A FRAMEWORK FOR DAMAGE INDEX CALCULATION IN LIGHT WOOD-FRAME
BUILDINGS

by
MD Sultanur Ashikin
B.Sc., Bangladesh University of Engineering and Technology, 2022

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

UNIVERSITY OF NORTHERN BRITISH COLUMBIA
April 2025
© MD Sultanur Ashikin, 2025

Abstract
Seismic events present significant challenges to the structural performance of buildings, with light
wood-frame structures being particularly susceptible due to their unique material variability,
reliance on non-structural components, and diverse construction practices. Existing seismic
damage models, such as the Park and Ang Damage Index (DI), have demonstrated utility for steel
and concrete structures but remain underdeveloped and unvalidated for light wood-frame
buildings. This research addresses these gaps by proposing a global-level calibration framework
for the β parameter in the Park and Ang DI model, tailored specifically for light wood-frame
structures. Unlike traditional component level calibration, the global approach emphasizes systemlevel behavior, capturing the cumulative effects of deformation and energy dissipation across the
entire structure.
The study integrates experimental data from benchmark tests conducted independent of this study
scope, the NEESWood project, to validate the accuracy of the calculated DI values against
observed damage patterns. By correlating DI values with actual damage, the research establishes
a comprehensive and validated methodology for assessing seismic damage in light wood-frame
buildings.
Furthermore, the proposed framework provides valuable insights into the progression of damage
under varying seismic intensities, offering thresholds that link DI values with observed structural
and non-structural damage. These findings significantly advance the practical application of the
Damage Index framework for light wood-frame structures, contributing to performance-based
seismic design and risk assessment efforts.

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Table of Content
ABSTRACT ................................................................................................................................................................II
TABLE OF CONTENT ........................................................................................................................................... III
LIST OF TABLES ................................................................................................................................................... VII
LIST OF FIGURES .................................................................................................................................................. IX
1

2

INTRODUCTION ..............................................................................................................................................1
1.1

BACKGROUND...............................................................................................................................................1

1.2

PROBLEM STATEMENT ..................................................................................................................................4

1.3

RESEARCH OBJECTIVES ................................................................................................................................ 6

1.4

THESIS STRUCTURE ......................................................................................................................................7

LITERATURE REVIEW ..................................................................................................................................9
2.1
2.1.1

OVERVIEW OF SEISMIC DAMAGE ASSESSMENT IN LIGHT WOOD-FRAME BUILDINGS ...................................9
Seismic Damage Assessment Practices....................................................................................................9

2.2

EVOLUTION OF DAMAGE INDICES IN STRUCTURAL HEALTH MONITORING ................................................. 10

2.3

ENERGY AND DEFORMATION BASED DAMAGE MODEL: PARK AND ANG DAMAGE INDEX ......................... 12

2.3.1

Park and Ang Damage Index Model ...................................................................................................... 13

2.3.2

Mathematical Expression of the Park and Ang Damage Index ............................................................. 14

2.3.3

Ultimate Displacement Parameter ........................................................................................................ 15

2.3.4

Equivalent Yield Force Parameter ........................................................................................................ 16

2.3.5

Component Level Parameter Values Derived from Experimental Shear Wall Test .............................. 17

2.3.6

Beta 𝜷 Parameter .................................................................................................................................. 19

2.3.7

Finite Element Modeling of Light Wood Frame Building...................................................................... 20

2.3.8

Global Level Modeling of Light Wood Frame Building ....................................................................... 21

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2.3.8.1

MSTEW Model Parameters and Their Effectiveness in Timber3D .............................................................. 22

2.3.8.2

Out-of-plane Stiffness of Light Wood Frame Buildings ............................................................................... 26

2.3.9
2.4

INCREMENTAL DYNAMIC ANALYSIS ........................................................................................................... 28

2.4.1
3

4

Mass Distribution in Numerical Modeling ............................................................................................ 27

FEMA Guidelines for Conducting IDA .................................................................................................. 29

SHAKING TABLE TESTS USED FOR DAMAGE OBSERVATION AND MODEL VALIDATION ... 32
3.1

BACKGROUND OF THE PROJECT .................................................................................................................. 32

3.2

TEST BUILDING ARCHITECTURE ................................................................................................................. 33

3.3

SHAKE TABLE SETUP .................................................................................................................................. 36

3.4

TEST PHASES .............................................................................................................................................. 37

3.5

GROUND MOTIONS ..................................................................................................................................... 39

3.5.1

Ground Motion Selection ....................................................................................................................... 39

3.5.2

Ground Motion Scaling ......................................................................................................................... 40

3.6

INSTRUMENTATION OF SHAKE TABLE TEST ................................................................................................ 43

3.7

OBSERVED DAMAGE IN PHASE 5 TESTING .................................................................................................. 43

NUMERICAL MODEL DEVELOPMENT ................................................................................................... 49
4.1

OVERVIEW OF TIMBER 3D AND NONLINEAR MODELING ............................................................................ 49

4.2

MODELING APPROACH................................................................................................................................ 50

4.2.1

Structural Representation ...................................................................................................................... 50

4.2.2

Master-Slave Nodal System ................................................................................................................... 50

4.2.3

Diaphragm and Shear Wall Modeling ................................................................................................... 50

4.2.4

Dynamic Analysis .................................................................................................................................. 51

4.2.5

Validation .............................................................................................................................................. 51

4.2.6

Spring Parameters ................................................................................................................................. 51

4.2.6.1

In-Plane Shear Spring Parameters ................................................................................................................. 51

4.2.6.2

Parallel Spring Theory .................................................................................................................................. 56

4.2.6.3

Out-of-Plane Bending Spring Parameters ..................................................................................................... 61

4.2.6.4

Nodal Restraints ............................................................................................................................................ 63

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4.2.6.5

Diaphragm Beam .......................................................................................................................................... 63

4.2.6.6

Mass Distribution .......................................................................................................................................... 66

4.2.6.7

Timber 3D Modeling .................................................................................................................................... 66

4.2.7
4.3

5

Damping Ratios in Phase 5 ................................................................................................................... 68
MODEL VALIDATION .................................................................................................................................. 68

4.3.1

Modal Analysis ...................................................................................................................................... 68

4.3.2

Structural Response ............................................................................................................................... 70

4.3.2.1

Displacement Response ................................................................................................................................ 70

4.3.2.2

Force Time History ....................................................................................................................................... 74

4.3.2.3

Global Hysteresis .......................................................................................................................................... 76

4.3.2.4

Energy Dissipation ........................................................................................................................................ 77

4.3.2.5

Roof Displacement Profile ............................................................................................................................ 79

DAMAGE INDEX MODEL CALIBRATION ............................................................................................... 83
5.1

INCREMENTAL DYNAMIC ANALYSIS (IDA) OF THE NEESWOOD BUILDING............................................... 85

5.2

IDA CURVE ................................................................................................................................................ 88

5.2.1

Scattered Plot Observed Trends: ........................................................................................................... 88

5.2.2

Median Curve ........................................................................................................................................ 90

5.3

PUSHOVER ANALYSIS OF NEESWOOD TWO STORY NUMERICAL MODEL .................................................. 92

5.4

GLOBAL BETA CALIBRATION CALCULATION FOR THE BENCHMARK TWO-STORY LIGHT WOOD FRAME

BUILDING ................................................................................................................................................................. 93

6

5.4.1

Scaled Response Spectrum Northridge Earthquake .............................................................................. 94

5.4.2

Global Response .................................................................................................................................... 95

5.4.3

Beta Value Sample Calculation ............................................................................................................. 97

DAMAGE INDEX CALCULATION AND DAMAGE CORRELATION ................................................ 100
6.1

DAMAGE INDEX CALCULATION FOR PHASE 5, TEST 8: NUMERICAL ANALYSIS OF BENCHMARK RESPONSE
101

6.1.1

Sample DI Calculation for Wall 1Y First Floor .................................................................................. 103

6.1.2

Global Damage Index Calculation ...................................................................................................... 104

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7

6.2

DAMAGE CORRELATION ........................................................................................................................... 106

6.3

CORRELATING DAMAGE ACROSS A RANGE OF INTENSITY LEVELS........................................................... 108

CONCLUSION ............................................................................................................................................... 117
7.1

8

FUTURE WORK ......................................................................................................................................... 118

REFERENCES................................................................................................................................................ 121

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List of Tables
Table 1 Summary of test phases and building configurations ...................................................... 38
Table 2 Ground Motion Information for NEESWood Benchmark Tests ..................................... 41
Table 3 Summary of Observed Damage in Phase 5 ..................................................................... 48
Table 4 First story in plane shear spring parameters in x direction .............................................. 54
Table 5 Second story in plane shear spring parameters in x direction.......................................... 54
Table 6 First story in plane shear spring parameters in y direction .............................................. 55
Table 7 Second story in plane shear spring parameters in y direction.......................................... 55
Table 8 Case Study: E27 Wall and Combined Parameters ........................................................... 58
Table 9 Combined MSTEW backbone parameters for in-plane shear springs ............................. 60
Table 10 Out-of-plane stiffness of the shear walls ....................................................................... 62
Table 11 Equivalent diaphragm beam element properties ............................................................ 65
Table 12. Damping ratio of Phase 5 structure used in the numerical model ................................ 68
Table 13 Comparison of modal periods between the benchmark test model and numerical model
....................................................................................................................................................... 70
Table 14. Summary of Validation Results – Phase 05 Test 08 ..................................................... 82
Table 15. Key information on 11 significant earthquakes used in the IDA analysis, including their
year of occurrence, magnitude, location, and notable features. .................................................... 87
Table 17. Wall-wise DI values and corresponding energy dissipation ....................................... 102
Table 16. Table presenting the calculated Damage Index (DI) for each wall on the first and second
floors of the NEESWood two-story light wood frame numerical model. The Northridge
earthquake, scaled by a factor of 1.2, was utilized for the dynamic analysis of the Timber 3D
model. The DI values are tabulated for the corresponding walls using calibrated Beta values. 103
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Table 18. Component-wise Damage Index (DI) calculation for the NEESWood two-story light
wood frame structure utilizing numerical response of Northridge earthquake ground motion with
scale factor 1.20 .......................................................................................................................... 105
Table 19. Peak Ground Acceleration (PGA) in X and Y directions from NEESWood benchmark
tests used in numerical analysis and obtained Global DI from numerical response ................... 110
Table 20. Comparison of Global DI values obtained from numerical response and experimental
benchmark test response, demonstrating the validity of the beta calibration and the reliability of
the developed framework. ........................................................................................................... 114

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List of Figures
Figure 1. (a) 𝐷𝑢𝑙𝑡 and 𝐹𝑦𝑖𝑒𝑙𝑑 as a function of nail spacing (b) 𝛽 as a function of nail spacing and
damage limit state. (Van De Lindt, 2005)(c) schematic representation of edge and inside nail
spacing of a typical shear wall (d) schematic of the test set-up for shear wall testing (Van De Lindt,
2005) ............................................................................................................................................. 18
Figure 2. Backbone curves of MSTEW model (Pan et al., 2018) ................................................ 23
Figure 3 Elevation view of the NEESWood two-story residential project building (Christovasilis
et al., n.d., 2009) ........................................................................................................................... 34
Figure 4 Floor plan layour of the NEESWood project building (Christovasilis et al., n.d., 2009)
....................................................................................................................................................... 35
Figure 5 Isometric view of the project building............................................................................ 35
Figure 6 (a) Extension frame of shake tables connected by steel link structure, and (b) Foundation
of Test Building under Construction building (Christovasilis et al., n.d., 2009) .......................... 36
Figure 7 South-east external view of the benchmark structure after the installation of the exterior
stucco finish (Christovasilis et al., n.d., 2009) .............................................................................. 42
Figure 8 Cracking and Spalling of Stucco at the Bottom of Garage Wall (Christovasilis et al., n.d.,
2009) ............................................................................................................................................. 44
Figure 9 Cracking and Spalling of Stucco at the Corner of Garage Wall Opening (Christovasilis et
al., n.d., 2009) ............................................................................................................................... 45
Figure 10 Cracking and separation of sill plate through entire length of garage narrow wall piers
(Christovasilis et al., n.d., 2009) ................................................................................................... 45
Figure 11 Cracking of stud above hold-down anchor (Christovasilis et al., n.d., 2009) .............. 46
Figure 12 Separation of Gypsum Wallboard from Ceiling (Christovasilis et al., n.d., 2009) ...... 46
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Figure 13 Horizontal Cracking of Gypsum Wallboard (Christovasilis et al., n.d., 2009) ............ 47
Figure 14 Cracking and Buckling of Gypsum Wallboard at Door Opening (Christovasilis et al.,
n.d., 2009). Table below summarises the damage observed and shown above: ........................... 47
Figure 15 Shear wall plan for the NEESWood two story light wood frame building (a) First Floor
(b) Second Floor ........................................................................................................................... 52
Figure 16 Equivalent in-plane shear spring system ...................................................................... 57
Figure 17 MSTEW hysteresis backbone curve used in this study for numerical model development
(a) E27 wall - Phase 03 (b) Gypsum wall board (Pan et al., 2018) (c) Stucco (Pan et al., 2018) . 59
Figure 18 MSTEW back bone curve for combined action of Phase 3 shear wall, GWB and Stucco
....................................................................................................................................................... 59
Figure 19 Wall line plan of the NEESWood two story building .................................................. 63
Figure 20 Diaphragm equivalent beam (a) first floor level (b) second floor level ....................... 65
Figure 21 Timber 3D numerical model of NEESWood two-story light wood frame building .... 67
Figure 22 Comparison of mode shapes obtained from the shake table test (benchmark test) and
the Timber 3D numerical model for the NEESWood two-story light wood-frame building. ...... 69
Figure 23 Comparison of nodal displacement time history between the benchmark structure shake
table test response and numerical model response for Phase 05 Test 08 – Shear wall E16 in Y
direction in 1st floor roof ............................................................................................................... 72
Figure 24 Comparison of nodal displacement time history between the benchmark structure shake
table test response and numerical model response for Phase 05 Test 08 – Shear wall E1 in X
direction in 1st floor roof ............................................................................................................... 72

x

Figure 25 Comparison of nodal displacement time history between the benchmark structure shake
table test response and numerical model response for Phase 05 Test 08 – Shear wall E28 in Y
direction in 2nd floor roof .............................................................................................................. 73
Figure 26 Comparison of nodal displacement time history between the benchmark structure shake
table test response and numerical model response for Phase 05 Test 08 – Shear wall E17 in X
direction in 2nd floor roof. ............................................................................................................. 73
Figure 27 Base shear force time history comparison between the benchmark test (Phase 05 - Test
08) and the numerical response in X direction (longitudinal direction) ....................................... 75
Figure 28 Base shear force time history comparison between the benchmark test (Phase 05 - Test
08) and the numerical response in Y direction (transverse direction) .......................................... 75
Figure 29 Base shear force versus central roof displacement hysteresis loops for Phase 05 – Test
08. Panels (a) and (c) correspond to the benchmark shake table test results in the X (longitudinal)
and Y (transverse) directions, respectively. Panels (b) and (d) represent the corresponding
numerical model predictions for the X and Y directions. ............................................................. 76
Figure 30 Comparison of global hysteretic energy dissipation of the benchmark test structure and
the numerical model in X (longitudinal) direction ....................................................................... 78
Figure 31 Comparison of global hysteretic energy dissipation of the benchmark test structure and
the numerical model in Y (transverse) direction........................................................................... 79
Figure 32 Numerical model time history analysis deformed shape (15th sec) at scale 100 for Phase
05 Test 08 ...................................................................................................................................... 80
Figure 33 Comparison of maximum roof displacement profile between the benchmark test
structure and the numerical model in X direction for Phase 05 Test 08 ....................................... 81

xi

Figure 34 Comparison of maximum roof displacement profile between the benchmark test
structure and the numerical model in Y direction for Phase 05 Test 08. The table below summarizes
the validation briefly. .................................................................................................................... 81
Figure 35. Flowchart illustrating the systematic process for Damage Index (DI) model calibration,
including the development and validation of a numerical model, determination of global
parameters via pushover analysis, collapse intensity identification through Incremental Dynamic
Analysis (IDA), and global beta calibration based on global hysteresis responses. ..................... 84
Figure 36. IDA scattered data points for the NEESWood two story light wood frame building
Timber 3D model. 11 wide range of ground motion data and 174 corresponding dynamic analysis
result is utilized for this plot.s ....................................................................................................... 89
Figure 37. Median incremental dynamic analysis (IDA) curve illustrating the relationship between
drift ratio (%) and spectral acceleration (g). The curve represents the median response of the
NEESWood two story light wood frame building model based on scattered IDA points from
multiple ground motion records. The collapse point is identified at a drift ratio of 6.5% and spectral
acceleration of 1.65g, indicating the intensity level at which the structure reaches its collapse limit
state. .............................................................................................................................................. 90
Figure 38. This figure presents the pushover analysis curve, illustrating the relationship between
the base shear force and the roof displacement. The force values are expressed in kN, while the
displacement is in mm. The curve provides insights into the nonlinear behavior and lateral load
resistance of the structure under increasing displacement. ........................................................... 93
Figure 39. Response spectrum illustrating the variation of spectral acceleration 𝑆𝑎 with respect to
the period (T) for a single-degree-of-freedom (SDOF) system with 5% damping. The ground
motion was scaled to match the collapse intensity level of 1.65g at a period 0.30 seconds. ........ 95

xii

Figure 40. Hysteresis Curve of the System. This figure illustrates the hysteresis response of the
global system, showing the relationship between force (kN) and average roof displacement (mm).
The curve represents the cyclic behavior of the structure under repeated loading and unloading,
capturing its energy dissipation and stiffness degradation over successive cycles. ..................... 96
Figure 41. Cumulative Energy Dissipation Over Time. This figure displays the cumulative energy
dissipation of the system as a function of time (s). The plot highlights the energy absorbed by the
structure during cyclic loading, with energy values calculated in kilojoules (kJ). ....................... 97
Figure 42. Layout of the wall lines for the NEESWood two story light wood frame building .. 100
Figure 43. Observed damages for the NEESWood benchmark test after Phase 05 Test 08....... 107
Figure 44. Level of damage observed during different test phases of the NEESWood benchmark
test and corresponding global DI value for each of the tests based on numerical dynamic analysis
response....................................................................................................................................... 111
Figure 45. Flowchart outlining the step-by-step framework for seismic damage assessment of light
wood-frame buildings using Damage Index (DI). ...................................................................... 115

xiii

1 Introduction
1.1 Background
The study of seismic performance and damage in structures has been a critical focus in structural
engineering for decades. With the increasing need to ensure safety and minimize damage during
earthquakes, damage indices have emerged as an essential tool for assessing the vulnerability and
performance of various structural systems. Among the early models, the Park and Ang Damage
Index (DI) introduced in 1985 has been a landmark contribution to this field, providing a
framework for quantifying seismic damage through a combination of deformation and energydissipation measures (Y. Park & Ang, 1985; Y.-J. Park et al., 1987). This DI model has been
extensively used for steel and reinforced concrete structures, where its parameters are wellcalibrated based on established material and structural behavior under seismic loading.
While the Park and Ang DI proved effective for many structural types, its application to light
wood-frame buildings introduced unique challenges. Light wood-frame structures are widely used
in North America for their cost-effectiveness and favorable thermal properties. However, their
inherent material variability, construction diversity, and reliance on non-structural components
like stucco and sheathing make them particularly vulnerable under seismic loading. The original
DI parameters, especially the calibration factor β, were not tailored to account for the unique cyclic
behavior and failure modes of light wood-frame buildings. Consequently, early applications of the
DI to such structures often resulted in inconsistencies and inaccuracies, highlighting the need for
further development. Despite the widespread use of Damage Indices (DIs) for various structural
systems, no rigid framework or standardized guideline has been established for calculating the DI
specifically for light wood-frame buildings. The lack of a straightforward and rigorous approach
1

has created challenges in ensuring consistency and reliability when evaluating seismic
performance for these structures using Damage Index. This study aims to address this gap by
providing a systematic, step-by-step methodology for calibrating and applying the Damage Index
framework to light wood-frame buildings.
Over the years, efforts have been made to adapt and refine the seismic health and risk assessment
tools for light wood-frame structures. A significant milestone in this endeavor was the initiation
of large-scale experimental studies, such as the NEESWood benchmark test project. This project
aimed to address the seismic vulnerabilities of light wood-frame buildings and provide data
(independent of this study and only publicly available data is utilized for validation and correlation
in this study) to enhance seismic risk assessment tools like Damage Index.
The NEESWood project, conducted at the University at Buffalo, investigated the seismic
performance of two-story wood-frame residential buildings. Using real-world seismic data, such
as ground motions from the Northridge Earthquake, researchers examined the progression of
damage across structural and non-structural components under varying intensities. The findings
underscored the role of construction details, such as nail spacing and wall configurations, in
influencing damage patterns and structural stability (Christovasilis et al., n.d.; van de Lindt, 2009).
This experimental campaign not only expanded the understanding of seismic damage in woodframe buildings but also provides damage details and response data that can be utilized in
validation and calibration of different damage index models. Specifically, the β parameter in the
Park and Ang DI, which accounts for material and connection behavior under cyclic loading, was
found to vary significantly in light wood-frame structures due to factors like nail spacing, sheathing
type, and retrofitting strategies. Incremental Dynamic Analysis (IDA) validated by this
NEESWood benchmark test structure has been utilized for beta calibration purpose in this study.

2

To further advance the understanding of seismic performance and refine the application of the
Damage Index (DI) framework for light wood-frame buildings, this study undertook a detailed and
systematic approach leveraging data from the NEESWood benchmark project. As discussed
earlier, Incremental Dynamic Analysis (IDA) was employed as the primary tool for calibrating the
beta parameter in the Park and Ang DI equation, which reflects the hysteretic behavior of structural
components. This calibration formed the backbone of the study, ensuring the Damage Index
accurately represented the unique cyclic behavior and failure mechanisms of light wood-frame
structures.
The core methodology involved several critical steps. First, a nonlinear structural model of the
NEESWood two-story light wood-frame benchmark structure was developed using the Timber3D
MATLAB package. This package enabled precise modeling of the building’s nonlinear dynamic
response, accounting for the specific material properties, connection details, and structural
configurations. Ground motion data, including records from the Northridge Earthquake, were
applied to simulate the seismic behavior under varying intensities.
The beta parameter calibration was conducted through a range of ground motion intensities using
IDA. This analysis helped establish a global beta values tailored to the NEESWood two story light
wood-frame benchmark structure, ensuring that the DI framework reflected the unique material
and connection behavior of the light wood-frame building. Once the beta calibration was complete,
the model was rigorously validated against observed responses from the NEESWood benchmark
tests. This validation ensured that the numerical model reliably predicted the seismic performance
and damage patterns observed during the actual tests, providing confidence in the calibrated beta
values.

3

Following validation, the calibrated beta values were used to calculate the Damage Index for each
structural component under various seismic scenarios. The calculated DI values were then
compared to observed damage from the benchmark tests to evaluate their reliability and accuracy.
This comparison demonstrated how well the calibrated beta values captured the progression of
damage across different intensities and structural configurations.
The study also extended the analysis beyond a single intensity level, conducting DI calculations
for a series of progressively increasing ground motion intensities. This allowed for an exploration
of how damage evolved with seismic intensity, providing insights into the relationship between
the Damage Index and the severity of observed damage. By observing trends in DI values and
corresponding structural responses, the study captured critical transitions, such as the onset of
significant cracking or near-collapse behavior, highlighting the robustness of the calibrated
Damage Index framework.
Overall, this comprehensive study represents a significant contribution to the field by providing a
systematic methodology for calibrating and validating the Damage Index framework for light
wood-frame buildings. The results not only offer a reliable tool for performance-based seismic
assessment but also pave the way for future studies to refine damage quantification methods and
improve structural design practices.

1.2 Problem Statement
The assessment of seismic damage in structures has relied heavily on the development of
frameworks like the Park and Ang Damage Index (DI), which quantify damage by combining
deformation and energy-dissipation parameters. While these frameworks have been extensively
calibrated and validated for steel and reinforced concrete structures, their application to light

4

wood-frame buildings remains inadequate. Light wood-frame structures are characterized by
significant variability in materials, construction practices, and reliance on non-structural
components such as sheathing and finishes, making them particularly complex to assess using
existing damage index frameworks. This inherent variability and the diverse ways in which light
wood-frame buildings respond to seismic events have highlighted the need for a tailored damage
index framework.
Unlike steel and concrete structures, light wood-frame buildings exhibit unique failure modes,
such as nail slip, sheathing degradation, and interaction between structural and non-structural
elements. These behaviors are influenced by factors such as wall configurations, nail spacing, and
construction quality, creating a level of uncertainty that is yet to be addressed by rigorous Damage
Index based damage correlation. Furthermore, existing frameworks often rely on global
assumptions that fail to capture the nuanced behavior of individual components, which is essential
for understanding the overall seismic performance of light wood-frame structures.
To date, there has been no systematic effort to develop or calibrate a comprehensive damage index
framework specifically tailored to light wood-frame buildings. Such a framework requires detailed
observations and modeling of individual building behaviors to account for the variability inherent
in these structures.
This lack of a tailored and reliable damage index framework limits the ability to assess and predict
the seismic performance of light wood-frame buildings accurately. Addressing this gap is essential
for ensuring the safety and resilience of these widely used structures, particularly in regions prone
to seismic activity.

5

1.3 Research Objectives
This research is focused on addressing critical limitations in the calibration of the β parameter
within the Park and Ang Damage Index (DI) as it applies to light wood-frame buildings. Unlike
steel or reinforced concrete structures, light wood-frame buildings exhibit unique variability and
complexity due to their construction methodologies and material properties. The β parameter,
which captures cyclic loading behavior and calibrates the DI equation to correlate anticipated
damage in real scale, has not yet been calibrated at a global level for these structures. This lack of
calibration hinders the model's accuracy and utility in assessing seismic damage for light woodframe buildings. To bridge this gap, this study aims to demonstrate a framework for global-level
β calibration, moving beyond the impracticality of wall-by-wall calibration approaches and
addressing the need for a more holistic understanding of the seismic behavior of entire structures.
By integrating results with experimental result from large-scale studies such as NEESWood
(Christovasilis et al., 2007; Van de Lindt, 2009), the research will validate β values and calculated
DI values to see if they align well with observed damage patterns or not.
The objectives of this study can be summarized as follows:
1. Demonstrating a Global-Level Calibration of the β Parameter for Light Wood Frame
Structure: Demonstrate a global-level calibration of the β parameter in the Park and Ang
Damage Index (DI) framework tailored for light wood-frame buildings, addressing their
unique seismic behavior and structural characteristics.
2. Establishing a Comprehensive and Validated Framework for Damage Index
Calculation: Develop a step-by-step, comprehensive guideline for calculating the Damage
Index (DI) for light wood-frame buildings. This framework is validated by correlating the
6

calculated DI values to the actual damage observed during benchmark experimental tests,
ensuring the methodology is both accurate and reliable for practical seismic damage
assessment.

1.4 Thesis Structure
This thesis is organized into seven chapters, each addressing a critical component of the study:
•

Chapter 1: Introduction

This chapter provides the background, problem statement, and objectives of the study, outlining
the motivation and significance of developing a validated Damage Index (DI) framework tailored
for light wood-frame buildings.
•

Chapter 2: Literature Review

A comprehensive review of existing seismic damage assessment practices, the evolution of
damage indices, and the Park and Ang Damage Index model. The chapter also discusses
parameters critical for DI calculation, such as ultimate displacement, equivalent yield force, and
beta calibration, and explores global-level modeling methodologies.
•

Chapter 3: Shaking Table Tests for Validation

This chapter introduces the benchmark NEESWood two-story test building, detailing its
architecture, test setup, shaking table instrumentation, and damage observations from Phase 5
testing, which serve as validation data for the proposed framework.
•

Chapter 4: Numerical Model Development

Focused on the development and validation of the Timber 3D numerical model, this chapter
explains the modeling approach, including structural representation, master-slave systems,
diaphragm modeling, and dynamic analysis, followed by detailed validation using modal and
response spectrum analyses.
7

•

Chapter 5: Damage Index Model Calibration

This chapter introduces the global beta calibration process, starting from Incremental Dynamic
Analysis (IDA) to identify collapse intensities, pushover analysis, and dynamic analysis of the
benchmark model. A sample beta value calculation is also presented, highlighting the importance
of global-level calibration.
•

Chapter 6: Damage Index Calculation and Correlation

This chapter demonstrates the application of the calibrated DI framework, including componentlevel and global-level damage index calculations. The calculated values are validated against
observed damage from the NEESWood tests, and trends across varying seismic intensity levels
are analyzed to assess the reliability of the methodology.
•

Chapter 7: Conclusion

The thesis concludes by summarizing the study’s contributions, emphasizing the validated
framework for DI calculation, and providing recommendations for future research on light woodframe buildings.

8

2 Literature Review
2.1 Overview of Seismic Damage Assessment in Light Wood-Frame Buildings
Seismic damage assessment is a fundamental aspect of earthquake engineering, aimed at
quantifying damage levels to predict building performance and mitigate risks during earthquakes.
While general frameworks for damage assessment are well-established for steel and concrete
structures, their application to light wood-frame buildings presents unique challenges due to the
distinctive behavior of these structures under seismic loads. Light wood-frame buildings, widely
used for residential purposes in North America, require specific adaptations to existing
methodologies to account for their variability in material properties, reliance on non-structural
components, and diverse construction practices (Van de Lindt et al., 2010).
2.1.1 Seismic Damage Assessment Practices
For steel and reinforced concrete structures, damage assessment frameworks have traditionally
relied on methodologies that integrate deformation-based indices, such as inter-story drift, with
energy-dissipation measures. Tools like the Park and Ang Damage Index (DI) (Park & Ang, 1985)
have been extensively used for these structures due to their clear cyclic response behavior, ductile
failure modes, and well-established calibration parameters. These approaches utilize a
combination of experimental data, numerical modeling, and Incremental Dynamic Analysis (IDA)
to quantify structural damage levels under varying seismic intensities. While these methods have
been successful for steel and concrete buildings, their direct application to light wood-frame
buildings is often problematic. Light wood-frame structures exhibit highly redundant load paths
and rely significantly on interactions between structural and non-structural components, such as
sheathing, nails, and stucco. This results in unique damage progression mechanisms, including
9

localized failures, material cracking, and degradation of non-structural components, which are not
adequately captured by traditional frameworks.
For light wood-frame structures, damage assessment frameworks need to address their distinct
characteristics, including material variability and highly distributed load-sharing mechanisms.
Several key methodologies for seismic performance evaluation have emerged, including:
a) Experimental Testing: Large-scale experimental studies, such as those conducted under the
NEESWood project, have been critical in identifying the damage progression mechanisms of light
wood-frame buildings. These studies utilize shake tables to replicate earthquake scenarios and
capture detailed failure modes, such as the separation of sheathing from framing and loss of nail
connections (van de Lindt, 2008).
b) Numerical Modeling: Advanced numerical modeling tools, such as Timber3D, are tailored for
simulating the nonlinear response of light wood-frame structures. These models incorporate
component-level behaviors, including hysteretic behavior of shear walls and energy dissipation
mechanisms, and are validated using experimental data to ensure reliability (Christovasilis et al.,
2007).
c) Hybrid Approaches: Hybrid approaches combining numerical simulations with empirical and
experimental data provide a robust framework for damage assessment. For instance, the calibrated
beta parameter in the Park and Ang DI has been adapted using global structural response metrics
from numerical model, ensuring the framework aligns with observed damage patterns specific to
light wood-frame buildings.

2.2 Evolution of Damage Indices in Structural Health Monitoring
The concept and development of damage indices have advanced significantly over the years to
meet the growing demand for precise tools to evaluate seismic damage and assess the health of
10

structures. A damage index is a quantitative measure that combines parameters such as
deformation and energy dissipation to represent the extent of damage sustained by a structure
under seismic loads. Early approaches relied on simple deformation-based metrics, offering a
rudimentary understanding of structural performance during earthquakes. However, as research
expanded, it became evident that these basic metrics were insufficient to capture the complex,
nonlinear behavior of structures during seismic events. This led to the evolution of more advanced
damage index models, incorporating cyclic loading effects, cumulative energy dissipation, and
other parameters critical to accurately reflecting the progressive nature of seismic damage. These
refined models have become essential tools in performance-based seismic design and structural
health assessment.
One of the earliest breakthroughs was the Park and Ang Damage Index (DI), introduced in 1985.
This model combined deformation parameters with energy dissipation metrics, offering a more
comprehensive framework for evaluating seismic damage in steel and reinforced concrete
structures (Park & Ang, 1985). Its ability to integrate multiple damage mechanisms into a single
numerical value marked a significant step forward in structural health monitoring, setting the
foundation for subsequent models.
As understanding of seismic behavior deepened, researchers began exploring more specialized
approaches. Displacement-based damage indices emerged as an extension of basic deformation
models, relying on measurable displacement thresholds to estimate damage levels (Iranmanesh &
Ansari, 2014). While these indices provided a straightforward and practical method for damage
assessment, they often failed to account for energy dissipation—a critical factor in materials like
reinforced concrete and wood that exhibit significant cyclic degradation.

11

Recognizing this limitation, energy-based damage indices were introduced to capture the
cumulative effects of seismic energy input. These models emphasized the role of energy absorption
and dissipation in determining structural health, making them particularly valuable for structures
subject to repeated loading (Xu et al., 2012). However, their application required precise
calibration to account for the distinct hysteretic behaviors of different materials and structural
systems.
Building on these advancements, researchers sought to integrate localized and global perspectives
of structural damage. This effort led to the development of the Global Damage Index (GDI), which
combined displacement and energy metrics into a holistic assessment framework (Pan et al.,
2020a). The GDI bridged the gap between local damage states—such as those observed in specific
structural elements—and the overall performance of complex systems. While effective for highrise buildings and reinforced concrete frames, its adaptation for light wood-frame structures
remains a challenge due to their unique reliance on non-structural components and connections.
Over time, these developments have shaped the field of structural health monitoring, providing a
range of tools tailored to different materials and structural systems. Yet, the application of these
indices to light wood-frame buildings is still evolving, requiring further research to address their
unique seismic response characteristics.

2.3 Energy and Deformation Based Damage Model: Park and Ang Damage
Index
Damage indices have become reliable tools in seismic damage assessment, providing numerical
measures to evaluate structural performance during earthquakes. The Park and Ang Damage Index
(1985), combining deformation parameters and energy dissipation, is widely used for reinforced
concrete and steel structures due to its ability to capture seismic behavior comprehensively (Park
12

& Ang, 1985). Displacement-based models, focusing solely on deformation thresholds, are
effective for straightforward assessments but lack precision for cyclic loading effects (Iranmanesh
& Ansari, 2014). Energy-based indices address this limitation by incorporating cumulative energy
absorption, offering enhanced applicability for materials with hysteretic behaviors (Xu et al.,
2012). These indices have been widely integrated into tools like fragility curves and Incremental
Dynamic Analysis (IDA), further solidifying their role in both research and practical seismic risk
assessment (Vamvatsikos & Cornell, 2002).

2.3.1 Park and Ang Damage Index Model
The Park and Ang Damage Index (1985) is a landmark contribution to the field of earthquake
engineering, reflecting a paradigm shift in how seismic damage is quantified and assessed. Before
its establishment, seismic damage assessment primarily relied on simple deformation-based
measures or observational damage scales, such as the Modified Mercalli Intensity (MMI) scale,
which, while useful, lacked the precision and quantifiability required for advanced structural
analysis and design. These methods could not adequately capture the complex, cumulative effects
of seismic loading on structures, particularly under repeated and cyclic stresses.
The Park and Ang Damage Index introduced a systematic framework that combined two critical
parameters: deformation and energy dissipation. By integrating maximum deformation
(displacement) and cumulative hysteretic energy, the model addressed the shortcomings of earlier
methods that focused solely on peak displacements. This dual-component approach provided a
more comprehensive measure of structural damage by accounting for both the immediate and
cumulative effects of seismic forces. It enabled engineers and researchers to evaluate structural
performance beyond simple elastic or plastic thresholds, paving the way for more accurate
predictions of collapse and failure.
13

The innovation of the Park and Ang Damage Index lies in its ability to move beyond traditional
elastic and plastic thresholds, providing a nuanced understanding of structural behavior under
seismic forces. It formed the basis for modern seismic design practices by enabling damage
quantification in terms of engineering demand parameters (EDPs) such as drift and energy
dissipation, paving the way for tools like fragility curves and Incremental Dynamic Analysis (IDA)
(Vamvatsikos & Cornell, 2002). Furthermore, its applicability to various structural systems—
including reinforced concrete, steel, and more recently, light wood-frame buildings—demonstrates
its versatility and enduring relevance in addressing the unique challenges posed by diverse
structural types and seismic conditions (Park & Ang, 1985; Xu et al., 2012).
2.3.2 Mathematical Expression of the Park and Ang Damage Index
The Park and Ang Damage Index (DI) is formulated as a dimensionless parameter that quantifies
the cumulative damage sustained by a structure under seismic loading. The key motivation behind
developing a dimensionless equation is to ensure that the damage measure remains independent of
absolute scale, making it applicable across different structural systems, loading conditions, and
material properties.
Unlike traditional displacement-based indices, which rely solely on peak response parameters, the
Park and Ang Damage Index integrates both maximum deformation and hysteretic energy
dissipation, capturing the cumulative effects of cyclic loading.
The general dimensionless form of the Park and Ang Damage Index is expressed as:
𝐷𝐼 =

𝐷𝑚𝑎𝑥
𝐷𝑢

𝐸

+ 𝛽 ⋅ 𝐹 ⋅𝐷𝑖
𝑦

𝑢

(1)

where:
DI = Park and Ang Damage Index
𝐷𝑚𝑎𝑥 = Maximum displacement
14

𝐷𝑢 = Ultimate displacement capacity
β = Empirical calibration parameter
𝐸𝑖 = Cumulative hysteretic energy dissipation
𝐹𝑦 = Equivalent yield force
This equation presents two fundamental damage components:
Deformation-based component: The first term,

𝐷𝑚𝑎𝑥
𝐷𝑢

represents the ratio of peak displacement to

ultimate displacement, providing a direct measure of how close the structure is to its failure limit.
𝐸

Energy-based component: The second term, β ⋅ 𝐹 ⋅𝐷𝑖 , accounts for the effect of cyclic energy
𝑦

𝑢

dissipation, reflecting the cumulative inelastic deformations sustained by the structure over the
duration of seismic loading.
2.3.3 Ultimate Displacement Parameter
The Ultimate Displacement Parameter (𝐷ult ) is a critical factor in the Damage Index (DI) equation,
representing the maximum allowable displacement a structure or component can sustain before
failure. For shear walls, this parameter is typically determined through experimental monotonic or
cyclic testing, as discussed extensively in the literature (e.g., (Van De Lindt, 2005)). Such tests
involve applying increasing lateral loads to isolated wall specimens with different nail spacings.
These experiments have provided standardized values for shear walls commonly used in light
wood-frame buildings, facilitating damage index calibration at the component level.
However, when performing global beta calibration for an entire structure, the definition and
determination of 𝐷ult must shift to reflect the collective behavior of the building under seismic
loads. For full-story or full-structure models, the Ultimate Displacement Parameter represents the
roof displacement at the anticipated collapse state of the building. This collapse level is
15

characterized by the point at which no base shear force is observed, as captured in the global
pushover curve of the numerical model. Unlike component-level tests, the global 𝐷ult is derived
from pushover analysis of the entire building model and must account for the dynamic interactions
between structural and non-structural elements, as well as the unique properties of the specific
building under consideration. The distinction between component-level 𝐷ult and global 𝐷ult is
crucial. While experimental values from shear wall tests can guide initial estimates, the ultimate
displacement for global beta calibration must be determined for the specific building being
analyzed.
2.3.4 Equivalent Yield Force Parameter
The Equivalent Yield Force Parameter (𝐹y ) quantifies the force at which a structure or component
transitions from elastic to inelastic behavior. Similar to 𝐷ult , 𝐹y has been extensively studied for
shear walls through experimental testing.
For global beta calibration, 𝐹y must represent the equivalent yield force of the entire building rather
than individual components. This parameter is derived from the global pushover curve, capturing
the force at which the entire structure transitions from elastic to inelastic behavior. Unlike the
experimentally determined 𝐹y for shear walls, the global 𝐹y accounts for the cumulative
contributions of all structural and non-structural components, as well as their interactions during
seismic loading. The pushover analysis of the numerical model provides a comprehensive
framework for determining this parameter, ensuring that it reflects the unique properties and
configuration of the specific building under analysis.

16

2.3.5 Component Level Parameter Values Derived from Experimental Shear Wall Test
To date, many studies (Van De Lindt, 2004) have been done to evaluated these two key parameters
and through that, it is well-established that experimental monotonic testing is essential for
accurately determining them. However, to perform monotonic shear wall tests for each building to
calculate the Damage Index (DI) is neither time-efficient nor practical. Nevertheless, wood-frame
buildings are constructed according to standard guidelines that standardize construction
procedures for wood shear walls; for example, the use of 2x4 studs is common in stick-frame wood
construction. Yet, a significant variable in wood shear walls is nail spacing, which directly
influences the strength properties of the wall. Consequently, research has focused on this variable
when determining the two key parameters for wood shear walls.
𝐹𝑦𝑖𝑒𝑙𝑑 = −0.16𝑠 + 38.5

(2)

𝐷𝑢𝑙𝑡 = 0.28𝑠 + 121

(3)

In a study conducted by Van De Lindt in 2005 on wood frame shear walls, static displacement
tests were performed on various shear wall specimens with different nail spacing configurations
(76 mm, 102 mm, and 152 mm). Figure 1(c) shows typical schematic of a wood shear wall where
the edge nails (highlighted in red) are spaced closely together, while the nails on the inside
(highlighted in blue) are spaced farther apart. Figure 1(d) presents the schematic of the test setup
used by Van De Lindt for conducting experiments, which provided the parameters for the DI
equation. The findings of this study (Van De Lindt, 2005) led to the proposal of relationships
between nail spacing and the corresponding equivalent yield force and ultimate displacement.
These proposed relationships as shown in the equation (2) and (3), are graphically presented in
Figure 1(a), illustrating the correlation between nail spacing and 𝐷𝑢𝑙𝑡 as well as 𝐹𝑦𝑖𝑒𝑙𝑑 for wood
shear walls. Here, s is the nail spacing in mm and 𝐷𝑢𝑙𝑡 & 𝐹𝑦𝑖𝑒𝑙𝑑 are in mm and KN respectively.

17

(a)

(b)

(c)

(d)

Figure 1. (a) 𝐷𝑢𝑙𝑡 and 𝐹𝑦𝑖𝑒𝑙𝑑 as a function of nail spacing (b) 𝛽 as a function of nail spacing and
damage limit state. (Van De Lindt, 2005)(c) schematic representation of edge and inside nail
spacing of a typical shear wall (d) schematic of the test set-up for shear wall testing (Van De Lindt,
2005)

18

Another study (Pei et al., 2013) conducted on 9 different wood shear wall specimens under two
different loading protocol to investigate the limit strength. The study outcome shows very similar
yield strength for different nail schedules which supports the proposed correlation by Van De
Lindt. Additionally, this study by Pei et al. also suggests that vertical load has very insignificant
impact on equivalent yield force determination which reasonably justifies the adoption of this
proposed relationship with nail spacing for shear walls at different story level for multistory wood
building. A separate study (He et al., 1999) for monotonic loading on wood shear wall with varying
amount of opening and nail spacing (76, 102 and 152 mm) has also shown similar result for both
displacement and yield force as the proposed relationship. Finally, wood shear wall testing under
ATC-71 project (Update Seismic Rehabilitation Guidance Program Definition and Guidance
Development: Part -1: Workshop Proceeding, 2008) by Federal Emergency Management Agency
(FEMA) suggests and further validates the proposed correlation discussed.
2.3.6 Beta 𝜷 Parameter
The practicality of the DI model in assessing damage of any building greatly depends on 𝛽 value.
The 𝛽 value calibrates the DI model and helps to establish a realistic limit state for damage. Study
(Y.-J. Park et al., 1987) on concrete and steel building shows reliably constant 𝛽 value, 0.05 and
0.025 correspondingly. However, 𝛽 for wood building is highly variable ranging from 0.05 to
more than 1.00 (Pan et al., 2020b). Hence, appropriately determining 𝛽 value for wood shearwall
is the biggest challenge in Damage Index (DI) calculation for wood building.
Incremental Dynamic Analysis (IDA) is one way of determining the β value for wood shear walls
by identifying collapse intensity levels under earthquakes, marked by the IDA curve slope
dropping below 5% (Liang, 2007). Nonlinear dynamic analysis with a damage index (DI) of 1.00
(Liang et al., 2011)integrates hysteretic energy to solve for β according to equation 4.

19

𝛽=

𝐷
(𝐷𝐼 − 𝐷𝑚𝑎𝑥 ) ∗ 𝐹𝑦 ∗ 𝐷𝑢𝑙𝑡
𝑢𝑙𝑡

(4)

∫ 𝑑𝐸

2.3.7 Finite Element Modeling of Light Wood Frame Building
Finite Element Modeling (FEM) has been a cornerstone of research in understanding the dynamic
behavior of light wood frame buildings under seismic and wind loading. It enables the detailed
representation of components such as framing members, sheathing panels, and connections,
allowing for the simulation of deformation, energy dissipation, and failure mechanisms. FEM is
widely utilized in advanced software like ABAQUS, ANSYS, and SAP2000 to explore the
performance of wood structures at both component and system levels.
While FEM provides a powerful tool for analyzing wood frame structures, its application is
hindered by several limitations:
a) Computational Challenges: Finite element modeling (FEM) requires solving highly
nonlinear equations to account for material properties, connection slip behavior, and
dynamic interactions. This complexity becomes particularly pronounced when analyzing
multi-story buildings or conducting nonlinear time-history simulations. For instance,
(Kasal et al., 1994) emphasized the computational burden of capturing detailed
nonlinearities in the connections and materials, especially for full-structure simulations.
Similarly, Folz and Filiatrault (2001) highlighted the challenges of achieving convergence
in dynamic analyses, which often translate into long computation times, making FEM
computationally expensive for large-scale applications.
b) Modeling Challenges: The inherent nonlinear behavior of wood and its connections, such as
nail slip, hold-down deformations, and sheathing-to-framing interactions, is a critical
challenge in FEM analysis. Kasal et al. (1994) meticulously modeled these nonlinearities,
20

providing insight into their significant influence on the global response of wood-frame
buildings. However, simplified approaches, such as those noted by Pang and Rosowsky
(2010) and Cattari et al. (2014), often struggle to replicate these interactions accurately,
leading to potential discrepancies in predicting the overall structural performance.
c) Mesh Dependency and Scalability: FEM models are sensitive to mesh quality, with finer
meshes needed to capture localized stress concentrations and deformations. This increases
computational cost and can lead to numerical instability in dynamic simulations of large
systems (Pei et al., 2013).
d) Boundary and Interaction Assumptions: Assumptions regarding diaphragm rigidity,
base fixity, and interaction between wall panels and diaphragms often simplify the model
but reduce accuracy. These assumptions are particularly limiting for light wood frame
structures, where semi-rigid behavior significantly affects global performance (van de
Lindt et al., 2010).
e) Practical Limitations in Routine Design: The complexity and computational demands of
FEM make it impractical for routine engineering design. Practitioners often favor
simplified methods, as FEM requires significant expertise in defining material models,
interaction effects, and boundary conditions (Filiatrault & Folz, 2002).
2.3.8 Global Level Modeling of Light Wood Frame Building
Numerical modeling plays a vital role in understanding the dynamic behavior of light wood-frame
buildings and shear walls under seismic loads. These models provide insights into deformation
mechanisms, energy dissipation, and failure patterns, enabling better design and retrofit strategies.
Early numerical models for wood-frame buildings relied on finite element methods (FEM) to
represent the nonlinear response of wood-frame structures. These methods used detailed
21

representations of studs, sheathing panels, and connections through beam elements, plane-stress
elements, and nonlinear springs, respectively (Estrella et al., 2020). Despite their accuracy, such
models were computationally expensive, limiting their applicability in routine design.
Simplified models such as SAWS (Seismic Analysis of Light wood frame Structures) emerged to
address these limitations. This lumped-mass model assumes rigid diaphragms and uses tenparameter hysteretic models for shear walls, balancing computational efficiency and accuracy. It
has been widely used for low-rise wood-frame buildings (Pei & Van De Lindt, 2009).
Similarly, the CASHEW (Cyclic Analysis of Shear Walls) model introduced an effective means
of simulating the nonlinear force-displacement behavior of wood-frame shear walls using
simplified spring elements. The subsequent M-CASHEW model expanded on this by adding
capabilities to account for cyclic degradation and computational optimization, making it a widely
applicable tool for both research and practical design scenarios.
2.3.8.1 MSTEW Model Parameters and Their Effectiveness in Timber3D
The Modified Stewart Hysteretic Model (MSTEW) represents a critical advancement in simulating
the nonlinear cyclic behavior of light wood-frame shear walls and diaphragms under seismic
loading. Evolving from the foundational work of Stewart (1987), which introduced a hysteretic
model for degrading and pinched structures, MSTEW incorporates additional parameters to
address the unique mechanical behaviors observed in timber structures, including stiffness
degradation, strength degradation, and energy dissipation. Over time, this model has been refined
and integrated into structural analysis platforms, such as Timber3D, to accurately simulate the
performance of light wood-frame buildings during seismic events.
The MSTEW model’s development is rooted in early work on cyclic hysteretic behavior,
specifically targeting wood-frame structures. Stewart (1987) laid the groundwork by formulating
22

a model capable of capturing pinching effects and nonlinear responses in general structural
systems. Building on this, (Folz & Filiatrault, 2001) extended these concepts to light wood-frame
shear walls, introducing hysteretic parameters that accounted for cyclic degradation and load
reversals.
Subsequent studies, such as those by (Pang et al., 2007), incorporated evolutionary parameters into
hysteretic models, enhancing their applicability to timber shear walls subjected to seismic loading.
The MSTEW model emerged as a further refinement, explicitly tailored to simulate the unique
mechanical characteristics of wood-frame structures, such as nail slip, rocking mechanisms, and
panel interactions. This evolution culminated in its integration into computational tools like
Timber3D, which facilitated its use in large-scale analyses, including projects like NEESWood,
that investigated seismic resilience in wood-frame buildings (Pang & Rosowsky, 2010).
Key Characteristics of MSTEW Model
a) Backbone Curve:

Figure 2. Backbone curves of MSTEW model (Pan et al., 2018)

23

The backbone curve as shown in the Figure 2, is central to the MSTEW model, defining the
primary load-deformation behavior of shear walls. It includes elastic, post-elastic, and ultimate
strength regions, ensuring the representation of nonlinear behaviors, including stiffness
degradation at higher displacements (Ventura et al., 2021). This curve is calibrated using
experimental data from shear wall tests to ensure accuracy in predictions.
b) Cyclic Degradation:
MSTEW introduces parameters to simulate cyclic degradation, accounting for the reduction in
stiffness and strength during repeated loading cycles. These parameters are particularly relevant
for wood-frame buildings, which exhibit significant hysteretic energy dissipation under seismic
forces (Estrella et al., 2020).
c) Pinching Effect:
Pinching in the force-displacement hysteresis loop, caused by the slipping of nails and connectors,
is explicitly modeled in MSTEW. This feature is critical for capturing the realistic dynamic
response of shear walls, particularly under long-duration ground motions (Pan et al., 2018).
d) Energy Dissipation:
Energy dissipation is a key parameter that measures the cumulative energy absorbed by the shear
walls during seismic events. MSTEW effectively models this parameter, providing insights into
the structure’s ability to resist collapse under severe cyclic loading (Ventura et al., 2021) .
Parameters of the MSTEW Model:
The Modified Stewart Hysteresis Model (MSTEW) incorporates a comprehensive set of
parameters that enable it to simulate the nonlinear and cyclic behaviors of light wood-frame shear
walls and diaphragms under seismic loading with precision. These parameters are designed to

24

represent critical aspects of material and connection behavior, including stiffness degradation,
energy dissipation, and pinching effects, which are common in light wood-frame construction.
Key Parameters of the MSTEW Model
a) Initial Stiffness, 𝐾0
Represents the stiffness of the spring at the beginning of loading.
b) Reloading Stiffness, 𝐾𝑝
Governs stiffness during reloading phases after unloading.
c) Maximum Backbone Force, 𝐹𝑢
Peak force on the backbone curve.
d) Force Intercept of Backbone, 𝐹0
y-Intercept of the initial linear stiffness line on the backbone.
e) Displacement at 𝐹𝑢
Displacement where the maximum backbone force 𝐹𝑢 is reached.
f) Pinching Parameters – 𝑟1, 𝑟2 , 𝑟3 and 𝑟4
Control the degree of pinching in the hysteresis loop and the shapes of unloading/reloading paths:
o 𝑟1: Pinching during unloading.
o 𝑟2 : Pinching during reloading.
o 𝑟3 : Controls backbone curve stiffness changes.
o 𝑟4 : Adjusts post-yield stiffness.
g) Strength Degradation Factor, α
Controls how the strength reduces after repeated cyclic loading.
h) Stiffness Degradation Factor, β
Governs the reduction in stiffness with increasing cyclic deformation.
25

2.3.8.2 Out-of-plane Stiffness of Light Wood Frame Buildings
The out-of-plane stiffness of light-frame buildings, particularly shear walls, is a critical aspect of
their structural behavior, especially in seismic zones. While in-plane stiffness determines the shear
wall’s ability to resist lateral loads, out-of-plane stiffness is essential for ensuring the overall
stability and load transfer mechanisms of the building. This is particularly relevant in light-frame
wood buildings, which are characterized by their relatively low stiffness compared to other
construction systems like reinforced concrete or steel (Véliz et al., 2023).
Out-of-plane stiffness contributes significantly to the holistic performance of a building under
seismic loads. It influences load redistribution between structural and non-structural components
and ensures that diaphragms and shear walls interact effectively to resist complex loading
scenarios. Neglecting or inaccurately representing this parameter can lead to underestimated
deformations and unsafe design outcomes. The bending stiffness component, which governs outof-plane deformation, can be represented mathematically as (Véliz et al., 2024):
𝐾bending =

2𝐻 3
3𝐸𝐴ext 𝐿2

Here:
𝐾bending : Bending stiffness, representing the wall’s resistance to out-of-plane deformation.
H : Height of the shear wall.
E : Elastic modulus of the material (e.g., sheathing or framing components).
𝐴ext : Effective cross-sectional area of the shear wall in the bending plane.
L : Span length of the wall.

26

This equation, derived from the principles of mechanics of materials, captures the flexural rigidity
of the wall system under out-of-plane loads. The height ( H ) and span length ( L ) are critical
geometric parameters that define the wall’s susceptibility to bending deformations, while the
elastic modulus ( E ) and cross-sectional area ( 𝐴ext ) account for the material and geometric
properties that influence stiffness.
2.3.9 Mass Distribution in Numerical Modeling
The distribution of mass within light-frame timber diaphragm systems plays a crucial role in
accurately modeling their dynamic behavior under seismic loads. In numerical modeling, mass is
often assigned using a lumped mass approach to simplify the analysis while maintaining fidelity
to the structural behavior. This method involves distributing seismic weights to critical points,
such as diaphragm nodes or shear wall connections, to represent the inertia forces during seismic
events (Pang & Rosowsky, 2010).
Typically, master nodes are introduced at key diaphragm locations, with masses distributed
proportionally based on the structural and non-structural components. These master nodes are
connected to slave nodes through rigid elements, ensuring that the mass is transferred and engaged
in the overall system response. The seismic weights are calculated based on the total structural and
applied loads, accounting for variations across different building components and construction
phases (Folz & Filiatrault, 2001).
The diaphragm’s mass distribution affects how loads are transferred between diaphragms and
shear walls, influencing the interaction between in-plane and out-of-plane forces. An effective

27

mass distribution model must consider both horizontal and vertical load paths, ensuring that the
simulated seismic response closely matches real-world behavior (Véliz et al., 2024).

2.4 Incremental Dynamic Analysis
Incremental Dynamic Analysis (IDA) is a crucial methodology in seismic performance
assessment, providing a systematic framework to evaluate structural response under increasing
levels of ground motion intensity. In this study, IDA plays a key role in determining collapse
intensity, which is essential for calibrating the β parameter in the Park and Ang Damage Index
(DI) framework for light wood-frame buildings. The collapse intensity defines the seismic demand
level at which the structure reaches its ultimate limit state, allowing for a more accurate globallevel damage assessment.
By incrementally scaling a suite of ground motion records and performing nonlinear dynamic
analyses, IDA provides a comprehensive understanding of structural behavior under extreme
loading conditions. This methodology enables the identification of critical intensity measures, such
as peak ground acceleration (PGA) and spectral acceleration (Sa(T)), that correspond to key
performance thresholds, including yielding, peak strength, and collapse. Given the unique
characteristics of light wood-frame structures—such as load redistribution, nonlinear energy
dissipation, and complex failure mechanisms—IDA serves as an indispensable tool for
establishing realistic collapse criteria.
Incremental Dynamic Analysis (IDA) is a performance-based seismic assessment method that
involves subjecting a structural model to a series of ground motion records, incrementally scaled

28

to increasing intensity levels. This procedure provides a detailed picture of how structures
transition from elastic to inelastic behavior and ultimately to collapse.
The IDA methodology was pioneered by Vamvatsikos and Cornell (2002) in their seminal work
on performance-based earthquake engineering. It has since been widely adopted for seismic
vulnerability assessment, particularly in conjunction with FEMA guidelines for evaluating
structural collapse capacity (FEMA P695, 2009). IDA produces a set of response curves, known
as IDA curves, which depict the relationship between ground motion intensity and structural
response parameters such as maximum inter-story drift, base shear, or roof displacement.
2.4.1 FEMA Guidelines for Conducting IDA
The Federal Emergency Management Agency (FEMA) has played a pivotal role in shaping the
methodological framework for seismic performance assessment through its detailed
publications—FEMA P695 (2009) and FEMA P58 (2012). These documents outline rigorous
procedures for conducting Incremental Dynamic Analysis (IDA), a core technique used in
performance-based earthquake engineering (PBEE). IDA facilitates a nuanced understanding of
how structures behave under progressively increasing seismic intensities, culminating in the
identification of their collapse capacities.
The strength of the FEMA guidelines lies in their ability to standardize the IDA process, ensuring
consistency, comparability, and reliability across various studies and engineering applications. By
following these protocols, researchers and engineers can systematically quantify structural
vulnerabilities and calibrate damage metrics using a scientifically grounded approach.

29

The key steps in the IDA process, as outlined in the FEMA P695 and P58 documents, are
elaborated below:
2.4.1.1 Selection of Ground Motion Records
The first and foundational step in IDA is the careful selection of earthquake ground motion records
that are representative of the seismic hazard at the target site. This involves curating a suite of
ground motions that spans a broad spectrum of earthquake characteristics, including:
•

Magnitude range

•

Source-to-site distances

•

Fault types (e.g., strike-slip, reverse, normal)

•

Site soil conditions and spectral content

These records should be chosen based on probabilistic seismic hazard analysis (PSHA) results and
in accordance with criteria recommended by FEMA and the Pacific Earthquake Engineering
Research (PEER) Center. The goal is to ensure statistical representativeness, spectral
compatibility, and hazard consistency, which are critical for achieving robust and generalizable
IDA outcomes.
2.4.1.2 Scaling of Ground Motions
Once selected, each ground motion is incrementally scaled to various intensity levels—typically
using spectral acceleration (Sa) at a specific period or peak ground acceleration (PGA) as the
intensity measure (IM). This scaling allows for the exploration of the structure’s behavior across
a wide range of seismic demands.

30

Through this process, analysts can trace the transition from elastic to nonlinear and inelastic
responses, ultimately reaching the point of global or local collapse. The progressive scaling is
crucial for constructing IDA curves that plot the chosen IM against an Engineering Demand
Parameter (EDP) such as inter-story drift ratio or roof displacement, offering a visual
representation of performance degradation.
2.4.1.3 Nonlinear Dynamic Analysis
The core of IDA lies in performing nonlinear time-history analyses (NLTHA) on a detailed
structural model subjected to each scaled ground motion. These models, often built using finite
element methods (FEM) or equivalent simulation techniques, must capture a comprehensive range
of response behaviors, including:
•

Material and geometric nonlinearities

•

Stiffness and strength degradation

•

Energy dissipation through hysteresis

•

Damage propagation and failure mechanisms

This analytical phase produces rich datasets from which IDA curves are generated. The shape and
critical points of these curves—especially the collapse point—provide direct insight into the
structure’s seismic resilience, damage tolerance, and fragility. Moreover, these outputs serve as
essential inputs for collapse fragility curves and for validating damage indices used in
performance-based design.

31

3 Shaking Table Tests Used for Damage Observation
and Model Validation
3.1 Background of the Project
Light wood frame structures have long been a staple of residential construction, particularly in
regions of moderate to high seismicity. Historically, these structures have demonstrated
commendable life safety performance during earthquakes. However, significant structural and
non-structural damage has often been observed, even in low-rise configurations, highlighting
vulnerabilities in their seismic behavior. The height of light wood frame buildings has traditionally
been limited to four to six stories due to several factors, including:
a) Dynamic Response Uncertainties: A limited understanding of the seismic response of
mid-rise light wood frame structures has posed challenges to their adoption in active
seismic zones.
b) Non-Structural Limitations: Issues such as fire safety requirements and damage to nonstructural finishes have restricted the widespread use of taller light wood frame
construction.
c) Lack of Global Seismic Design Philosophy: Existing building codes for engineered wood
construction are component-based, focusing on individual elements rather than adopting a
global approach that considers the interactions between structural components.
These factors, compounded by the lack of clarity in load paths during earthquake shaking, have
constrained the use of wood to low-rise buildings. This limitation has reduced the competitiveness
of the wood construction industry relative to steel and concrete alternatives, particularly in the U.S.
and international markets.
32

Recognizing these challenges, the NEESWood Project was conceived as part of the National
Science Foundation’s George E. Brown Jr. Network for Earthquake Engineering Simulation
(NEES). The project’s mission is to advance the seismic design of light wood frame structures,
enabling their use in mid-rise buildings while addressing vulnerabilities in low-rise configurations.
This study builds upon previously conducted research by incorporating benchmark data from the
NEESWood two-story light wood frame shake table test. While the experiment itself was not part
of this study, its data played a key role in validating the numerical analyses and shaping the
methodology developed herein.

3.2 Test Building Architecture
The test structure utilized in the NEESWood benchmark testing is a two-story townhouse,
representing one unit of a three-unit townhouse configuration, as illustrated in Figure 3 and Figure
5. This design provides approximately 1800 square feet of living space with an attached two-car
garage. The structure is modeled as a “production house,” reflecting typical construction practices
of the 1980s and 1990s in Northern or Southern California.
The townhouse follows engineered construction principles compliant with the seismic provisions
of the 1988 Uniform Building Code. The overall height of the building, from the first-floor slab to
the roof eaves, is 18 feet, and its total weight is approximately 40 tons (80 kips). These architectural
details make the structure a representative sample for assessing light wood frame behavior under
seismic loads.
The exterior walls of the structure consist of a layered system, including:
a) Exterior finish: 7/8-inch stucco.
b) Sheathing: 7/16-inch oriented strand board (OSB).
c) Interior finish: 1/2-inch gypsum wallboard.
33

(a)

(b)
Figure 3 Elevation view of the NEESWood two-story residential project building (Christovasilis
et al., n.d., 2009)
The structural framing of the shear walls employs 2x4 dimensional lumber, except for the first
level of the garage, which uses 2x6 lumber. The framing includes double members for the top
plates and end studs, while the sole plate and interior studs are single members. Stud spacing is
maintained at 16 inches on-center. Conventional corner hold-downs are used to mitigate
overturning and ensure the racking mode of deformation during seismic events.
34

Figure 4 Floor plan layour of the NEESWood project building (Christovasilis et al., n.d., 2009)
The floor plan includes functional spaces such as living, dining, and bedroom areas as shown in
the Figure 4, demonstrating typical residential configurations.

Figure 5 Isometric view of the project building

35

3.3 Shake Table Setup
The experimental test setup for the NEESWood benchmark structure was carried out at the
Structural Engineering and Earthquake Simulation Laboratory (SEESL) at the University at
Buffalo. Utilizing two tri-axial shake tables, the testing accommodated the full-scale two-story
townhouse to simulate dynamic earthquake loading. Each shake table, weighing approximately 50
tons, was extended with 7 m x 7 m steel frames and connected through a rigid steel link structure
to support the building’s weight while minimizing vertical deflection as depicted in the Figure 6.
This setup ensured the accurate simulation of seismic responses over a continuous platform.
The foundation of the test building was constructed with threaded A-307 steel rods that were bolted
to the existing hole patterns in the extension frame. Anchor bolts were placed at critical locations,
reinforced with 2-1/4 in. x 2-1/4 in. x 1/4 in. steel plate washers. At hold-down device locations,
5/8 in. diameter rods were employed, while 1/2 in. diameter rods were used elsewhere. A 2-1/4 in.
layer of grout was installed beneath pressure-treated sill plates to emulate a true concrete
foundation. The friction between the sill plate and the grout was intended to represent realistic
base resistance conditions.

(a)

(b)

Figure 6 (a) Extension frame of shake tables connected by steel link structure, and (b) Foundation
of Test Building under Construction building (Christovasilis et al., n.d., 2009)

36

This experimental setup was designed to evaluate the dynamic response of the full-scale
townhouse structure under seismic loading conditions. The setup also served as a benchmark for
calibrating numerical models and for understanding load path behavior and structural interactions
during earthquake events

3.4 Test Phases
The NEESWood benchmark testing program consisted of five distinct test phases, each
representing a specific construction configuration of the two-story light wood frame townhouse.
These phases were designed to systematically evaluate the dynamic behavior of the structure as
various construction components and supplemental systems were incorporated. Table 1 provides
a summary of these phases:
Phase 1: Wood Structural Elements Only
This phase included only the wood structural elements without any additional sheathing or
supplemental damping systems. The focus was on establishing a baseline understanding of the
bare structural response of the light wood frame system under seismic loading conditions.
Phase 2: Incorporation of Passive Fluid Dampers
Phase 2 involved the addition of passive fluid dampers integrated into selected wood shear walls.
This configuration was tested to assess the influence of supplemental damping systems on energy
dissipation and overall seismic performance.
Phase 3: Addition of Gypsum Wallboard (Load-Bearing Walls Only)
In this phase, the structure from Phase 1 was supplemented with 1/2-inch thick gypsum wallboard
fastened to the structural (load-bearing) walls using #6-1-1/4 inch long screws at 16 inches oncenter (O.C.). The testing aimed to determine the contribution of interior finishes to the stiffness
and damping characteristics of the structure.
37

Phase 4: Gypsum Wallboard on All Walls and Ceilings
Building on Phase 3, this phase involved the installation of 1/2-inch thick gypsum wallboard on
all walls (16 inches O.C.) and ceilings (12 inches O.C.). This configuration was tested to further
evaluate the role of extensive interior sheathing in modifying the dynamic behavior of the
structure.
Table 1 Summary of test phases and building configurations
Test Phase Test Building Configuration
Phase 1

Wood structural elements only

Phase 2

Test Phase 1 structure with passive fluid dampers incorporated into
selected wood shear walls

Phase 3

Test Phase 1 structure with 1/2 in. thick gypsum wallboard installed
with #6-1-1/4 in. long screws @ 16 in. O.C. on structural (loadbearing) walls

Phase 4

Test Phase 3 structure with 1/2 in. thick gypsum wallboard installed
with #6-1-1/4 in. long screws on all walls (16 in. O.C.) and ceilings
(12 in. O.C.)

Phase 5

Test Phase 4 structure with 7/8 in. thick stucco installed with 16-gauge
steel wire mesh and 1-1/2 in. long leg staples @ 6 in. O.C. on all
exterior walls

Phase 5: Full Building Configuration with Stucco Exterior
The final phase represented the complete construction of the building with all inclusive
components. The structure included 7/8-inch thick stucco on the exterior walls, reinforced with
38

16-gauge steel wire mesh and 1-1/2 inch long leg staples at 6 inches O.C. This phase also retained
the gypsum wallboard configuration from Phase 4. Phase 5 provided the most realistic
representation of the building’s full-scale performance under seismic loading, capturing the
combined effects of structural, non-structural, and exterior finishes.
In this study, Phase 5 is the primary focus as it reflects the complete configuration of the test
building, incorporating all structural and non-structural elementsGround Motions
In the experimental phase of the NEESWood project, a comprehensive suite of ground motion
records was employed to evaluate the seismic performance of a two-story light-frame wood
structure under progressively increasing levels of earthquake excitation. This test series was
conducted at the University at Buffalo, and the building was constructed in phases to allow for
sequential assessment of structural performance with and without various architectural finishes
and retrofits. Notably, only data from Phases 3, 4, and 5 were considered for this study, as the
structure was not fully completed during Phases 1 and 2, rendering those early datasets unsuitable
for reliable damage assessment and dynamic response analysis.
3.4.1 Ground Motion Selection
The seismic excitations used in these tests were derived from two real historical earthquake
records, both originating from the 1994 Northridge Earthquake in California:
•

Canoga Park (CP): Representing ordinary ground motion, recorded approximately 15.8
km from the fault rupture (Topanga Canyon, USC Station 90053). This record served as a
primary input for mid-to-moderate seismic intensities. It includes three orthogonal
components (east-west, north-south, and vertical), although only the horizontal
components were considered in this study, in accordance with the modeling and validation
strategies adopted in Chapter 4.
39

•

Rinaldi (RN): Representing near-fault motion, recorded just 7.1 km from the fault rupture
(Rinaldi Receiving Station, DWP Station 77). This record embodies a more intense shaking
profile, characteristic of maximum credible earthquake (MCE) scenarios, typically
associated with a 2% probability of exceedance in 50 years (return period of 2475 years).

3.4.2 Ground Motion Scaling
The Canoga Park records were systematically scaled using amplitude-scaling factors ranging from
0.12 to 1.20, simulating a wide range of seismic intensities—from minor shaking to design-basis
earthquake (DBE) levels and beyond. Specifically, a scaling factor of 1.20 was adopted to simulate
DBE-level shaking (equivalent to a 10% probability of exceedance in 50 years, or a 475-year return
period). The progression of ground motion intensities allowed for the observation of the structure’s
transition from elastic to nonlinear behavior, and ultimately towards localized and global damage
accumulation.
The Rinaldi record was scaled to a factor of 1.0, corresponding to MCE-level ground motion, with
Peak Ground Accelerations (PGAs) substantially higher than those observed in Canoga Park cases.
This provided the necessary stimulus to evaluate performance under severe seismic demands,
thereby offering a basis for benchmarking collapse-level or near-collapse structural behavior.
The Table 2 below provides a detailed breakdown of the applied ground motions, including the
test ID, ground motion source, scaling factors, and corresponding PGAs in both the X and Y
directions. These ground motions, in conjunction with detailed instrumentation (including
accelerometers and string potentiometers), enabled the research team to evaluate component-level,
story-wise, and global-level damage indices under a range of seismic demands. The rigorous
application of these records also conforms with FEMA guidelines for IDA (Incremental Dynamic

40

Analysis), making the study's findings robust and generalizable across a wide spectrum of woodframe seismic performance assessments.
Table 2 Ground Motion Information for NEESWood Benchmark Tests
Test ID Ground Motion X (scale factor) PGA (g) X Direction Y (scale factor) PGA (g) Y Direction
P3S1 Canoga Park
P3S2 Canoga Park
P3S3 Canoga Park
P3S4 Canoga Park
P4S1 Canoga Park
P4S2 Canoga Park
P4S3 Canoga Park
P4S4 Canoga Park
P5S1 Canoga Park
P5S2 Canoga Park
P5S3 Canoga Park
P5S4 Canoga Park
P5S5 Canoga Park
P5S6 Canoga Park
P5S7 Canoga Park
P5S8 Canoga Park
P5S11 Rinaldi

0.12
0.12
0.53
0.53
0.12
0.12
0.53
0.53
0.12
0.12
0.53
0.53
0.86
0.86
1.20
1.20
1.00

0.04
0.04
0.19
0.19
0.04
0.04
0.19
0.19
0.04
0.04
0.19
0.19
0.31
0.31
0.43
0.43
0.47

0.12
0.12
0.53
0.53
0.12
0.12
0.53
0.53
0.12
0.12
0.53
0.53
0.86
0.86
1.20
1.20
0.00

0.05
0.05
0.22
0.22
0.05
0.05
0.22
0.22
0.05
0.05
0.22
0.22
0.36
0.36
0.50
0.50
0.00

3.4.3 Description of Test Phase 5 Protocol
Test Phase 5 was the culminating stage of the NEESWood benchmark testing and aimed to
comprehensively evaluate the seismic performance of the fully finished test structure, inclusive of
all structural and non-structural components. This phase incorporated the application of exterior
stucco wall finishes to simulate construction practices typical of California homes built in the
1980s or 1990s. The stucco application included multiple steps: the installation of a vaporpermeable, water-resistant tar paper, followed by a 16-gauge steel wire mesh attached to the
exterior walls using staples spaced 6 inches on center. The plastering process consisted of three
41

coats: two base coats of 3/8-inch thickness each and a final finishing coat of 1/8 inch. Figure 7
shows the finished benchmark structure before initiation of phase 05.

Figure 7 South-east external view of the benchmark structure after the installation of the exterior
stucco finish (Christovasilis et al., n.d., 2009)
Unique to Phase 5, the tri-axial motion represented Seismic Test Level 5, the most severe condition
within the experimental protocol, simulating the maximum credible earthquake scenario. To
enhance realism and illustrate potential non-structural vulnerabilities, the structure was fully
furnished as though occupied by a family of four. Anchored non-structural components, including
furniture and appliances, were installed in accordance with established standards. For example,
one heater in the garage was anchored to the wall, while the other remained unanchored. These
configurations were designed to evaluate the performance of non-structural elements under seismic
excitation.
42

3.5 Instrumentation of Shake Table Tests
Instrumentation is a critical component of experimental studies, providing precise data to evaluate
structural responses under dynamic loading. The project building for the NEESWood shake table
tests incorporated an array of sensors designed to capture comprehensive measurements, including
acceleration, displacement, and force data.
More than 70 accelerometers were installed to monitor the dynamic behavior of the structure.
These accelerometers captured data in two horizontal directions (east-west and north-south) and
the vertical direction.
To capture absolute and relative displacements, 21 linear string potentiometers were deployed.
Their specific uses included:
a) Monitoring absolute displacements between the shake tables and the test structure
relative to a stationary reference system.
b) Measuring racking deformations of shear walls through diagonally oriented
potentiometers.
c) Capturing inter-story drifts by measuring floor diaphragm displacements.
Force sensors included more than 50 load cells installed to measure tensile axial forces in key
structural elements, such as:
a) Shear transfer anchor bolts.
b) Hold-down anchor bolts of first-floor shear walls.

3.6 Observed Damage in Phase 5 Testing
During Phase 5 of the NEESWood benchmark shake table test, the building was subjected to highintensity seismic loading, resulting in a range of structural and non-structural damage. Notable
forms of damage included cracking, spalling, material separation, and deformation, predominantly
43

in highly stressed regions such as wall bases, corners, and connection interfaces. The observations
provide valuable insight into the vulnerability of exterior finishes, sill plates, anchorage zones, and
gypsum wallboards under strong lateral and vertical seismic demands.
Cracking and significant spalling of the exterior stucco were observed at the base of the garage
wall. This damage likely resulted from concentrated stresses near the foundation during seismic
excitation, leading to the detachment of the stucco layer and exposing the underlying surface.

Figure 8 Cracking and Spalling of Stucco at the Bottom of Garage Wall (Christovasilis et al., n.d.,
2009)
Severe cracking appeared at the corner of the garage wall opening, accompanied by spalling. The
damage concentrated at the structural stress points around the corners, where the forces were
amplified due to openings in the wall.

44

Figure 9 Cracking and Spalling of Stucco at the Corner of Garage Wall Opening (Christovasilis et
al., n.d., 2009)
The sill plate at the narrow pier of the garage wall exhibited cracking and separation along its
entire length. This resulted from the high inter-story drifts experienced during seismic loading.
The observed damage demonstrates the vulnerability of sill plates at narrow wall segments.

Figure 10 Cracking and separation of sill plate through entire length of garage narrow wall piers
(Christovasilis et al., n.d., 2009)

45

Vertical cracking occurred at the stud immediately above the hold-down anchor. The damage
indicates the transfer of seismic forces through the anchoring system, creating tensile stresses in
the wood stud that exceeded its capacity.

Figure 11 Cracking of stud above hold-down anchor (Christovasilis et al., n.d., 2009)
Large sections of the gypsum wallboard were separated from the ceiling, indicating significant
deformation and failure in the ceiling connections. This damage highlights the challenges in
maintaining ceiling integrity under tri-axial seismic loads.

Figure 12 Separation of Gypsum Wallboard from Ceiling (Christovasilis et al., n.d., 2009)
46

Horizontal cracking was evident along the second-floor level, reflecting the influence of interstory drift. The cracks followed the drywall seams and were exacerbated by the lateral deformation
of the building.

Figure 13 Horizontal Cracking of Gypsum Wallboard (Christovasilis et al., n.d., 2009)
The gypsum wallboard near the door opening exhibited significant cracking and buckling. The
structural discontinuity around the opening led to localized stress concentrations, causing the
wallboard to deform and fail.

Figure 14 Cracking and Buckling of Gypsum Wallboard at Door Opening (Christovasilis et al.,
n.d., 2009). Table below summarises the damage observed and shown above:
47

A detailed summary of the damage types and their locations is presented in Table 3.
Table 3 Summary of Observed Damage in Phase 5
Damage Location

Description of Damage

Base of garage wall

Cracking and spalling of exterior stucco

Corner of garage wall opening

Cracking and stucco detachment

Sill plate at narrow wall pier

Full-length cracking and separation

Stud above hold-down anchor

Vertical splitting of the stud

Ceiling (gypsum wallboard)

Separation of gypsum wallboard from ceiling

Second-floor drywall seam

Horizontal cracking along gypsum wallboard seams

Door opening area

Cracking and buckling of gypsum wallboard

48

4 Numerical Model Development
4.1 Overview of Timber3D and Nonlinear Modeling
Timber3D is a specialized numerical modeling framework tailored for the analysis of light wood
frame buildings subjected to lateral loads, such as seismic events. Developed within the MATLAB
environment, Timber3D integrates nonlinear hysteretic material models and advanced
computational techniques to capture the complex behavior of light wood structures at various
scales, from connection details to full building systems.
The framework consists of three interconnected modules:
a) Connection-Level Analysis: Focused on deriving nonlinear hysteresis properties
of fasteners and connections, such as nails, screws, and hold-downs.
b) Assembly-Level Analysis: Designed for simulating the nonlinear behavior of shear
walls and diaphragms under cyclic loads.
c) Building-Level Analysis: Extends the assembly-level simulation to entire
structures, incorporating interactions between diaphragms, walls, and load paths.
This modularity allows for a comprehensive understanding of the behavior of wood frame
structures, offering capabilities for both static pushover and dynamic nonlinear time history
analyses. By representing physical systems using frame and frame-to-frame link elements (F2F),
Timber3D enables accurate predictions of structural performance while accounting for localized
deformations and energy dissipation mechanisms.

49

4.2 Modeling Approach
4.2.1 Structural Representation
The Timber3D numerical model utilizes a hybrid approach, combining frame elements for primary
load-bearing members and frame-to-frame link elements (F2F) to capture nonlinear interactions at
interfaces:
Frame Elements: Represent components such as studs, beams, and columns, modeled as
deformable members connected at master nodes.
Frame-to-Frame Links (F2F): Represent sheathing-to-framing connections and are designed
with six degrees of freedom, capturing nonlinear hysteretic behavior for load path interactions.
4.2.2 Master-Slave Nodal System
To optimize computational efficiency, Timber3D employs a master-slave node system:
Master Nodes: Represent key structural points, such as diaphragm centroids and load transfer
joints, ensuring accurate global load distribution.
Slave Nodes: Condensed into master nodes via a nodal condensation technique, reducing
computational complexity while maintaining localized response accuracy.
4.2.3 Diaphragm and Shear Wall Modeling
Diaphragms: Modeled using rigid beam elements at the base, first floor, and second floor to define
their geometry. The diaphragms are assigned predefined stiffness values to replicate semi-rigid
behavior and load transfer mechanisms between shear walls and floors.
Shear Walls: Modeled as nonlinear springs calibrated from experimental hysteresis data,
incorporating hold-down effects, energy dissipation, and uplift responses.

50

4.2.4 Dynamic Analysis
Timber3D supports nonlinear dynamic analyses using ground motion records to simulate realworld earthquake scenarios. Time history analyses are conducted using numerical integration
method to evaluate global structural responses, such as:
o Roof displacement profiles.
o Hysteretic energy dissipation.
o Base shear forces and moment distributions.
4.2.5 Validation
The Timber3D framework has been validated against experimental benchmarks, including shake
table tests and static cyclic analyses. These validations demonstrate close agreement between
numerical predictions and experimental results for hysteretic energy dissipation, displacement
responses, and global structural behavior.
Through its modular design and robust modeling capabilities, Timber3D provides a powerful tool
for understanding and optimizing the performance of light wood frame buildings under seismic
and lateral loads.
4.2.6 Spring Parameters
4.2.6.1 In-Plane Shear Spring Parameters
In this study for developing the numerical model of the NEESWood two story light wood frame
building, in-plane shear springs are used to represent the load-deformation behavior of the shear
walls along the wall lines in a light-frame wood building. The springs are designed to replicate the
aggregate stiffness and strength characteristics of each shear wall and are calibrated based on
experimental and numerical studies.

51

(a)

(b)
Figure 15 Shear wall plan for the NEESWood two story light wood frame building (a) First Floor
(b) Second Floor

52

Figure 15 illustrates the shear wall plan of the NEESWood two-story light-frame building,
showcasing the layout of the shear walls on both the first and second floors. The figure provides
detailed wall IDs, such as E1, E2, E3, and others, which correspond to specific shear walls within
the structure. These wall IDs are used for referencing the structural springs in the building for
modeling and analysis purposes.
The parameters for the shear walls for the NEESWood two-story building were obtained from the
study by (Pang & Rosowsky, 2010). The tables below (Table 4, Table 5, Table 6 and Table 7)
outline the key hysteretic parameters for walls across both stories of the structure in the
longitudinal and transverse directions. These include essential attributes such as initial stiffness
(K₀), force intercepts (F₀, Fᵢ), deformation parameters (Δ, r₁, r₂, r₃, r₄), and maximum forces (Fᵤ).
Each of these parameters plays a critical role in capturing the dynamic behavior of the walls under
seismic loading.
The parameter values were derived using the MSTEW model, a specialized shear wall analysis
tool developed to predict non-linear force-displacement responses for timber shear walls. MSTEW
accounts for various factors, including nail slip behavior, shear panel deformation, and anchorage
effects.

53

Table 4 First story in plane shear spring parameters in x direction
Wall ID

Ko

r1

r2

r3

r4

F0 (kN)

Fi (kN)

Δ (mm)

α

β

(kN/mm)
E1

2.57

0.04

-0.06

1.01

0.06

18.14

2

57.3

1

1.2

E2

2.59

0.05

-0.05

1.01

0.06

16.75

1.63

54.9

0.9

1.2

E35

2.88

0.04

-0.04

1.01

0.06

23.74

2.58

57.1

1

1.2

E4

2.55

0.04

-0.05

1.01

0.05

22.51

1.88

72.6

1

1.2

E5

1.81

0.05

-0.06

1.01

0.08

15.76

1.54

64.3

1

1.2

E9

2.66

0.04

-0.06

1.01

0.05

28.13

2.29

70.5

1

1.2

E10

2.42

0.03

-0.07

1.01

0.07

29.26

2.38

64.4

1

1.5

E12

0.78

0

-0.08

0.82

0.13

21.39

1.78

102.4

1

1.2

E37

0.83

0.02

-0.03

0.74

0.04

4.44

0.09

42.9

1

1.2

E36

4.04

0.03

-0.04

1.01

0.05

37.01

3.34

64.7

1

1.2

Fi (kN)

Δ

Table 5 Second story in plane shear spring parameters in x direction
Wall ID

Ko

r1

r2

r3

r4

F0 (kN)

(kN/mm)

α

β

(mm)

E17

2.73

0.026 -0.098

1.01

0.051 29.31

3.5

82.5

0.99

1.37

E18

1.83

0.017 -0.04

1.01

0.049 19.37

1.2

66.3

0.99

1.26

E19

3.68

0

-0.059

1.01

0.04

42.46

2.13

42.8

0.99

1.25

E20

3.71

0

-0.059

1.01

0.057 42.9

3.93

42.8

0.95

1.15

E24

2.22

0.035 -0.079

1.01

0.075 23.66

2.45

51.2

0.99

1.2

E25

1

0.027 -0.03

1.01

0.045 13.16

1.42

95.1

0.95

1.15

E33

1.4

0.081 -0.038

1.01

0.08

1.33

37.3

0.95

1.15

E31

0.61

0.039 -0.046

1.01

0.024 3.1

0.27

35.3

1

1.29

E30

2.84

0

-0.047

1.01

0.055 34.23

3.19

53.7

0.8

1.2

E22

0.6

0.02

-0.034

1.01

0.03

0.35

41.8

0.99

1.24

11.07

2.81

54

Table 6 First story in plane shear spring parameters in y direction
Wall
ID

Ko
r1
(kN/mm)

r2

r3

r4

F0
(kN)

Fi (kN)

Δ
(mm)

α

β

E6
E8
E11
E13
E16
I1
I27

1.07
2.6
1.85
2.18
1.36
2.26
1.96

-0.055
-0.041
-0.027
-0.05
-0.063
-0.005
-0.038

0.455
0.834
0.699
1.4
0.861
0.32
1.01

0.062
0.077
0.034
0.055
0.053
0.094
0.044

15.7
45.39
12.67
23.08
15.4
22.08
19.66

1.71
2.07
1
1.93
1.76
2.39
1

48.6
106.9
88.3
62.4
78.9
43.1
88.1

0.95
0.95
0.91
0.95
0.85
0.95
0.94

1.15
1.25
1.21
1.2
1.25
1.2
1.15

0.026
0.03
0.071
0.031
0.1
0.048
0.046

Table 7 Second story in plane shear spring parameters in y direction

Wall ID

Ko
(kN/mm)

r1

r2

r3

r4

F0 (kN)

Fi (kN)

Δ (mm)

α

β

E21

0.51

0.01

-0.04

0.88

0.08

5.42

0.43

39.3

1

1.3

E23

1.54

0.01

-0.02

1.01

0.06

23.48

1.24

39.8

1

1.2

E26

1.85

0.02

-0.05

0.48

0.08

22.23

2.5

37.9

1

1.4

E32

1.93

0.06

-0.06

0.72

0.06

12.31

1.19

34.1

0.9

1.3

E29

1.27

0.01

-0.02

1.01

0.01

2.96

0.24

38.6

1

1.2

E28

1.11

0.04

-0.01

0.52

0.03

6.83

0.61

70.3

1

1.3

E27

1.27

0.01

-0.02

1.01

0.01

2.96

0.24

38.6

1

1.2

However, in seismic modeling of light-frame shear walls, accurately capturing the behavior of
different components such as structural studs, gypsum wallboards, and stucco is crucial. Each of
these elements contributes to the wall’s overall in-plane stiffness and strength, with unique
mechanical properties and hysteresis behavior.
The data presented in the tables above corresponds to Phase 3 of the two-story building tested
during the shake table experiments.

55

The complete seismic behavior of the building as a whole, incorporating additional elements such
as stucco in later phases, cannot be accurately captured without a comprehensive approach that
accounts for the interactions between all components across all phases. Specifically:
o In Phase 4, the GWBs were extended to cover all walls and ceilings, introducing
additional stiffness and damping contributions.
o In Phase 5, the inclusion of 22.2 mm thick stucco on the exterior further enhanced
the structural capacity by significantly increasing the lateral stiffness and energy
dissipation of the system.
To model the full-scale seismic behavior of the building across all phases, it becomes necessary to
develop a framework that integrates the contributions of all components—including structural
elements, GWBs, and stucco—into a unified representation. This is essential for understanding the
interaction between these layers and predicting the global response of the structure under seismic
loading.
To that purpose, spring theory provides an efficient and reliable solution. By representing each
component as a nonlinear spring with calibrated parameters and combining them in parallel (Zhou,
n.d.), the collective behavior of the building can be modeled effectively. To create a representative
model of the combined wall behavior, we employed the parallel spring theory, which assumes that
the stiffness of multiple components connected in parallel adds linearly.
4.2.6.2 Parallel Spring Theory
The parallel spring theory is based on the principle that when multiple spring elements are
connected in parallel as shown in the Figure 16, their combined stiffness is the sum of their
individual stiffness values.

56

Figure 16 Equivalent in-plane shear spring system
This approach assumes that all the spring components experience the same deformation under
applied loads, which is consistent with the physical behavior of a composite shear wall. The total
stiffness 𝐾total is given by:
K total = K studs + K gypsum + K stucco
For other parameters, such as yield force ( 𝐹0 ) and deformation ( Δ ), a weighted average approach
was used. This weighting ensures that the contributions of each material are proportional to their
stiffness, reflecting their relative influence on the overall wall behavior. The weighted average is
calculated as:
Pcombined =

K studs Pstuds + K gypsum Pgypsum + K stucco Pstucco
K total

Where, P represents the parameter being combined (e.g., 𝐹0 , Δ).
For the purpose of developing the numerical model in this study, the parameters for gypsum
wallboard (GWB) and stucco were obtained from the literature by Pan et al. (2018). This study
provided the necessary MSTEW model parameters for these materials, which were then combined
with the spring parameters given in the table for Phase 3 of the NEESWood two-story light-frame
57

building. The GWB and stucco parameters were effectively treated as parallel springs, combined
with the Phase 3 springs to represent the in-plane shear behavior of the composite wall system in
the numerical simulations.
The E27 shear wall has been investigated as a demonstration of how the combined parameters
were utilized in the numerical modeling on this study. Its phase 03 parameters (Table 07) were
combined with those of gypsum wallboard and stucco to create a representative model of the
composite wall system. The table below provides the tabulated values for the individual
components and their combined parameters, reflecting their in-plane shear behavior.
Table 8 Case Study: E27 Wall and Combined Parameters
Component

Ko

r1

r2

r3

r4

F0 (kN)

Fi (kN)

(kN/m

Δ

α

β

(mm)

m)
E27 Wall

1.27

0.01

-0.02

1.01

0.01

2.96

0.24

38.6

1

1.2

Stucco

1.09

0.07

-0.27

1

0.01

32.6

3.6

71.88

0.8

1.1

Gypsum

0.45

0.05

-0.02

1.01

0.01

2.76

0.44

39.62

0.9

1.65

Combined

2.81

0.046

-0.109

1.01

0.009

15.28

1.46

55.75

0.9

1.32

Figure 17 illustrates the MSTEW hysteresis backbone curves for the individual components used
in this study for numerical model development. Figure 17(a) represents the backbone curve of the
E27 wall for Phase 3, while Figure 17(b) and Figure 17(c) display the backbone curves for gypsum
wallboard and stucco, respectively, derived from Pan et al. (2018). These curves characterize the
force-displacement relationship and highlight the distinct hysteretic behaviors of each component.

58

(a)

(b)

(c)

Figure 17 MSTEW hysteresis backbone curve used in this study for numerical model development
(a) E27 wall - Phase 03 (b) Gypsum wall board (Pan et al., 2018) (c) Stucco (Pan et al., 2018)
Figure 18, in contrast, depicts the backbone curve for the combined wall system, which integrates
the contributions of the E27 wall (phase 03), gypsum wallboard, and stucco. The combined
backbone curve demonstrates the aggregated response, incorporating the stiffness and hysteretic
properties of all three components, effectively representing the global behavior of the composite
shear wall under seismic loading.

Figure 18 MSTEW back bone curve for combined action of Phase 3 shear wall, GWB and Stucco
59

Table 9 Combined MSTEW backbone parameters for in-plane shear springs
Wall ID
E1 Combined
E2 Combined
E35 Combined
E4 Combined
E5 Combined
E9 Combined
E10 Combined
E12 Combined
E37 Combined
E36 Combined
E17 Combined
E18 Combined
E19 Combined
E20 Combined
E24 Combined
E25 Combined
E33 Combined
E31 Combined
E30 Combined
E22 Combined
E6 Combined
E8 Combined
E11 Combined
E13 Combined
E16 Combined
I1 Combined
I27 Combined
E21 Combined
E23 Combined
E26 Combined
E32 Combined
E29 Combined
E28 Combined
E27 Combined

K0
(kN/m
m)
4.11
4.13
4.42
4.09
3.35
4.2
3.96
2.32
2.37
6.58
4.27
3.37
5.22
5.25
4.76
3.54
2.94
2.15
4.38
2.13
2.61
4.14
3.39
3.72
2.9
4.18
3.88
2.05
3.08
3.39
3.47
2.81
2.65
2.81

r1

r2

r3

r4

F0 (kN) Fi (kN)

Δ
(mm)

α

β

0.042
0.052
0.042
0.042
0.052
0.042
0.032
0.002
0.022
0.032
0.034
0.031
0.019
0.019
0.041
0.038
0.053
0.049
0.016
0.028
0.042
0.038
0.055
0.041
0.059
0.049
0.046
0.026
0.032
0.038
0.051
0.027
0.045
0.027

-0.073
-0.063
-0.053
-0.063
-0.073
-0.073
-0.083
-0.093
-0.043
-0.053
-0.085
-0.067
-0.072
-0.072
-0.085
-0.054
-0.048
-0.046
-0.054
-0.041
-0.055
-0.045
-0.037
-0.046
-0.05
-0.025
-0.04
-0.058
-0.038
-0.054
-0.061
-0.033
-0.017
-0.033

1.01
1.01
1.01
1.01
1.01
1.01
1.01
0.82
0.74
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
0.627
0.922
0.795
1.24
0.939
0.701
0.934
0.818
0.936
0.726
0.804
0.936
0.697
0.936

0.053
0.053
0.053
0.043
0.073
0.043
0.063
0.103
0.023
0.043
0.044
0.046
0.037
0.045
0.061
0.039
0.062
0.021
0.043
0.024
0.054
0.063
0.035
0.053
0.049
0.065
0.046
0.058
0.053
0.059
0.053
0.033
0.038
0.033

20.14
18.85
25.65
24.17
18.22
31.05
32.18
23.52
10.89
40.1
24.88
17.11
31.88
31.9
22.18
13.46
11.92
4.13
26.57
3.69
19.75
32.7
17.11
21.63
17.85
25.54
20.99
10.16
17.68
17.24
12.56
8.38
9.54
8.38

59.48
57.81
58.47
73.3
65.43
71.78
66.68
102.9
46.84
66.35
77.78
64.07
47.69
47.69
52.87
84.3
46.96
41.32
53.98
45.92
53.7
84.47
80.94
63.77
74.49
53.27
73.63
55.27
52.5
51.55
47.66
50.58
64.6
50.58

0.92
0.82
0.92
0.92
0.92
0.92
0.92
0.92
0.92
0.92
0.92
0.92
0.92
0.91
0.92
0.91
0.91
0.92
0.86
0.92
0.92
0.91
0.91
0.91
0.89
0.91
0.91
0.92
0.92
0.92
0.89
0.92
0.93
0.92

1.32
1.32
1.32
1.32
1.32
1.32
1.62
1.32
1.32
1.32
1.32
1.32
1.32
1.28
1.32
1.28
1.28
1.35
1.28
1.31
1.28
1.33
1.31
1.28
1.33
1.3
1.26
1.32
1.28
1.35
1.32
1.28
1.32
1.28

2.68
2.31
3.11
2.47
2.11
3.14
3.23
2.17
1.17
4.74
3.18
1.88
2.54
3.72
2.96
1.92
1.63
0.92
3.12
0.87
2.09
2.61
1.58
2.28
2.14
2.83
1.83
1.26
2.18
2.85
1.63
1.29
1.24
1.29

Similarly, the same methodology employed for the E27 shear wall, involving the integration of
spring parameters for the structural studs, gypsum wallboard, and stucco, was also applied to the
remaining shear walls. For each wall, the parameters were combined using the parallel spring
60

theory, where individual contributions were aggregated to capture the global in-plane shear
behavior of the composite system. The combined parameters for the walls are listed in Table 9.
4.2.6.3 Out-of-Plane Bending Spring Parameters
In this study, linear springs were employed in the out-of-plane direction to replicate the bending
behavior of each shear wall. The out-of-plane bending stiffness of the each shear walls, 𝐾bending ,
was calculated using the equation (Véliz et al., 2024):
𝐾bending =

2𝐻 3
3𝐸𝐴ext 𝐿2

Here:
H = 3048 mm (wall height),
E = 10,000 N/mm2 (elastic modulus of wood and sheathing materials),
The effective cross-sectional area (𝐴ext ) was calculated based on the contributions of different wall
components, including studs, sheathing (gypsum wallboard and stucco), and framing elements.
The total 𝐴ext = 18.01 mm2 /mm was derived as follows:
Studs Contribution: 𝐴studs = 9.68 mm2 /mm, based on the stud spacing (400 mm) and their
cross-sectional area (38 × 89 mm).
Sheathing Contribution: The effective thicknesses of gypsum wallboard and stucco were used to
calculate their respective contributions. For gypsum, 𝑡 = 12.7 mm , and for stucco, 𝑡 = 22.2 mm ,
resulting in combined contributions of 8.33 mm2 /mm.

61

Table 10 lists out the bending stiffness of the linear spring that is used in the numerical model in
this study to incorporate the out-of-plane stiffness of the shear walls.
Table 10 Out-of-plane stiffness of the shear walls
Wall ID
E1
E2
E35
E4
E5
E6
E9
E10
E12
E13
E16
E36
E37
I27
I1
E17
E18
E19
E20
E21
E22
E23
E24
E25
E26
E27
E28
E29
E30
E31
E32
E33
E34

Length (mm)
2950
2930
3350
3430
2440
990
3430
3430
3430
3430
2930
3350
2520
3430
3350
5870
3350
4620
6870
990
990
4650
3350
3430
3430
2930
1500
1500
5870
2520
2520
3430
2290

𝑲𝒃𝒆𝒏𝒅𝒊𝒏𝒈 (kN/mm)
0.02804
0.02825
0.0226
0.02156
0.04535
0.27324
0.02156
0.02156
0.02156
0.02156
0.02825
0.0226
0.04302
0.02156
0.0226
0.00169
0.01071
0.00058
0.00172
0.00172
0.00117
0.00185
0.00112
0.00104
0.00104
0.00174
0.00174
0.00268
0.00169
0.00456
0.00456
0.00104
0.00185

62

4.2.6.4 Nodal Restraints
In this study, the vertical stiffness of the building model was constrained by fixing the degree of
freedom in the Z direction for master nodes, ensuring no vertical deformation in the model. This
approach aligns with the methodology outlined in Pang and Rosowsky (2010), where master nodes
were assigned only two in-plane translational degrees of freedom (X and Y directions) and one
rotational degree of freedom. The absence of a vertical degree of freedom in the model reflects the
assumption of rigid vertical connectivity, effectively simulating the shear wall’s behavior under
in-plane loading.
4.2.6.5 Diaphragm Beam
The semi-rigid behavior of the diaphragms in the NEESWood benchmark structure was modeled
using linear two-node beam elements. The layout of the beam elements are depicted in the Figure
20. These elements connect master nodes placed along transverse wall lines (2, 4, 5, and 6) as
shown in Figure 19 on the floor and roof diaphragms, allowing for relative movement in the
transverse (N–S) direction. Each master node retains one rotational and two in-plane translational
degrees of freedom, simulating the semi-rigid diaphragm behavior.

Figure 19 Wall line plan of the NEESWood two story building
The stiffness matrix for the two-node beam elements was derived using classical beam theory:

63

where:
E: Elastic modulus (12,410 MPa for Douglas Fir),
L: Length of the beam element (see Table 4 for specific lengths),
A: Cross-sectional area,
I: Moment of inertia.

The moment of inertia (I) for each diaphragm segment was calculated using the diaphragm stiffness
obtained from its backbone curve. The backbone curve was generated through monotonic pushover
analysis of diaphragm segments Pang and Rosowsky (2010), yielding a stiffness parameter (𝑲𝒅 )
corresponding to the slope of the linear portion of the curve.
The relationship for I is:
𝐼=

𝐾𝑑 𝐿3
𝐸

Using 𝐾𝑑 = 0.0742 kN/mm (example value for B2, middle floor segment):
1.

Convert 𝐾𝑑 to consistent units: 𝐾𝑑 = 74.2 N/mm.

2.

Substitute into the equation:

74.2 × (3.35 × 103 )3
𝐼=
12,410 × 106

3.

Compute I: 𝐼 = 22,476 cm4 .

64

This process was repeated for each diaphragm segment using their respective 𝐾𝑑 values obtained
from pushover analyses.
Table 11 summarizes the beam properties, including elastic modulus, effective moment of inertia
(I), and length (L):
Table 11 Equivalent diaphragm beam element properties
Element
ID
B1
B2
B3
B4
B5
B6

Location
Floor west
Floor middle
Floor east
Roof west
Roof middle
Roof east

(a)

E (MPa)

I (cm^4)

12410
12410
12410
12410
12410
12410

265556
22476
261810
224765
16649
191466

L (m)
5.87
3.35
6.86
5.87
3.35
6.86

(b)

Figure 20 Diaphragm equivalent beam (a) first floor level (b) second floor level
The calculated I values provided an accurate representation of the diaphragm’s bending resistance.
By incorporating these beam elements, the model effectively captured the semi-rigid behavior of
the diaphragms, including load redistribution and transverse deformations. The stiffness properties
derived from the backbone curves ensured realistic simulation of diaphragm behavior under
seismic loading conditions.

65

4.2.6.6 Mass Distribution
For the numerical modeling of the benchmark structure in Phase 05, the mass distribution was
implemented to accurately reflect the building’s dynamic behavior. The weights for the
diaphragms on the first and second floors were allocated based on the structural configuration and
applied uniformly across the master and slave nodes.
The total weight assigned to the first-floor diaphragm was 133.45 kN. This weight was distributed
uniformly along the master nodes of the first-floor diaphragm. The allocation ensured that the inplane behavior of the first-floor diaphragm was accurately captured, enabling proper interaction
with the supporting shear walls.
The second-floor diaphragm included a total weight of 186.34 kN, composed of 103 kN from the
second-floor level and 83.34 kN from the roof diaphragm load. This combined weight was
distributed across the master nodes on the second-floor diaphragm to account for its in-plane
behavior and on the slave nodes to represent the roof load effects.
4.2.6.7 Timber 3D Modeling
The numerical model of the NEESWood two-story light wood-frame building (Test Phase 05) was
developed in Timber 3D as shown in the Figure 21 to simulate the dynamic response and seismic
behavior of the structure. This section outlines the modeling approach and high-level design
considerations.
Rigid beam elements (with very high modulus of elasticity) were used to define the diaphragm
geometry at three distinct levels: the base, first floor, and second floor. These rigid beam elements
served to transfer loads from the slave nodes to the diaphragm beam and the shear walls, ensuring
effective load redistribution within the system. The diaphragm stiffness itself was not governed by
these rigid beam elements but was instead defined by six dedicated beam elements running in the
66

longitudinal direction. These longitudinal beams captured the semi-rigid behavior of the
diaphragms during seismic events and accounted for their deformation characteristics.

Figure 21 Timber 3D numerical model of NEESWood two-story light wood frame building
Frame-to-frame 3D spring elements were employed to connect the diaphragms across the floors,
simulating the interaction between structural components. The spring elements accounted for the
in-plane shear stiffness of the shear walls and their interaction with the diaphragms. For the outof-plane behavior, bending stiffness values were incorporated into the spring elements, reflecting
the wall components’ ability to resist out-of-plane loads.
Master nodes were assigned at critical locations in the diaphragm to represent the center of mass
and capture the diaphragm’s overall translational and rotational behavior. Slave nodes were
distributed along the edges of the diaphragm and connected to the master nodes, ensuring accurate
load redistribution and maintaining the building’s structural integrity.
For simulating vertical stiffness, the degrees of freedom in the Z-direction were fixed at both floor
levels. This ensured that the vertical stiffness did not influence in-plane load transfer but allowed
accurate modeling of gravity and axial loads on the shear walls and diaphragm connections.

67

4.2.7 Damping Ratios in Phase 5
Damping ratios for Phase 5—the final and fully constructed stage of the two-story wood-frame
building—provide key insights into the system’s energy dissipation capacity under near-complete
structural and non-structural configurations. This phase included all architectural finishes such as
gypsum board and stucco, which are known to significantly influence dynamic behavior. The table
below presents the initial damping ratios for the first three vibration modes during Phase 5:
Table 12. Damping ratio of Phase 5 structure used in the numerical model
Mode
1
2
3

Damping Ratio (%)
17.9
17.1
5.0

4.3 Model Validation
4.3.1 Modal Analysis
The modal periods obtained from the Timber 3D numerical model for Phase 5 are compared to the
experimental periods recorded during the shake table test (benchmark test).
Table 13 provides a modal period comparison and
Figure 22 compares their corresponding mode shapes for the first three modes of vibration. These
modal periods serve as an essential measure of dynamic behavior, reflecting the structural stiffness
and mass distribution.
Mode 1: The benchmark full scale model and numerical model periods for the first mode show a
close agreement, with the numerical model slightly overestimating the period. This discrepancy is
attributed to minor variations in the diaphragm stiffness and nodal fixity in the numerical model.

68

Mode 2: The second mode, representing torsional behavior, exhibits an excellent match between
the experimental and numerical periods, with a negligible difference of only -2.5%. This validates
the semi-rigid diaphragm assumptions and mass distribution accuracy used in the Timber 3D
model.
Shake Table Test (Benchmark Test)

Timber 3D Numerical Model

Mode 1

Mode 1

Mode 2

Mode 2

Mode 3

Mode 3

Figure 22 Comparison of mode shapes obtained from the shake table test (benchmark test) and
the Timber 3D numerical model for the NEESWood two-story light wood-frame building.

69

Mode 3: The third mode shows the largest deviation, with the numerical model overestimating the
period by approximately 12.60%. This difference may stem from simplifications in modeling local
shear wall deformations or assumptions in the distribution of stiffness along the building.
Table 13 Comparison of modal periods between the benchmark test model and numerical model
Mode
1
2
3

Shake Table Test(sec)
0.286
0.198
0.127

Numerical Model Period (sec)
0.31
0.193
0.143

The numerical model captures the essential dynamic characteristics of the NEESWood two-story
light wood-frame building, as evidenced by the close agreement between the experimental and
numerical modal periods. These results demonstrate the Timber 3D model’s robustness in
predicting the behavior of light wood-frame structures under seismic loads.
The slight deviations observed highlight the influence of modeling assumptions, including
diaphragm stiffness, mass distribution, nodal fixity and material properties. Overall, the
comparison validates the numerical modeling approach adopted in this study for Phase 5 of the
structure. This alignment reinforces confidence in the use of the Timber 3D framework for
accurately simulating seismic performance in light wood-frame buildings.
4.3.2 Structural Response
4.3.2.1 Displacement Response
The displacement responses shown in Figure 23 to Figure 26 illustrate a comparative analysis of
nodal displacement time-history for the benchmark shake table test and the numerical model. The
responses correspond to specific shear walls, as indicated in Figure 19, and represent the behavior
of the structure at selected nodes under seismic excitation.
70

Observations:
a) Figure 23: The numerical simulation exhibits strong agreement with the benchmark shake
table test results, effectively replicating both the amplitude and phase characteristics of the
observed dynamic behavior. The oscillatory patterns and gradual decay of motion after the
peak seismic input are well captured by the model. Notably, the residual displacement—
visible after approximately 30 seconds—settles around -20 mm, indicating permanent
deformation in the structural system due to inelastic response. This residual drift confirms
energy dissipation and plastic behavior within the structural components, aligning with
expectations for damage accumulation during strong seismic excitation.
b) Figure 24: The displacement response of shear wall E1 in the X-direction (1st-floor roof)
demonstrates a slight deviation in peak displacement magnitudes between the numerical
and test responses. However, the overall trend and oscillation frequency are consistent,
validating the robustness of the numerical model in this direction.
c) Figure 25: For shear wall E28 in the Y-direction (2nd-floor roof), the numerical model
captures the general displacement trend but exhibits slight underprediction in the amplitude
of peak displacements. This variance might be attributed to minor simplifications in the
model assumptions for the semi-rigid diaphragm interaction.
d) Figure 26: The displacement response for shear wall E17 in the X-direction (2nd-floor
roof) shows strong alignment between the numerical predictions and the benchmark test.
Both responses follow similar oscillatory patterns with closely matching peak values,
indicating that the model effectively represents the system’s dynamics in this direction.
The numerical model effectively replicates the benchmark shake table test results for all analyzed
cases, despite minor discrepancies in amplitude. These deviations can be linked to assumptions in

71

material damping, semi-rigid diaphragm behavior, and connection modeling within the numerical
framework.

Figure 23 Comparison of nodal displacement time history between the benchmark structure shake
table test response and numerical model response for Phase 05 Test 08 – Shear wall E16 in Y
direction in 1st floor roof

Figure 24 Comparison of nodal displacement time history between the benchmark structure shake
table test response and numerical model response for Phase 05 Test 08 – Shear wall E1 in X
direction in 1st floor roof
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Figure 25 Comparison of nodal displacement time history between the benchmark structure shake
table test response and numerical model response for Phase 05 Test 08 – Shear wall E28 in Y
direction in 2nd floor roof

Figure 26 Comparison of nodal displacement time history between the benchmark structure shake
table test response and numerical model response for Phase 05 Test 08 – Shear wall E17 in X
direction in 2nd floor roof.

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4.3.2.2 Force Time History
The base shear force time-history comparisons between the benchmark test (Phase 05 – Test 08)
and the numerical model are presented in Figure 27 and Figure 28 for the longitudinal (X-axis)
and transverse (Y-axis) directions, respectively. In the benchmark test, the base shear force was
calculated by considering the average acceleration response from the building corners, as captured
by accelerometers strategically placed at these locations. These average accelerations were
multiplied by the tributary mass to compute the base shear forces in both longitudinal and
transverse directions.
As shown in Figure 27, the peak base shear force in the benchmark test was close to 130 kN, while
the numerical model predicted a peak value of 135 kN. The timing of these peaks is closely aligned,
occurring within less than a millisecond of each other during the most significant seismic motion.
The numerical model effectively replicates the amplitude and frequency characteristics observed
in the benchmark test, with minor deviations attributed to simplifications in the modeling
assumptions.
In the transverse direction, as illustrated in Figure 28, the peak base shear force in the benchmark
test reached just over 305 kN, compared to the numerical model’s prediction of 310 kN. Similar
to the longitudinal axis, the timing of the peaks aligns closely. The numerical model captures the
primary dynamic behavior, including the oscillation trends and energy dissipation observed in the
benchmark test data.
The comparison reveals that the numerical model not only replicates the peak values with a margin
of error of less than 5%, but it also captures the general trends, including the oscillation frequency
and decay patterns. These results validate the robustness of the modeling approach and its ability
to simulate the complex interactions of diaphragm, shear wall, and gravity load components under

74

seismic loading. However, minor discrepancies in the amplitude and phase may be attributed to
idealized boundary conditions and simplifications in material properties in the numerical model.

Figure 27 Base shear force time history comparison between the benchmark test (Phase 05 - Test
08) and the numerical response in X direction (longitudinal direction)

Figure 28 Base shear force time history comparison between the benchmark test (Phase 05 - Test
08) and the numerical response in Y direction (transverse direction)

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4.3.2.3 Global Hysteresis
The hysteresis loops shown in Figure 29 depict the relationship between base shear force and
central roof displacement for Phase 05 – Test 08, comparing results from the benchmark shake
table test and the numerical model.

(a)

(b)

(c)

(d)

Figure 29 Base shear force versus central roof displacement hysteresis loops for Phase 05 – Test
08. Panels (a) and (c) correspond to the benchmark shake table test results in the X (longitudinal)
and Y (transverse) directions, respectively. Panels (b) and (d) represent the corresponding
numerical model predictions for the X and Y directions.

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Figure (a) and (c) represent the benchmark test results for the X (longitudinal) and Y (transverse)
directions, respectively, while panels (b) and (d) show the corresponding numerical model
predictions. The central roof displacement was derived by averaging the displacements measured
at the roof corners for both the benchmark structure and the numerical model. The base shear force
reflects the global structural resistance against the applied seismic loads. The loops indicate the
energy dissipation and non-linear behavior of the system under cyclic loading, which is essential
for understanding the structural response.
The shape and area enclosed by the loops highlight the structure’s capacity for energy dissipation.
The similarity in loop shapes between the benchmark test and numerical model demonstrates the
accuracy of the modeling approach in capturing global hysteretic behavior.
4.3.2.4 Energy Dissipation
Figure 29 illustrates the base shear force versus central roof displacement hysteresis loops for both
the benchmark shake table test and the numerical model in the longitudinal (X) and transverse (Y)
directions. These loops provide critical insights into the global hysteretic behavior of the structure,
which forms the basis for analyzing the energy dissipation patterns shown in Figure 30 and Figure
31.
Panels (a) and (c) in Figure 29 represent the hysteresis loops derived from the benchmark shake
table test for the X and Y directions, respectively. The broader shapes of these loops indicate
significant energy dissipation due to the non-linearities in the physical structure, such as material
yielding and connection deformation under seismic loading. Panels (b) and (d) correspond to the
numerical model’s predictions for the same directions. The slightly narrower loops in these panels
reflect the calibrated stiffness and damping properties assumed in the numerical model, yet they
still capture the overall global behavior with high fidelity.
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In Figure 30, the global hysteretic energy dissipation in the longitudinal direction shows agreement
between the shake table test results and the numerical model predictions. The benchmark test
indicates a slightly faster rate of energy dissipation at the initial stages, primarily due to the direct
interaction between the structural elements and seismic inputs. However, by the mid-to-late stages
of the simulation, both the test and the numerical model converge, displaying comparable energy
dissipation patterns. The peak energy dissipation observed in the numerical model closely follows
the benchmark test, validating the model’s effectiveness in capturing the global hysteretic
behavior.

Figure 30 Comparison of global hysteretic energy dissipation of the benchmark test structure and
the numerical model in X (longitudinal) direction
Figure 31 provides a similar comparison for the transverse direction. Here, the numerical model
successfully replicates the energy dissipation trends observed in the benchmark test. Both curves
follow a steady increase, particularly after the 15-second mark, when the seismic inputs reach peak
amplitudes. The observed variance in the rate of dissipation during the initial phase might
attributed to the assumptions regarding semi-rigid diaphragm behavior in the numerical model.

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Despite this, the peak energy dissipation values and the overall cumulative energy trends closely
align, demonstrating the robustness of the model in the transverse direction.

Figure 31 Comparison of global hysteretic energy dissipation of the benchmark test structure and
the numerical model in Y (transverse) direction
4.3.2.5 Roof Displacement Profile
The roof displacement profiles of the benchmark test and the numerical model provide essential
insights into the structural performance under seismic loading, as depicted in Figure 33 and Figure
34. Figure 32 showcases the deformed shape of the numerical model under the seismic excitation
for Phase 05 Test 08 shaking level.
Figure 33 and Figure 34 compare the maximum roof displacement profiles between the shake table
test and the numerical model in the X (longitudinal) and Y (transverse) directions. In the X
direction, both experimental and numerical results display a consistent linear displacement
gradient, with the highest displacement occurring at the roof level. The alignment of the two
profiles demonstrates the model’s ability to replicate the benchmark structure’s global

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deformation. Slight differences observed near the second-floor level might attributed to the
simplified assumptions about diaphragm stiffness in the numerical representation.
Similarly, in the Y direction, the displacement profiles maintain a comparable trend, with the
numerical model closely following the experimental results. Minor deviations are observed in the
roof displacement at the second-floor level, likely resulting from the assumptions regarding semirigid diaphragm behavior in the numerical model. Despite these differences, the overall
displacement patterns agree well, confirming the model’s ability to capture the transverse
structural response.

Figure 32 Numerical model time history analysis deformed shape (15th sec) at scale 100 for Phase
05 Test 08

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Figure 33 Comparison of maximum roof displacement profile between the benchmark test
structure and the numerical model in X direction for Phase 05 Test 08

Figure 34 Comparison of maximum roof displacement profile between the benchmark test
structure and the numerical model in Y direction for Phase 05 Test 08. The table below summarizes
the validation briefly.

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Table 14. Summary of Validation Results – Phase 05 Test 08

Validation Item

Benchmark
Value

Modal Period – Mode
0.286
1 (sec)
Modal Period – Mode
0.198
2 (sec)
Modal Period – Mode
0.127
3 (sec)
Residual
Displacement (E16 - ~-20 mm
Y dir)
Peak Displacement
~55 mm
(E1 - X dir)
Base Shear – X
~130 kN
Direction
Base Shear – Y
~305 kN
Direction
Peak Base Shear
~18.2 sec
Timing (X/Y)
Energy Dissipation –
~2.4 kJ
Final (X Direction)
Energy Dissipation –
~18.7 kJ
Final (Y Direction)
Roof Displacement Linear
Profile (X Direction) gradient
Roof Displacement Linear
Profile (Y Direction) gradient
Full,
Global Hysteresis
nonlinear
Loop Shape
cycles

Numerical
Model

Difference

% Difference /
Match

0.310

+0.024 sec

+8.4%

0.193

-0.005 sec

-2.5%

0.143

+0.016 sec

+12.6%

~-20 mm

0 mm

100% match

~50 mm

-5 mm

~9% underprediction

~135 kN

+5 kN

~3.8% overprediction

~310 kN

+5 kN

~1.6% overprediction

~18.2 sec

< 1 ms

Excellent match

~2.3 kJ

-0.1 kJ

~4% deviation

~18.2 kJ

-0.5 kJ

~2.7% deviation

Linear
gradient
Linear
gradient
Closely
matching
shape

Minor difference at
<10 mm deviation
2nd fl.
Minor difference at
<10 mm deviation
2nd fl.
Slightly narrower

High visual
agreement

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5 Damage Index Model Calibration
The calibration of key parameters is a critical step in implementing the Park and Ang Damage
Index (DI) framework for light wood-frame buildings. Unlike steel or reinforced concrete
structures, light wood-frame buildings exhibit unique seismic behaviors due to their distributed
load paths, reliance on non-structural components, and inherent material variability. These factors
necessitate a tailored approach to parameter calibration, ensuring the DI equation accurately
reflects the collective seismic response of the building.
When discussing parameter calibration, it is important to distinguish between two types of
parameters: the global beta (β) model parameter and the global-level structural parameters,
namely global ultimate displacement (𝐷ult ) and equivalent yield force (𝐹𝑦 ) . For global beta
calibration, these parameters must be determined specifically for the entire structural system, as
opposed to the component-level values commonly derived from shear wall testing. While existing
literature provides significant data on component-level ultimate displacement and yield force
through shear wall testing, these values are insufficient for system-level calibration. Instead, global
parameters must be obtained through pushover analysis of the entire structure, capturing its holistic
response under lateral loading.
Figure 35 outlines the systematic process for calibrating these global parameters and the beta
model. The process begins with the development and validation of a high-fidelity numerical model
of the structure. Pushover analysis is then conducted to identify the global 𝐷ult and 𝐹𝑦 . Incremental
Dynamic Analysis (IDA) follows to determine the collapse intensity of the building, and dynamic
analysis is performed to generate global hysteresis responses, in the weaker direction of the
building where critical seismic vulnerabilities are most pronounced. These steps culminate in the

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calculation of a single β value for the entire system, ensuring consistency and reliability in damage
assessments.
This chapter provides a detailed overview of this calibration process, emphasizing its significance
in advancing the Damage Index framework to account for the unique challenges posed by light
wood-frame buildings.

Figure 35. Flowchart illustrating the systematic process for Damage Index (DI) model calibration,
including the development and validation of a numerical model, determination of global
parameters via pushover analysis, collapse intensity identification through Incremental Dynamic
Analysis (IDA), and global beta calibration based on global hysteresis responses.

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5.1 Incremental Dynamic Analysis (IDA) of the NEESWood Building
Incremental Dynamic Analysis (IDA) is a powerful method used to assess the seismic
performance of structures by subjecting them to a suite of ground motions scaled incrementally
in intensity. For this study, the NEESWood light wood frame building numerical model,
developed in Timber 3D, was utilized to perform the IDA under 11 distinct ground motion
records (Pacific Earthquake Engineering Research Center, 2013) from earthquakes of varying
characteristics. These ground motions, listed in the Table 15, include a range of magnitudes,
locations, and notable seismic features, reflecting diverse seismic behaviors.
The purpose of Incremental Dynamic Analysis (IDA) is to capture the nonlinear response of a
structure as the earthquake intensity increases. This method provides a detailed understanding of
how a structure transitions from elastic to inelastic behavior, eventually reaching failure under
extreme seismic loads. The analysis helps identify critical seismic parameters which are essential
for performance-based design and for quantifying the global Damage Index (DI).
The IDA process employs a diverse set of earthquake ground motions with varying magnitudes,
site conditions, and seismic characteristics to provide a robust and comprehensive evaluation of
structural behavior under different scenarios. This variability ensures accurate assessment of
performance, resilience, and safety across a range of earthquake intensities. The primary goal of
IDA is to produce plots that graphically represent spectral acceleration versus structural response,
such as drift. These plots are instrumental in evaluating structural performance, calibrating the beta
parameter for damage index equations through energy dissipation and displacement trends, and

85

identifying critical thresholds like maximum drift and displacement to inform performance
objectives and failure criteria.
The 11 ground motions were selected to encompass a wide range of seismic events with diverse
characteristics, including:
a) Magnitude and Duration: Covering small to large-magnitude earthquakes (e.g., 5.9 for
Saguenay to 7.4 for Manjil Earthquake), reflecting both short and long-duration shaking.
b) Geographic and Soil Variations: Events from different locations, such as Mexico City
(amplified effects due to soil conditions) and Kobe, Japan (severe urban ground shaking),
capture variations in soil conditions, seismic sources, and geographic regions.
c) Near-Field vs. Far-Field Effects: Including near-field events like Northridge and Chi-Chi
earthquakes and far-field events such as Val-des-Bois to account for differences in rupture
characteristics.
d) Spectral Characteristics: Events with varied frequency content and energy dissipation
profiles, enabling comprehensive assessment of the structure’s dynamic properties.
These ground motions simulate a wide spectrum of seismic scenarios, ensuring that the results
from the IDA analysis are representative and encompass real-world conditions. The diverse ground
motions provide a basis for understanding the structural response under varying seismic demands.

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Table 15. Key information on 11 significant earthquakes used in the IDA analysis, including their
year of occurrence, magnitude, location, and notable features.
Earthquake
Northridge
Earthquake

Year
1994

Magnitude
6.7

Location
Los Angeles,
California, USA

Christchurch
Earthquake

2011

6.2

Christchurch, New
Zealand

Mexico Earthquake

1985

8

Mexico City, Mexico

Val-des-Bois
Earthquake

2010

5

Quebec, Canada

Saguenay
Earthquake

1988

5.9

Quebec, Canada

Manjil Earthquake

1990

7.4

Iran

Loma Prieta
Earthquake

1989

6.9

San Francisco,
California, USA

Landers
Earthquake

1992

7.3

California, USA

Chi-Chi Earthquake

1999

7.6

Taiwan

Kobe Earthquake

1995

6.9

Kobe, Japan

Cape Mendocino
Earthquake

1992

7.2

Northern California,
USA

Notable Features
Caused extensive damage
and high accelerations;
one of the costliest
earthquakes.
Severe ground shaking in
urban areas; major
liquefaction.
Amplified effects due to
soil conditions; significant
loss of life and
infrastructure.
Moderate ground motion;
rare event for eastern
Canada.
High-frequency shaking;
unusual location for
significant seismic
activity.
Devastating impact in
rural areas; significant
loss of life.
Occurred during World
Series; caused collapse of
freeway structures.
Large surface ruptures;
influenced future seismic
design.
Extensive fault rupture;
caused significant
structural and
geotechnical failures.
Severe ground shaking in
urban areas; highlighted
the importance of seismic
retrofits.
Significant shaking and
surface faulting; caused
landslides and
infrastructure damage.

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5.2 IDA Curve
The IDA scatter plot in the Figure 36 represents the spectral acceleration ( 𝑆𝑎 ) plotted against the
drift ratio ( % ) for the NEESWood two-story light wood frame building model, subjected to a
diverse range of 11 earthquake ground motions. The results from 174 dynamic analyses are
presented, showcasing a clear trend in structural response under increasing seismic intensity.
5.2.1 Scattered Plot Observed Trends:
a) Initial Elastic Behavior:
For low drift ratios (0% to approximately 1%), the data points exhibit a linear trend, indicating that
the structure is behaving elastically. In this region, spectral acceleration ( 𝑆𝑎 ) increases
proportionally with the drift ratio, reflecting the structure’s ability to resist seismic forces without
significant deformation or damage.
b) Transition to Nonlinear Behavior:
Beyond a drift ratio of approximately 1%, the slope of the curve decreases, showing that the
structural response becomes nonlinear. This behavior represents the onset of inelastic
deformations, where damage mechanisms like yielding or minor cracking might start to occur.
c) Increased Nonlinearity and Damage:
For higher drift ratios (around 2% to 4%), the spread of data points increases significantly. This
indicates variability in response due to the differing characteristics of ground motions. The
structure absorbs energy through inelastic mechanisms, such as connection slip and material
yielding.
d) Plateau and Limit Behavior:
Beyond a drift ratio of approximately 5%, spectral acceleration reaches a near-plateau, particularly
for the higher-intensity ground motions. This trend implies that the structure is nearing or has
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reached its performance limits, with significant energy dissipation through damage and limited
additional resistance.
e) Scatter in Higher Drift Ratios:
At drift ratios exceeding 6%, the scatter among data points increases substantially, reflecting the
diversity in ground motion effects and indicating significant structural degradation. This region
may correspond to partial or complete failure mechanisms, where performance objectives are
likely exceeded.

Figure 36. IDA scattered data points for the NEESWood two story light wood frame building
Timber 3D model. 11 wide range of ground motion data and 174 corresponding dynamic analysis
result is utilized for this plot.s

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5.2.2 Median Curve
The median curve as shown in the Figure 37 illustrating the relationship between drift ratio and
spectral acceleration was derived from multiple earthquake data sets to represent a central trend
across various seismic events. First, drift ratios were standardized on a uniform range (0% to 12%)
with 1,000 points to ensure consistency across all datasets, and spectral acceleration values were
interpolated linearly. At each drift ratio, the median value was computed to capture the central
tendency while reducing the influence of outliers. To enhance readability and ensure smoothness,
a Savitzky-Golay filter (Savitzky & Golay, 1964) was applied with a window length of 51 points
and a polynomial order of 3, balancing trend preservation with noise reduction. The resulting
median curve, displayed as a dashed red line, provides a clear and interpretable trend that
highlights the central response of drift ratio and spectral acceleration across all earthquake events,
suitable for further analysis and comparison.

Figure 37. Median incremental dynamic analysis (IDA) curve illustrating the relationship between
drift ratio (%) and spectral acceleration (g). The curve represents the median response of the
NEESWood two story light wood frame building model based on scattered IDA points from
multiple ground motion records. The collapse point is identified at a drift ratio of 6.5% and spectral
90

acceleration of 1.65g, indicating the intensity level at which the structure reaches its collapse limit
state.
This median curve, graphically represents the relationship between drift ratio (%) and spectral
acceleration (𝑺𝒂 ) for the NEESWood two-story light wood frame building model subjected to
multiple ground motion records. This curve reflects the aggregate response of the structure to
varying earthquake intensities, capturing the trend of increasing drift ratios as spectral acceleration
rises. A critical feature of this curve is its distinct transition from an initial steep slope to a plateau
region, where drift ratio increases minimally despite rising spectral acceleration. This transition
highlights the shift in structural behavior from elastic and nonlinear responses to near-collapse
conditions.
The collapse point, marked at a drift ratio of 6.5% and spectral acceleration of 1.65g, is identified
where the curve flattens significantly. This flattening signifies that additional increases in seismic
demand yield negligible displacement increases, indicating that the structure has reached its
performance limit. Justifying the selection of 6.5% drift as the collapse point, it represents the
logical and observable threshold at which the structure’s deformation capacity is effectively
exhausted. While literature (Christovasilis et al., 2009) often suggests a predefined collapse point
based on slope change or drift thresholds, such as 7%, the observed behavior of the NEESWood
model supports the choice of 6.5%. At this level, the structural response demonstrates a transition
into a near-failure state, making it a rational and evidence-based definition of collapse for this
analysis.

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5.3 Pushover Analysis of NEESWood Two Story Numerical Model
Pushover analysis is a static nonlinear analysis technique widely used to assess the seismic
performance of structures by progressively applying lateral forces or displacements to a numerical
model. For the calibration of the beta (β) parameter in the Damage Index (DI) framework,
pushover analysis plays a critical role in determining global-level parameters, such as the global
ultimate displacement (𝐷ult ) and equivalent yield force (𝐹𝑦 ).
In this study, the pushover analysis is performed on the validated numerical model of the light
wood-frame building, where lateral forces are incrementally applied until the structure reaches a
predefined displacement or collapse state. The analysis provides insights into the nonlinear
behavior of the system, including key parameters like lateral load resistance, stiffness degradation,
and post-peak behavior. The resulting pushover curve, as illustrated in Figure 38, represents the
relationship between the base shear force (kN) and the average roof displacement (mm).
The parameters 𝐷ult (225 mm) and 𝐹𝑦 (158 KN) extracted from this curve are essential for
calibrating the global beta value. Unlike component-level parameters, which are derived from
individual shear walls, these global parameters account for the collective behavior of the entire
structure, including interactions between structural and non-structural components. This ensures
that the beta calibration reflects the seismic response of the building as a whole, enabling accurate
damage assessment for light wood-frame structures under seismic loading.

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Figure 38. This figure presents the pushover analysis curve, illustrating the relationship between
the base shear force and the roof displacement. The force values are expressed in kN, while the
displacement is in mm. The curve provides insights into the nonlinear behavior and lateral load
resistance of the structure under increasing displacement.

5.4 Global Beta Calibration Calculation for the Benchmark Two-story Light
Wood Frame Building
The calibration of the beta (β) parameter is a pivotal step in implementing the Park and Ang
Damage Index (DI) framework to assess seismic damage in light wood-frame buildings. This study
focuses on calibrating β specifically for the Northridge earthquake ground motion since the
Damage Index values are correlated to the observed damage during the benchmark test where
Northridge ground motion data was utilized. Given the variability in seismic intensity and
characteristics across different earthquakes, the beta parameter must be uniquely calibrated for
each event. This ensures that the DI framework accurately reflects the seismic demands imposed
by a specific earthquake on the structure.

93

For the Northridge earthquake, the calibration process involves conducting Incremental Dynamic
Analysis (IDA) to extract key global structural response parameters, such as roof displacement
and base shear force. These parameters are used to generate a global hysteresis curve, from which
the maximum displacement (𝐷max ) and hysteretic energy (E) are determined. These values serve
as the inputs for calibrating the global β value, ensuring that it represents the collective behavior
of the structure under the specific seismic loading conditions of the Northridge event.
5.4.1 Scaled Response Spectrum Northridge Earthquake
Figure 39 presents the response spectrum for the Northridge earthquake ground motion, which was
utilized in the NEESWood benchmark test for Phase Five. The response spectrum illustrates the
variation of spectral acceleration (𝑆𝑎 ) as a function of the structural period (T) for a single-degreeof-freedom (SDOF) system with 5% damping. The spectral acceleration intensity level was scaled
to match the collapse intensity observed during the IDA analysis for the NEESWood light woodframe building (Fundamental period is about 0.30 sec), which was identified at 1.65g.
To achieve the target spectral acceleration of 1.65g, the original Northridge earthquake ground
motion data was scaled using a scaling factor of 2.06. Thus, it was made sure that the input motion
accurately represent the collapse conditions for the NEESWood structure during the dynamic
analysis.

94

Figure 39. Response spectrum illustrating the variation of spectral acceleration (𝑆𝑎 ) with respect
to the period (T) for a single-degree-of-freedom (SDOF) system with 5% damping. The ground
motion was scaled to match the collapse intensity level of 1.65g at a period 0.30 seconds.

With the scaled Northridge earthquake ground motion data representing the collapse conditions at
1.65g, the next step involves performing dynamic analysis to extract the global structural response
necessary for the beta (β) calibration process.
5.4.2 Global Response
Under the global response analysis, the dynamic response for the scaled Northridge earthquake
ground motion (calibrated to the collapse intensity of 1.65g) is presented. The response was
captured from multiple points on the roof, and the average displacement values were computed to
generate a comprehensive system-level hysteresis curve Figure 40. This plot highlights the cyclic

95

behavior of the structure under seismic loading, showcasing maximum displacement and stiffness
degradation.
Additionally, the cumulative energy dissipation over time was calculated and is illustrated in
Figure 41. This plot represents the total energy absorbed by the structure during the loading cycle,
providing insights into the system’s capacity to dissipate seismic energy. These parameters,
derived from global system-level responses, form the basis for beta calibration and ensure that the
calibrated value accurately reflects the overall seismic performance of the structure.

Figure 40. Hysteresis Curve of the System. This figure illustrates the hysteresis response of the
global system, showing the relationship between force (kN) and average roof displacement (mm).
The curve represents the cyclic behavior of the structure under repeated loading and unloading,
capturing its energy dissipation and stiffness degradation over successive cycles.

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Figure 41. Cumulative Energy Dissipation Over Time. This figure displays the cumulative energy
dissipation of the system as a function of time (s). The plot highlights the energy absorbed by the
structure during cyclic loading, with energy values calculated in kilojoules (kJ).
5.4.3 Beta Value Sample Calculation
To advance the assessment of seismic performance for the NEESWood light wood-frame building,
the next critical step involves the calibration calculation of the beta (β) parameter within the
Damage Index (DI) framework. Having identified the collapse intensity through Incremental
Dynamic Analysis (IDA) and obtained the corresponding dynamic responses, including maximum
displacement and cumulative energy dissipation, we now focus on determining the β value. The
following section provides a detailed example of the beta calculation process, showcasing the
methodology and step-by-step derivation of the β value based on global system response data
maximum displacement of roof 𝐷max , energy dissipation (𝐸𝑖 ), ultimate displacement (𝐷u ), and

97

yield force (𝐹y ) values, highlighting the methodology employed in calibrating beta for individual
walls.

𝐷𝐼 =

𝐷max
𝐸𝑖
+β⋅
𝐷ultimate
𝐹𝑦 ⋅ 𝐷ultimate

Where:
DI = 1 (collapse level)
𝐷max = Maximum displacement during dynamic analysis (from the table) = 60.36 mm
𝐷ultimate = Ultimate displacement = 225 mm (pushover curve)
𝐸𝑖 = Energy dissipation = 89.5 kN-mm
𝐹𝑦 = Equivalent yield force = 158 kN (pushover curve)
β = Calibration parameter to be determined
Step-by-Step Calculation:
a) Reorganize the Equation for Beta:
Solve for β using the given equation:

β=

𝐷
𝐷𝐼 − 𝐷 max

ultimate

𝐸𝑖
𝐹𝑦 ⋅ 𝐷ultimate

𝐷

b) Calculate 𝐷 max :
ultimate

𝐷max
60.36
=
= 0.27
𝐷ultimate
225

98

𝐸

c) Calculate 𝐹 ⋅𝐷 𝑖
𝑦

ultimate

:
𝐹𝑦 ⋅ 𝐷ultimate = 158 ⋅ 225 = 35,550 kN-mm
𝐸𝑖
89.5 ∗ 1000
=
= 2.52
𝐹𝑦 ⋅ 𝐷ultimate
35,550

d) Substitute Values into the Beta Equation:
β=

β=

1 − 0.27
2.52

0.73
= 0.29
2.52

The global beta calibration has determined a beta (β) value of 0.29, providing a reliable parameter
for implementing the Damage Index (DI) framework tailored to NEESWood two story light woodframe building. This calibrated beta value is now ready for use in component-wise DI calculations,
which will ultimately contribute to the calculation of the global-level DI under varying intensity
levels of the Northridge earthquake, paving the way for detailed damage assessments and further
performance evaluations.

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6 Damage Index Calculation and Damage Correlation
The Damage Index (DI) is a vital metric used to quantify the extent of seismic damage in structures,
providing insights into both localized and global damage. The process of DI calculation begins at
the component level, where individual structural elements, such as walls or frames, are evaluated
based on their dynamic response. Component-level DI values are determined by analyzing key
parameters, including maximum displacement and cumulative energy dissipation during seismic
events. These values capture the unique damage characteristics of each component, enabling a
detailed assessment of their performance under seismic loads.
Once the component-level DI values are computed, they are aggregated to determine the Global
Damage Index (DI). This involves weighting the contribution of each component based on its
energy dissipation relative to the entire structure, thereby offering a holistic view of the building’s
overall damage state. The DI reflects the cumulative effects of deformation and energy dissipation
across all components, providing a comprehensive measure of the structure’s seismic vulnerability.

Figure 42. Layout of the wall lines for the NEESWood two story light wood frame building

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The NEESWood two-story light wood-frame building, the subject of this study, consists of 16
distinct wall lines—8 on the first floor and 8 on the second floor. Each wall is identified by its
orientation (X or Y direction) and contributes uniquely to the structural system’s seismic response.
Figure 42 illustrates the layout of these walls, which were analyzed individually to calculate their
respective DI values. These component-level results were subsequently integrated into the Global
Damage Index calculation, facilitating a robust evaluation of the building’s performance under
varying levels of seismic intensity. This hierarchical approach ensures a thorough understanding
of both localized damage mechanisms and the overall structural response.

6.1 Damage Index Calculation for Phase 5, Test 8: Numerical Analysis of
Benchmark Response
The purpose of this study is to calibrate the Damage Index (DI) equation to accurately predict the
actual damage that a structure might sustain during a given earthquake. By refining the DI
equation, the framework aims to bridge the gap between analytical predictions and observed
seismic damage, thereby offering a reliable tool for performance-based seismic design and
assessment. The Damage Index serves as a critical parameter for quantifying structural
performance by combining maximum displacements, cumulative energy dissipation, and
calibrated beta values, which represent the hysteretic characteristics of each structural component.
Building on the groundwork laid in Chapter 5, where the beta parameter was calibrated for each
walls, we are now equipped to proceed with an actual dynamic analysis. This next step involves
obtaining the seismic response of individual components of the structure under ground motions
and utilizing the calibrated beta values to calculate the Damage Index. This allows for a direct
comparison between analytical predictions and physical observations, ensuring that the calibrated
equation reflects realistic damage scenarios.
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The Northridge earthquake ground motion scaled by a factor of 1.2 was used for the dynamic
analysis as a first step. This specific scaling was chosen to replicate the intensity observed during
Phase 5 Test 8 of the NEESWood benchmark experiments, where real damage was documented.
By aligning the scaled intensity with experimentally observed damage, the calculated DI values
can be cross-validated against physical damage patterns, ensuring the accuracy and robustness of
the framework.
Table 16. Wall-wise DI values and corresponding energy dissipation

Wall
Wall 1y
Wall 2x
Wall 3y
Wall 4x
Wall 5y
Wall 6x
Wall 7y
Wall 8x
Wall 1y
Wall 2x
Wall 3y
Wall 4x
Wall 5y
Wall 6x
Wall 7y
Wall 8x

Floor
first floor
first floor
first floor
first floor
first floor
first floor
first floor
first floor
second floor
second floor
second floor
second floor
second floor
second floor
second floor
second floor

𝑫𝒎𝒂𝒙m)
17.89
2.53
12.73
7.40
28.78
6.55
32.05
5.60
12.79
0.93
10.39
2.85
20.41
2.71
19.26
2.19

Energy Dissipation
(kN-mm)
6177.58
6675.46
5337.27
10193.20
9126.95
10107.47
9085.07
10183.98
5442.14
2557.48
5711.34
4272.81
8458.68
4755.21
8143.07
4563.74

DI
0.66
0.60
0.55
0.94
0.99
0.93
1.01
0.93
0.56
0.23
0.57
0.39
0.88
0.43
0.84
0.41

The focus on component-level damage allows for a detailed assessment of localized structural
behavior, which is critical for understanding how individual walls contribute to the global
structural response. Table 17 summarizes the DI calculations for all 16 walls of the two-story
NEESWood light wood frame model, separated into first and second floors. These DI values were

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computed using the calibrated beta parameters and reflect the maximum displacement and energy
dissipation recorded during the dynamic analysis under the scaled Northridge ground motion.
Table 17. Table presenting the calculated Damage Index (DI) for each wall on the first and second
floors of the NEESWood two-story light wood frame numerical model. The Northridge
earthquake, scaled by a factor of 1.2, was utilized for the dynamic analysis of the Timber 3D
model. The DI values are tabulated for the corresponding walls using calibrated Beta values.
6.1.1 Sample DI Calculation for Wall 1Y First Floor
The Global Level Damage Index (Global DI) represents the overall seismic damage of the structure
by aggregating the contributions of individual component-level damage indices (𝐷𝐼𝑖 ) weighted by
their energy dissipation. This section presents the step-by-step calculations to derive the Global DI
using the results from Table 17.
The Damage Index (𝐷𝐼𝑖 ) for each wall is calculated using the following formula:
𝐷𝐼𝑖 =

𝐷max,𝑖
β𝑖 ⋅ 𝐸𝑖
+
𝐷alt
𝐹𝑦 ⋅ 𝐷alt

Where:
𝐷max,𝑖 : Maximum displacement of the i-th component (mm).
𝐷alt : Ultimate displacement capacity of the wall (𝐷alt = 149.56 mm) (ref- Figure 1)
β𝑖 : 0.29
𝐸𝑖 : Energy dissipated by the 𝑖 − 𝑡ℎ component from Table 17 =6177.58 KN-mm
𝐹𝑦 : Yield strength of the wall (𝐹𝑦 = 22.12 kN). (ref- Figure 1)
As an example, consider Wall 1y on the first floor:
𝐷max,𝑖 = 17.89 mm
β𝑖 = 0.29
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𝐸𝑖 = 6177.58 kN-mm
Substituting the values:
𝐷𝐼1𝑦,first floor =

17.89 0.29 ⋅ 6177.58
+
149.56 22.12 ⋅ 149.56

𝐷𝐼1𝑦,first floor = 0.66
6.1.2 Global Damage Index Calculation
The Global Damage Index (DI) serves as a critical parameter for assessing the overall performance
and integrity of a structure during seismic events. Unlike component-level DIs, which quantify
damage for individual structural elements, the Global DI provides a holistic measure of the
cumulative damage sustained by the entire structure. It synthesizes the contributions of all
structural components by accounting for their respective energy dissipation capacities and their
damage indices.
To compute the Global DI, a weighting factor (𝝀𝒊 ) is assigned to each component based on the
proportion of energy it dissipates relative to the total energy dissipation of all components. The
weighting factor ensures that components with higher energy dissipation have a greater influence
on the Global DI, reflecting their critical role in the structural response.
This section outlines the detailed calculations performed to derive the Global DI for the
NEESWood two-story light wood-frame structure, using the numerical response data from the
Northridge earthquake scaled by a factor of 1.2. A sample calculation for the Wall 1Y at the first
floor level is demonstrated.
As discussed earlier, the weighting factor (λ𝑖 ) represents the proportion of energy dissipated by
each wall relative to the total energy dissipated by all walls:
λ𝑖 =

𝐸𝑖
𝐸total
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Where:
16

𝐸total = ∑ 𝐸𝑖 = 110791 kN-mm
𝑖=1

For Wall 1y on the first floor:
λ1𝑦,first floor =

6177.58
= 0.06
110791

The Global DI is computed as the weighted sum of the individual DIs:
16

𝐷𝐼global = ∑ λ𝑖 𝐷𝐼𝑖
𝑖=1

Table 18. Component-wise Damage Index (DI) calculation for the NEESWood two-story light
wood frame structure utilizing numerical response of Northridge earthquake ground motion with
scale factor 1.20
Wall

Floor

Wall 1y
Wall 2x
Wall 3y
Wall 4x
Wall 5y
Wall 6x
Wall 7y
Wall 8x
Wall 1y
Wall 2x
Wall 3y
Wall 4x
Wall 5y
Wall 6x
Wall 7y
Wall 8x

first floor
first floor
first floor
first floor
first floor
first floor
first floor
first floor
second floor
second floor
second floor
second floor
second floor
second floor
second floor
second floor

Component
𝑫𝑰𝒊
0.66
0.60
0.55
0.94
0.99
0.93
1.01
0.93
0.56
0.23
0.57
0.39
0.88
0.43
0.84
0.41

Lambda
𝛌𝒊
0.06
0.06
0.05
0.09
0.08
0.09
0.08
0.09
0.05
0.02
0.05
0.04
0.08
0.04
0.07
0.04

𝝀𝒊 𝑫𝑰𝒊
0.04
0.04
0.03
0.09
0.08
0.08
0.08
0.09
0.03
0.01
0.03
0.02
0.07
0.02
0.06
0.02

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Table 18 presents the component-wise Damage Index (DI) calculations for the NEESWood twostory light wood-frame structure. The table summarizes the maximum displacement, energy
dissipation, calibrated beta, and computed DI values for each wall on both the first and second
floors. Additionally, the weighting factor and its contribution to the Global DI are listed, providing
insights into the relative importance of each wall in the overall structural response.
Summing the 𝜆𝑖 𝐷𝐼𝑖 values for all walls:
16

𝐷𝐼global = ∑ λ𝑖 𝐷𝐼𝑖 = 0.76
𝑖=1

6.2 Damage Correlation
The primary purpose of this section is to establish a correlation between the calculated Global
Damage Index (DI) from the numerical dynamic analysis and the observed damage from the
corresponding benchmark test, specifically Phase 05 Test 08 of the NEESWood two-story light
wood-frame building. The calculated Global DI for this test was 0.76, and this value is used as a
basis for understanding the severity and extent of damage visible in the benchmark test. By
comparing numerical predictions with actual damage, this analysis aims to validate the calibration
of the Damage Index equation and assess its reliability for predicting real-world structural
performance.
The photographs in Figure 43 illustrate the types of damage sustained during the seismic
benchmark test. The observed damage includes both structural and non-structural failures:
Cracking in Gypsum Wallboard:

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Figure 43. Observed damages for the NEESWood benchmark test after Phase 05 Test 08

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Extensive diagonal, horizontal, and localized cracks were observed near wall intersections and
openings, such as doors and windows. These cracks suggest that the gypsum wallboard
experienced significant shear and tensile forces due to seismic shaking.
Spalling of Stucco:
The exterior stucco layer exhibited spalling around corners and edges of walls, indicating localized
material failure due to high stress concentrations. Spalling is particularly prominent near
connections and load-transfer regions.
Buckling and Crushing:
Evidence of buckling in wallboards and crushing of drywall corners demonstrates areas subjected
to compressive stresses exceeding material limits. These types of damage often occur in areas of
inter-story drift or concentrated force transfer.
Localized Connection Failures:
Cracking and separation were noted along sill plates and wall intersections, highlighting critical
points of weakness where forces exceeded connection capacity.

6.3 Correlating Damage Across a Range of Intensity Levels
Following the correlation of observed damage with the calculated Global Damage Index (DI) for
Test Phase 5, Test 8, it is equally critical to expand this analysis to a broader range of intensity
levels. The benchmark structure used for the NEESWood project was fully furnished and
constructed to simulate real-world conditions. This provides a unique opportunity to investigate
how the structure responds to varying seismic intensities and how observed damage aligns with
calculated DIs across different scenarios.

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By analyzing a series of additional tests under Test Phase 5, which were conducted using a wide
variety of ground motion intensity levels, we can better understand the progression of structural
damage. These tests are essential for:
a) Exploring Intensity-Dependent Damage:
Different earthquake intensity levels elicit varying degrees of structural response, ranging from
minor cracking and spalling to extensive deformation and potential collapse. By correlating
observed damage with calculated DIs across these tests, we can validate the robustness of the
damage index framework.
b) Identifying Damage Trends:
The analysis of damage under varying seismic intensities helps reveal trends, such as the onset of
significant cracking or the transition to collapse-level damage. Understanding these trends is vital
for assessing building resilience and identifying critical performance thresholds.
As seismic intensity increases, damage typically transitions from localized non-structural damage
to widespread structural failures. Investigating these transitions helps refine performance
objectives and establish a more comprehensive understanding of structural behavior. The results
of these tests will further illuminate how the Global DI captures the cumulative effects of
displacement, energy dissipation, and hysteretic behavior under increasing earthquake intensity.
To build upon this analysis, it is essential to correlate the calculated Global Damage Index (DI)
values with the seismic intensity parameters used during these benchmark tests. Table 19 provides
a summary of the Peak Ground Acceleration (PGA) values in both the X and Y directions, which
represent the seismic intensity levels applied to the benchmark structure in the numerical analysis.
These PGA values serve as the input for the dynamic simulations, while the corresponding
calculated Global DI values offer a quantitative measure of the structural response and damage

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under each intensity scenario. By presenting this table, we aim to link the seismic intensity levels
with the predicted structural performance, enabling a comprehensive assessment of how well the
calculated Global DI reflects the observed damage trends.
Table 19. Peak Ground Acceleration (PGA) in X and Y directions from NEESWood benchmark
tests used in numerical analysis and obtained Global DI from numerical response

Test ID
Phase 5, Test 3
Phase 5, Test 6
Phase 5, Test 11

PGA(g) in X
Direction
0.19
0.31
0.47

PGA(g) in Y
Direction
0.22
0.36
0.47

Global Damage
Index
0.20
0.52
0.83

The correlation between the calculated global Damage Index (DI) and the observed damage
provides a comprehensive understanding of how the structure responds to varying seismic
intensities. The tabulated results in Table 19 present numerical evidence of structural performance
and its degradation under increasing ground motion levels. To further validate and contextualize
these findings, visual documentation of the damage observed during the corresponding benchmark
tests is presented. These figures illustrate the progression of damage at various DI levels, offering
a qualitative perspective that complements the numerical analysis. By examining the visual
damage and its alignment with the calculated DI, we can critically assess the accuracy and
applicability of the DI framework in capturing real-world structural behavior.

110

Figure 44. Level of damage observed during different test phases of the NEESWood benchmark
test and corresponding global DI value for each of the tests based on numerical dynamic analysis
response

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The observed damage trends corresponding to the global Damage Index (DI) values reveal a
progressive increase in structural damage as the DI increases, providing a clear correlation between
the numerical analysis and the physical test results. Here’s an analytical breakdown of the trends:
a) DI = 0.20 (Minimal Damage):
Observed damage is primarily non-structural, with minor cracks evident on wall surfaces
and localized areas. This level of damage corresponds to minor seismic excitations, where
the structure remains within the elastic range or experiences minimal inelastic behavior.
The DI value of 0.20 accurately reflects this early stage of damage, signifying minor energy
dissipation and limited displacement.
b) DI = 0.52 (Moderate Damage):
Damage observations reveal significant spalling of the stucco, diagonal cracking around
wall openings, and detachment of non-structural components. The increase in DI indicates
that the structure has transitioned to moderate inelastic behavior, with energy dissipation
concentrated around joints and weak points. The observed damage aligns with numerical
predictions, emphasizing the structural vulnerability at this stage, particularly in areas of
high stress concentration.
c) DI = 0.83 (Severe Damage):
The damage becomes widespread, with visible signs of structural compromise such as large
cracks, extensive spalling, and partial failure of wall sections. Internal non-structural
components show extensive deformation, and localized collapse in certain regions
becomes evident. The high DI value reflects substantial energy dissipation and large
displacements, indicative of near-collapse conditions. The numerical predictions provide a

112

strong correlation to the observed damage, underscoring the validity of the damage index
framework.
In addition to calculating the Global Damage Index (DI) from the numerical model response, this
study further reinforces the validity of the proposed framework by computing the Global DI
directly from the benchmark test response.
The comparison between the Global Damage Index (DI) values derived from the numerical model
and those obtained from the experimental benchmark test indicates a generally consistent trend,
validating the core assumptions of the proposed framework and beta calibration process. However,
some discrepancies—particularly in mid- and high-intensity tests—highlight areas where the
validation remains relatively weak and presents opportunities for improvement. The lack of model
optimization, while intentional to preserve generality, limited the accuracy of response prediction,
especially in replicating nuanced hysteretic behavior. Simplified assumptions regarding material
uniformity, connection behavior, and boundary conditions further contributed to deviations from
experimental results, which inherently captured more complex energy dissipation mechanisms
such as fastener slip and material degradation. Moreover, the experimental setup itself had
limitations, including potential noise in sensor data and constrained instrumentation coverage,
which may have affected the precision of measured displacements and forces. To strengthen the
validation, future work should incorporate targeted calibration, probabilistic modeling of
construction variability, and higher-resolution experimental data. These enhancements would
improve the predictive fidelity of the numerical model and elevate the reliability of the DI
framework in capturing real-world seismic performance of wood-frame structures.

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Table 20. Comparison of Global DI values obtained from numerical response and experimental
benchmark test response, demonstrating the validity of the beta calibration and the reliability of
the developed framework.
P05T03

P05T06

P05T08

P05T11

Numerical Model

0.20

0.52

0.76

0.83

Benchmark Test

0.13

0.58

0.61

0.79

By applying the same Damage Index frameworks, but utilizing the displacement and energy
dissipation observed during the actual shake table test, the experimental Global DI was determined.
The calculated values align well with those derived from the numerical model, indicating that the
beta calibration performed for the numerical model accurately reflects the real-world behavior of
the structure under seismic loading. This additional validation step further confirms that the
developed methodology is a reliable tool for assessing seismic damage in light wood-frame
buildings.
The results of this study showcase the effectiveness of the developed Damage Index (DI)
framework for assessing seismic damage in light wood-frame buildings. The systematic approach,
outlined in the flowchart (Figure 45), provides a robust and repeatable methodology for evaluating
structural performance under varying seismic intensities.

114

Figure 45. Flowchart outlining the step-by-step framework for seismic damage assessment of light
wood-frame buildings using Damage Index (DI).
The framework begins with the development of a validated numerical model of the structure,
which captures the unique characteristics of light wood-frame buildings, including their
redundancy, load-sharing mechanisms, and material variability. This model forms the foundation
for subsequent steps, such as the identification of collapse intensity through Incremental Dynamic
Analysis (IDA). The global beta (β) parameter calibration process ensures that the DI equation
accurately reflects the cumulative behavior of the structure as a whole.
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The results demonstrate a strong correlation between calculated DI values and observed damage
patterns during the NEESWood benchmark tests. For example, at a DI of 0.20, minimal damage
was observed, primarily consisting of minor cracks in non-structural components. As the DI
increased to 0.52, moderate damage, including spalling and cracking around wall openings,
became evident. At a DI of 0.83, the damage transitioned to severe, with large cracks, spalling,
and partial structural failure observed. These trends validate the capability of the DI framework to
accurately capture and predict the progression of structural damage.
In conclusion, the results affirm that the developed framework is a practical and reliable tool for
assessing seismic damage in light wood-frame buildings. By integrating numerical and
experimental data, it bridges the gap between theoretical predictions and real-world observations.
The methodology is not only a step forward in damage assessment but also a critical tool for
advancing performance-based seismic design and resilience planning for light wood-frame
structures.

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7 Conclusion
This thesis presents a comprehensive and validated framework for calculating the Global Damage
Index (DI) specifically tailored to light wood-frame buildings, representing a major advancement
in seismic performance assessment for this widely used construction type. By addressing the
limitations of traditional component-based damage models, the study introduces a global-level
methodology that captures the cumulative and system-wide behavior of light-frame structures
under seismic loading conditions.
The proposed framework integrates nonlinear numerical modeling, Incremental Dynamic Analysis
(IDA), pushover analysis, and experimental validation using data from the NEESWood two-story
light-frame wood building shake table test. This multidimensional approach enables accurate
prediction of global damage while maintaining sensitivity to both structural and non-structural
failure mechanisms.
A key contribution of the study is the calibration of the β parameter in the Park and Ang Damage
Index equation, customized for the dynamic characteristics of wood-frame systems. The
calibration process utilized critical global response parameters such as roof displacement and base
shear force, derived from scaled ground motion simulations of the 1994 Northridge earthquake.
The model’s predictions were cross-validated against physical observations from full-scale testing,
revealing a strong correlation between computed DI values and actual damage patterns.
To enhance interpretability, the study establishes damage classification thresholds based on the
computed DI values:
•

DI < 0.25 corresponds to minor, non-structural damage, such as superficial cracking or
detachment of finishes.

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•

DI between 0.25 and 0.60 marks the transition to major non-structural damage and
initiation of structural damage, typically affecting sill plates, anchorage regions, and local
deformation zones.

•

DI > 0.60 indicates extensive structural damage, with possible system instability or
collapse potential, and reflects significant compromise in lateral load-resisting elements.

These thresholds provide a practical means to interpret DI outputs and connect numerical
predictions to real-world consequences. While the thresholds are supported by strong experimental
validation, they are preliminary and should be refined further through the development of damage
fragility curves and broader datasets encompassing varying ground motions and building
typologies.
The framework developed here offers substantial benefits for engineering practice, postearthquake assessment, and retrofitting strategies. It equips engineers, researchers, and decisionmakers with a quantifiable and scalable tool to evaluate seismic vulnerability and prioritize
structural interventions. Moreover, by bridging the gap between localized damage measures and
holistic building behavior, this approach lays the groundwork for more robust risk models and
resilience-based design tools for wood-frame construction.
In conclusion, this study marks a significant step forward in the seismic evaluation of light woodframe buildings. Future research should aim to extend the framework to multi-story and hybrid
systems, incorporate long-duration and near-fault ground motions, and enhance calibration
through a statistical, multi-building dataset to support region-wide seismic resilience efforts.

7.1 Future Work
While this thesis establishes a robust and validated framework for the calculation of the Damage
Index (DI) tailored to light wood-frame buildings, there remains considerable scope for refining
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and expanding the methodology. The work presented represents a critical foundation, but future
research is essential to enhance its applicability and precision.
A key area for advancement lies in the development of damage fragility curves specifically for
light wood-frame construction. Unlike steel and concrete buildings, where well-defined fragility
functions and limit-state criteria have been developed, light wood-frame structures lack systematic
studies that connect DI values with observed physical damage. The threshold classifications
proposed in this study—ranging from minor non-structural to severe structural damage—serve as
initial estimates but require further calibration through large-scale experimental campaigns and
analytical studies. Future work should incorporate a wide range of seismic inputs, including
various ground motion types (e.g., crustal and subduction earthquakes) and intensity levels, as well
as diverse building geometries and configurations.
Additionally, the global-level beta calibration process introduced in this thesis must be validated
across more complex structural systems, such as multi-story light-frame buildings. This will
involve additional experimental testing and refined numerical modeling to ensure that the
interaction between structural and non-structural components is accurately captured under
different loading conditions. Incorporating advanced material models, such as nonlinear hysteretic
behavior and degradation effects, along with soil-structure interaction, could provide a more
comprehensive understanding of seismic performance.
Further research should also aim to establish quantitative limit-state criteria based on DI values.
By correlating specific DI thresholds with defined damage states—such as reparable non-structural
damage, localized structural yielding, or near-collapse—engineers can adopt this framework in
practical seismic design, retrofitting, and post-earthquake assessment strategies. Doing so will help

119

align light wood-frame assessment methods with those already available for reinforced concrete
and steel structures.
In conclusion, while this thesis lays the groundwork for DI-based seismic assessment in light
wood-frame buildings, continued research toward the development of fragility curves, DI-based
limit states, and enhanced modeling approaches will be instrumental in advancing this
methodology into a widely accepted and applicable engineering tool for seismic risk mitigation.

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