 )
The term (σ/μ), referred to as the coefficient of variation of the loading, is calculated as:
( ⁄ )
√
(𝐵
𝑠
)
( 30 )
Where K is set as 0.10 for Exposure B, CeH is a similar factor that accounts for the exposure
at the top of the building, B is the background turbulence factor, s is the size reduction factor
100
of the structure, F is the gust energy ratio at the natural frequency of the building, and
is
the damping ratio in the structure. Because the structure is not expected to undergo plastic
deformation during wind loading, the previous 5% damping ratio is no longer appropriate as
a significant proportion of that ratio comes from energy dissipation due to inelastic
deformation in the members of the structure. Instead a ratio of 2% is adopted based on
recommendations from the NBCC (NRC, 2010).
The background turbulence factor, B, is calculated through the following integral:
𝐵
∫
[
𝑥𝐻
][
𝑥𝑤 ] [
𝑥
(
] 𝑥
( 31 )
𝑥 )
Where H is the building height, and w is the effective (average) building width:
𝑤
∑ 𝑤
∑
( 32 )
The size reduction factor, s, of a structure is calculated as:
𝑠
𝜋
[
8 𝐻
𝑉
][
𝑉
𝑤
]
( 33 )
Where fn is the natural frequency of the building, and VH is the mean wind speed at the top of
the building, defined from:
𝑉
𝑉
𝑉√
( 34 )
√
The reference velocity pressure q, was defined earlier for Vancouver as 0.48 kPa.
101
The gust energy factor, F, is defined as the following function based on the wave number as
follows:
𝑥
(
( 35 )
𝑥 )
Where xo is defined as:
⁄𝑉
𝑥
( 36 )
The gust energy factor as a function of wave number is illustrated in Figure 72.
Figure 72: Gust Energy Ratio as a Function of Wave Number
Finally, the peak factor, gp, is calculated as:
√ 𝑙 𝜐
√ 𝑙 𝜐
( 37 )
Where the time, T is taken as 3600 sec and the average fluctuation rate, υ, is defined as:
102
𝜐
√
𝑠
𝑠
𝐵
( 38 )
For which all the variables have previously been defined.
5.3
Wind Analyses
The equations in the previous section were solved in order to determine the wind pressure
including dynamic effects, Pe, for each model. This pressure was applied both laterally to the
exterior nodes of the building models and upwards on the roof nodes of the models according
to Figure 71. The pressure was applied as forces on nodes according to their tributary area.
Gravity loads and snow were also applied according to the relevant load combinations as
specified in the NBCC (NRC, 2010):
1) 1.4DL + 1.4WL + 0.5LL
2) 0.9DL + 1.4WL + 0.5SL
Static analyses were run in OpenSees with the wind acting in both major directions of the
models for both load cases. Second order P-Delta effects were included in the analyses.
5.4
Results of Wind Analyses
The result of each structure was taken as the maximum result from the two directions and
two wind analysis cases. The results for the suite of models are illustrated in Figure 73a.
Acceptable performance under wind loading is defined in the NBCC as a maximum
interstorey drift of h/500, or 0.2%, (NRC, 2010). This interstorey drift limit is chosen to
preserve occupant comfort in a significant wind event. Adding this limit to the figure and
then excluding the models that did not meet this performance objective yields the results
shown in Figure 73b. Option 1 models are limited to 8 stories; Option 2 and 3 models are
103
limited to 16 stories; and Option 4 models and FFTT system, as design for this study, may be
limited to about 22 stories.
(a)
(b)
Figure 73: (a) Wind Loading Interstorey Drift Results and (b) with h/500 limits
5.5
Discussion of Wind Analyses
The results presented in the previous section show that even in a moderately high seismic
zone, such as Vancouver, BC, wind loading may govern the design of tall wood buildings,
such as the FFTT system. These results agree with the conclusions of Reynolds et al. (2012),
that tall timber structures may be susceptible to significant wind induced vibrations. Since
timber buildings are relatively light and flexible compared to steel and concrete structures,
these significant wind effects, which are normally only problematic in much taller buildings,
104
begin to affect shorter timber high-rise structures. In order to remedy the wind effects either
the stiffness or mass of the structures may have to be increased (Reynolds et al., 2012).
Reynolds et al., (2012) also note that stiffness in timber joints tends to decrease over their
lifetime through repeated loading, and that this would change the dynamic characteristics of
these structures over their lifetime and more susceptible to wind later in their lifespan. This
would both increase the dynamic effects of wind, and make the lateral force resisting system
more flexible, so it would displace more under lateral loading. Combined, these two effects
could considerably increase the deflections under wind, as well as seismic loading. Whether
or not this may be a problem in the timber-steel beam connections required by the FFTT
system has not been thoroughly investigated at this point in time but should not be neglected
by potential designers.
105
Chapter 6: Force Reduction Factor Study
6.1
Seismic Force Modification Factors in the NBCC
One of the benefits of the research presented herein is that a framework for modeling the
FFTT system and its four options was developed. This framework may be useful for other
studies about the behavior of the FFTT system. As an example, the framework for the models
developed in this thesis was also used to study proposed seismic force reduction factors for
the FFTT structural system.
One of the seismic design approaches specified in the NBCC (NRC, 2010) is the Equivalent
Static Force Procedure (ESFP). This procedure is meant as a simple process that can be used
for seismic design of regular structures. It begins by taking a design spectrum (usually the
2% in 50 year 5% damped spectrum for the building site) and an estimate of a structures
weight and fundamental period (determined either through code equations of finite element
models), and an importance factor (1.0 for normal buildings). Then, a design elastic base
shear is determined by multiplying the weight of the structure by the spectral acceleration
from the design spectrum at the fundamental period of the structure (force equals mass times
acceleration) and then by the importance factor. A higher mode factor is also applicable to
more flexible buildings that may have a significant contribution from higher modes. This
method gives a reasonable estimate of the elastic base shear expected by a structure under
design seismic loading. The base shear can then be distributed along the height of the
structure in a reverse triangular shape to get the design forces at each level and for each
component in the structure.
106
The NBCC (NRC, 2010) does not require structures to behave purely inelastically during rare
earthquake events. Due to this, two reduction factors may be used to reduce the design base
shear of a structure based on its expected inelastic behavior. The first is an overstrength
factor, Ro, which accounts for reserve structural capacity from sources such as member
oversizing in design and strain hardening of materials. The second is a ductility factor, Rd,
which accounts for the lower forces induced in a structure behaving inelastically compared to
an equivalent elastic structure and is related to the ductility able to be provided by a structural
system. In this case, ductility refers to the ability to deform inelastically past yielding. More
ductile systems can deform further before degrading in strength, which allows them to be
designed with lower forces.
Figure 74 illustrates the application of the ductility reduction factor based on the equal
displacement approximation proposed by Newmark and Hall (1982). In this figure μ is the
displacement ductility and Rμ is the ductility reduction factor (Rd in the NBCC). Ve is the
elastic base shear, Vi, is the inelastic base shear, Δy, is the yielding displacement, and Δmax is
the maximum displacement obtained by either system. Based on the work by Newmark and
Hall (1982), it can be shown that for structures with periods greater than 0.5 sec, that the
displacement of an equivalent structure behaving elastically or inelastically will be
approximately equal. It can also be shown that for structures that follow (or nearly follow)
this equal displacement approximation, that Rμ will equal μ. This is what the NBCC ESFP is
based on, since most typical structures will follow the equal displacement approximation.
The implication of this is that the force reduction allowed in the ESFP is directly equal to the
amount of expected ductility of the system. The NBCC (NRC, 2010) provides these factors
for most typical systems.
107
Figure 74: Ductility Factor Based on Equal Displacement Approximation
Note that Figure 74 only illustrates an idealized, elastically-perfectly-plastic, response. A
more realistic response would be more curved and include some strain hardening.
The use of the ESFP allows for efficient structural solutions since the design base shear can
be lowered significantly depending on the type of structural system being used. For example,
a ductile steel moment frame has a Rd equal to 5.0 and Ro equal to 1.5 (NRC, 2010), which
allows a 7.5 times reduction in the elastic base shear for design of this type of system.
6.2
Force Reduction Factor Study for the FFTT System
Currently, no provisions regarding the seismic force reduction factor are given in the NBCC
for hybrid timber-steel systems such as the FFTT system. The study by Pei et al. (2013) (see
Section 2.3.5) proposed a ductility factor of 2.0 for CLT shear wall systems. However, this
value was based on ductility provided by the wall hold-downs and may not be appropriate for
a CLT shear wall system such as the FFTT system, in which ductility is provided through
108
yielding of steel beams which interconnect the CLT panels. Due to this mechanism, the
FFTT system may behave more like the ductile steel moment frame, which is allowed to be
designed with a ductility factor of 5.0 according to the NBCC (NRC, 2010). A study was
carried out by Zhang et al.1 to address this issue using simplified two dimensional and more
complex three-dimensional structural models of the FFTT Option 1 system to assess the
expected ductility of this system.
6.2.1
Two Dimensional Model
The two dimensional models were developed similar to the models in Chapter 3 of this
thesis, with material properties based on the same tests by Bhat (2013). The models were
designed using an ESFP using several ductility factors from 1.5 to 6.0 and an assumed Ro of
1.5 based on the Vancouver design spectrum. Models were developed in OpenSees for three,
six, nine, and 12 storey buildings. All ductility was assumed to be provided by the yielding of
the steel beams and thus the wall hold downs/base connection and gravity system were not
modelled. This simplified model is illustrated in Figure 75, which shows the CLT walls,
modelled with shell elements; the steel beams, modelled using elastic beam elements with
concentrated plasticity idealized with the Pinching4 material (Lowes et al., 2004); and a PDelta (leaning) column to include second order nonlinear geometric effects (P-Delta effects)
applied to the shear walls by the weight of the structure not directly applied to the walls.
1
Zhang, X., Fairhurst M., Tannert, T. (2014). Ductility Estimation for a Novel Timber-Steel Hybrid System.
Submitted and Under Review.
109
Figure 75: Simplified Model Illustration (Zhang et al., 2014)
The 22 FEMA P695 (FEMA, 2009) far-field ground motion set was modified to match the
Vancouver spectrum and applied to each model to get a reliable estimation of the interstorey
drift expected. Figure 76 presents an exemplarily cumulative distribution function (CDF) for
a three storey model designed with different ductility factors.
Figure 76: Example CDF for a 12 Storey Model Design with Different Rd Factors (Zhang et al.)
110
An acceptable ductility factor was considered one that limited interstorey drift to 2.5% with
an 80% probability of non-exceedance. Based on the all the models considered and two
different ground motion scaling techniques, an Rd of 5.0 was proposed.
6.2.2
Three Dimensional Model
In order to support the FFTT ductility factor study, the OpenSees framework for the FFTT
system as presented in Chapter 3 of this thesis was considered. Based on the proposed
ductility factor of 5.0 and overstrength factor of 1.5, a 12 storey Option 1 model was
redesigned using an ESFP. The resulting beam sections chosen are summarized in Table 16.
No other aspects of the model were varied from the previous study except that the base of the
structure and the glulam frame system were pinned in order to be consistent with the
assumptions made for the simplified models.
Table 16: 12 Storey Option 1 Model Beam Sections Design with RdRo = 7.5
6.2.3
Stories
Section
Yielding Moment (kN·m)
1-3
W360x33
163.5
4-6
W250x22
78.3
7-9
W250x22
78.3
10-12
W150x18
41.4
Ground Motion Record Selection and Scaling
An essential step in any nonlinear time history analysis is the selection and scaling of ground
motion time history records to use for the analyses. Typically 7 records are chosen and the
mean response from the record set is used for design or assessment of a structure (Deierlein
et al., 2010; NRC, 2010) and scaled to a design acceleration spectrum (2% in 50 year 5%
111
damped spectrum in the NBCC (NRC, 2010)). The records should be chosen to match the
characteristics (distance, magnitude, fault-type, duration, etc.) of a ground motion expected at
the site of the structure being assessed and should be similar to the design spectrum so that
adequate scaling can be achieved with low or moderate scaling factors. This helps to ensure
the motions will be reasonable realistic and representative of a similar possible earthquake
event at the building location.
In order to choose suitable records, first a site de-aggregation was carried out for the
proposed location of the fictional structure: Vancouver, BC, using EZFrisk software
(McGuire, 1995). The purpose of this is to de-aggregate all the sources that contribute to the
design acceleration spectrum at the period of the structure (T = 2.0 seconds) so that ground
motions can be selected to best represent the hazard at the site of the proposed structure. The
resulting distance and magnitude de-aggregations for Vancouver, BC at 2 seconds, which is
the fundamental period of the model, are presented in Figure 77a and b, respectively.
(a)
(b)
Figure 77: Vancouver, BC Site Hazard De-aggregation at 2 Seconds for (a) Distance and (b) Magnitude
112
The ground motions listed in Table 17 were chosen to match as closely as possible to these
two types of event while maintaining similar spectral values between 0.2T-1.5T to the
Vancouver design spectrum. All of these records were from shallow crustal source type
earthquakes, which are similar to the type of earthquake commonly used for assessment of
structures in Vancouver (relatively short, high frequency motions). All ground motions were
downloaded from the PEER strong-motion ground motion database (Chiou et al., 2008).
The linear scaling factors used to scale the ground motions for the first scaling approach are
also summarized in Table 17. In this approach, the average geometric means (geomeans) of
the ground motions were scaled to match the average of the Vancouver spectrum between
periods of 0.2T-1.5T seconds on average. As a second modification method, the motions
were also spectrally matched in both directions to the Vancouver spectrum for this same
period range. To accomplish this matching, the motions were modified in the time domain
through the wavelet algorithm proposed by Abrahamson (1992) and Hancock et al. (2006)
using the commercially available SeismoMatch program (Seismosoft, 2013). Figure 78
shows the spectral values of the ground motion suite obtained using these two common
record scaling methods.
These two hazard matching methods were chosen to gain insight into the effect of how
ground motion modification could impact the results. The linearly scaled records are much
more variable, even in period range of the structure since it is only the average of the spectra
that matches the target spectrum. Therefore, these records are predicted to produce more
scattered results. The spectrally matched motions agree very well with the specified design
spectrum at and around the period range of the structures, making them a potentially viable
choice for the analysis of the structure. However, it has been theorized that the smooth
113
spectrum over the matched period range may lower the demand in the structures (Atkinson
and Macais, 2009) and limit some of the natural variability of the results of the motions.
Table 17: Ground Motion Summary
Record
Magnitude
Name
Station
Epicentral
Distance (km)
Scaling
Factor
1
6.7
Northridge
Beverly Hills Mulhol
13.3
0.50
2
7.1
Hector Mine
Hector
26.5
0.90
3
6.9
Kobe, Japan
Nishi-Akashi
8.7
0.70
4
7.5
Kocaeli, Turkey
Arcelik
53.7
1.60
5
6.9
Loma Prieta
Capitola
9.8
0.75
6
6.5
Superstition
Hills
Poe Road
(temp)
11.2
1.00
7
7.6
Chi-Chi, Taiwan
CHY101
32
0.65
(a)
(b)
Figure 78: Spectral Accelerations for (a) Linearly Scaled Motions and (b) Spectrally Matched Motions
114
6.2.4
Results from the Three Dimensional Model
The two suites of scaled motions were applied in the two directions of the model. Figure 79
and Figure 80 present the interstorey drift results for the two direction components of the two
scaling methods, respectively. The mean and 80th percentile results from the maximum
response observed from the seven motions are presented, along with the minimum and
maximum values to give insight into the range of results.
From these figures it can be seen that the maximum response was observed when the primary
component of the motions was applied in direction 2 (N-S direction of the building) of the
models, and that the mean interstorey drift response of the suite of results was approximately
2% drift. The 80th percentile drift was approximately 2.5%, which is reasonable and expected
given that the reduction factors were chosen to give 80% probability of non-exceedance at
2.5% drift (Zhang et al.1 ). Additionally it can be observed that the interstorey drift was
2
relatively constant over the height of the structures, meaning that the core walls were almost
rigid and rocked at their base, distributing damage over the height of the building, rather than
concentrating it at certain stories.
1
Zhang, X., Fairhurst M., Tannert, T. (2014). Ductility Estimation for a Novel Timber-Steel Hybrid System.
Submitted and Under Review.
115
(a)
(b)
Figure 79: Interstorey Drift Results for Matched Motions Applied in (a) Direction 1 and (b) Direction 2
cdc
(a)
(b)
Figure 80: Interstorey Drift Results for Matched Motions Applied in (a) Direction 1 and (b) Direction 2
Next, the beam plastic rotations at each storey are presented in Figure 81 and 83. As
mentioned earlier, beam plastic rotations are another commonly used performance
measurement. The results show a wide range of responses from the different motions.
116
However the mean response in the critical direction from both scaling methods is less than
0.05, which was the life safety criteria considered previously in Section 4.3.2.
(a)
(b)
Figure 81: Steel Beam Rotations Results for Scaled Motions Applied in (a) Direction 1 and (b) Direction 2
(a)
(b)
Figure 82: Steel Beam Rotations Results for Matched Motions Applied in (a) Direction 1 and (b)
Direction 2
117
Figure 83 and Figure 84 illustrate the maximum accelerations observed at each storey over
the suites of analyses. Accelerations peaked at the base and near the top of the structures, but
were within reasonable limits to maintain non-structural integrity. All results support the
results generated from the simplified two dimensional models and show that the proposed
reduction factors can lead to a design that satisfies all applicable life safety performance
criteria.
(a)
(b)
Figure 83: Storey Acceleration Results for Scaled Motions Applied in (a) Direction 1 and (b) Direction 2
118
(a)
(b)
Figure 84: Storey Acceleration Results for Matched Motions Applied in (a) Direction 1 and
(b) Direction 2
119
Chapter 7: Conclusions
7.1
Summary
This thesis presented the work done on the modeling and dynamic analyses of the FFTT
structural system. The FFTT system comprises four proposed structural layout options for the
design of high-rise (up to 30 stories) timber-steel composite structures. The modeling
included the nonlinear behavior of steel elements and connections with material models
calibrated to physical test results. The dynamic analyses comprised both dynamic earthquake
analyses with a suite of 10 bidirectional ground motions and wind analyses in accordance to
the NBCC guidelines (NRC, 2010). The entire suite of building layouts options and proposed
heights were analyzed. This included four different building options modelled with a range of
heights from 6 to 30 stories. In total over 800 nonlinear dynamic analyses were performed on
40 different models.
The results showed good seismic behavior in response to ground motions scaled to the
Vancouver 2% in 50 year design spectrum. The entire suite of models performed to an
acceptable level of performance considering mean interstorey drift, roof drift, steel beam
plastic rotation, timber stresses, and base shear. The taller structures were less affected by the
ground motions. The subsequent wind analyses, however, showed that wind load governed
the height limits of many models. As designed for this study, the models with heights above
22 stories did not meet the wind load serviceability limits.
A study about acceptable ductility reduction factors was also presented to highlight how the
models and framework developed for this thesis could be utilized outside the scope of this
120
study. The preliminary results presented herein indicate that higher Rd factors, up to 5.0, may
be appropriate for the FFTT timber-steel hybrid system.
7.2
Recommendations for Design
Based on the results presented in this thesis, the FFTT system may be viable for high rise
construction in earthquake prone regions. However, the tall and flexible structures will likely
be governed by wind loading rather than seismic loads. This means that the FFTT system
will need to be re-designed to provide either more stiffness or more mass to limit wind
induced vibrations. Such a change, however, will simultaneously increase the seismic
demand, so caution must be exercised and additional seismic analyses are required.
Designers must also consider the long term performance of the connections they design for
this type of structure to ensure stiffness does not degrade over long-term due to repeated
cyclic wind loading.
Also in structures governed by wind load, designers must ensure that adequate ductility can
be developed by the system, since if a structure is limited by its ductility the elastic seismic
force may become large enough to govern the design once again. Ductility factors of 2.0
have previously been considered for CLT construction (Pei et al., 2013), the FFTT system,
however, may be able to reach ductility factors of up to 5.0. Potential designers would be
encouraged to explore using higher ductility factors, up to and including 5.0, if acceptable
performance can be demonstrated. The resulting reduction in base shear demand will allow
for much more economic and competitive structural designs.
121
7.3
Recommendations for Future Studies
This thesis only scratched the surface of analyses that need to be performed in order to assess
the viability of the novel FFTT hybrid system. Further component-level physical tests
accompanied by sophisticated component finite element models will be required to optimize
the design of these components and to more accurately model and subsequently optimize the
design of these components. It is recommended that additional steel beam-CLT panel tests be
conducted to assess the performance of stronger wide flange steel sections when they are
embedded into CLT panels. Tests should also be performed to assess the stiffness of the
glulam and CLT-steel beam connections after repeated loading to determine if the long term
performance of the connections is acceptable. After the component-level behavior is better
understood, system level, large-scale static and possibly dynamic tests may be required to
gain better insight into the system level behavior.
Additionally, more design and testing needs to be implemented to the wall base connections
of the FFTT system. In order to develop the ductile, rocking failure mechanism in the system,
the CLT walls will have to be essentially pinned at their base and allowed to rock. Such a
boundary condition will require very stiff shear connections along with ductile hold-downs
that allow for yielding and plastic deformation without buckling or deteriorating over a
number of earthquake induced load cycles.
Others may want to investigate other components of this type of system including damping,
fire resistance, and its performance in regions with higher seismic demands. Additionally,
research into the reliability of the FFTT system when subjected to different material and
loading uncertainties will be required to ensure the ultimate feasibility of the system.
122
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Appendix A – FFTT Numerical Model Mode Shapes and Periods
This appendix summarizes the mode shapes and periods of the numerical FFTT models.
Table A1 presents the weight and fundamental periods of the FFTT numerical models and
compares them to a typical equivalent concrete structure.
Figures A1-A4 illustrate the first three mode shapes and periods of four typical FFTT
numerical models: a 12 storey Option 1 model, a 20 storey Option 2 model, and 20 storey
Option 3 model, and a 30 storey Option 4 model. For each of the four options these models
represent the typical mode shapes.
127
†
Table A1. FFTT Weight and Fundamental Periods Compared with a Typical Concrete Structure
Typical† Concrete
FFTT*
Height (stories)
Weight‡ (kN)
Period (sec)
Weight‡ (kN)
Period§ (sec)
6
11200
0.90
28600
0.44
7
13100
1.04
33400
0.49
8
15000
1.21
38200
0.54
9
16900
1.38
42900
0.59
10
18800
1.57
47700
0.64
11
20700
1.75
52500
0.69
12
22600
1.95
57200
0.73
13
26500
1.68
62000
0.78
14
28600
1.83
66800
0.82
15
30600
1.98
71500
0.87
16
32700
2.14
76300
0.91
17
34700
2.30
81100
0.95
18
36800
2.46
85800
1.00
19
38900
2.63
90600
1.04
20
40900
2.79
95400
1.08
21
44100
1.89
100100
1.12
22
46200
1.99
104900
1.16
23
48300
2.10
109700
1.20
24
50500
2.22
114500
1.24
25
52600
2.33
119200
1.27
26
54700
2.45
124000
1.31
27
56800
2.56
128800
1.35
28
58900
2.68
133500
1.39
29
61100
2.80
138300
1.42
30
63200
2.93
143100
1.46
* Option 1 for 6-12 stories; average of Options 2 and 3 for 13-20 stories; Option 4 for 21+ stories
†
‡
§
Assuming the same basic floor plan as the FFTT options with a 10kPa dead load
Dead load only
Period calculated as: T = 0.05h3./4 (NRC, 2010)
128
(a)
(b)
(c)
Figure A1: 12 Storey Option 1 (a) Mode 1; T1 = 1.95 sec (b) Mode 2; T2 = 1.74 sec
(c) Mode 3; T3 = 1.47 sec
129
(a)
(b)
(c)
Figure A2: 20 Storey Option 2 (a) Mode 1; T1 = 2.65 sec (b) Mode 2; T2 = 2.35 sec
(c) Mode 3; T3 = 1.85 sec
130
(a)
(b)
(c)
Figure A3: 20 Storey Option 3 (a) Mode 1; T1 = 2.94 sec (b) Mode 2; T2 = 2.58 sec
(c) Mode 3; T3 = 2.07 sec
131
(a)
(b)
(c)
Figure A4: 30 Storey Option 4 (a) Mode 1; T1 = 2.93 sec (b) Mode 2; T2 = 2.78 sec
(c) Mode 3; T3 = 2.13 sec
132