ABSTRACT OF THE DISSERTATION OF
Kraisorn Lucksiri for the degree of Doctor of Philosophy in Wood Science and Civil
Engineering presented on March 21, 2012.
Title: Development of Rapid Visual Screening Tool for Seismic Evaluation of WoodFrame Dwellings.
Abstract approved:
_____________________________________________________________________
Thomas H. Miller
Rakesh Gupta
During the past several decades, earthquakes have caused extensive damage to
buildings, including wood-frame, single-family dwellings, in the United States. In
order to mitigate future losses, existing buildings in earthquake prone areas should be
evaluated for their seismic safety. This is also an important issue for buildings in
Oregon due to the Cascadia subduction zone along its west coast.
One seismically vulnerable element observed in wood-frame, single-family dwellings
is the shear walls. In general, assessment of shear wall seismic performance can be
accomplished by a building-specific engineering calculation. Extra effort is required if
the effects of plan irregularity are a concern. This project aims to facilitate seismic
evaluation of wood-frame dwellings by proposing a new engineering-based rapid
visual screening method to examine the expected performance level of the structure’s
exterior shear walls to resist lateral forces from ground motions, including torsional
forces induced from plan irregularity.
In order to achieve the objective, SAPWood software was used to perform a series of
nonlinear time-history analyses for 480 representative models, covering different
combinations of shape parameters and shear wall opening-related parameters. The
evolutionary parameter hysteresis model was used to represent the load-displacement
relationship of structural panel-sheathed shear walls and a ten parameter CUREE
hysteresis model for gypsum wallboard sheathed walls. The calculated maximum
lateral drifts were used as basic information for the development of the new method.
Through the development process, the significance of both plan configuration and
shear wall openings were emphasized as they affect the overall seismic performance
of a building through building mass, lateral stiffnesses, and eccentricities. Within the
study range, single-family dwellings with two stories, a larger percentage of openings,
and having a garage door were shown to be more vulnerable to seismic events. Plan
configuration and shear wall openings were important features especially in houses
located in high 1 (0.5g ≤ Sa < 1.0g) and high 2 (1.0g ≤ Sa < 1.5g) seismicity regions, as
they could potentially lead to severe damage. For low and moderate seismicity, the
performance ranges from satisfying the collapse prevention limit to the immediate
occupancy limit.
The developed piRVS (plan irregularity Rapid Visual Screening) takes into
consideration the shape of the floor plan, number of stories, base rectangular area,
percent cutoff, and openings from doors/windows and garage doors, and supports
evaluation at the immediate occupancy (IO), life safety (LS), and collapse prevention
(CP) performance levels. The piRVS provides relatively more conservative
assessment results than FEMA 154 and ASCE 31 Tier 1. Its prediction for the two
applicable Northridge earthquake damage samples is reasonable. This method will
help architects, engineers, building officials, and trained inspectors in examining the
expected seismic performance of shear walls, considering the effects of plan
irregularity in wood-frame, single-family dwellings.
© Copyright by Kraisorn Lucksiri
March 21, 2012
All Rights Reserved
DEVELOPMENT OF RAPID VISUAL SCREENING TOOL FOR SEISMIC
EVALUATION OF WOOD-FRAME DWELLINGS
by
Kraisorn Lucksiri
A DISSERTATION
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Doctor of Philosophy
Presented March 21, 2012
Commencement June 2012
Doctor of Philosophy dissertation of Kraisorn Lucksiri presented on March 21, 2012.
APPROVED:
_____________________________________________________________________
Co-Major Professor, representing Civil Engineering
_____________________________________________________________________
Co-Major Professor, representing Wood Science
_____________________________________________________________________
Head of the School of Civil and Construction Engineering
_____________________________________________________________________
Head of the Department of Wood Science and Engineering
_____________________________________________________________________
Dean of the Graduate School
I understand that my dissertation will become part of the permanent collection of
Oregon State University libraries. My signature below authorizes release of my
dissertation to any reader upon request.
_____________________________________________________________________
Kraisorn Lucksiri, Author
ACKNOWLEDGMENTS
I would like to express my sincere gratitude and appreciation to all the people who
helped and inspired me during my Ph.D. study:
•
I especially would like to thank my advisors, Dr. Thomas Miller and Dr. Rakesh
Gupta, for giving me an opportunity to learn and pursue my goals at Oregon State
University. Their excellent guidance, technical expertise and continuous support
are deeply appreciated.
•
Special thanks and sincere gratitude to Dr. Thomas Miller. I am indebted to him
for his support and motivation through difficult periods in both my Masters and
Doctoral studies. I have been fortunate to study under his tutelage.
•
Dr. John van de Lindt and Dr. Shiling Pei for their continuous support throughout
the project.
•
Dr. Barbara Lachenbruch, Dr. Michael Scott, and Dr. Kate Lajtha for serving as
my dissertation committee members. Their suggestions and feedback on several
aspects of my research are really appreciated.
•
The Royal Thai Government for an opportunity and financial support.
•
All of my friends for their friendship and making my time at OSU memorable.
•
My father, mother, and family for the love, caring, support, and encouragement
they have unconditionally provided.
CONTRIBUTION OF AUTHORS
Dr. Thomas Miller, Dr. Rakesh Gupta, Dr. John van de Lindt, and Dr. Shiling Pei
were involved in all aspects of the work leading to this dissertation including advising
on data collection, analysis and help in writing the manuscripts.
TABLE OF CONTENTS
Page
Chapter 1: General Introduction .................................................................................... 1
Motivation .......................................................................................................... 1
Objectives and Scope ......................................................................................... 2
Technical Approach ........................................................................................... 3
Organization of the Dissertation ........................................................................ 5
Chapter 2: Effect of Plan Configuration on Seismic Performance of SingleStory, Wood-Frame Dwellings ..................................................................... 7
Abstract .............................................................................................................. 7
Introduction ........................................................................................................ 9
Plan Configuration Observation....................................................................... 10
Case Study Configurations............................................................................... 12
Structural Modeling ......................................................................................... 14
Ground Motions and Structural Analysis......................................................... 17
Results and Discussion..................................................................................... 19
Effect of Overall Shape Ratio .............................................................. 21
Effect of Percent Cutoff ....................................................................... 22
Effect of Cutoff Shape Ratio ................................................................ 23
Conclusions ...................................................................................................... 24
Acknowledgments ............................................................................................ 25
References ........................................................................................................ 25
TABLE OF CONTENTS (Continued)
Page
Chapter 3: A Procedure for Rapid Visual Screening for Seismic Safety of
Wood-Frame Dwellings with Plan Irregularity .......................................... 40
Abstract ............................................................................................................ 40
Introduction ...................................................................................................... 42
Methodology .................................................................................................... 44
Building Configuration Parameters...................................................... 44
Seismic Response Prediction ............................................................... 48
Results and Discussion..................................................................................... 52
Overall Seismic Performance............................................................... 52
Development of Grading Sheets .......................................................... 55
Conclusions ...................................................................................................... 57
Acknowledgments ............................................................................................ 58
References ........................................................................................................ 58
Chapter 4: Implementation of Plan Irregularity Rapid Visual Screening Tool
for Wood-Frame, Single-Family Dwellings ............................................... 71
Abstract ............................................................................................................ 71
Introduction ...................................................................................................... 73
Evaluation Methods ......................................................................................... 74
FEMA 154 (Rapid Visual Screening of Buildings for Potential
Seismic Hazards).................................................................................. 74
Tier 1 of ASCE 31-03 (Seismic Evaluation of Existing Buildings) .... 75
piRVS (Plan Irregularity Rapid Visual Screening) .............................. 76
TABLE OF CONTENTS (Continued)
Page
Methodology .................................................................................................... 76
Study Samples ...................................................................................... 76
Modeling Assumptions ........................................................................ 77
Level of Seismicity and Soil Types ..................................................... 77
Evaluation Methods and Assumptions ................................................. 78
Results and Discussion..................................................................................... 82
Uncertainties inherent in piRVS Performance Scores ......................... 82
Prediction Results between piRVS, ASCE 31 Tier 1, and FEMA
154 ........................................................................................................ 84
1994 Northridge Damage Predictions .................................................. 86
Conclusions ...................................................................................................... 89
Acknowledgments ............................................................................................ 90
References ........................................................................................................ 90
Chapter 5: General Summary, Conclusions, and Future Work.................................. 100
Summary ........................................................................................................ 100
Conclusions .................................................................................................... 102
Future work .................................................................................................... 104
Bibliography............................................................................................................... 106
Appendices ................................................................................................................. 110
LIST OF FIGURES
Figure
Page
2.1 Plan shape parameters and notation ....................................................................... 31
2.2 Summary of configurations based on observations of existing buildings ............. 32
2.3 Rectangular wood-frame house and its pancake model ......................................... 33
2.4 Response spectra of ground motion records (5% damping) .................................. 33
2.5 Summary of the selected worst-case-scenario models ........................................... 34
2.6 Median maximum drifts at Sa= 0.1g-2.0g for all case study models ..................... 36
2.7 Effect of shape ratio in terms of median maximum drifts at Sa= 0.5g ................... 36
2.8 Effect of shape ratio in terms of number of drifts exceeding 3% .......................... 37
2.9 Effect of percent cutoff in terms of median maximum drifts at Sa= 0.5g .............. 38
2.10 Effect of cutoff shape ratio and cutoff ratio on median maximum drifts............. 38
2.11 Effect of cutoff shape ratio and cutoff ratio ......................................................... 38
3.1 Composition of plan shapes ................................................................................... 64
3.2 Average performance grades of all models for each seismic region ..................... 65
3.3 Effect of base-rectangular area (1-story, R= 1.0)................................................... 65
3.4 Effect of base-rectangular area (2-story, R≠ 1.0) ................................................... 66
3.5 Effect of percent openings and garage door........................................................... 66
3.6 Effect of percent openings and garage door........................................................... 67
3.7 Histograms of maximum differences of Gavg among L, T, and Z shapes .............. 67
3.8 Grading sheet for 1-story L, T, and Z shapes......................................................... 68
3.9 Grading sheet for 2-story L, T, and Z shapes......................................................... 69
LIST OF FIGURES (Continued)
Figure
Page
4.1 Basic shape parameters for L-shape buildings ....................................................... 96
4.2 Example of a scoring table for one-story, L, T, Z shape buildings ........................ 96
4.3 Flowchart for selection of percent opening score modifiers .................................. 97
4.4 Comparisons of performance scores ...................................................................... 97
4.5 Ranges of score difference between piRVS and SAPWood .................................. 98
4.6 SAPWood performance scores for 40 one-story L-shape models ......................... 98
4.7 Seismic performance of sample houses on ASCE 41-06 performance scale......... 99
LIST OF TABLES
Table
Page
2.1 Randomly selected cities in each group ................................................................. 28
2.2 Determination of population weights among city groups ...................................... 28
2.3 Summary of observed parameters and selected ranges for modeling .................... 29
2.4 Comparison of seismic responses .......................................................................... 30
3.1 Observed areas of plan shapes from phase 1 (Lucksiri et al. 2012) ....................... 61
3.2 Base-rectangular areas selected for RVS development ......................................... 61
3.3 Selected shape ratios and percent cutoffs............................................................... 61
3.4 Example of case study matrix ................................................................................ 62
3.5 Summary of total number of representative models .............................................. 63
3.6 CUREE parameters for 2.4 m (8 ft) by 2.4 m (8 ft) GWB wall model .................. 63
3.7 Seismic region definition ....................................................................................... 63
3.8 Performance grade conversion criteria................................................................... 64
3.9 Minimum and maximum values of average performance grades (Gavg) ................ 64
4.1 Summary of 1-story sample models....................................................................... 93
4.2 Summary of 2-story sample models....................................................................... 93
4.3 Levels of Seismicity Definitions ............................................................................ 94
4.4 Summary of percent agreement between ASCE 31 Tier 1 and piRVS.................. 94
4.5 Summary of percent agreement between FEMA 154 and piRVS ......................... 95
4.6 Configuration details and dynamic properties of sample models from ATC38 .... 95
LIST OF APPENDICES
Appendix
Page
Appendix A: Configuration summary for phase 1 study ........................................... 111
Appendix B: Median maximum drifts for phase 1 study ........................................... 116
Appendix C: Case study matrices for phase 2 study .................................................. 121
Appendix D: piRVS grading sheets developed in phase 2 ........................................ 139
Appendix E: Configuration summary for phase 3 study............................................ 148
Appendix F: Modified piRVS grading sheet for phase 3 study ................................. 155
Appendix G: Summary of phase 3 analysis results.................................................... 164
LIST OF APPENDIX FIGURES
Figure
Page
D1 Grading sheet for 1-story rectangular shape ........................................................ 140
D2 Grading sheet for 1-story L, T, and Z shapes ....................................................... 141
D3 Grading sheet for 1-story T-shape (for 4,500 sq.ft. base area)............................. 142
D4 Grading sheet for 1-story U-shape ....................................................................... 143
D5 Grading sheet for 1-story U-shape (for 4,500 sq.ft. base area) ............................ 144
D6 Grading sheet for 2-story rectangular shape ........................................................ 145
D7 Grading sheet for 2-story L, T, Z shapes ............................................................. 146
D8 Grading sheet for 2-story U-shape ....................................................................... 147
E1 Wall side notations for each plan shape (phase 3)................................................ 148
F1 Modified grading sheet for 1-story rectangular shape .......................................... 157
F2 Modified grading sheet for 1-story L, T, and Z shapes ........................................ 157
F3 Modified grading sheet for 1-story T-shape ......................................................... 158
F4 Modified grading sheet for 1-story U-shape ......................................................... 159
F5 Modified grading sheet for 1-story U-shape ......................................................... 160
F6 Modified grading sheet for 2-story rectangular shape .......................................... 161
F7 Modified grading sheet for 2-story L, T, Z shapes ............................................... 162
F8 Modified grading sheet for 2-story U-shape ......................................................... 163
LIST OF APPENDIX TABLES
Table
Page
A1 Configuration details for R-Shape ....................................................................... 111
A2 Configuration details for L-Shape ........................................................................ 111
A3 Configuration details for T-Shape ........................................................................ 112
A4 Configuration details for U-Shape ....................................................................... 113
A5 Configuration details for Z-Shape ........................................................................ 114
B1 Median maximum drifts (in.) for R-Shape ........................................................... 116
B2 Median maximum drifts (in.) for L-Shape ........................................................... 117
B3 Median maximum drifts (in.) for T-Shape ........................................................... 118
B4 Median maximum drifts (in.) for U-Shape ........................................................... 119
B5 Median maximum drifts (in.) for Z-Shape ........................................................... 119
C1 Summary of 1-story rectangular shape models .................................................... 121
C2 Summary of 1-story L-shape models ................................................................... 122
C3 Summary of 1-story T-shape models ................................................................... 124
C4 Summary of 1-story U-shape models ................................................................... 126
C5 Summary of 1-story Z-shape models ................................................................... 128
C6 Summary of 2-story rectangular shape models .................................................... 130
C7 Summary of 2-story L- shape models .................................................................. 131
C8 Summary of 2-story T- shape models .................................................................. 133
C9 Summary of 2-story U- shape models .................................................................. 135
C10 Summary of 2-story Z- shape models ................................................................ 137
LIST OF APPENDIX TABLES (Continued)
Table
Page
E1 Configuration details for 1-story rectangular shape samples ............................... 149
E2 Configuration details for 1-story L-shape samples............................................... 150
E3 Configuration details for 1-story T-shape samples............................................... 151
E4 Configuration details for 1-story U-shape samples .............................................. 151
E5 Configuration details for 1-story Z-shape samples............................................... 152
E6 Configuration details for 2-story rectangular shape samples ............................... 153
E7 Configuration details for 2-story L-shape samples............................................... 154
E8 Configuration details for 2-story T-shape samples............................................... 154
E9 Configuration details for 2-story Z-shape samples............................................... 154
G1 Summary of analysis results (phase 3) for 1-story rectangular shape .................. 165
G2 Summary of analysis results (phase 3) for 1-story L-shape ................................. 166
G3 Summary of analysis results (phase 3) for 1-story T-shape ................................. 168
G4 Summary of analysis results (phase 3) for 1-story U-shape................................. 169
G5 Summary of analysis results (phase 3) for 1-story Z-shape ................................. 170
G6 Summary of analysis results (phase 3) for 2-story rectangular shape .................. 171
G7 Summary of analysis results (phase 3) for 2-story L-shape ................................. 172
G8 Summary of analysis results (phase 3) for 2-story T-shape ................................. 173
G9 Summary of analysis results (phase 3) for 2-story Z-shape ................................. 173
Development of Rapid Visual Screening Tool for Seismic Evaluation of Wood-Frame
Dwellings
CHAPTER 1: GENERAL INTRODUCTION
Motivation
Light-frame wood construction is by far the most common type for single-family
dwellings (SFD) in North America. It constitutes approximately 90% of all residential
buildings in the United States and up to 99% for the states of California and Oregon
(NIBS 2003). Any hazards that cause damage to this building type thus could lead to
extensive damage, injuries, and loss of life over a wide area. During the past several
decades, earthquakes such as the 1989 Loma Prieta and 1994 Northridge have shown
significant losses from damage and degradation of the overall strength and stability of
existing buildings, including wood-frame SFD. In order to mitigate future losses, the
existing buildings in an earthquake prone area should thus be evaluated for their
vulnerability and expected damage from a possible future earthquake. This is an
important issue for buildings in Oregon because the Cascadia subduction zone along
its west coast is a potential source of a major earthquake (magnitude 8 or larger)
(Nelson et al. 2006).
For decades, the Rapid Visual Screening (RVS) method has played an important role
in an early stage seismic performance evaluation of buildings. The RVS provides the
users, such as architects, engineers, building officials, and home owners, an
inexpensive and quick way to identify the potential sources of seismic deficiency and
obtain a preliminary recommendation of whether a more detailed analysis is
necessary. This is a very challenging task since the RVS is generally based on a
limited amount of information, essentially from a sidewalk survey. For wood-frame
SFD, some elements such as garage doors, unreinforced masonry chimneys, and
cripple walls may be easy to identify as obvious potential sources of damage. This is
however not the case for damage to shear walls, an important and commonly observed
2
seismically damaged element. Shear wall repair costs can be high (if repair is possible)
and, in fact, severe damage to shear walls can lead to injuries and loss of life.
Shear wall damage severity is related to many factors such as (i) characteristics of
ground motions at the building site (e.g. amplitude, duration, and frequency content),
(ii) dynamic characteristics of the building (e.g. natural frequency and damping), (iii)
load-resistance properties of the building (e.g. stiffness, strength, and ductility), and
(iv) inherent irregularities (e.g. plan irregularity due to large openings, garage doors,
and plan shape). These factors are generally taken into account in the detailed seismic
performance evaluation, but not in the RVS due to its complexity. For example,
assessment of shear wall adequacy and the expected seismic performance is not
directly included in the currently available RVS, FEMA 154 (FEMA 2002a).
Evaluation of the effect of plan irregularity on the overall seismic performance is very
limited in terms of detail, i.e. it is based only on an indication of the existence of plan
irregularity. A single-value score modifier was provided for each structural type (for
each seismicity region) to represent the effect of plan irregularity regardless of
building size, plan shape, number of floors, shear wall openings, and size of reentrant
corners. These limitations provide an impetus for this project.
Objectives and Scope
The objective of this study is to develop an engineering-based plan irregularity Rapid
Visual Screening (piRVS) method for the State of Oregon that: (i) takes into
consideration of the plan configuration, number of stories, shear wall openings, and
garage doors, and (ii) examines the adequacy and the expected seismic performance,
in terms of immediate occupancy, life safety, and collapse prevention, of wood-frame,
single-family dwellings to resist lateral forces resulting from ground motions and also
torsional forces induced from the plan irregularity.
The focus area for this study is the State of Oregon. Ten pairs of ground motion time
histories developed for nearby Seattle were selected for the analysis to represent three
3
types of seismic sources including (i) shallow crustal faults (at depths less than 10
km), (ii) subducting Juan de Fuca plate (at depths of about 60 km), and (iii) plate
interface at the Cascadia subduction zone. Application of the piRVS is thus suitable
for Oregon and the nearby area subject to the same or similar sources of ground
motions.
This study emphasized specifically the seismic performance of buildings considering
the additional torsional forces induced from plan irregularity. The proposed method
does not evaluate other sources of seismic vulnerabilities such as the stress
concentrations at reentrant corners, vertical irregularity, liquefaction, slope failure,
unreinforced masonry chimneys, foundation connections, etc.
Technical Approach
There are two main approaches to develop an RVS method: a category-based
approach and a building-specific approach. The category-based approach is generally
based on historical damage data and/or expert opinion. Unique details of buildings are
usually not included. An RVS method developed from this approach is thus
appropriate at the macroscopic level. The building-specific approach uses engineering
analysis to predict seismic response of buildings. This approach allows for inclusion of
unique details of buildings, an important issue for this study, however, an extensive
number of analyses can be involved. FEMA 154 (FEMA 2002a) is an example of a
category-based approach RVS method, especially in its initial development. Although
it is now based on engineering analysis, i.e. nonlinear pushover analysis, the unique
details of buildings are not included. The load-displacement properties for each
structural type are generally based on a few numbers of representative models. In
addition, the early development relied heavily upon historical damage data and expert
opinion. For example, plan irregularity is approximately addressed in the current
version of FEMA 154 by simply increasing the input spectral acceleration response
values by 50%.
4
Following the 1994 Northridge earthquake, numerous research and development
efforts for wood-frame buildings were carried out. In regards to structural modeling
and analysis, numerical models such as the 10-parameter CUREE hysteresis model
(Folz and Filiatrault 2004), the Evolutionary Parameter Hysteresis Model (EPHM)
(Pei et al. 2006), and pancake models (Folz and Filiatrault 2002), provide practical,
state-of-art models for seismic response prediction of wood-frame buildings. A
seismic analysis program for wood-frame buildings (SAPWood (Pei 2007)), which
incorporates the 10-parameter CUREE model, EPHM model, pancake model, and a
feature to perform multi-case, incremental dynamic analysis has been developed and
become an efficient tool to support a large number of analyses. These valuable
resources provide opportunities for this project to develop a RVS method by the
building-specific approach.
5
Organization of the Dissertation
This dissertation includes three manuscripts for three study phases covering from the
development background to implementation of the proposed method.
In the first manuscript (Chapter 2), numerical modeling and non-linear time-history
analyses were performed to investigate the effect of plan configuration on seismic
performance of single-story, wood-frame SFD. The study results highlight the
importance of plan configuration on seismic performance of single-story, wood-frame
dwellings. In addition, an approach to classify a wood-frame, SFD population into
groups based on the proposed shape parameters, which is a key basis for the
development of plan irregularity rapid visual screening in the second phase, was
introduced.
The second manuscript (Chapter 3) describes the development background of the
piRVS from selection of the configurations and combinations of shape parameters for
480 representative models, analysis assumption and procedures, conversion of the
computed maximum lateral drifts to seismic performance grades, to development of
the piRVS grading sheet. The study results also provide an overall picture of the
seismic performance for one- and two-story wood-frame SFD at each seismicity level.
The third manuscript (Chapter 4) presents an implementation of the piRVS on 124
samples. The obtained results were compared with (i) building-specific, non-linear
time-history analysis, and (ii) FEMA 154 and ASCE 31 Tier 1. In addition,
verification using two houses damaged in the 1994 Northridge Earthquake was also
performed.
Chapter 5 presents an overall summary, conclusions, and recommendations for future
work. Supporting data and tables for all three manuscripts are presented in a series of
supporting appendices, subsequently.
6
EFFECT OF PLAN CONFIGURATION ON SEISMIC PERFORMANCE OF
SINGLE-STORY, WOOD-FRAME DWELLINGS
Kraisorn Lucksiri, Thomas H. Miller, Rakesh Gupta, Shiling Pei, and John W. van de
Lindt
Natural Hazards Review
American Society of Civil Engineers
1801 Alexander Bell Drive
Reston, VA 20191, USA
Accepted for publication on June 6, 2011
Published 13(1): 24-33, February, 2012.
Published Online: DOI 10.1061/(ASCE)NH.1527-6996.0000061
7
CHAPTER 2: EFFECT OF PLAN CONFIGURATION ON SEISMIC
PERFORMANCE OF SINGLE-STORY, WOOD-FRAME DWELLINGS
Kraisorn Lucksiri1, Thomas H. Miller2, Rakesh Gupta3, Shiling Pei4, and John W. van
de Lindt5
Abstract
A numerical investigation is presented on effects of plan configuration on seismic
responses of single-story, wood-frame dwellings. 151 models were developed using
observations of 412 dwellings of rectangular, L, T, U, and Z shapes in Oregon. A
nonlinear, time-history program, Seismic Analysis Package for Woodframe Structures,
was the analysis platform. Models were analyzed for 10 pairs of biaxial ground
motions (spectral accelerations from 0.1g to 2.0g) for Seattle. Configuration
comparisons were made using median shear wall maximum drifts and occurrences of
maximum drifts exceeding the 3% collapse prevention limit. Plan configuration
significantly affects performance through building mass, lateral stiffnesses and
eccentricities. Irregular configuration tends to induce eccentricity and cause one wall
to exceed the allowable drift limit, and fail, earlier than others. Square-like buildings
usually perform better than long, thin rectangles. Classification of single-story
dwellings based on shape parameters, including size and overall aspect ratio, plan
shape, and percent cutoff area, can organize a building population into groups having
similar performance, and be a basis for including plan configuration in rapid visual
screening.
CE Database subject headings: seismic analysis; wood structures; configuration
8
1
Graduate Student. School of Civil and Construction Engineering and Dept. of Wood
Science and Engineering, Oregon State University, Corvallis, OR 97331. Email:
kraisorn.lucksiri@oregonstate.edu
2
Corresponding Author. Associate Professor. School of Civil and Construction
Engineering, Oregon State University, Corvallis, OR 97331. Email:
thomas.miller@oregonstate.edu
3
Professor. Dept. of Wood Science and Engineering, Oregon State University,
Corvallis, OR 97331. Email: rakesh.gupta@oregonstate.edu
4
Assistant Professor. Dept. of Civil and Environmental Engineering, South Dakota
State University, Brookings SD 57006. Email: Shiling.Pei@sdstate.edu
5
Professor and Drummond Chair. Dept. of Civil, Construction, and Environmental
Engineering, University of Alabama, Tuscaloosa, AL, 35487. Email:
jwvandelindt@eng.ua.edu
9
Introduction
Wood-frame construction is the most common structural type for houses in North
America. It is relatively light weight, flexible and inherently redundant in its force
resisting systems, all beneficial properties for buildings subjected to earthquakes.
However, the Northridge earthquake (Schierle 2003) has shown that small woodframe dwellings are seismically vulnerable to earthquake damage at different levels
from minor non-structural damage, i.e., gypsum wall board (GWB) cracking to an
uninhabitable level. Approximately, $20B of the $40B in losses caused by the
Northridge earthquake were the result of wood frame building damage, virtually all
residential.
Vulnerability assessment of wood-frame dwellings can be initiated by performing a
rapid visual screening (RVS) to obtain preliminary information on whether an
engineering evaluation and/or structural rehabilitation are needed. Examples of
currently available RVS tools are the second edition of FEMA 154 (FEMA 2002a), its
supporting document FEMA 155 (FEMA 2002b), and ATC 50 (ATC 2007). In ATC
50, some features such as foundation connections, cripple walls, and unreinforced
chimneys are relatively easy to identify and decide to rehabilitate as they are obviously
potential sources of damage. This is, however, not the case for features like plan
configuration (shape, including aspect ratio) and irregularity, where the effect varies
from case to case and depends on the type (re-entrant corner, door/window opening,
etc.) and degree of irregularity (size of door/window opening, offset ratio of re-entrant
corner, etc.). This limitation, found in both FEMA 154 and ATC 50, has become our
study motivation.
Inclusion of plan configuration and irregularity in an RVS procedure is a challenging
task, as wood-frame houses vary widely in layout. A numerical model is needed to
capture the complexity of building plan irregularities, and to provide realistic
predictions for a large number of analyses. Plan irregularity is approximately
10
addressed in FEMA 154 by simply increasing the input spectral acceleration response
values by 50%. Here, the Seismic Analysis Package for Woodframe Structures
(SAPWood) (Pei 2007, Pei and van de Lindt 2007) is used to directly handle effects of
plan configuration and irregularity.
This study initiates an approach to include plan configuration and irregularity in RVS.
The objectives are (i) to propose a way to classify single-story, wood-frame dwellings
into groups based on a set of shape parameters and (ii) to numerically investigate the
effect of plan irregularity, resulting from plan configuration, on seismic performance.
Other sources of plan irregularities such as unbalanced stiffnesses caused by large
openings (windows and garage doors) are not included at this stage, but will be a part
of the next study. Models for case study are all single-story buildings. The state of
Oregon is the focus area for the study. Comparisons of performance are based on
maximum shear wall drifts.
Plan Configuration Observation
There are numerous plan configurations possible for residential buildings but not all of
them are commonly used in design. Therefore, the first step was to determine
commonly used plan configurations (shapes) for single-story existing dwellings.
While reviewing construction drawings or an on-site survey of buildings would
provide more accurate data, a different approach was used to save time and cost for
the large number of houses throughout the state. Thus, Google Earth and Google
SketchUp were used. Google Earth displays satellite images of the earth’s surface
while Google SketchUp is a 3D modeling program capable of working together with
Google Earth.
The observation process was a two-step task: city selection and pin point (specific
coordinates within a selected city) selection. City selection was based on 241 Oregon
cities and their population obtained from the Census Bureau’s Population Estimates
Program (U.S. Census Bureau 2009), Vintage 2007. Based on their estimate, there are
11
168 cities (70%) that have population less than 5,000, but only 26 cities (11%) having
population over 20,000. To ensure that samples were collected from different size
cities, this study organized cities into: group A (0 < population ≤ 5,000), group B
(5000< population≤ 20,000), and group C (population> 20,000). Ten cities were then
randomly selected from each group as shown in Table 2.1. Five simple geometries
commonly used for wood-frame dwellings were selected for the study, including
rectangle, L, T, U, and Z shapes.
Before selection of pin points could be made from within a city, boundaries of the city
were established with two pairs of latitude and longitude lines embracing most of the
buildings in the city. This excluded lakes, forest, or agricultural lands with few
residential buildings. Pin points, located within that city boundary, were then
randomly generated in terms of latitude-longitude pairs. Guidelines for pin points and
sample selection were:
1. Each pin point represents the center of an observational area.
2. Houses that have shapes of interest, located within a 76.2 m. (250 ft.) radius
from the pin point, and within a residential area, are sample candidates.
3. Plan area of a sample house did not exceed 464 m2 (5,000 ft2).
4. A reentrant corner is considered to exist if it is at least 1.22x1.22 m. (4 x 4 ft.)
5. As many dwellings were assessed as possible for each pin point. However,
dwellings with exactly the same configuration were assessed only once.
6. Twenty pin points was the overall limit for each city.
The number of samples (for each plan shape) from each group was determined based
on the relative population among groups (A: B: C) which is approximately 1: 2: 7
(Table 2.2). With a limit of 20 pin points per city, total numbers of actual observed
12
samples were 95, 100, 84, 61, and 72 for rectangular, L, T, U, and Z shapes,
respectively. Figure 2.1 shows the details and notation for the observed parameters for
5 shapes of interest (rectangle, L, T, U, and Z shapes). Table 2.3 shows a summary of
observed parameters for these actual houses. These were used to determine the range
of parameters for model houses as shown in Table 2.3 as well.
Case Study Configurations
Dimensions of all observed buildings were transformed into two groups of parameters
as shown in Figure 2.1. The first group of “key parameters” are those used in the case
study matrix including (i) overall shape ratio, R, (ii) percent cutoff, Cp, (iii) cutoff
shape ratio, Rc, and (iv) cutoff ratio, Cr (for T, U and Z shapes). The R and Cp
parameters are related to overall floor proportions and the reduction in area cut off
from the base rectangle (a x b) that encloses the entire plan area. Rc reflects the shapes
of the cutoff areas while Cr indicates distribution of cutoff areas in a floor plan. For a
given set of R and Cp values, variation of Rc and Cr yields different plan shapes,
locations of exterior shear walls and, consequently, eccentricities between the center
of rigidity and center of mass of buildings. This is based on the assumption that unit
shear strength is the same for all wall lines. Different nail spacings for wall lines with
large openings should also be investigated. The second group of “supporting
parameters” defines the geometries of reentrant corners. Key parameters varied within
the most extreme values, with limits constrained by the supporting parameters. A
summary of all parameters is shown in Figure 2.1, with values in Table 2.3.
This study classifies buildings into 3 configuration levels: index level, sub-index level,
and sub-sub-index level. The index level classifies buildings by their shapes:
rectangles, L, T, U, and Z shapes, with overall box area (a x b) of 139 sq.m. (1,500
sq.ft.). The sub-index level includes index level buildings with a specific set of R and
Cp values. Three selected values of R and Cp, determined based on the observed mean
± 2* Standard Deviation (SD) range and the corresponding maximum and minimum
13
values, for each index level building are shown in the “Selected range” column in
Table 2.3. For example, for L- shape index buildings, the selected values are: R= 0.5,
0.75, 1.00, and Cp= 10%, 20%, and 30%; thus, nine L- shape sub-index groups with
different combinations of R and Cp, can be developed. Finally, each of the sub-index
level buildings was assigned Rc and Cr, based on the selected ranges shown in Table
2.3, to yield the final building shapes as follows:
•
L shape: Three different values of Rc were assigned to each sub-index to
represent the minimum and maximum cutoff shape ratios and a square cutoff.
•
T shape: For each sub-index, offset distances, f and d, were assumed equal.
Two cutoff ratios (1.0 and minimum) representing equal and unequal cutoffs
were included.
Equal cutoffs (Cr= 1.0): Three values of Rc1 were assigned to each
sub-index for minimum and maximum cutoff shape ratios and
square cutoffs. Since the offset distance f was assumed to equal d,
Rc1 = Rc2.
Unequal cutoffs (minimum Cr): Each of the sub-sub index buildings
developed earlier for equal cutoffs was used as a basis for the
unequal cutoffs case. With the distance f (and d) kept constant, the
distances c and e were varied to achieve the smallest Cr that kept
the supporting parameters within their ranges. For example,
buildings T1 and T4 are a pair, and their f and d distances are equal.
The c and e distances are equal for building T1, but not T4.
•
U shape: Equal leg lengths (e= g) were assumed, i.e. the cutoff ratio (Cr) is
zero, and there are equal widths (Rl= 1.0). Three values of Rc were assigned to
each sub-index building to represent the minimum and maximum cutoff shape
ratios and a square cutoff.
14
•
Z shape: Two cutoff ratios (Cr= 1.0 and minimum Cr) representing equal
cutoffs and unequal cutoffs were included. For each Cr, five combinations of
cutoff shape ratios were used including: (i) [min. Rc1, min. Rc2], (ii) [min. Rc1,
max. Rc2] (iii) [max. Rc1, min. Rc2], (iv) [max. Rc1, max. Rc2], and (v) [Rc1=
1.0, Rc2= 1.0]. The values of Cr, Rc1, and Rc2 are determined so the related
supporting parameters are still within their ranges.
Cases where the values of either Rc or Cr do not keep all supporting parameters in their
ranges were excluded. As a result, 151 sample models (Figure 2.2) are developed: 4
rectangles, 21 L- shapes, 35 T- shapes, 18 U- shapes, and 73 Z- shapes.
Structural Modeling
Buildings were modeled to represent typical wood-frame, single-story dwellings in
North America. Vertical elements consist of interior gypsum wallboard (GWB)
partition walls and exterior structural shear walls, all assumed to be 2.44 m. (8 ft.) in
height. 50% of each side of the building perimeter was assumed to consist of shear
walls, contributing to the lateral force resisting system. This 50% shear walls
assumption was selected to conservatively satisfy the residential codes adopted by the
state of Oregon over different periods of time, such as CABO (1989, 1995) and the
International Residential Code (ICC 2000). The requirements from CABO (1989,
1995) and ICC (2000) (for seismic design category A, B, and C) are to provide a
minimum of 1.22 m. (48 in) structural sheathing wall located at each end and at least
every 25 feet of wall length, but not less than 16% of braced wall line. For buildings
with seismic design category D1 or D2 (ICC 2000), a similar requirement is applied but
with the minimum wall lengths of 20% and 25% of braced wall line, respectively.
A pilot study was also performed in regards to percent openings in existing buildings.
Focusing on rectangular, L, T, U, and Z plan shapes, observations were made of 98
single-story dwellings in Corvallis, Oregon. It was found that the average percent
openings (resulting from doors and windows) along the long and short sides are 50%
15
(S.D.= 11%) and 20% (S.D.= 17%), respectively. The overall ranges are 20-75% on
the long side and 0-60% on the short side. Since most houses in Oregon have
structural sheathing around the entire perimeter with the same nailing schedule, the
50% assumption is thus considered a reasonable and conservative value for this
comparative study of plan shapes. The seismic performance of existing houses
designed with different amounts of openings will obviously vary, i.e. the more
openings, the less the stiffness and the greater the lateral drift. So, different
percentages of shear walls in braced wall lines and different wall design details will be
included in future work to further develop a rapid visual screening tool that supports
different levels of design and ages of construction across the existing building
inventory.
Lateral force resistance from gypsum wallboard partition walls was not included, but
will be taken into account in the next phase of the study. Horizontal elements consist
of the roof and ceiling. Seismic masses are lumped at the roof level with a uniform
distribution over the roof area, including roof, ceiling, partition wall, and shear wall
weight. Roof and ceiling dead loads are assumed to be 478 N/m2 (10 psf) and 191
N/m2 (4 psf), respectively. Wall dead loads are transferred to the roof diaphragm based
on tributary height. Magnitudes of shear wall and partition wall dead loads are based
on ASCE 7-05 (ASCE 2005) with a dead load of 527 N/m2 (11 psf) for exterior shear
walls and a uniformly distributed load per floor area of 718 N/m2 (15 psf) for partition
walls.
Structural modeling and analysis was performed using SAPWood v1.0 which
incorporates the “pancake” model (Folz and Filiatrault 2002), the Evolutionary
Parameter Hysteretic Model (EPHM) (Pei 2007), and a feature to perform multi-case
incremental dynamic analysis. In general, the pancake model degenerates an actual 3dimensional building into a 2- dimensional planar model. Diaphragms (floors and
roof) are connected by zero-height shear wall spring elements (Figure 2.3). All
diaphragms are assumed rigid with infinite in-plane stiffness, so the dynamic
16
responses of buildings can be defined by only 3 degrees of freedom per floor. With
this assumption, the model will only be able to capture the effect of torsional moment
due to eccentricity but not the stress concentration at reentrant corners.
An Evolutionary Parameter Hysteretic Model (EPHM) (Pang et al. 2007) was selected
to represent the nonlinear force-deformation relationship of shear walls. The model
uses exponential functions to trace the descending backbone and hysteresis loop.
Incorporated degradation rules for hysteretic parameters allow it to track stiffness and
strength degradation. Given appropriate parameters, the EPHM model provides a
better simulation of the post-peak envelope behavior than a linearly decaying
backbone model, and greater flexibility to represent the actual shear wall hysteresis
behavior.
Values of EPHM parameters are from a SAPWood database, generated at the
connector level using the SAPWood-NP program, where nail hysteresis data, obtained
from cyclic loading tests of nailed sheathing to stud connections (Pei 2007), were used
to determine average shear wall parameters. Within the database, parameters for
standard shear wall lengths (e.g. 2ft, 4ft, and 8ft) were calculated based on nail
connection behavior. Linear interpolation was used to obtain parameters for different
wall lengths. Since shear wall configurations of the screened buildings can be
different, it is considered conservative and appropriate to use minimum values in the
database for other ductility- related parameters. Nail spacings for edge and field are 15
mm (6 in.) and 30 mm (12 in.), respectively, with a stud spacing of 406 mm (16 in.).
EPHM parameters for this specific wall configuration are described in the SAPWood
software and user’s manual (Pei and van de Lindt 2007).
Dynamic energy dissipation behavior in wood-frame buildings results from both
viscous and hysteretic damping. Wood-frame buildings subjected to strong motion are
estimated to have an average damping ratio of 10% - 20% (Camelo et al. 2001; Folz
and Filiatrault 2002), with more damping for larger displacements. For this study, the
17
majority of the damping will be accounted for by nonlinear hysteresis damping in the
EPHM springs. A viscous damping ratio of 0.01 was used based on SAPWood model
verification (Pei and van de Lindt 2009, van de Lindt et al., 2010), where analyses
with a very small viscous damping ratio (usually 0.01) yielded good agreement with
shake table test results.
Ground Motions and Structural Analysis
All 151 models were analyzed to determine the maximum lateral drifts in any of the
walls. Ten pairs of ground motion time histories developed for Seattle (Somerville et
al. 1997), having probabilities of exceedance of 2% in 50 years (typically associated
with collapse prevention performance), were used. These ground motions were
developed considering 3 types of seismic sources including (i) shallow Seattle crustal
faults (at depths less than 10 km), (ii) subducting Juan de Fuca plate (at depths of
about 60 km), and (iii) plate interface at the Cascadia subduction zone (about 100 km
west of Seattle). This suite of ground motions includes the 1992 Mendocino, 1992
Erzincan, 1949 Olympia, 1965 Seattle, 1985 Valpariso, 1978 Miyagi-oki, and several
simulated ground motions representing deep and shallow interplate earthquakes.
Detailed information on these ground motions and their reference numbers which are
specified as SE21 to SE40, can be found on the website
<nisee.berkeley.edu/data/strong_motion/sacsteel/motions/se2in50yr.html>.
From Baker (2007), it was observed that “if the records were selected to account for
the peaked spectral shape of ‘rare’ ground motions, then the records could be safely
scaled up to represent rare (i.e., high Sa) ground motions while still producing the
same structural response values as unscaled ground motions.” The selected suite
involves ‘rare’ ground motions, and response spectra for these ground motions (5%
damping) are shown in Figure 2.4. A similar suite of ground motions was applied to a
wide variety of building types and natural frequencies in FEMA (2008), and the
selected suite is used for the short period, single story houses in this study.
18
The scaling used is unbiased and implemented with the intention to fix the intensity in
one excitation direction while keeping the intensity ratio between the two components
from the original record, partially because building damage is often driven by
excitation in one direction. However, although a common procedure in many
situations including shake table testing, this scaling is not as robust as some other
possible methods (such as using the geometric means of the two horizontal
components).
Each of these ground motions was scaled based on the spectral acceleration (Sa) of a
single degree of freedom system with a damping ratio of 0.05 and a natural period of
0.2 seconds before being applied to the structural models. Twenty Sa targets were used
in the study ranging from 0.1g to 2.0g at 0.1 g steps. Ground motion scaling was
performed so that when the first component of ground motion reached the specified Sa,
the same scaling factor was used for the second component. Each orthogonal pair of
ground motions was applied twice (rotated 90 degrees) on each model.
A total of 60,400 analyses were conducted with 151 models, 10 ground motions each
applied twice, and ground motions scaled to 20 different levels. Two different
measures of seismic response were determined for each model at each Sa target: (i)
median of maximum drifts of shear walls and (ii) number of drifts exceeding the 3%
collapse prevention limit. Each scaled ground motion pair was applied to the structure
twice, thus resulting in 2 sets of outputs. Maximum wall drift from both applications
of the ground motion pair was considered the maximum drift for that ground motion,
thus giving 10 maximum drifts from 10 ground motion pair inputs. All ten maximum
drifts were used to determine the “median maximum drift”. Mean maximum drift was
not used here since some impractical large drifts are obtained from the numerical
analyses. Total number of times that maximum drifts exceeded 3% for a particular
spectral acceleration is called “number of drifts exceeding 3%.” While not directly
related to the probability of collapse, the number of drifts exceeding 3% quantifies the
number of events causing severe damage/collapse using the suite of ten ground
19
motions selected for this study, and allows one to compare extreme performance for
different configurations.
Results and Discussion
The overall box area (a x b), overall shape ratio, and percent cutoff are parameters that
affect the dynamic characteristics of buildings as they relate to the overall mass and
stiffness along both major axes of a floor plan. In this study, the fundamental periods
of vibration for all models were found to range from 0.135 sec to 0.219 sec. Natural
periods of the first 3 modes of vibration for each of the worst-case-scenario models
(explained later in this section) are displayed on top of each model in Figure 2.5. In
general, the longest natural period corresponds to one of the lateral displacement
modes, usually parallel to the short side of the building. The second mode is often the
lateral displacement mode in the perpendicular direction. The third mode is typically
the torsional mode. Accordingly, the following results can be observed:
•
A square shape (R= 1.0) better distributes the external shear walls along both
major directions, i.e. providing similar stiffnesses. On the other hand, those
with long, thin shapes (R≠ 1.0) are stiffer in the long direction but more
flexible in the short. The square shapes thus tend to have shorter fundamental
periods than the more rectangular shapes. For example, the fundamental
periods for rectangular shape models (R1, R2, R3, and R4 in Figure 2.5) with
overall shape ratios of 0.35, 0.50, 0.75, and 1.0 are 0.219 sec, 0.200 sec, 0.180
sec, and 0.168 sec, respectively.
•
The spacing of the natural periods is also affected by the overall shape of the
building. The more slender the plan shape, the larger the spacing between
mode 1 and mode 2 periods. Square-like buildings tend to have approximately
the same natural periods in modes 1 and 2, except for U-shapes which have
increased lateral stiffness in one direction from the walls forming the cutoff
area. Natural periods for mode 3 were found to slightly increase as the plan
20
shapes become more slender. For all of these worst-case-scenario models, the
average natural periods for the first, second, and third modes are 0.169 sec
(S.D.= 0.015), 0.139 sec (S.D.= 0.012), and 0.100 sec (S.D.= 0.005),
respectively.
•
For plan shapes with a particular combination of overall box area and shape
ratio, the larger the percent cutoff area, the shorter the fundamental period.
This is because the total seismic mass is reduced while the total lateral stiffness
in both directions remains the same. For example, for L-shape models (Figure
2.5) with R= 0.5, the fundamental periods are 0.191 sec, 0.182 sec, and 0.173
sec for 10, 20, and 30 percent cutoff areas, respectively.
For the same box area, the L, T, U and Z-shapes have reduced seismic mass compared
to the R-shape. Only the U-shape has increased wall mass and increased stiffness. The
R-shape thus tends to have the longest fundamental period while the U-shape tends to
have the shortest. For example, for worst-case-scenario models (Figure 2.5) with
R=0.50 and Cp= 10%, the fundamental periods for rectangle (Cp= 0%), L, T, U, and Z
shapes are 0.200 sec, 0.191 sec, 0.191 sec, 0.169 sec, and 0.191 sec, respectively.
The results and discussion above are for the initial dynamic properties of models.
Figure 2.6 shows the observed variations in seismic performance when the
degradation of shear wall stiffness is included. Figure 2.6 is a plot of median
maximum drifts versus spectral acceleration for all 151 models. Any median
maximum drift that exceeds the 3% collapse prevention limit (73 mm (2.88 in.)) is
displayed as 73 mm. This figure shows that, at low Sa (e.g. Sa≈ 0.0g-0.5g), the
variation of median maximum drifts is small with the small ground excitations. The
middle range (Sa≈ 0.5g-1.3g) is where the effect of shape parameters becomes
obvious. Median maximum drifts are highly scattered. In this range, U shapes have the
lowest variation partly due to the smaller number of case study samples (N= 18). As
can be seen from Figure 2.2 that the total numbers of samples for rectangle, L, T, U,
21
and Z shapes are 4, 21, 35, 18, and 73, respectively. Another reason is due to the
assumption that the cutoff area for the U shape is center-located (as explained earlier).
Thus, the eccentricity is developed on one axis only. This is contrast to Z-shape
samples with a larger variation, where the total number of models is 73 and, in
addition, changes in the two cutoff areas cause different levels of eccentricity along
two major axes. Similarly, large gaps in drifts of the rectangular models are due to the
nonlinearity and small number of samples (N= 4). For the upper range (Sa> 1.3g),
most of the median drifts tend to exceed 75 mm, thus the plots converge to this drift
limit.
Effect of Overall Shape Ratio
Figures 2.7a to 2.7d show examples of the correlation between overall shape
(aspect) ratio R and median maximum drifts at Sa= 0.5g for L- shapes (percent
cutoff Cp= 30%), T- shapes (Cp= 20%), U- shapes (Cp= 15%), and Z- shapes
(Cp= 20%), respectively. These examples show trends in results over a range of
different shapes with different percent cutoffs. For the same total floor area,
buildings tend to perform better (smaller drift) as their shape ratios approach
1.0, or as the overall shapes become more square-like. This trend is consistent
for all except some U- shapes where performance is observed to be similar or
even better at shape ratios less than 1.0. This improvement in lateral load
resistance is because extra lengths of shear wall are added on the short side due
to the cutoff area in the U- shape. While this additional wall length enhances
the performance for U- shapes with a smaller shape ratio (e.g. R= 0.5), it does
not appear to benefit larger shape ratios (e.g. R= 1.0, 1.3), since lateral load
resistance in the other major direction has become more critical.
Figure 2.8 shows how overall building shape ratio affects the seismic
performance in terms of number of incidences where maximum drifts exceed
the 3% collapse prevention limit when excited by the 10 different ground
22
motions. Plots include five levels of Sa: 0.1g, 0.5g, 1.0g, 1.5g, and 2.0g.
Comparisons are made among buildings with the same shape and total floor
area (same percent cutoff). In this comparison, no model exceeded the 3%
limit at Sa= 0.1g. For Sa= 0.5g, number of drifts exceeding 3% ranges from 1 to
2 times. At this level, effect of shape ratio is not clearly visible since the
spectral acceleration is relatively low. Most ground motions did not cause
excessive drifts except for two: the 1992 Mendocino and 1978 Miyagi-oki.
Effect of shape ratio (lower number of drifts exceeding 3% as R approaches
1.0) is more obvious for the intermediate range, i.e. Sa= 1.0g and 1.5g, while
most models exceeded the 3% drift limit from all 10 ground motions when Sa =
2.0g.
Effect of Percent Cutoff
For buildings with the same base rectangle (a x b), variation in percent cutoff
(from the base rectangle) directly affects at least two factors that influence
seismic performance of buildings: eccentricity and seismic mass. By increasing
the percent cutoff, the size of reentrant corners increase, and this produces
larger eccentricity between centers of rigidity and mass. For example, for Lshape models with R= 0.5, the eccentricities along the length and width (ex, ey)
for L1 (Cp= 10%), L4 (Cp= 20%), and L5 (Cp= 30%) are (0.37m, 0.05m),
(0.79m, 0.15m), and (1.11m, 0.34m), respectively. However, increasing the
percent cutoff also reduces seismic mass which, in turn, often leads to smaller
drift. Results from this study have shown that for buildings with the same base
rectangle, maximum drift decreases as percent cutoff increases (Figure 2.9).
Thus, within the study range, the effect of mass reduction over-rides the effect
of eccentricity. Examples of this correlation between percent cutoff and
median maximum drifts at Sa= 0.5g for L- shapes (R= 0.50) and Z- shapes
(R=0.75) are shown in Figures 9a and 9b, respectively.
23
Effect of Cutoff Shape Ratio
Although cutoff shape ratio (aspect ratio of area cutoff from base rectangle)
affects eccentricities along both major axes of a building, within the range
studied, it does not cause a major difference in seismic performance for
buildings of the same overall shape and total floor area. Figure 2.10 shows
seismic response in terms of median maximum drifts compared among
buildings of the same sub-index group (i.e. same shape, overall shape ratio,
and percent cutoff), so, differences in drifts result from the variation of cutoff
ratio and cutoff shape ratio. Figure 2.10a shows that, for T- shape models with
R= 1.00, Cp= 20%, and Sa= 1.0g, median maximum drift varies over a narrow
range from 28-34 mm. For Z-shapes with R= 0.75, Cp= 30%, Sa= 1.0g (Figure
2.10b), median maximum drift similarly ranges from 28-35 mm. Comparisons
of these two groups are shown again in terms of number of drifts exceeding
3% in Figures 2.11a and 2.11b, where the plots show that, within the range of
cutoff area shape ratios and cutoff ratios examined, performances of buildings
with the same overall shape, R, and percent cutoff, Cp, are usually identical.
Thus, use of one worst-case-scenario model (for example, L1) from each group
of sub-sub-index buildings (L1, L2, L3) to represent the seismic performance
of its corresponding sub-index buildings of the same shape, R, and Cp (Lshape, R= 0.5 and Cp= 10%) is reasonable.
Selection of a worst-case-scenario model for each sub-index level was thus performed
by comparison of median maximum drifts over a range of spectral accelerations. The
lower bound for comparison is assumed to be the Sa value that induces approximately
12.7 mm (0.5 in.) median maximum drift, while the upper bound is that producing
73.1 mm (2.88 in.) median maximum drift (3%). The comparison generally covers
approximately a 0.5g range. The model that has the largest median maximum drift
(over the range of spectral accelerations) is considered the worst-case-scenario model
for that particular sub-index group. Figure 2.5 shows a summary of worst-case-
24
scenario models. Comparison of seismic responses in terms of number of drifts
exceeding the 3% limit for the selected worst-case-scenario models at Sa= 1.0g is
shown in Table 2.4. In general, the number of simulations with drifts exceeding 3%
ranges from 2 to 7, showing building performance differences with changes in plan
configuration.
In addition, an unsymmetrical plan tends to cause maximum drift to occur on a
particular wall side more often than the others. Generally, the wall located farthest
away from the center of rigidity tends to have the maximum drift most frequently. For
each worst-case-scenario model, the percentage of times a wall side has either the
maximum drift or exceeds 3% drift, resulting from all 400 analyses (10 ground
motions pairs applied in 2 orthogonal directions, and 20 spectral acceleration scalings)
is summarized in Figure 2.5.
Conclusions
Effect of plan configuration on seismic performance of single-story wood-frame
dwellings has been examined by (i) establishing a practical configuration range for
small, wood-frame dwellings, and proposing an appropriate set of shape parameters,
and (ii) utilizing a recently developed and verified numerical model for wood-frame
building and shear walls for the analyses.
Seismic performance of small, wood-frame dwellings has been shown (for example, in
Table 2.4) to strongly depend on the overall plan proportions (shape ratio, R) and
amount of reduction in area from the base rectangle (percent cutoff, Cp). For buildings
with the same floor area, those with square-like base rectangles perform relatively
better than those with long, thin base rectangles. For a particular size base rectangle (a
x b), maximum shear wall drifts generally decrease as the percent cutoff area (Cp)
increases because of reduced mass. Variation of the proportions in cutoff area (cutoff
shape ratio Rc), considered within a practical range, has a relatively smaller effect on
seismic performance than R and Cp. U-shape buildings with small shape ratio (e.g., R=
25
0.5) can benefit from extra wall length (i.e., increased total stiffness) in the short
direction. Such benefits do not occur for U-shapes with shape ratio closer to 1.0 since
the critical load resistance direction has changed.
This study reveals the importance of plan configuration identification in efforts such
as rapid visual screening. Classification of single-story wood-frame dwellings by
shape, size (a * b), shape ratio (R), and percent cutoff (Cp) has been shown to be
capable of organizing a large population of buildings into a definite number of
building groups with similar seismic performance. Plan configuration screening of
existing buildings can thus be made by assuming them to perform similarly to the
analyzed worst-case scenario models of the same shape, size, R, and Cp.
This approach will be used as a basis for the development of an improved rapid visual
screening method considering the complexity of different combinations of
configuration, base-rectangular area, numbers of stories, windows and doors openings,
and garage doors. Comparison of results between this approach and the simpler,
current FEMA 154 (which simply increases the input spectral acceleration by 50% for
a plan irregularity) will be made.
Acknowledgments
The authors are grateful for the financial support of this project by the Royal Thai
Government, the School of Civil and Construction Engineering, and the Department of
Wood Science and Engineering, Oregon State University.
References
American Society of Civil Engineers (ASCE). (2005). “Minimum Design Loads for
Buildings and Other Structures.” ASCE/SEI 7-05, American Society of Civil
Engineers, New York.
Applied Technology Council (ATC). (2007). “Seismic Rehabilitation Guidelines for
Detached, Single Family, Wood-Frame Dwellings.” ATC 50-1, Redwood City,
CA.
26
Baker, J. W. (2007). “Measuring bias in structural response caused by ground motion
scaling.” Proceedings, 8th Pacific Conference on Earthquake Engineering,
Nangyang Technological University, Singapore, 8.
Camelo, V.S., Beck, J.L. and Hall, J.F. (2001). “Dynamic characteristics of
woodframe structures.” CUREE Publication No. W-11, Richmond, CA.
Council of American Building Officials (CABO). (1989). “CABO One and Two
Family Dwelling Code.” CABO 1989 Edition, Falls Church, VA.
Council of American Building Officials (CABO). (1995). “CABO One and Two
Family Dwelling Code.” CABO 1995 Edition, Falls Church, VA.
Federal Emergency Management Agency (FEMA). (2002a). “Rapid Visual Screening
of Buildings for Potential Seismic Hazards: A Handbook.” FEMA 154,
Washington, D.C.
Federal Emergency Management Agency (FEMA). (2002b). “Rapid Visual Screening
of Buildings for Potential Seismic Hazards: Supporting Documentation.”
FEMA 155, Washington, D.C.
Federal Emergency Management Agency (FEMA). (2008). “Quantification of
Building Seismic Performance Factors.” FEMA P-695, Washington, D.C.
Folz, B. and Filiatrault, A. (2002). “A computer program for seismic analysis of
woodframe structure.” CUREE Publication No. W-21, Richmond, CA.
International Code Council (ICC). (2000). “International Residential Code for Oneand Two-Family Dwellings.” IRC 2000, Falls Church, VA.
Pang, W.C., Rosowsky, D.V., Pei, S. and van de Lindt, J.W. (2007). “Evolutionary
Parameter hysteretic Model for Wood Shear Walls.” ASCE Journal of
Structural Engineering, 133(8), 1118-1129.
Pei, S. (2007). “Loss analysis and loss based seismic design for woodframe
structures.” Ph.D. thesis, Department of Civil and Environmental Engineering,
Colorado State University, Fort Collins, CO.
Pei, S. and van de Lindt, J. W. (2007). “User’s Manual for SAPWood for Windows.”
<http://www.engr.colostate.edu/NEESWood/sapwood.shtml> (Dec. 10, 2007).
Pei, S. and van de Lindt, J.W. (2009). “Coupled shear-bending formulation for seismic
analysis of stacked wood shear wall systems.” Earthquake Engineering and
Structural Dynamics, 38(14), 1631-1647.
27
Schierle, G. G. (2003). “Northridge earthquake field investigations: Statistical analysis
of woodframe damage.” CUREE Publication No. W-09, Richmond, CA.
Somerville, P., Smith, N., Punyamurthula, S. and Sun, J. (1997). “Development of
Ground Motion Time Histories for Phase 2 of the FEMA/SAC Steel Project.”
Report No. SAC/BD-97/04, SAC Joint Venture for the Federal Emergency
Management Agency, Washington, D.C.
U.S. Census Bureau, Population Division. (2009). “Population estimates-Vintage 2007
Archive.” <http://www.census.gov/popest/archives/2000s/vintage_2007/>
(Mar. 2, 2009).
van de Lindt, J. W., Pei, S., Liu, H. and Filiatrault, A. (2010). “Three-dimensional
seismic response of a full-scale light-frame wood building: Numerical
study.” Journal of Structural Engineering, 136(1), 56-65.
28
Table 2.1 Randomly selected cities in each group
Group A
Group B
City
Group C
No.
City
Population* No.
Population* No.
A-1
Nyssa
3,026 B-1
Canby
15,602 C-1
Corvallis
51,125
A-2
Shady Cove
2,299 B-2
Molalla
7,115 C-2
Redmond
23,769
A-3
Gervais
2,416 B-3
Sutherlin
7,201 C-3 Beaverton
90,704
A-4
Coburg
1,021 B-4
Wilsonville
18,814 C-4
Albany
47,239
A-5
Yoncalla
1,047 B-5
Talent
6,150 C-5
Keizer
35,312
A-6 North Plains
1,813 B-6
Central Point
16,447 C-6
Medford
72,186
A-7
Heppner
1,371 B-7
Lebanon
14,836 C-7 Springfield
56,666
A-8
Brownsville
1,620 B-8
North Bend
9,672 C-8 Woodburn
22,044
A-9
Siletz
A-10
Joseph
1,098 B-9 Happy Valley
959 B-10
Troutdale
City
Population*
11,599 C-9
Newberg
22,193
15,366 C-10
Salem
151,913
*Source: U.S. Census Bureau, 2009
Table 2.2 Determination of population weights among city groups
Group
Total*
A
B
C
Population
0-5,000
5,001-20,000
> 20,000
No. of cities
168
47
26
241
Total population
219,894
492,927
1,854,266
2,567,087
Relative population
8.6%
19.2%
72.2%
100.0%
Sample weight
1
2
7
10
*Source: U.S. Census Bureau, 2009
29
Table 2.3 Summary of observed parameters and selected ranges for modeling
Shapes
Rect.
N = 95
L- Shape
N = 100
T- Shape
N = 84
U- Shape
N = 61
Z- Shape
N = 72
Parameters
Observed ranges
Mean ± 2SD
Selected ranges
R
0.29 to 1.00
0.36 to 0.98
0.35, 0.50, 0.75, 1.00
R
0.48 to 1.00
0.57 to 1.08
0.50, 0.75, 1.00
Cp
3% to 31%
3% to 34%
10%, 20%, 30%
Rc
0.13 to 3.00
-0.19 to 1.68
0.20, 1.00, 1.60
c/a
0.12 to 0.70
0.20 to 0.70
0.20 to 0.70
d/b
0.11 to 0.63
0.12 to 0.59
0.20 to 0.60
R
0.43 to 1.47
0.44 to 1.27
0.50, 1.00, 1.30
Cp
8% to 38%
6% to 33%
10%, 20%, 30%
Cr
0.14 to 1.00
0.07 to 1.16
0.20, 1.00
Rc1
0.21 to 6.00
-0.75 to 3.62
0.30, 1.00, 3.60
Rc2
0.23 to 11.25
-0.96 to 5.74
0.30, 1.00, 5.80
e/c
0.14 to 2.00
0.01 to 1.29
0.20 to 1.30
d/f
0.60 to 2.12
0.6 to 1.52
1.00
c/a
0.13 to 0.61
0.12 to 0.49
e/a
0.07 to 0.36
0.04 to 0.33
0.10 to 0.50
d/b
0.15 to 0.71
0.14 to 0.70
f/b
0.13 to 0.73
0.12 to 0.69
R
0.36 to 1.35
0.44 to 1.27
0.5, 1.0, 1.3
Cp
3% to 27%
1% to 20%
5%, 10%, 15%
Cr
0 to 4.67
-0.87 to 2.66
0
0.20 to 0.70
Rl
0.47 to 1.38
0.52 to 1.25
1.00
Rc
0.17 to 3.25
-0.59 to 2.29
0.20, 1.00, 2.30
c/b
0.62 to 1.00
0.67 to 1.09
1.0
e/b
0.14 to 0.62
0.14 to 0.52
0.20 to 0.60
h/a
0.06 to 0.48
0.03 to 0.34
0.10 to 0.40
R
0.54 to 1.00
0.59 to 1.01
0.50, 0.75, 1.00
Cp
9% to 39%
10% to 34%
10%, 20%, 30%
Rc1
0.14 to 3.50
-0.24 to 2.21
0.20, 1.00, 2.20
Rc2
0.14 to 6.00
-1.05 to 4.81
0.20, 1.00, 4.80
Cr
0.20 to 1.00
0.13 to 1.03
0.30, 1.00
c/a
0.15 to 0.71
0.13 to 0.63
0.20 to 0.70
e/a
0.07 to 0.65
-0.05 to 0.55
0.10 to 0.60
d/b
0.12 to 0.70
0.15 to 0.64
0.20 to 0.60
f/b
0.08 to 0.65
0.09 to 0.67
0.10 to 0.60
e/c
0.17 to 2.00
-0.086 to 1.46
0.20 to 1.50
f/d
0.25 to 2.01
0.29 to 1.68
0.30 to 1.60
30
Table 2.4 Comparison of seismic responses in terms of number of drifts exceeding the
3% limit based on the selected worst-case-scenario models at Sa= 1.0g
Shape
Ratio
0.35
Cp (%)
Rect
L
0
7
N/A
0
7
N/A
5
N/A
N/A
10
N/A
7
0.5
15
N/A
N/A
20
N/A
7
30
N/A
5
0
6
N/A
5
N/A
N/A
10
N/A
6
0.75
15
N/A
N/A
20
N/A
3
30
N/A
3
0
5
N/A
5
N/A
N/A
10
N/A
3
1.0
15
N/A
N/A
20
N/A
3
30
N/A
2
5
N/A
N/A
10
N/A
N/A
15
N/A
N/A
1.3
20
N/A
N/A
30
N/A
N/A
Note: N/A= Not Analyzed configurations
T
U
Z
N/A
N/A
N/A
7
N/A
7
5
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
3
N/A
3
2
N/A
6
N/A
3
2
N/A
N/A
6
5
4
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
3
3
3
N/A
N/A
6
5
5
N/A
N/A
N/A
N/A
N/A
7
N/A
7
5
N/A
N/A
6
N/A
3
3
N/A
N/A
3
N/A
3
2
N/A
N/A
N/A
N/A
N/A
31
Figure 2.1 Plan shape parameters and notation
Note: For T and Z shapes, (c * d) > (e * f)
32
Figure 2.2 Summary of configurations based on observations of existing buildings
33
Figure 2.3 Rectangular wood-frame house and its pancake model
Figure 2.4 Response spectra of ground motion records (5% damping)
34
Figure 2.5 Summary of the selected worst-case-scenario models, percentage of times
maximum drifts occur on each wall side, natural periods of first 3 modes of vibration
T1, T2, T3 (displayed on top of each model)
35
Figure 2.5 (continued) Summary of selected worst-case-scenario models, percentage
of times maximum drifts occur on each wall side, natural periods of first 3 modes of
vibration T1, T2, T3 (displayed on top of each model)
36
Median maximum drifts, mm
0.0 0.5 1.0 1.5 2.0
Shape: L
0.0 0.5 1.0 1.5 2.0
Shape: T
Shape: U
Shape: Z
Shape: Rect
75
50
25
0
0.0 0.5 1.0 1.5 2.0
0.0 0.5 1.0 1.5 2.0
0.0 0.5 1.0 1.5 2.0
Spectral acceleration, g
Shape ratio
(c) U shape, Cp= 15%
1.25
1.00
0.75
0.50
10
5
0
1.25
1.25
1.00
0.75
0.50
0
15
1.00
5
(b) T shape, Cp= 20%
Median maximum drifts, mm
10
0.25
Median maximum drifts, mm
(a) L shape, Cp= 30%
Shape ratio
0.75
Shape ratio
0
0.50
1.25
1.00
0.75
0.50
0
5
0.25
5
10
0.25
10
Median maximum drifts, mm
15
0.25
Median maximum drifts, mm
Figure 2.6 Median maximum drifts at Sa= 0.1g-2.0g for all case study models
Shape ratio
(d) Z shape, Cp= 10%
Figure 2.7 Effect of shape ratio in terms of median maximum drifts at Sa= 0.5g
Sa: 0.5
Sa: 1
1.00
0.75
0.50
1.00
0.75
0.50
Sa: 0.1
Sa: 1.5
Sa: 2
1.00
0.75
0.50
1.00
0.75
0.50
1.00
0.75
10
8
6
4
2
0
0.50
No. of drifts exceeding 3%
37
Shape ratio
Sa: 0.5
Sa: 1
1.00
0.75
0.50
1.00
0.75
0.50
Sa: 0.1
Sa: 1.5
Sa: 2
1.00
0.75
0.50
1.00
0.75
0.50
1.00
0.75
10
8
6
4
2
0
0.50
No. of drifts exceeding 3%
(a) Rectangular shape
Shape ratio
Sa: 0.1
Sa: 1
1.00
0.75
0.50
1.00
0.75
Sa: 0.5
Sa: 1.5
Sa: 2
1.00
0.75
0.50
1.00
0.75
0.50
1.00
0.75
10
8
6
4
2
0
0.50
No. of drifts exceeding 3%
0.50
(b) L- shape, Cp 30%
Shape ratio
(c) Z- shape, Cp 10%
Figure 2.8 Effect of shape ratio in terms of number of drifts exceeding 3%
5
0
Percent cutoff
(a) L shape, R= 0.50
10
5
0
0
5
10
15
20
25
30
Median maximum drifts, mm
10
0
5
10
15
20
25
30
Median maximum drifts, mm
38
Percent cutoff
(b) Z shape, R= 0.75
40
30
20
10
0
Z34
Z35
Z36
Z37
Z38
Z39
Z40
Z41
Z42
Z43
Median maximum drifts, mm
40
35
30
25
20
15
10
5
0
T22
T23
T24
T25
T26
T27
Median maximum drifts, mm
Figure 2.9 Effect of percent cutoff in terms of median maximum drifts at Sa= 0.5g
Model
Model
(a)
(b)
Model
(a)
9
8
7
6
5
4
3
2
1
0
Z34
Z35
Z36
Z37
Z38
Z39
Z40
Z41
Z42
Z43
No. of drifts exceeding 3%
9
8
7
6
5
4
3
2
1
0
T22
T23
T24
T25
T26
T27
No. of drifts exceeding 3%
Figure 2.10 Effect of cutoff shape ratio and cutoff ratio on median maximum drifts:
(a) T- shape, R= 1.00, Cp= 20%, Sa= 1.0g; (b) Z- shape, R= 0.75, Cp= 30%, Sa= 1.0g
Model
(b)
Figure 2.11 Effect of cutoff shape ratio and cutoff ratio in terms of number of drifts
exceeding 3% (a) T- shape, R= 1.00, Cp= 20%, Sa= 1.0g (b) Z- shape R= 0.75, Cp=
30%, Sa= 1.0g
39
A PROCEDURE FOR RAPID VISUAL SCREENING FOR SEISMIC SAFETY
OF WOOD-FRAME DWELLINGS WITH PLAN IRREGULARITY
Kraisorn Lucksiri, Thomas H. Miller, Rakesh Gupta, Shiling Pei, and John W. van de
Lindt
Engineering Structures
Elsevier Inc.
3251 Riverport Lane
Maryland Heights, MO 63043, USA
Accepted for publication on December 8, 2011
Published, 36(3): 351-359, March, 2012.
Published Online: DOI 10.1016/j.engstruct.2011.12.023
40
CHAPTER 3: A PROCEDURE FOR RAPID VISUAL SCREENING FOR
SEISMIC SAFETY OF WOOD-FRAME DWELLINGS WITH PLAN
IRREGULARITY
Kraisorn Lucksiri1, Thomas H. Miller2, Rakesh Gupta3, Shiling Pei4, and John W. van
de Lindt5
Abstract
This paper highlights the development of a rapid visual screening (RVS) tool to
quickly identify, inventory, and rank residential buildings that are potentially
seismically hazardous, focusing on single-family, wood-frame dwellings with plan
irregularity. The SAPWood software was used to perform a series of nonlinear timehistory analyses for 480 representative models, covering different combinations of
plan shapes, numbers of floors, base-rectangular areas, shape aspect ratio, area
percentage cutoffs, window and door openings, and garage doors. The evolutionary
parameter hysteresis model was used to represent the load-displacement relationship
of structural panel-sheathed shear walls and a ten parameter CUREE hysteresis model
for gypsum wallboard sheathed walls. Ten pairs of ground motion time histories were
used and scaled to four levels of spectral acceleration at 0.167g, 0.5g, 1.0g, and 1.5g.
An average seismic performance grade for each model was generated based on the
predicted maximum shear wall drifts. Five seismic performance grades: 4, 3, 2, 1, and
0, are associated with the 1% immediate occupancy drift limit, 2% life safety limit, 3%
collapse prevention limit, 10% drift, and exceeding 10% drift, respectively. The
obtained average seismic performance grades were used to develop a new RVS tool
that is applicable for checking the seismic performance of either existing or newly
designed single-family, wood-frame dwellings. It examines the adequacy of the
structure’s exterior shear walls to resist lateral forces resulting from ground motions,
including torsional forces induced from plan irregularity.
Key Words: seismic analysis, wood structures, configuration
41
1
Graduate Student. School of Civil and Construction Engineering and Dept. of Wood
Science and Engineering, Oregon State University, Corvallis, OR 97331. Email:
kraisorn.lucksiri@oregonstate.edu
2
Corresponding Author. Associate Professor. School of Civil and Construction
Engineering, Oregon State University, Corvallis, OR 97331. Email:
thomas.miller@oregonstate.edu
3
Professor. Dept. of Wood Science and Engineering, Oregon State University,
Corvallis, OR 97331. Email: rakesh.gupta@oregonstate.edu
4
Assistant Professor. Dept. of Civil and Environmental Engineering, South Dakota
State University, Brookings SD 57006. Email: Shiling.Pei@sdstate.edu
5
Professor and Drummond Chair. Dept. of Civil, Construction, and Environmental
Engineering, University of Alabama, Tuscaloosa, AL, 35487. Email:
jwvandelindt@eng.ua.edu
42
Introduction
Damage caused to residential wood-frame dwellings from the 1994 Northridge,
California earthquake has raised concerns. It is estimated that approximately 48,000
housing units were rendered uninhabitable (Schierle 2003), and estimated property
loss in residential wood-frame buildings was at least $20 billion. Private insurance
companies paid a total of about $12.3 billion in claims, with approximately $9.5
billion (78% of total) for residential claims (Kircher et al. 1997). Damage was found
to range from minor non-structural damage to a severe, non-habitable level.
In general, the simplest damage and loss estimation procedures for existing buildings
involve rapid visual screening (RVS) where the evaluation is primarily based on visual
inspection with no engineering calculations involved. For single-family, wood-frame
dwellings, the currently available RVS tools are the second edition of FEMA 154
(FEMA 2002a), its supporting document, FEMA 155 (FEMA 2002b), and ATC 50-1
(ATC 2007). These tools were, however, found to have some limitations which
provide the impetus for this study. First, FEMA 154 was originally developed for
macroscopic loss estimation for a large inventory of buildings, so its application to
building-specific cases is not recommended. Second, although ATC 50-1 was
developed specifically for detached, single-family, wood-frame dwellings, and it looks
at a house as an integrated unit with considerations of various vulnerability sources
that affect seismic performance, it was, however, particularly developed for the city
of Los Angeles. Finally, indications of potential seismic vulnerability sources in both
RVS tools are based on a simple “yes” or “no” categorization, which is only really
suitable for identifying the presence of building features such as unreinforced masonry
chimneys and cripple walls. This approach may not be appropriate for plan irregularity
where the effect varies from case to case and depends on the type (re-entrant corner,
door/window opening, etc.) and degree of irregularity (size of door/window opening,
offset ratio of re-entrant corner, etc.). Almost all houses in the US have some type of
plan irregularity and many have vertical irregularities as well.
43
This paper describes the development of an RVS tool for examining plan irregularity
in single-family, wood-frame dwellings. This is the second phase of the study. In
phase 1, basic data were developed and a numerical investigation performed on the
effect of plan configuration on seismic performance of single-family, wood-frame
dwellings (Lucksiri et al. 2012). 151 models were developed using observations of
412 dwellings of rectangular, L, T, U, and Z shapes in Oregon. A nonlinear, timehistory program, Seismic Analysis Package for Woodframe Structures, was the
analysis platform. Models were analyzed for 10 pairs of biaxial ground motions
(spectral accelerations from 0.1g to 2.0g) for Seattle. Configuration comparisons were
made using median shear wall maximum drifts and occurrences of maximum drifts
exceeding the 3% collapse prevention limit. Phase 1 showed that plan configuration
significantly affects performance through building mass, lateral stiffnesses and
eccentricities. Irregular configuration tends to induce eccentricity and cause one wall
to exceed the allowable drift limit, and fail, earlier than others. Square-like buildings
usually perform better than long, thin rectangles. Classification of single-family
dwellings based on shape parameters, including size and overall aspect ratio, plan
shape, and percent cutoff area, can organize a building population into groups having
similar performance, and be a basis for including plan configuration in rapid visual
screening.
The objective of this paper (Phase 2) is to develop a rapid visual screening tool for
single-family wood-frame dwellings with plan irregularity that can be used by the
same audience as FEMA 154 (FEMA 2002a), including building officials and
inspectors, government agencies, insurance companies and private-sector building
owners, to identify, inventory, and rank buildings that are potentially seismically
hazardous. The new RVS tool also uses the same concept of “sidewalk survey”
approach and a “data collection form” in which the screener can complete the
evaluation based on visual observations from the exterior. In this project, only the
effect of plan irregularity on torsional forces was examined, and the effect of stress
44
concentrations at reentrant corners was not included. Non-linear, time-history analysis
was used to study variations in plan configuration including plan shapes, sizes,
window and door openings, and garage doors. Future work will include an
implementation of this new RVS tool for more realistic building configurations and
openings in walls. The results will be compared to predictions from FEMA 154
(FEMA 2002a) and tier 1 of ASCE/SEI 31 (ASCE 2003).
Methodology
The development methodology is organized into two parts: (i) building configuration
parameters and (ii) building seismic response prediction.
Building Configuration Parameters
Selection of the building configuration parameters, discussed in the following
sections, for the models was considered based on two aspects. First, the range
of parameters covers the typical variations in plan shapes and plan irregularity
found in a particular type of building. Second, each model represents the
worst-case scenario for dwellings of similar configurations. Details of selected
configuration parameters were summarized into 2 groups: (i) shape parameters
and (ii) openings-related parameters.
Shape Parameters
Shape parameters are used to specify plan shape configurations of
buildings. A set of parameters including plan shape, base-rectangular area,
overall shape ratio, and percent cutoff, introduced in Lucksiri et al.
(Lucksiri et al. 2012) was used.
As illustrated in Figure 3.1, each building plan originates from a baserectangular area of size a x b. Overall shape ratio, R, (R= b/a), is used to
represent the overall proportions of a plan shape, i.e. a square plan shape
(R= 1.0) or a rectangular plan shape (R≠ 1.0). For rectangular, L, and Z
45
shapes, the dimension “a” is always assigned to be longer than “b”. For T
and U shapes, “a” always refers to the side shown in the figure and can
either be longer or shorter than “b”. This base-rectangular area is then cutoff to achieve a particular plan shape. The cutoff areas are shown in Figure
3.1 as grey-shaded portions. Percent cutoff (Cp) area indicates the amount
of cutoff area relative to the area of the base rectangle, and is also a way to
specify the relative size of reentrant corners. The value of Cp is always less
than 1.0. For example, percent cutoff area equals 100*[(c*d)/(a*b)] for the
L-shape in Figure 3.1.
To specify the configuration for a plan shape, two additional parameters
are required: cutoff shape ratio, Rc, and cutoff ratio, Cr (for T and Z
shapes). Cutoff shape ratio represents the direction of cutoff area relative to
the base dimension “a”. For example, it is the ratio of dimension “c”
(parallel to “a”) to “d” (parallel to “b”) for the L-shape shown in Figure
3.1. Rc can either be smaller or greater than 1.0. Cutoff ratio is used for T
and Z shapes to indicate the relative size between two cutoff areas. For the
T-shape, cutoff ratio equals the ratio of (the smaller) cutoff area 1 to (the
larger) cutoff area 2. The maximum value of cutoff ratio is 1 (equal cutoff
areas). Thus, the selected shape parameters are summarized as follows:
i.
Plan Shape
Five plan shapes commonly used in the design of single-family,
wood-frame dwellings were selected, including rectangles, L, T, U,
and Z shapes.
ii.
Base-Rectangular Area
The overall upper limit of the base-rectangular area is 465 m2 (5000
ft2). This selection was based on the FEMA 154 (FEMA 2002a)
definition for the W1 structural type, light wood-frame, residential
46
and commercial buildings with floor area less than 465 m2 (5000
ft2). Observed data from phase 1 on areas for various plan shapes
are shown in Table 3.1. Although the data collected using Google
Earth may include some 2-story buildings, they were used directly
for base-rectangular area selection for 1 story models. Selections
for 2-story buildings were based on the FEMA 154 definition for
W1 alone. A summary of the selected base-rectangular areas is
shown in Table 3.2.
iii.
Shape Ratio and Percent Cutoff
For both shape ratio and percent cutoff, upper and lower bounds
determined from phase 1, the observed mean ± 2* standard
deviations (SD) with considerations of the corresponding maximum
and minimum values, were used. The upper bound of shape ratio
(R= 1.0) represents square plan shapes, while the lower bound (R≠
1.0) represents rectangular shapes. The upper and lower bounds of
percent cutoff represent building plans with large and small
reentrant corners, respectively. Table 3.3 summarizes the selected
values for both parameters.
For each combination of shape parameters in Table 3.3, the final shape for
each model, specified by cutoff shape ratio and cutoff ratio, was based on
the worst-case-scenario model determined from Lucksiri et al. (2012).
Selection of a worst-case-scenario model, for each combination of R and
Cp, was performed by comparison of median maximum drifts of models
with variations of Rc, and Cr (for T and Z shapes) over a range of spectral
accelerations, Sa. The lower bound was assumed to be the Sa value that
induces approximately 12.7 mm (0.5 in.) median maximum drift, and the
upper bound is that producing 73.1 mm (2.88 in.) median maximum drift
47
(3%). The model that has the largest median maximum drift (over the range
of spectral accelerations) is considered the worst-case-scenario.
Openings-Related Parameters
Two sources of openings included in the development were windows and
doors, and garage doors. The amount of windows and doors is specified in
terms of percent openings which is the relative length (horizontal
dimension) of windows and doors compared to the length of the wall where
they are located. Openings were made in walls in both major directions of
the buildings. For rectangular shapes (R≠ 1.0), it is common to have more
windows and door openings along the long side than the short, so four
different combinations of percent openings (Long % | Short %) were
included: 60|30, 60|0, 30|15, and 30|0. For square shapes (R= 1.0),
percentage openings were assumed to be equal on walls in both major
directions, and the 60|60 and 30|30 combinations were included.
Models were also analyzed for cases with and without a garage door
opening. When a garage door is present, its location was assumed to be on
the most critical wall (a wall where maximum drift tends to occur, as
described in Lucksiri et al. (2012) to enhance the effect of torsion. This,
however, limits the size of a garage door to the length of the most critical
wall. As a result, a 3.05 m (10-ft) wide single car garage door is assumed
for dwellings with total net floor area less than or equal to 279 m2 (3,000
ft2), and a 5.49 m (18-ft) wide double car garage door is assumed for
dwellings with total net floor area greater than 279 m2 (3,000 ft2).
Based on these parameter variations and combinations, a set of representative
models was created. Table 3.4 shows an example of a case study matrix for 1story, 139 m2 (1,500 ft2) base-rectangular area, L-shape models where 24
representative models were produced. Case study matrices for other models
48
with different shapes and numbers of stories were set up similarly and are
given in Lucksiri (2012). As a result, a total of 480 representative models was
obtained as summarized in Table 3.5.
Seismic Response Prediction
Structural Modeling
In general, a structural model consists of a vertical shear wall, and
horizontal elements which include the roof, ceiling, and floor. Shear walls
are located on the perimeter of the plan shape with structural sheathing
panels on one side and gypsum wallboard on the other. Story height is
assumed to be 2.44 m (8 ft). Wall dead loads are transferred to the roof
diaphragm based on tributary height. Magnitudes of shear wall and
partition wall dead loads were based on ASCE 7-05 (ASCE 2005) with a
dead load of 527 N/m2 (11 psf) for exterior shear walls and a uniformly
distributed load per floor area of 718 N/m2 (15 psf) for partition walls. For
horizontal elements, seismic mass includes the roof, ceiling, and floor, as
478 N/m2 (10 psf), 191 N/m2 (4 psf), and 383 N/m2 (8 psf), respectively.
Structural elements of the buildings are assembled into a “pancake” model
configuration (Folz and Filiatrault 2002) where horizontal diaphragms are
connected by zero-height shear wall spring elements. The pancake model
assumes all diaphragms to be rigid with infinite in-plane stiffness, and
captures the effect of torsional moment due to eccentricities.
Structural Panel Sheathed Shear Walls
An evolutionary parameter hysteretic model (EPHM) (Pei 2007; Pang et al.
2007) was selected to represent the nonlinear force-deformation
relationship of structural panel sheathed shear walls as it is capable of
providing a better simulation of the post-peak envelope behavior than a
49
linearly decaying backbone model. Values of EPHM parameters are from a
SAPWood database generated at the connector level using the SAPWoodNP program. Linear interpolation was used to obtain parameters for
different wall lengths. Since shear wall configurations can be different, it is
considered conservative and appropriate to use minimum values in the
database for other ductility- related parameters. The assumed nail spacing
values for edge and field are 150 mm (6 in.) and 300 mm (12 in.),
respectively, with a stud spacing of 406 mm (16 in.). EPHM parameters for
this specific wall configuration are described in the SAPWood software
and user’s manual (Pei and van de Lindt 2007).
Gypsum Wallboard Sheathed Walls
The contribution of gypsum wallboard (GWB) sheathed walls was included
in the analysis. Since the degradation of GWB is sudden, the CUREE 10parameter model was considered suitable for representing the loaddeformation relationship. Parameters used (Table 3.6) were based on the
available set of parameters for a 2.4 m x 2.4 m (8 ft x 8 ft) GWB wall (Folz
and Filiatrault 2004). It was assumed that the initial stiffness (K0) and
ultimate capacity (F0) are proportional to the wall length for walls with
lengths other than 2.4 m (8 ft). This CUREE hysteretic model was
superimposed with the EPHM model to build up exterior shear walls with a
structural panel on the exterior surface and GWB on the interior surface.
Ground Motion Suite
Ten pairs of ground motion time histories developed for Seattle
(Somerville et al. 1997), having probabilities of exceedance of 2% in 50
years (typically associated with collapse prevention performance), were
used. These ground motions were developed considering 3 types of seismic
sources including (i) shallow Seattle crustal faults (at depths less than 10
50
km), (ii) the subducting Juan de Fuca plate (at depths of about 60 km), and
(iii) the plate interface at the Cascadia subduction zone (about 100 km west
of Seattle).
Damping Ratio
For this study, the majority of the damping is accounted for by nonlinear
hysteresis damping in the EPHM springs. A viscous damping ratio of 0.01
was used based on SAPWood model verification (Pei and van de Lindt
2009; van de Lindt et al. 2010), where analyses with a very small viscous
damping ratio (usually 0.01) yielded good agreement with shake table test
results.
Nonlinear Time-History Analysis
SAPWood v1.0 was the analysis platform. The natural period of each
building was determined based on the seismic mass, height of the building,
floor plan configuration, and amount of shear wall openings. Examples of
the variation in natural period were illustrated in Lucksiri et al. (2012). A
period of 0.2 sec was used only for ground motion scaling, i.e. each input
record was scaled based on the spectral acceleration (Sa) of a single degree
of freedom system with a damping ratio of 0.05 and a natural period of 0.2
sec. Ground motion scaling was performed so that when the first
component of ground motion reached the specified Sa, the same scaling
factor was then applied to the second component. The scaling used is
unbiased and implemented with the intention to fix the intensity in one
excitation direction while keeping the intensity ratio between the two
components the same as the original record, partially because building
damage is often driven by excitation in one direction. However, although a
common procedure in many situations including shake table testing, this
51
scaling is not as robust as some other possible methods (such as using the
geometric means of the two horizontal components).
Each orthogonal pair of ground motions was applied twice (rotated 90
degrees) to each model. The Sa targets were the upper limits of Sa specified
for each seismic region in FEMA 154 (FEMA 2002a) (Table 3.7).
However, the high seismicity region was separated into High 1 and High 2
regions with their corresponding Sa limits of 1.0g and 1.5g, respectively, to
increase the resolution of the high seismic region categories. Accordingly,
for each level of spectral acceleration, ten maximum shear wall drifts
resulting from the ten input ground motions were obtained through
nonlinear time history analysis.
Seismic Performance Grade
The proposed RVS method uses numerical seismic performance grades,
ranging from 0 to 4, to classify different performance levels. Similar to the
FEMA 154 (FEMA 2002a), the higher score represents better seismic
performance for the buildings. The conversion criteria used to transform
the analysis results, i.e. maximum shear wall drifts, to performance grades
are summarized in Table 3.8. Conceptually, grades 4, 3, and 2 are
associated with the 1% immediate occupancy (IO) drift limit, 2% life
safety (LS) limit, and 3% collapse prevention (CP) limit, respectively.
For each model, at a particular level of Sa, the conversion was made for
each of the ten maximum drifts (resulting from ten input ground motions).
The average performance grade (Gavg) was determined by averaging all ten
performance grades accordingly to represent the overall performance of the
modeled structure.
52
Results and Discussion
Overall Seismic Performance
The overall seismic performance of the studied models is presented and
discussed. It is emphasized that no interior shear walls or interior partition
walls are considered in the analyses as it is assumed that the structural details
are obtained from a “side-walk survey” only. There is a bias in the approach to
overestimate the response of larger residential buildings with many interior
walls that are neglected in the analysis.
Table 3.9 shows the overall ranges of average performance grades for all the
models when classified by number of floors and base-rectangular area.
Distributions of these grades are also shown in Figure 3.2. In general, across
all selected ground motions, group 1-S has the best performance and is the
group of single-story buildings with small base-rectangular areas, while group
2-L, 2-story models with large base-rectangular area, is the group that performs
worst. Single-story houses generally perform better than 2- story houses even
of a small size.
As shown in Table 3.9, for the low seismicity region, all single story models
satisfy the objective of immediate occupancy, i.e. all Gavg scores equal 4.0. For
2-story models, Gavg ranges from 3.4 to 4.0 for low seismicity, indicating that
lateral and torsional forces from ground motion do not cause severe damage.
The worst performance (Gavg= 3.4) is in the range of the life safety to
immediate occupancy performance limits. For the moderate seismicity area, all
models were able to meet the objective of collapse prevention with the overall
range of seismic performance grades from 2.9 to 4.0 and 1.8 to 3.8 for singlestory and 2-story dwellings, respectively.
High 1 and high 2 seismic regions are where the effects of plan configuration
and plan irregularity become more obvious and earthquake-induced damage
53
can be severe. For high 1, wide ranges of grades were observed from 0.9 to 3.2
and 0.4 to 2.6 for 1-story and 2-story models, respectively. For high 2, the
single-story group continues to have a wide range with the minimum grade as
low as 0.2 and a maximum grade of 3.2. However, at this level, none of the 2story models was able to meet the collapse prevention objective, and grades
range from 0.1 to 1.1.
Figure 3.3 shows the relationship between base-rectangular area and average
performance grades for 1-story, square, models. In general, average
performance grade decreases as the base-rectangular area increases. For 1story models, this effect was not evident in the low seismicity region where all
models perform well, but it becomes clearer for moderate seismicity. For high
1, the grades, especially the lower bounds, decrease as the base-rectangular
area increases. This is because the effects of increased mass (from an increased
base-rectangular area) and the nonlinear properties of shear walls become more
obvious at this level of spectral acceleration. For high 2, while the lower
bounds approach zero, the trend is still observable for the upper bounds. This
same trend was also found for 2-story, rectangular models (Figure 3.4). Since
the first story shear walls are supporting seismic mass from the second floor in
addition, the effect was observable even for low seismicity.
The amount (percentage) of openings and a garage door directly affect the
overall lateral stiffness of buildings. As a result, for buildings with the same
base-rectangular area and percent cutoff, the more openings present, the worse
is the seismic performance. Examples are shown in Figures 3.5 and 3.6. Figure
3.5 is for a 1-story, L-shape, 139 m2 (1,500 ft2) base-rectangular area, R= 0.5,
and Cp= 10%, while Figure 3.6 is for a 2-story, L-shape, 2x232 m2 (2x2,500
ft2) base-rectangular area, R= 0.5, Cp= 10%. Buildings tend to perform worse
as the opening on the short side becomes larger, i.e. comparisons made
between 30|00 vs 30|15 or 60|00 vs 60|30 percent openings cases. For buildings
54
with the same configuration and window/door percent openings, the presence
of a garage door generally decreases their seismic performances, as expected
(i.e. comparisons made between a triangular dot (with garage door) and a
circular dot (no garage door) at each level of percent openings. The plots also
show the effects of shear wall nonlinearity in that when a garage door is
present on a wall having window/door openings, it tends to have a stronger
negative effect on seismic performance than having a garage door installed on
a solid wall (for example, the comparison with and without a garage door,
between the 60|00 and 60|30 cases). However, this trend did not exist for high
2 seismicity for 1-story, and high 1 and high 2 for 2-story, since the ground
motions are so severe that they cause Gavg to approach zero regardless of the
amount of percent openings.
Figure 3.7 shows histograms of the maximum difference of Gavg between L, T,
and Z shapes of the same configuration and plan irregularity. The comparison
was made for all 48 cases of single story models and 48 cases for 2-story
models. For all seismicity regions, the range of difference that has the highest
frequency is 0.0 to 0.1. For more than 80% of all cases, the differences are less
than 0.3. This implies a strong similarity in seismic performance for these
building shapes because these three shapes, when having the same baserectangular area and percent cutoff, have the same seismic mass as well as the
total lateral stiffness along both major directions. The observed differences of
Gavg result from different eccentricity characteristics due to variation in
numbers and locations of cutoff areas. So, it is considered reasonable to use the
minimum grades (among the comparable L, T, and Z shapes) to develop
scoring tables which are applicable for these plan shapes.
55
Development of Grading Sheets
The intent of the grading sheet development is to provide a simple evaluation
form that would allow an inspector to assign a building its seismic
performance grade (reflecting its plan shape and irregularities) that represents
the expected seismic performance at a specified level of spectral acceleration.
Grading sheets were developed separately for each group of single-family,
wood-frame dwellings classified by plan shape and number of floors. For each
group, the grading sheet is a single page except for that of single- story T and
U shapes where an extra page for the 4,500 ft2 base-rectangular area was
added. Figure 3.8 shows the grading sheet for 1-story L, T, and Z shapes.
The grading sheet is organized into 5 areas as shown in Figure 3.8. The top left
area (area #1) shows plan shapes and defines parameters. Next to the shapes is
a scale showing the relationship between the final score and the expected
performance level. The middle left area (area #2) is provided for shape
parameter calculation. An area to sketch a plan view of the structure is located
at the bottom left of the page (area #3). The top right area (area #4) is for basic
information about the building and RVS, such as the address, date, and name
of screeners. A space to record the expected spectral response (Sa) for the site
under considerations is also provided. The remaining space (area #5) on the
right side is where the scoring table is located.
All (1,920) average performance grades (Gavg) obtained from the analysis of
480 models at 4 levels of Sa were arranged into their corresponding locations in
the scoring table (the grading sheet is organized by plan shape and number of
floors). The table was designed to have a similar appearance and scoring
concept as FEMA 154 (FEMA 2002a), where the scoring consists of 3 major
components: basic score (BS), score modifiers (SMs), and final score (FS),
where FS = BS – SMs. For this new RVS tool, the basic score refers to the
56
average performance grade of a basic model. For square plan shapes (R= 1.0),
basic models are those with the least openings, i.e., 30|30 percent openings
with no garage door. Similarly, for rectangular plan shapes (R≠ 1.0), basic
models are the models with 30|0 percent openings with no garage door. The
basic scores and score modifiers were determined for each group of models
having the same plan shape, number of floors, overall shape ratio, baserectangular area, and percent cutoff. The difference in Gavg between models
having different percent openings (without garage door) compared to the basic
model is reflected in percent opening score modifiers. The maximum
differences in Gavg between the “with-garage” and “without-garage” cases,
determined from all pairs, were used as the garage door score modifier for the
group. An example of the developed grading sheet for 1-story for L, T, and Z
shapes is shown in Figure 3.8. Figure 3.9 shows part of a grading sheet (areas 1
and 5) for 2-story L, T, and Z shapes.
An example application of the grading sheet is illustrated in Figure 3.8, where
a single story L-shape building is examined. The observed plan configuration
data were recorded and shown in area 2. The building has a base-rectangular
area of 279 m2 (3,000 ft2), percent cutoff of 9.7%, and a garage door. Percent
openings along the long and short sides were estimated to be 60% and 30%,
respectively. The overall plan configuration was sketched in area 3. Assuming
that Life Safety was the performance objective, the 2008 U.S. Geological
Survey (USGS) National Seismic Hazard Maps with 10% probability of being
exceeded in 50 years were used. The expected spectral acceleration, calculated
including the site coefficient, was determined based on the procedure in
ASCE/SEI 31 (ASCE 2003), and was assumed equal to 1.0 for this example.
As a result, from the high 1 scoring table, the basic score for this building is
3.0. The score modifiers for window and door openings and garage door are 1.1 and -0.6, respectively. This leads to a final score of 1.3 which is less than
57
2.0, so the building fails to meet the collapse prevention drift limit and a more
detailed investigation is recommended.
Conclusions
1. The new rapid visual screening (RVS) tool, developed in this study, examines
the adequacy of single-family, wood-frame dwellings in Oregon to resist
lateral forces resulting from ground motions and torsion induced from plan
irregularity. The evaluation procedure takes into consideration the shape of the
floor plan, number of stories, base-rectangular area, percent cutoff, and
openings from doors/windows and garage doors.
2. Application of the proposed RVS tool does not cover other sources of seismic
vulnerabilities such as the effects of forces at reentrant corners, vertical
irregularity, liquefaction, slope failure, unreinforced masonry chimneys, and
foundation connections. Other issues such as different nail spacing for wall
lines with large openings should also be further investigated.
3. The tool can be used together with FEMA 154 to identify whether a building
with a particular plan shape and plan irregularity, focusing on torsional effects,
can be potentially hazardous. Since performance grades from the new RVS
method relate the predicted maximum shear wall drifts to immediate
occupancy, life safety, and collapse prevention limits, the screener can use a
final score of 2.0, which relates to collapse prevention performance, as a cutoff
grade. It is also possible to incorporate this tool into Tier 1 (screening phase) of
ASCE/SEI 31 to check the adequacy of the exterior shear walls in an existing
building.
4. Using non-linear time-history analysis with pancake model, the effect of
torsion due to mass eccentricities is included. Duration of ground motion
shaking and number of cycles are taken into account through the numerical
58
integration of the equation of motion. Since the development was based on a
worst-case-scenario concept, and the representative models were based only on
structural details observable from a side-walk survey (no contributions from
any interior walls were included), the predicted results are considered to be
reasonable and conservative for evaluations to meet the target performance
objectives.
5. When ignoring the contributions from interior walls, increasing the baserectangular area degrades the overall seismic performance. Buildings with two
stories, a larger percentage of openings, and having a garage door were found
to be more vulnerable to seismic events, as expected. In general, plan shape
and plan irregularity were found to be important features especially in houses
located in high 1 and high 2 seismicity regions, as they could potentially lead
to severe damage. For low and moderate seismicity, the performance ranges
from satisfying the collapse prevention limit to the immediate occupancy limit.
Acknowledgments
The authors are grateful for the financial support of this project by the Royal Thai
Government, the School of Civil and Construction Engineering, and the Department of
Wood Science and Engineering, Oregon State University.
References
American Society of Civil Engineers (ASCE). (2003). “Seismic Evaluation of Existing
Buildings.” ASCE/SEI 31-03, American Society of Civil Engineers, Reston,
VA.
American Society of Civil Engineers (ASCE). (2005). “Minimum Design Loads for
Buildings and Other Structures.” ASCE/SEI 7-05, American Society of Civil
Engineers, New York.
Applied Technology Council (ATC). (2007). “Seismic Rehabilitation Guidelines for
Detached, Single Family, Wood-Frame Dwellings.” ATC 50-1, Redwood City,
CA.
59
Federal Emergency Management Agency (FEMA). (2002a). “Rapid Visual Screening
of Buildings for Potential Seismic Hazards: A Handbook.” FEMA 154,
Washington, D.C.
Federal Emergency Management Agency (FEMA). (2002b). “Rapid Visual Screening
of Buildings for Potential Seismic Hazards: Supporting Documentation.”
FEMA 155, Washington, D.C.
Folz, B. and Filiatrault, A. (2002). “A computer program for seismic analysis of
woodframe structure.” CUREE Publication No. W-21, Richmond, CA.
Folz, B. and Filiatrault, A. (2004). “Seismic analysis of woodframe structures. I:
model formulation.” Journal of Structural Engineering, 130(9), 1353-1360.
Kircher, C.A., Reitherman, R.K., Whitman, R.V. and Arnold, C. (1997). “Estimation
of earthquake losses to buildings.” Earthquake Spectra, 13(4), 703-720.
Lucksiri, K., Miller, T.H., Gupta, R., Pei, S. and van de Lindt, J.W. (2012). “Effect of
plan configuration on seismic performance of single-story, wood-frame
dwellings.” Natural Hazards Review, 13(1), 24-33.
Lucksiri, K. (2012). “Development of rapid visual screening tool for seismic
evaluation of wood-frame dwellings.” Ph.D. dissertation, Oregon State
University, Corvallis, OR.
Pang, W.C., Rosowsky, D.V., Pei, S. and van de Lindt, J.W. (2007). “Evolutionary
Parameter hysteretic Model for Wood Shear Walls.” ASCE Journal of
Structural Engineering, 133(8), 1118-1129.
Pei, S. (2007). “Loss analysis and loss based seismic design for woodframe
structures.” Ph.D. thesis, Department of Civil and Environmental Engineering,
Colorado State University, Fort Collins, CO.
Pei, S. and van de Lindt, J. W. (2007). “User’s Manual for SAPWood for Windows.”
<http://www.engr.colostate.edu/NEESWood/sapwood.shtml> (Dec. 10, 2007).
Pei, S. and van de Lindt, J.W. (2009). “Coupled shear-bending formulation for seismic
analysis of stacked wood shear wall systems.” Earthquake Engineering and
Structural Dynamics, 38(14), 1631-1647.
Schierle, G. G. (2003). “Northridge earthquake field investigations: Statistical analysis
of woodframe damage.” CUREE Publication No. W-09, Richmond, CA.
60
Somerville, P., Smith, N., Punyamurthula, S. and Sun, J. (1997). “Development of
Ground Motion Time Histories for Phase 2 of the FEMA/SAC Steel Project.”
Report No. SAC/BD-97/04, SAC Joint Venture for the Federal Emergency
Management Agency, Washington, D.C.
van de Lindt, J. W., Pei, S., Liu, H. and Filiatrault, A. (2010). “Three-dimensional
seismic response of a full-scale light-frame wood building: Numerical
study.” Journal of Structural Engineering, 136(1), 56-65.
61
Table 3.1 Observed areas of plan shapes from phase 1 (Lucksiri et al. 2012)
Observed Net Floor Area, m2 (ft2)
Plan Shape
Minimum
Average
Maximum
Rectangle
52 (560)
162 (1,747)
297 (3,200)
L
72 (780)
185 (1,987)
293 (3,150)
T
88 (948)
215 (2,310)
387 (4,170)
U
173 (1,860)
247 (2,661)
436 (4,688)
Z
100 (1,074)
203 (2,185)
308 (3,316)
Table 3.2 Base-rectangular areas selected for RVS development
No. of
Stories
1
Baserectangular
Area
Plan Shape
Rectangle
L
T
U
Z
139 m2
(1,500 ft2)
X
X
X
X
X
279 m2
(3,000 ft2)
X
X
X
X
X
X
X
2
418 m
(4,500 ft2)
2
2x116 m2
(2x1,250 ft2)
X
X
X
X
X
2x232 m2
(2x2,500 ft2)
X
X
X
X
X
Table 3.3 Selected shape ratios and percent cutoffs
R
0.5
Cp (%)
Rect.
L
T
0
x
10
x
x
x
30
x
x
x
x
x
x
x
0
10
x
15
30
1.3
Z
x
5
1.0
U
x
x
x
5
x
15
x
62
Table 3.4 Example of case study matrix for 1-story, 139 m2 base-rectangular area, Lshape models
L1
X
X
X
X
L2
X
X
X
X
L3
X
X
X
X
L4
X
X
X
X
L5
X
X
X
X
L6
X
X
X
X
L7
X
X
X
X
L8
X
X
X
X
Garage Door
30|0
30|15
30|30
60|0
60|30
Percent Openings
60|60
30
Percent
Cutoff
10
1.0
Shape
Ratio
0.5
279 m2
No.
139 m2
Baserectangular
Area
X
X
X
L9
X
X
X
X
L10
X
X
X
X
L11
X
X
X
X
L12
X
X
X
X
L13
X
X
X
X
L14
X
X
X
X
L15
X
X
X
X
L16
X
X
X
X
L17
X
X
X
X
L18
X
X
X
X
L19
X
X
X
L20
X
X
X
L21
X
X
X
X
L22
X
X
X
X
L23
X
X
X
X
L24
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
63
Table 3.5 Summary of total number of representative models
Number of representative models
Shape
1-story
2-story
Total
R
24
24
48
L
48
48
96
T
72
48
120
U
72
48
120
Z
48
48
96
480
Table 3.6 CUREE parameters for 2.4 m (8 ft) by 2.4 m (8 ft) GWB wall model
Value
Parameter
K0
2.60 kN/mm (14,846 lb/in)
F0
3.56 kN (800 lb)
F1
0.80 kN (179.8 lb)
r1
0.029
r2
-0.017
r3
1
r4
0.005
xu
24.00 mm (0.9449 in)
0.8
α
1.1
β
Table 3.7 Seismic region definition
Region of
Seismicity
Z1: Low
Z2: Moderate
High
Z3: High 1
Z4: High 2
Spectral Acceleration
(short period or 0.2 sec)
FEMA 154 This project
< 0.167g
< 0.167g
≥ 0.167g
≥ 0.167g
< 0.50g
< 0.50g
≥ 0.50g
≥ 0.50g
< 1.00g
≥ 1.00g
< 1.50g
64
Table 3.8 Performance grade conversion criteria
Grade
Conversion Criteria
Max. drift≤ 1% (IO)
4
3
2
1
0
1% < max. drift ≤ 2% (LS)
2% < max. drift ≤ 3% (CP)
3% < max. drift ≤ 10%
Max. drift> 10%
Table 3.9 Minimum and maximum values of average performance grades (Gavg)
classified by number of floors and base-rectangular area
1
Number
of
Floors
1
2
1
1-L
279 (3,000)
4.0
4.0
3.2
4.0
1.1
3.2
0.2
2.3
3
1
1-XL
418 (4,500)
4.0
4.0
2.9
3.9
0.9
3.1
0.2
1.4
4
2
2-S
2x166 (2x1,250)
3.7
4.0
2.6
3.8
0.8
2.6
0.2
1.1
5
2
2-L
2x232 (2x2,500)
3.4
4.0
1.8
3.4
0.4
1.6
0.1
0.7
No
LOW
MODERATE
HIGH 1
HIGH 2
*Group
Code
Base-rectangular
Area, m2 (ft2)
min
max
min
max
min
max
min
max
1-S
139 (1,500)
4.0
4.0
3.2
4.0
1.8
3.2
0.6
3.2
*Group code is designated as: number of floors – relative size of base-rectangular area
(S: small, L: large, XL: extra large)
Figure 3.1 Composition of plan shapes in terms of base-rectangular area (a x b) and
cutoff areas (grey-shaded)
No.of.floor: 1
No.of.floor: 2
4
3
2
1
Z4-HI2
Z3-HI1
Z2-MOD
Z1-LOW
Z4-HI2
Z3-HI1
Z2-MOD
0
Z1-LOW
Average performance grade
65
Seismic region
Figure 3.2 Average performance grades of all models for each seismic region
Average performance grade
100 250 400
Z1-LOW
Z2-MOD
100 250 400
Z3-HI1
Z4-HI2
4
3
2
1
0
100 250 400
100 250 400
Base-rectangular area (m2)
Figure 3.3 Effect of base-rectangular area (1-story, R= 1.0)
66
100 250 400
Average performance grade
Z1-LO W
Z2-M O D
100 250 400
Z3-HI1
Z4-HI2
4
3
2
1
0
100 250 400
100 250 400
2 x Base-rectangular area (m 2 )
Z1-LOW
Z2-MOD
Z3-HI1
Z4-HI2
4
3
2
1
0
3000
3015
3030
6000
6030
3000
3015
3030
6000
6030
3000
3015
3030
6000
6030
3000
3015
3030
6000
6030
Average performance grade
Figure 3.4 Effect of base-rectangular area (2-story, R≠ 1.0)
Percent openings
Figure 3.5 Effect of percent openings and garage door (1-story, L-shape, 139 m2
(1,500 ft2) base-rectangular area, R= 0.5, Cp= 10%)
Note: Triangular dots represent cases with garage door.
Circular dots represent cases with no garage door.
Z1-LOW
Z2-MOD
Z3-HI1
Z4-HI2
4
3
2
1
0
3000
3015
3030
6000
6030
3000
3015
3030
6000
6030
3000
3015
3030
6000
6030
3000
3015
3030
6000
6030
Average performance grade
67
Percent openings
Figure 3.6 Effect of percent openings and garage door (2-story, L-shape, 2x232 m2
(2x2,500 ft2) base-rectangular area, R= 0.5, Cp= 10%)
Z1-Low
Z2-M od
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Note: Triangular dots represent cases with garage door.
Circular dots represent cases with no garage door.
Z3-Hi1
Z4-Hi2
80
60
40
20
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
0
M aximum differences of G avg
Figure 3.7 Histograms of maximum differences of Gavg among L, T, and Z shapes
68
Figure 3.8 Grading sheet for 1-story L, T, and Z shapes
69
Figure 3.9 Grading sheet for 2-story L, T, and Z shapes
70
IMPLEMENTATION OF PLAN IRREGULARITY RAPID VISUAL
SCREENING TOOL FOR WOOD-FRAME, SINGLE-FAMILY DWELLINGS
Kraisorn Lucksiri, Thomas H. Miller, Rakesh Gupta, Shiling Pei, and John W. van de
Lindt
Journal of Earthquake Engineering
Taylor & Francis
325 Chestnut Street
Suite 800
Philadelphia, PA 19106, USA
In review
Published Online: N/A
71
CHAPTER 4: IMPLEMENTATION OF PLAN IRREGULARITY RAPID
VISUAL SCREENING TOOL FOR WOOD-FRAME, SINGLE-FAMILY
DWELLINGS
Kraisorn Lucksiri1, Thomas H. Miller2, Rakesh Gupta3, Shiling Pei4, and John W. van
de Lindt5
Abstract
A plan irregularity rapid visual screening method for seismic performance assessment
of wood-frame, single-family dwellings is presented. Results from 124 samples were
compared with (i) building-specific, non-linear time-history analysis, and (ii) FEMA
154 and ASCE 31 Tier 1. Verification using two houses damaged in the 1994
Northridge Earthquake is presented. The method includes effects of shape, torsional
forces from eccentricity, and is based on conservative values of shear wall capacities
and a non-linear time-history analysis. The method is relatively more conservative
than ASCE 31 Tier 1 and FEMA 154, and provides conservative but reasonable
predictions of actual earthquake damage.
Short Title: Case Study for Plan Irregularity Screening Tool
CE Database subject headings: seismic analysis; wood structures; rapid visual
screening
72
1
Graduate Student. School of Civil and Construction Engineering and Dept. of Wood
Science and Engineering, Oregon State University, Corvallis, OR 97331. Email:
kraisorn.lucksiri@oregonstate.edu
2
Corresponding Author. Associate Professor. School of Civil and Construction
Engineering, Oregon State University, Corvallis, OR 97331. Email:
thomas.miller@oregonstate.edu
3
Professor. Dept. of Wood Science and Engineering, Oregon State University,
Corvallis, OR 97331. Email: rakesh.gupta@oregonstate.edu
4
Assistant Professor. Dept. of Civil and Environmental Engineering, South Dakota
State University, Brookings SD 57006. Email: Shiling.Pei@sdstate.edu
5
Professor and Drummond Chair. Dept. of Civil, Construction, and Environmental
Engineering, University of Alabama, Tuscaloosa, AL, 35487. Email:
jwvandelindt@eng.ua.edu
73
Introduction
Economic losses due to major earthquakes have been extensive, including to
residential buildings or single family dwellings (SFD). For example, the dollar loss to
SFD from the 1994 Northridge Earthquake was at least $20 billion (Kircher et al.
1997). In the City of Los Angeles, a total of 40,010 (of the existing 442,994) SFD
were damaged (Schierle 2003). Damage was observed on different elements such as
garage doors, chimneys, cripple walls, partition walls, and shear walls. The total repair
cost for SFD was estimated to be more than $414 million, and for those with shear
walls damaged, the estimated average shear wall repair cost was as much as $ 11,819
per building. Damage to shear walls demonstrates the load path is reasonably defined
but shear capacity to resist ground motion forces is lacking in many of these SFD.
Many existing wood-frame SFD were non-engineered in their design. Some were
code-prescribed but the level of damage from a major earthquake is unknown. For
engineered structures, they are designed to provide life safety, and not damage control.
The inherent torsion due to eccentricity is also not typically included in the design
practice of SFD due to the non-engineer designer. The adequacy of shear walls in
existing wood-frame SFD to resist both direct shear and torsional shear (due to
eccentricity) from future earthquakes thus should be evaluated.
This paper presents the method and results of the third and final phase of a project
whose objective was to develop a rapid visual screening (RVS) tool for evaluating
seismic performance of wood-frame SFD. The first phase (Lucksiri et al. 2012a)
introduced an approach to classify wood-frame SFD based on shape parameters
including the number of floors, plan shape, base area, percent cutoff area, and percent
openings, as shown in Figure 4.1 for L-shape buildings. That study showed that, when
neglecting contributions from interior walls, seismic performance of wood-frame SFD
of the same size (base area), shape, and percent openings, is strongly dependent on the
overall plan proportions (shape ratio) and amount of reduction in area from the base
rectangle (percent cutoff). The second phase (Lucksiri et al. 2012b) developed a plan
74
irregularity rapid visual screening (piRVS) method which takes into consideration the
shape of the floor plan, number of stories, base-rectangular area, percent cutoff, and
openings from doors/windows and garage doors. It was found that plan shape and plan
irregularity were important features especially in houses located in high 1 (Sa= 1.00g)
and high 2 (Sa= 1.50g) seismicity regions. For low and moderate seismicity, the
performance ranges from satisfying the collapse prevention limit to the immediate
occupancy limit. This third phase is on piRVS implementation with three study
objectives as follows:
i.
To determine uncertainties inherent in piRVS scores that result from
configuration differences between piRVS index models and an actual house
population.
ii.
To compare prediction results from piRVS (Lucksiri et al. 2012b) to FEMA
154 (FEMA 2002a) and ASCE 31 Tier 1 (ASCE 2003).
iii.
To compare the prediction results from piRVS, Tier 1 of ASCE 31, and FEMA
154 to examples of 1994 Northridge Earthquake house damage.
Evaluation Methods
Fast and qualitative methods for building seismic hazard evaluation were mainly
developed to preliminary identify the inherent sources of seismic deficiencies in
buildings and to obtain a recommendation of whether a more detailed analysis should
be performed. The assessment generally involves building inspection and/or simple
calculations. This study focuses on three methods that can be applied to SFD building
types including:
FEMA 154 (Rapid Visual Screening of Buildings for Potential Seismic
Hazards)
FEMA 154 (FEMA 2002a) was developed by the Federal Emergency
Management Agency to identify, inventory, and rank buildings that are
75
potentially seismically hazardous. FEMA 154 methodology is based on a
“sidewalk survey” of a building. A simple data collection form is provided for
each seismicity area which was classified as low-, moderate-, and highseismicity based on the expected response acceleration. The process starts by
the determination of a basic structural hazard (BSH) score based on the
primary lateral load resisting system. Score modifiers (SMs) are selected to
incorporate effects of height, plan irregularity, vertical irregularity, year built,
and soil types. For plan irregularity, just one SM was provided for each
structural type and each seismicity regardless of level of irregularity severity
(e.g. size of reentrant corners). A final score (S) is obtained by summation of
the BSH and all applicable SMs. FEMA 154 performance scores were based
on spectral displacements of representative models and predictions from
nonlinear static analysis. The properties of representative models, i.e. building
capacity curves and fragility curves, were obtained from HAZUS 99 (NIBS
1999). The suggested cutoff score (S= 2) is related to 1% probability of
collapse. Buildings with final scores of 2 or less are suggested to have more
detailed evaluation.
Tier 1 of ASCE 31-03 (Seismic Evaluation of Existing Buildings)
ASCE 31 (ASCE 2003) is a three-tiered evaluation process. Tier 1 summarizes
potential deficiencies through the provided checklists and simple calculations.
The checklist is a compliant/non-compliant evaluation system, with no
performance scoring. For light wood frames, a simple procedure for demandcapacity checking of shear walls is provided. With an appropriate ductility
related m-factor, shear stresses are checked against the suggested shear wall
capacity. Tier 2 and 3 provide more detailed evaluation guidelines focusing on
the potential deficiencies as indentified in Tier 1. ASCE 31 evaluates buildings
at immediate occupancy (IO) and life safety (LS) performance limits.
76
piRVS (Plan Irregularity Rapid Visual Screening)
piRVS (Lucksiri et al. 2012b) was developed for seismic performance
evaluation of wood-frame SFD, with plan irregularity. The tool examines the
adequacy of the structure’s exterior shear walls to resist lateral forces resulting
from ground motions, including torsional forces induced from plan irregularity
but does not cover other sources of seismic deficiencies such as cripple walls,
anchor bolts, chimneys, and vertical irregularities. It uses the concept of a
sidewalk survey with a similar scoring procedure to FEMA 154. Selection of
the BSH score is based on the number of floors, plan shape, base area, shape
ratio, and percent cutoff area. Selection of the SMs is based on percent
openings along short and long directions, and garage doors. A final score (S) is
obtained by summation of the BSH score and all applicable SMs. Performance
scores were based on spectral displacements from a set of representative
models and predictions using nonlinear time-history analysis. piRVS supports
evaluation at immediate occupancy (IO), life safety (LS), and collapse
prevention (CP) performance targets with the suggested cutoff scores of 3.5,
2.5, and 1.5, respectively.
Methodology
Study Samples
There are two sets of samples studied. The first set includes 124 wood-frame
SFD in Oregon; 95 one-story houses from Corvallis (Table 4.1) and 29 twostory from Salem and Portland (Table 4.2). Observation was performed
through image data of Google Earth, with the limitation that not all wall sides
can be observed. It was assumed that the percent openings on the unobserved
sides are equal to the weighted average (by length) of the percent openings of
the observed walls along the same direction. The second set of samples was
selected from 530 buildings damaged in the 1994 Northridge Earthquake (ATC
77
2000). Applicable buildings were W1 type (light-frame) with floor area less
than 464 m2 (5,000 ft2), and having damage on the exterior walls. Eleven
houses qualified but only two were usable. Exclusion of the other nine
buildings was due to one of the following: having complex plan shapes,
ground motions were not recorded, unable to locate/observe on Google Earth,
no reference photo, and roofing material unclear. Image from Google Earth
permitted a simulated sidewalk-survey. An assumption was made for percent
openings on the unobservable side, as discussed.
Modeling Assumptions
Simplified models were used to represent these structures. The following
assumptions were used in this study. Building structural system was assumed
to be made of vertical shear walls, and horizontal diaphragm elements
including roof, ceiling, and floor. Exterior shear walls are structural-sheathed
on one side and gypsum wallboard-sheathed on the other. Lateral loads were
resisted by exterior shear walls only. Story height is at 2.44 m (8 ft). A dead
load of 527 N/m2 (11 psf) was assumed, based on ASCE 7-05 (ASCE 2005),
for shear walls and a uniformly distributed load per floor area of 718 N/m2 (15
psf) for partition walls. Seismic masses for roof, ceiling, and floor, were 478
N/m2 (10 psf), 191 N/m2 (4 psf), and 383 N/m2 (8 psf), respectively. Sample
buildings were assumed to have no vertical irregularity and built before 1976,
in other words, before the initial adoption of seismic codes such as the 1976
UBC (ICBO 1976) for engineered structures, and also before the first editions
of the current International Residential Code (IRC) (ICC 2012) for prescribed
designs of houses.
Level of Seismicity and Soil Types
Level of seismicity was classified as low, moderate, or high based on design
spectral acceleration (Table 4.3) at short period (0.2 sec) and 1.0 sec. In
78
piRVS, the high seismicity was separated into 2 ranges to increase the
resolution. As defined in ASCE 31 (ASCE 2003), the design spectral
acceleration is a function of the expected MCE and the site adjustment factors.
The site adjustment factor covers five different site classes from class A (hard
rock) to class E (soft clay). The seismicity level for ASCE 31 and piRVS thus
depends on site class. Differently, FEMA 154 defines seismicity based on site
class “B” which refers to rock with an average shear wave velocity between
762 to 1,524 m/s (2,500 to 5000 ft/sec).
In this study, comparisons between piRVS and ASCE 31 Tier 1 were made at
the upper limits of each seismicity, i.e. at 0.167g, 0.500g, 1.000g, and 1.500g.
For comparisons between piRVS and FEMA 154, site class B was assumed.
Since the site adjustment factor for site class B equals 1.0, the level of
seismicity for a building comparison for FEMA 154 and piRVS is always the
same.
Evaluation Methods and Assumptions
FEMA 154
Study samples were considered to be the W1 building type, defined as light
wood-frame residential and commercial buildings smaller than or equal to
464 m2 (5,000 ft2). Three BSH scores were obtained, one for each
seismicity. SMs for plan irregularity were applied for L-, T, U, and Z-shape
samples due to reentrant corners. Since all dwellings were assumed to be
built before 1976, the post-benchmark SMs were not applied. Samples with
final scores of 2 or greater were tagged as “Pass”, otherwise, as “Fail”.
FEMA 154’s cutoff level (at S= 2.0) is related to 1% probability of
collapse. ASCE 31 and piRVS use different performance limits including
immediate occupancy (1% drift for piRVS, IO), life safety (2% drift for
piRVS, LS), and collapse prevention (3% drift for piRVS, CP). Additional
79
back-calculation was performed for the FEMA 154 S = 2 cutoff score to
obtain percent lateral drifts that correspond to such a level of probability of
collapse. Based on the BSH definition (FEMA 2002b) and default values
for building capacity curves and fragility curves (NIBS 1999), percent
lateral drifts at the S = 2 cutoff score for high-, moderate- and lowseismicity are 4.8%, 4.8%, and 3.8%, respectively. The percent lateral
drifts for high and moderate seismicity regions are equal because they
share the same values of drift ratio (NIBS 1999) that define a damage state.
Although the drift limits are different, evaluation results were compared
between FEMA 154 and the piRVS at the CP limit.
ASCE 31 Tier 1
The shear wall shear stress check in ASCE 31 Tier 1 is based on a
performance-based methodology using pseudo lateral forces. This means
that a pseudo lateral force was applied to a structure to obtain an “actual”
displacement during a design earthquake. The pseudo lateral force was
calculated using Equation (1).
V = C Sa W
(1)
where C= modification factor to relate expected maximum inelastic
displacements to displacements calculated for linear elastic response; Sa=
spectral acceleration (g’s); and W= effective seismic weight. Modification
factor is based on the number of stories. For wood frames, C equals 1.3 and
1.1 for one-story and two-story buildings, respectively.
The pseudo lateral force (Eq. 1) is distributed vertically to determine story
shear at each floor level using the prescribed methods in Section 3.5.2.2
(ASCE 2003). The story shear was then used to calculate average the shear
stress in shear walls (Eq. 2). Since the analysis is linear, the (pseudo
80
lateral) force to reach the expected displacement is unrealistically high. The
ductility-related m-factor was used to reduce the pseudo lateral force to a
more realistic level.
vavg = (Vj/Lw)/m
(2)
where Vj= story shear at level j (in accordance with Section 3.5.2.2 of
ASCE 31); m = component modification factor: m = 4.0 for life safety
limit, m = 2.0 for immediate occupancy limit; Lw= summation of shear wall
length in the direction of loading.
For evaluations at both life safety and immediate occupancy limits, the
shear stresses in shear walls calculated from equation (2) were checked
against the 14.6 kN/m (1,000 plf) capacity limits for structural panel
sheathing shear walls, as specified in Section 4.4.2.7.1 of ASCE 31.
Sample models with maximum shear stress lower than this limit were
tagged as “Pass”, otherwise, tagged as “Fail”.
piRVS
Modifications were made in the piRVS scoring tables (Lucksiri et al.
2012b) to reduce performance score variations due to inspectors. The
modification rules were selected in such a way to minimize the overall
score differences (of all study models) between the piRVS and buildingspecific case analyses using SAPWood (Pei and van de Lindt 2009), a
nonlinear time history analysis software developed specifically for light
frame wood structures. These rules could be adjusted and would affect the
level of conservatism of piRVS relative to FEMA 154 and ASCE 31 Tier
1. For BSH, more specific ranges were specified for base area, shape ratio,
and percent cutoff area. For example, in the unmodified tables, users would
have to select the percent cutoff areas for single-story L-shape houses to be
81
either 10% or 30%. The new tables modified these numbers to ≤20% and >
20%, respectively. An example of the updated scoring table for one-story,
L, T, Z shape buildings at high 1 seismicity is as shown in Figure 4.2. In
addition, a flowchart was developed to assist selection of SMs for percent
openings (Figure 4.3).
The observed configuration details were used directly as piRVS input
except for percent openings in which two average values, one along each
major direction, were used. For garage doors, the SMs are included only
when a garage is parallel to the short direction of a building. This is
because the development of piRVS assumed a garage door to be on the
most critical side, a wall side where maximum drift tends to occur most
often (see, for example, Filiatrault et al 2010, van de Lindt et al 2010), and
which is usually one of the walls on the short direction. The cutoff scores
for piRVS for IO, LS, and CP limits are 3.5, 2.5 and 1.5, respectively.
Building-Specific Case Analysis using SAPWood
Building-specific case analysis follows the same procedures as in the
piRVS development (Lucksiri et al. 2012b). In general, the analysis is
based on nonlinear time-history analysis using the SAPWood software.
The evolutionary parameter hysteresis model (EPHM) (Pei et al. 2006) was
used to represent the load-displacement relationship of structural panelsheathed shear walls. Values of the EPHM parameters are from a
SAPWood database (Pei 2007) and linear interpolation was used to obtain
parameters for different wall lengths. The assumed nail spacing values for
edge and field are 150 mm (6 in.) and 300 mm (12 in.), respectively, with a
stud spacing of 406 mm (16 in.). A ten parameter CUREE hysteresis model
(Folz and Filiatrault 2004) was used to represent the load-displacement
relationship for gypsum wallboard-sheathed walls. The “pancake” model
82
(Folz and Filiatrault 2002) was used for structural modeling. Ten pairs of
ground motion time histories developed for Seattle (Somerville et al.
1997), having probabilities of exceedance of 2% in 50 years were used.
The analysis results, i.e. maximum shear wall drifts, were converted to
performance grade from 0 (worst) to 4 (best). Conceptually, grades of 4, 3,
2, 1, and 0 are associated with the 1% immediate occupancy (IO) drift
limit, 2% life safety (LS) limit, 3% collapse prevention (CP) limit, drifts
greater than 3% up to 10%, and drifts greater than 10%, respectively.
Results and Discussion
Uncertainties inherent in piRVS Performance Scores
The performance scores from piRVS were compared against the reference
scores from building-specific analysis using SAPWood. Figure 4.4 shows
comparisons for 40 one-story L-shape models (out of all 95 one-story models)
at high 1 seismicity. The higher score implies better performance (i.e. less
drift). An ideal piRVS would provide the same score for each model and thus
give the same plots. Using piRVS, although not perfectly matched, the plots
are similar and the scores scatter about the same level (approximately S= 2.5,
for this case). Cases with large score differences were partly due to limitations
of piRVS to cover some extreme configurations, and insufficient resolution of
piRVS shape parameters. For example, the score difference for model number
9 (Fig. 4.4) is -1.7. The piRVS final score was based on a SM for 30%|15%
openings (30% along long direction and 15% along short direction) while the
actual openings are 72%|16%. The provided SM thus does not support this
extreme case well where the percent openings on the long direction of the
observed building is much higher than that of the index models. Large percent
openings along the length can also change the critical direction of a building
since the long direction may become weaker than the short direction. Another
example related to the resolution of shape parameter is for model number 27.
83
Note that the piRVS for L-shape models was developed based on two levels of
shape ratio; 0.50 (for rectangle-like) and 1.00 (for square-like). The assumed
shape ratio range for square-like shapes in this study is from 0.85 to 1.00,
Model 27 (shape ratio= 0.84) was thus considered as rectangular-like and its
piRVS score is 1.8. With a SAPWood score of 3.4, the score difference is 1.6.
The difference would reduce to 0.8 if the model was considered as square-like
and the piRVS score improves to 2.6. Increasing the piRVS shape ratio
resolution could be a benefit for this case.
Figure 4.5 summarizes the score differences (SAPWood - piRVS) for all
models in a box plot format. Box widths show the middle 50% of the data. A
line within each box shows the median. Whiskers show the 10th to 90th
percentile range. For single-story dwellings, medians are generally within ±
0.10 ranges, except for moderate seismicity where the median equals 0.50. The
overall score differences are within the ± 0.80 range; minimal at low, peaked at
high 1, and reduced at high 2 seismicity. At low seismicity, the difference is
minimal due to low seismic demand. All models are subject to small drifts as
illustrated in Fig. 4.6 with all one-story L-shape models at low seismicity at
scores of 4.0.
At moderate seismicity, the range of the score difference increases. Most of the
models remain at a SAPWood score of 4.0 (Fig. 4.6). The piRVS scores
decrease earlier, thus the score differences initiate on the positive side. For
high 1 seismicity, the range of score difference is peaked as the buildings
behave more nonlinearly. Figure 4.6 shows that the majority of SAPWood
scores reduce to 2.0 to 3.5. Unlike moderate seismicity, the score differences
are now on both positive and negative sides. A possible reason is that the effect
of nonlinearity, torsional moment due to eccentricity, and load redistribution,
become more obvious. The range of score difference decreases at high 2
84
seismicity since the performance score of 1.0 covers a wider range of percent
drifts from more than 3% up to 10%.
For two-story dwellings, medians of the difference are also within ± 0.10
ranges. The overall score differences are within a ± 0.50 range, thus relatively
less variation than for a one-story. This is partly because the set of two-story
models have less configuration variations than for one-story models. For
example, from Table 4.1 and 4.2, two-story samples generally cover narrower
ranges of base area as well as overall width to length ratio. There are also less
two-story sample models (N= 29) than one-story models (N= 95).
Prediction Results between piRVS, ASCE 31 Tier 1, and FEMA 154
piRVS vs ASCE 31 Tier 1
Table 4.4 shows comparison results in terms of percent “Fail” and “Pass”
agreement. The percent agreement ranges from as low as 7% up to 100%.
The perfect (100%) agreements are observed for low seismicity where the
seismic demand is very low. The percentages tend to, but not always,
reduce at the moderate and high 1 seismicities before increasing again at
high 2 seismicity. piRVS is seen to be relatively more conservative than
ASCE 31 Tier 1. It predicts failures roughly 1 step (in seismicity level)
ahead of ASCE 31.
The conservatism of piRVS is partly because the effects of torsional forces
from eccentricity, dynamic loadings, nonlinearity, and force redistribution
were included. The difference in shear wall capacity can also be a major
factor. piRVS assumed shear walls with 8d nails and a nail spacing for the
edge and field of 150 mm (6 in.) and 300 mm (12 in.), respectively. Stud
spacing was assumed at 406 mm (16 in.). The ultimate capacity used in
piRVS development for a 2.40 x 2.40-m (8 x 8-ft) shear wall is
approximately 8.90 kN/m (610 plf). ASCE 31 does not specify
85
configuration details of a shear wall but suggests a shear capacity of 14.6
kN/m (1,000 plf). References such as Report 154 (Tissell 1993) and
Pardoen et al. (2000) show that typical 2.40 x 2.40-m (8 x 8-ft) shear walls
using 8d nails, with 150 mm (6 in.) nail spacing value for the edge and 300
mm (12 in.) for the field, generally have a shear capacity within this range,
i.e. from 8.76 kN/m (600 plf) to 14.6 kN/m (1,000 plf). Variations in shear
capacity depend on factors such as blocked and unblocked conditions, and
sheathing material and thickness. Shear wall capacity used in piRVS is thus
closer to the lower bound while the ASCE 31 value is closer to the upper
bound.
The last column of Table 4.4, percent agreement (2), shows the recalculated percent agreement after revising the ASCE 31 shear capacity to
10.2 kN/m (700 plf). Selection of the 10.2 kN/m (700 plf) is somewhat
arbitrary but is within the 8.76 kN/m (600 plf) to 14.6 kN/m (1,000 plf)
range, and closer to the value used in piRVS. While this revision improves
the overall agreement, a more careful study is recommended.
piRVS vs FEMA 154
The piRVS is sensitive to plan configuration as can be seen from Fig. 4.4
where the piRVS scores for one-story L-shape models at high 1 seismicity
vary across the group models. Differently, the FEMA 154 scores (Fig. 4.4)
are at a constant value since all models use the same FEMA 154 basic
score of 4.4 with the same SM for plan irregularity of -0.5. As a result,
their final scores are 3.9 (S= 4.4 – 0.5).
Table 4.5 shows a summary of percent agreement between FEMA 154 and
piRVS for all models. FEMA 154 does not predict any failures at all
seismicities. piRVS is more conservative as it starts to provide warnings at
high 1. The results show very good agreement (100%) between the two
86
methods for low and moderate seismicity. Percent agreement starts to
reduce at high 1 and becomes worse at high 2 where the agreement drops
to 20% and 0% for one-story and two-story buildings, respectively.
Conservatism of piRVS may due to two reasons. First, the drift limits were
different. piRVS collapse prevention limit is associated with 3% drift while
the FEMA 154 cutoff score is associated with 4.8% drift for high- and
moderate-, and 3.8% drift for low-seismicity. Second, their index models,
assumptions, and analysis approach are different. FEMA 154 was
developed based on standard build capacity curves (NIBS 1999)
representing load-displacement properties of typical W1 type buildings.
For piRVS, the load-displacement properties of buildings depend on
different combinations of shape parameters. Effects of torsional moment
due to eccentricity, nonlinearity, load redistribution, and dynamic loadings
are included. Lateral load resistance contribution from interior wall is
excluded.
1994 Northridge Damage Predictions
Selected houses from ATC 38, “USC021-GTZ-21” and “USC053-ER-01”, are
designated house 1 and house 2, respectively. Comparisons were qualitatively
made between the observed conditions and the predictions from piRVS, ASCE
31 Tier 1, and FEMA 154.
Observed Damage Conditions
The observed damage conditions for both houses can be summarized as
follows:
House 1: The overall damage condition is moderate meaning that
repairable structural damage has occurred. Existing elements can be
repaired in-place without substantial demolition or replacement.
87
Percent structural element damage was estimated to be 1% to 10%.
Diagonal cracks were found in the north wall.
House 2: The overall damage condition is moderate. Percent structural
element damage was approximate 1% to 10%. Moderate damage was
on exterior walls.
The damage description above was used to describe both houses in terms
of the ASCE 41-06 (ASCE 2007) performance scale (i.e. IO, LS, and CP
limits). Since shear wall damage is present but repairable, both houses were
considered to “fail” the IO limit but “pass” the LS limit. Figure 4.7 shows
the ASCE 41-06 performance scale, the corresponding damage description,
and the seismic performance for both sample houses.
Predicted Damage Conditions
The overall configuration details, natural periods, and spectral
accelerations for both houses are summarized in Table 4.6. The natural
periods were determined using SAPWood based on the observed
configuration and an assumption that interior walls were spaced every 4.57
m (15 ft). With the provided response spectra (ATC 2000), the spectral
accelerations for both sample houses were determined.
The obtained spectral accelerations were used directly in the ASCE 31 Tier
1 calculation. Building effective seismic weight was calculated based on
the assumed values described earlier. The calculated pseudo lateral force
(Eq. 1) for house 1 and house 2 are 511 kN (115.0 kips) and 388 kN (87.3
kips), respectively. The calculated maximum shear stresses (equation 2) for
house 1 are 32.8 kN/m (2,246 plf) (at IO) and 16.4 kN/m (1,123 plf) (at
LS) which means that house 1 fails both the IO and LS (shear capacity=
14.6 kN/m (1,000 plf) for both performance limits). The prediction is for
88
somewhat more severe damage than observed. The extent of damage
beyond the LS limit is unknown. For house 2, the calculated maximum
shear stresses are 16.6 kN/m (1,137 plf) (at IO) and 8.29 kN/m (568 plf) (at
LS), so it fails the IO but passes the LS limit. This is considered slightly
unconservative since the predicted damage level is the same as the
observed even though the interior wall contribution has not been included.
Tier 1 of ASCE 31 thus provides reasonable predictions although they
could be slightly unconservative for some cases.
The FEMA 154 evaluation was performed using the high-seismicity data
sheet. The only applicable SM is for plan irregularity. The final score for
house 1 is 4.4 (S= 4.4 – 0), and for house 2 is 3.9 (S= 4.4 – 0.5). Both
houses thus pass the cutoff score. FEMA 154 provides correct predictions
in that neither collapsed. However, how well these houses would perform
at the higher performance limits (i.e. at IO, LS, and CP) is unidentified.
The piRVS evaluation was made at high 1 seismicity. Based on their
configuration details (Table 4.6), the BSH scores are 2.9 and 3.0 for house
1 and house 2, respectively. The SMs for both houses are equal at 1.1. The
garage door score modifier is not included since it is not in the short
direction. As a result, the performance scores for house 1 and house 2 are
1.8 (S= 2.9 – 1.1) and 1.9 (S= 3.0 – 1.1), respectively. Both houses fail the
IO (cutoff score= 3.5) and LS (cutoff score= 2.5), but pass the CP limit
(cutoff score= 1.5). For these two buildings, the piRVS prediction is
conservative as it predicts somewhat more severe damage (one
performance level difference) than observed.
89
Conclusions
Plan Irregularity Rapid Visual Screening (piRVS) is a new method to predict the
expected seismic performance level of wood-frame, single family dwellings with plan
irregularity with regards to the Immediate Occupancy (IO), Life Safety (LS), and
Collapse Prevention (CP). The method is able to reasonably evaluate seismic
performance for building-specific cases as the variation in final scores, relative to
building-specific nonlinear time history analyses, is generally within the ± 0.80 range
for 1-story (N= 95) models and ± 0.50 range for 2-story (N= 29) models.
piRVS is relatively more conservative than ASCE 31 Tier 1. It predicts failures earlier
than ASCE 31 Tier 1, roughly one step in seismicity level ahead. In other words, for a
particular performance level, ASCE 31 Tier 1 allows a building to withstand a more
severe seismic intensity than the piRVS. The benefits of piRVS over ASCE 31 are (i)
the effects of torsional forces from eccentricity, dynamic loadings, nonlinearity, and
force redistribution are included, and (ii) piRVS shear wall capacity is closer to the
lower bound.
The piRVS is also relatively more conservative than FEMA 154. This is felt to be
reasonable because the piRVS evaluation uses the CP limit while FEMA 154 uses 1%
probability of collapse (higher drift limits). The benefits of piRVS are that (i) effects
of plan configurations and eccentricities are directly included, (ii) contributions from
interior walls are neglected which is conservative for sidewalk-survey-based
evaluations, and (iii) its non-linear dynamic analysis background is more rigorous.
The piRVS provides reasonable damage predictions for Northridge Earthquake
damage samples. By excluding shear resistance from interior walls, the piRVS
predicts slightly more damage (one performance level difference) than observed.
Among the three methods, it is the only one that provides a seismic performance
assessment for all of the ASCE 41 performance levels (IO, LS, and CP).
90
Overall, piRVS is an engineering-based rapid visual screening method for wood-frame
SFD with plan irregularity. While the piRVS covers many different combinations of
shape parameters, the evaluation method is simple and thus suitable for rapid visual
screening. It provides reasonable and conservative predictions. It is believed that the
piRVS is an effective tool for use in rapid visual screening of wood-frame SFD.
Acknowledgments
The authors are grateful for the financial support of this project by the Royal Thai
Government, the School of Civil and Construction Engineering, and the Department of
Wood Science and Engineering, Oregon State University.
References
American Society of Civil Engineers (ASCE). (2003). “Seismic Evaluation of Existing
Buildings.” ASCE/SEI 31-03, American Society of Civil Engineers, Reston,
VA.
American Society of Civil Engineers (ASCE). (2005). “Minimum Design Loads for
Buildings and Other Structures.” ASCE/SEI 7-05, American Society of Civil
Engineers, New York.
American Society of Civil Engineers (ASCE). (2007). “Seismic Rehabilitation of
Existing Buildings.” ASCE/SEI 41-06, American Society of Civil Engineers,
Reston, VA.
Applied Technology Council (ATC). (2000). “Database on the Performance of
Structures Near Strong-Motion Recordings: 1994 Northridge, California,
Earthquake.” ATC-38, Redwood City, CA.
Federal Emergency Management Agency (FEMA). (2002a). “Rapid Visual Screening
of Buildings for Potential Seismic Hazards: A Handbook.” FEMA 154,
Washington, D.C.
Federal Emergency Management Agency (FEMA). (2002b). “Rapid Visual Screening
of Buildings for Potential Seismic Hazards: Supporting Documentation.”
FEMA 155, Washington, D.C.
91
Filiatrault, A., Christovasilis, I.P., Wanitkorkul, A. and van de Lindt, J.W. (2010).
“Experimental seismic response of a full-scale light-frame wood building.”
Journal of Structural Engineering, 136(3), 246-254.
Folz, B. and Filiatrault, A. (2002). “A computer program for seismic analysis of
woodframe structure.” CUREE Publication No. W-21, Richmond, CA.
Folz, B. and Filiatrault, A. (2004). “Seismic analysis of woodframe structures. I:
model formulation.” Journal of Structural Engineering, 130(9), 1353-1360.
International Code Council (ICC). (2012). International Residential Code,
Washington DC.
International Conference of Building Officials (ICBO). (1976). Uniform Building
Code, Whittier, CA.
Kircher, C.A., Reitherman, R.K., Whitman, R.V. and Arnold, C. (1997). “Estimation
of earthquake losses to buildings.” Earthquake Spectra, 13(4), 703-720.
Lucksiri, K., Miller, T.H., Gupta, R., Pei, S. and van de Lindt, J.W. (2012a). “Effect of
plan configuration on seismic performance of single-story, wood-frame
dwellings.” Natural Hazards Review, 13(1), 24-33.
Lucksiri, K., Miller, T.H., Gupta, R., Pei, S. and van de Lindt, J.W. (2012b). “A
procedure for rapid visual screening for seismic safety of wood-frame
dwellings with plan irregularity.” Engineering Structures, 36(3), 351-359.
National Institute of Building Sciences (NIBS). (1999). Earthquake Loss Estimation
Methodology HAZUS, Technical Manual, Vol. 1, Washington, D.C.
Pang, W.C., Rosowsky, D.V., Pei, S. and van de Lindt, J.W. (2007). “Evolutionary
Parameter hysteretic Model for Wood Shear Walls.” ASCE Journal of
Structural Engineering, 133(8), 1118-1129.
Pardoen, G.C., Kazanjy, R.P., Freund, E., Hamilton, C.H., Larsen, D., Shah, N. and
Smith, A. (2000). “Results from the City of Los Angeles-UC Irvine shear wall
test program.” Paper 1.1.1 on CD in Proc 6th World Conf on Timber Eng, 31
July to 3 Aug 2000, Whistler, BC.
Pei, S. (2007). “Loss analysis and loss based seismic design for woodframe
structures.” Ph.D. thesis, Department of Civil and Environmental Engineering,
Colorado State University, Fort Collins, CO.
92
Pei, S., van de Lindt, J.W., Rosowsky, D.V. and Pang, W. (2006). “Next generation
hysteretic models for development of a performance-based seismic design
philosophy for woodframe construction.” 8th National Conference on
Earthquake Engineering, San Francisco, CA.
Pei, S. and van de Lindt, J.W. (2009). “Coupled shear-bending formulation for seismic
analysis of stacked wood shear wall systems.” Earthquake Engineering and
Structural Dynamics, 38(14), 1631-1647.
Schierle, G. G. (2003). “Northridge earthquake field investigations: Statistical analysis
of woodframe damage.” CUREE Publication No. W-09, Richmond, CA.
Somerville, P., Smith, N., Punyamurthula, S. and Sun, J. (1997). “Development of
Ground Motion Time Histories for Phase 2 of the FEMA/SAC Steel Project.”
Report No. SAC/BD-97/04, SAC Joint Venture for the Federal Emergency
Management Agency, Washington, D.C.
Tissell, J. R. (1993). “Wood Structural Panel Shear Walls.” Report 154, APA – The
Engineered Wood Association, Tacoma, WA.
van de Lindt, J. W., Pei, S., Liu, H. and Filiatrault, A. (2010). “Three-dimensional
seismic response of a full-scale light-frame wood building: Numerical
study.” Journal of Structural Engineering, 136(1), 56-65.
93
Table 4.1 Summary of 1-story sample models
1-Story Dwellings (Corvallis, OR)
No. of
Samples
Avg. Base
Area, m2 (ft2)
Base Area
Ranges, m2
(ft2)
Overall
Width to
Length Ratio
Rect.
L
T
U
Z
20
40
16
7
12
157
(1,693)
239
(2,569)
276
(2,974)
245
(2,642)
283
(3,049)
89
(960)
to
259
(2,788)
0.41
to
0.95
84
(900)
to
361
(3,888)
0.45
to
1.00
98
(1,050)
to
438
(4,712)
0.43
to
0.96
190
(2,040)
to
301
(3,240)
0.57
to
0.96
202
(2,176)
to
357
(3,848)
0.53
to
1.00
Table 4.2 Summary of 2-story sample models
2-Story Dwellings (Salem and Portland, OR)
No. of
Samples
Average
Based Area,
m2 (ft2) (per
floor)
Based Area
Ranges, m2
(ft2) (per
floor)
Overall
Width to
Length Ratio
Rect.
L
T
U
Z
15
10
2
N/A
2
116
(1,253)
136
(1,459)
196
(2,108)
N/A
207
(2,224)
61
(660)
to
184
(1,976)
0.43
to
1.00
85
(912)
to
241
(2,592)
0.62
to
1.00
171
(1,840)
to
221
(2,376)
0.81
to
0.87
N/A
N/A
172
(1,848)
to
242
(2,600)
0.95
to
0.96
94
Table 4.3 Levels of Seismicity Definitions
Level of
seismicity
Design short-period spectral response acceleration
parameter, SDS
High
ASCE 31
< 0.167g
≥ 0.167g
< 0.500g
≥ 0.500g
FEMA 154
< 0.167g
≥ 0.167g
< 0.500g
≥ 0.500g
Z3: High 1
-
-
Z4: High 2
-
-
Z1: Low
Z2: Moderate
Design spectral response
acceleration parameter at
a one-second period, SD1
piRVS
< 0.167g
≥ 0.167g
< 0.500g
≥ 0.500g
< 1.000g
≥ 1.000g
< 1.500g
< 0.067g
≥ 0.067g
< 0.200g
≥ 0.200g
≥ 0.200g
≥ 0.200g
Table 4.4 Summary of percent agreement between ASCE 31 Tier 1 and piRVS for all
models
No. of
Floors
Performance
Level
Immediate
Occupancy
1
Life Safety
Immediate
Occupancy
2
Life Safety
Seismicity
Level
No. of
Samples
Low
No. of Failures
Percent
Agreement
Percent
Agreement
(2)
ASCE 31
piRVS
95
0
0
100%
100%
Moderate
95
0
45
53%
52%
High 1
High 2
95
95
40
90
95
95
42%
95%
93%
100%
Low
95
0
0
100%
100%
Moderate
95
0
0
100%
100%
High 1
95
0
21
78%
77%
High 2
95
3
91
7%
58%
Low
29
0
0
100%
100%
Moderate
29
3
25
24%
62%
High 1
29
28
29
97%
100%
High 2
29
29
29
100%
100%
Low
29
0
0
100%
100%
Moderate
29
0
1
97%
55%
High 1
29
3
29
10%
100%
High 2
29
18
29
62%
100%
Note: Percent agreement (2) was determined after revising ASCE 31 shear capacity to
10.2 kN/m (700 plf)
95
Table 4.5 Summary of percent agreement between FEMA 154 and piRVS for all
models
No. of
Floors
1
2
Performance
Level
No. of Failures
Seismicity
Level
No. of
Samples
FEMA 154
piRVS
Percent
Agreement
Low
95
0
0
100%
Moderate
95
0
0
100%
High 1
95
0
4
96%
High 2
95
0
76
20%
Low
29
0
0
100%
Collapse
Prevention
Collapse
Prevention
Moderate
29
0
0
100%
High 1
29
0
18
38%
High 2
29
0
29
0%
Table 4.6 Configuration details and dynamic properties of sample models from
ATC38
Model
Plan
Shape
Base
Area,
m2, (ft2)
Shape
Ratio
Percent
Cutoff
Percent
Openings
(Long |
Short)
House
1
Rect.
(1-story)
291
(3,136)
0.33
N/A
75 | 60
House
2
L
(1-story)
285
(3,072)
0.75
8
60 | 60
Garage
Door
Yes
(on long
dir.)
Yes
(on long
dir.)
Ground
Motion
Station
ID
Natural
Period
(sec)
Spectral
Acc. (g)
USC-21
0.132
0.91
USC-53
0.114
0.75
96
Figure 4.1 Basic shape parameters for L-shape buildings
Figure 4.2 Example of a scoring table for one-story, L, T, Z shape buildings at high 1
seismicity
97
Figure 4.3 Flowchart for selection of percent opening score modifiers
Figure 4.4 Comparisons of performance scores between piRVS, SAPWood, and
FEMA 154 for 40 one-story L-shape models at high 1 seismicity
98
No.of.Fl: 1
Score Differences
(SAPWood - piRVS)
1.0
No.of.Fl: 2
0.5
0.0
-0.5
-1.0
1-LOW
2-MOD
3-Hi1
4-Hi2
1-LOW
2-MOD
3-Hi1
4-Hi2
Level of Seismicity
Figure 4.5 Ranges of score difference between piRVS and SAPWood for all models
4.5
Performance Scores
4
3.5
3
2.5
2
1.5
1
0.5
0
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
Model Number (1-story, L-shape)
LOW
MOD
HI 1
HI 2
Figure 4.6 SAPWood performance scores for 40 one-story L-shape models at each
seismicity level
99
Observed performance level (on IO, LS, and CP scales)
based on damage description for both models
IO
No Damage
LS
CP
1% prob. of
collapse
2 Northridge
Houses
Distributed minor
hairline cracking of
gypsum and plaster
veneers
Moderate
loosening of
connections and
minor splitting of
members
Collapse
Connection loose.
Nails partially
withdrawn. Some
splitting of members
and panels. Veneer
dislodged
Figure 4.7 Seismic performance of sample houses on ASCE 41-06 performance scale
100
CHAPTER 5: GENERAL SUMMARY, CONCLUSIONS, AND FUTURE
WORK
Summary
Damage to shear walls in wood-frame, single-family dwellings during earthquakes is
examined, and is a concern for the Pacific Northwest due to the Cascadia subduction
zone. With a goal to mitigate future seismic damage, a rapid visual screening (RVS)
method has been developed to facilitate seismic performance evaluation of the
structure’s exterior shear walls considering torsional forces induced from plan
irregularity. The development of plan irregularity RVS (piRVS) encompassed a
variety of efforts, including:
1. Introducing shape parameters
A set of shape parameters was introduced to (i) specify a plan configuration
(shape and dimensions) in a format that can be used in the RVS and (ii)
organize the wood-frame SFD population into a definite number of groups
having similar seismic performance.
2. Configuration observations on existing wood-frame SFD
Observations were made to obtain the typical ranges of plan shape
configurations and shear wall openings from the building population. The
observation results allowed this study to exclude impractical configurations. It
also provides guidelines for selection of the configurations and shape
parameter ranges to be included in the piRVS.
3. Development of 480 index models
Wood-frame SFD come in many different configurations, e.g. shapes, sizes,
and shear wall openings. These properties directly reflect the dynamic
properties and load-resistance properties of a building. As a result, 480 index
101
models were developed to cover different combinations of shape parameters
and opening-related parameters.
4. Seismic responses for 480 representative models were determined based on:
a. Rigorous engineering approach
Nonlinear time-history analysis was used. Effects of dynamic loadings,
shaking durations, and frequency contents are directly included in the
analysis.
b. Verified numerical models of wood-frame buildings
Ten-parameter CUREE model and EPHM models were used for
modeling of gypsum-sheathed walls and shear walls, respectively.
These models are capable of representing the nonlinear, hysteretic loaddisplacement behavior of walls. Pancake models were used for
structural modeling. With a rigid-diaphragm assumption, effects of
torsional forces from plan irregularity were captured.
5. Development of a method to facilitate the rapid visual screening process
The obtained analysis results of all representative 480 models are in terms of
maximum lateral drifts. Transformation of this data set into a simple format
that supports RVS and allows an inspector to assign a building its seismic
performance grade is needed.
6. Implementation of the piRVS
An implementation phase was set up to provide insights into the new piRVS.
The evaluation results from piRVS were compared to FEMA 154 and ASCE
Tier 1. Verification of piRVS method using two houses damaged in the 1994
Northridge Earthquake was also performed.
102
Conclusions
Plan Irregularity Rapid Visual Screening (piRVS) is a new RVS method to predict the
expected seismic performance level of wood-frame, single family dwellings in Oregon
with plan irregularity. It can be used by architects, engineers, building officials, and
trained inspectors, to examine shear wall adequacy to resist lateral forces resulting
from ground motions and torsion induced from plan irregularity. The piRVS explicitly
considers the characteristics of building configurations including floor plan shape,
number of stories, base rectangular area, percent cutoff, and openings from
doors/windows and garage doors and, thus, should provide accurate RVS results
suitable for building-specific cases. In addition, since the piRVS was developed based
on an engineering approach where all the development procedures and assumptions
were clearly specified, its development framework provides the basis for future
improvements as well as extensions of the method for other seismic-prone areas.
The study to investigate effects of plan configurations on seismic performance of
wood-frame SFD (phase 1) showed that:
1) Square-like (shape ratio approaches 1.0) buildings usually perform better than
long, thin rectangles as it better distributes shear walls in both major directions
than long, thin rectangles.
2) Long, thin U-shapes may have improvements in their lateral load resistance
along the short direction due to the extra lengths of shear wall, caused by the
cutoff area in the U- shape, that are added on the short side.
3) The positive and negative effects of cutoff area on the overall seismic
performance were also observed. The positive effect is that, for a base
rectangle, the cutoff area reduces the overall seismic mass which generally
leads to smaller drifts. The negative effect is that cutoff area induces
eccentricity between centers of rigidity and mass and, as a result, causes one
103
critical wall to exceed the allowable drift limit, and fail, earlier than others.
This leads to a concern for cases where large openings (windows/garage doors)
are present on the critical wall where the negative effect can be significantly
enhanced. These findings emphasize that plan configuration is an important
issue for an RVS of single-story wood-frame SFD.
4) Classification of single-story wood-frame SFD based on shape parameters,
including size and overall aspect ratio, plan shape, and percent cutoff area, is
capable of organizing a building population into groups having similar
performance.
From the phase 2 study, it can be concluded that:
1) When ignoring the contributions from interior walls, increasing the baserectangular area degrades the overall seismic performance.
2) Plan shape and plan irregularity should be a concern especially for houses
located in high 1 and high 2 seismicity regions, as the buildings may fail to
meet the collapse prevention objective. For low and moderate seismicity, the
performance ranges from satisfying the collapse prevention limit to the
immediate occupancy limit.
3) The effect of each parameter (such as percent openings, garage doors) depends
on seismicity level. For example, the seismic performance score for a building
in low seismicity (Sa= 0.167g) may not be different when a garage door was
added. This is because the ground motion intensity is so small that the
difference is not significant. When the seismic intensity increases, the score
differences (between with and without garage doors) tends to be more
significant as the buildings start to yield and behave nonlinearly. These
findings thus emphasize the importance of shape parameters as well as the
benefits of using nonlinear time-history analysis in the development.
104
Study results from an implementation phase (phase 3) showed that:
1) The piRVS is relatively more conservative than ASCE 31 Tier 1. The
conservatism may be partly due to the effects of torsional forces, dynamic
loadings, nonlinearity, and force redistribution included in the piRVS and, in
addition, the shear wall capacity assumed in piRVS is closer to the lower
bound.
2) The piRVS is relatively more conservative than FEMA 154 which is felt to be
reasonable because the piRVS evaluation uses the CP limit while FEMA 154
uses 1% probability of collapse (higher drift limits).
3) The piRVS provides reasonable damage predictions for the two applicable
Northridge earthquake damage samples. By excluding shear resistance from
interior walls, the piRVS predicts slightly more damage (one performance
level difference) than observed.
Future work
Further work is recommended in the following areas:
1) Inclusion of interior partition walls in piRVS. This would improve the
capability of piRVS to support an RVS for dwellings where access to the
interior or information about the interior is available, and can also be a useful
guideline for the design of new dwellings.
2) A study to verify/improve FEMA 154 scores by using the predicted spectral
displacement obtained from nonlinear time-history analysis in SAPWood.
3) Improvements of the resolution of factors (such as floor area and percent
openings) and seismic intensity in piRVS to reduce the inherent uncertainties.
105
4) A more thorough study for 2-story wood-frame SFD since this group of
buildings generally have highly complex shapes and the second floor does not
always have the same plan shape as the first floor.
5) Extension of piRVS output to the estimated repair cost (in addition to
performance levels) which is useful information for decision-making for
designers, home-owners, and the insurance industry.
106
BIBLIOGRAPHY
American Society of Civil Engineers (ASCE). (2003). “Seismic Evaluation of Existing
Buildings.” ASCE/SEI 31-03, American Society of Civil Engineers, Reston,
VA.
American Society of Civil Engineers (ASCE). (2005). “Minimum Design Loads for
Buildings and Other Structures.” ASCE/SEI 7-05, American Society of Civil
Engineers, New York.
American Society of Civil Engineers (ASCE). (2007). “Seismic Rehabilitation of
Existing Buildings.” ASCE/SEI 41-06, American Society of Civil Engineers,
Reston, VA.
Applied Technology Council (ATC). (2000). “Database on the Performance of
Structures Near Strong-Motion Recordings: 1994 Northridge, California,
Earthquake.” ATC-38, Redwood City, CA.
Applied Technology Council (ATC). (2007). “Seismic Rehabilitation Guidelines for
Detached, Single Family, Wood-Frame Dwellings.” ATC 50-1, Redwood City,
CA.
Baker, J. W. (2007). “Measuring bias in structural response caused by ground motion
scaling.” Proceedings, 8th Pacific Conference on Earthquake Engineering,
Nangyang Technological University, Singapore, 8.
Camelo, V.S., Beck, J.L. and Hall, J.F. (2001). “Dynamic characteristics of
woodframe structures.” CUREE Publication No. W-11, Richmond, CA.
Council of American Building Officials (CABO). (1989). “CABO One and Two
Family Dwelling Code.” CABO 1989 Edition, Falls Church, VA.
Council of American Building Officials (CABO). (1995). “CABO One and Two
Family Dwelling Code.” CABO 1995 Edition, Falls Church, VA.
Federal Emergency Management Agency (FEMA). (2002a). “Rapid Visual Screening
of Buildings for Potential Seismic Hazards: A Handbook.” FEMA 154,
Washington, D.C.
Federal Emergency Management Agency (FEMA). (2002b). “Rapid Visual Screening
of Buildings for Potential Seismic Hazards: Supporting Documentation.”
FEMA 155, Washington, D.C.
107
Federal Emergency Management Agency (FEMA). (2008). “Quantification of
Building Seismic Performance Factors.” FEMA P-695, Washington, D.C.
Filiatrault, A., Christovasilis, I.P., Wanitkorkul, A. and van de Lindt, J.W. (2010).
“Experimental seismic response of a full-scale light-frame wood building.”
Journal of Structural Engineering, 136(3), 246-254.
Folz, B. and Filiatrault, A. (2002). “A computer program for seismic analysis of
woodframe structure.” CUREE Publication No. W-21, Richmond, CA.
Folz, B. and Filiatrault, A. (2004). “Seismic analysis of woodframe structures. I:
model formulation.” Journal of Structural Engineering, 130(9), 1353-1360.
International Code Council (ICC). (2000). “International Residential Code for Oneand Two-Family Dwellings.” IRC 2000, Falls Church, VA.
International Code Council (ICC). (2012). International Residential Code,
Washington DC.
International Conference of Building Officials (ICBO). (1976). Uniform Building
Code, Whittier, CA.
Kircher, C.A., Reitherman, R.K., Whitman, R.V. and Arnold, C. (1997). “Estimation
of earthquake losses to buildings.” Earthquake Spectra, 13(4), 703-720.
Lucksiri, K. (2012). “Development of rapid visual screening tool for seismic
evaluation of wood-frame dwellings.” Ph.D. dissertation, Oregon State
University, Corvallis, OR.
Lucksiri, K., Miller, T.H., Gupta, R., Pei, S. and van de Lindt, J.W. (2012a). “Effect of
plan configuration on seismic performance of single-story, wood-frame
dwellings.” Natural Hazards Review, 13(1), 24-33.
Lucksiri, K., Miller, T.H., Gupta, R., Pei, S. and van de Lindt, J.W. (2012b). “A
procedure for rapid visual screening for seismic safety of wood-frame
dwellings with plan irregularity.” Engineering Structures, 36(3), 351-359.
National Institute of Building Sciences (NIBS). (1999). Earthquake Loss Estimation
Methodology HAZUS, Technical Manual, Vol. 1, Washington, D.C.
National Institute of Building Science (NIBS). (2003). “Multi-hazard Loss Estimation
Methodology, Earthquake Model.” HAZUS-MH MR3 Technical Manual,
Washington, D.C.
108
Nelson, A. R., Kelsey, H. M. and Witter, R. C. (2006). “Great earthquakes of variable
magnitude at the Cascadia subduction zone.” Quaternary Research, 65(3),
354-365.
Pang, W.C., Rosowsky, D.V., Pei, S. and van de Lindt, J.W. (2007). “Evolutionary
Parameter hysteretic Model for Wood Shear Walls.” ASCE Journal of
Structural Engineering, 133(8), 1118-1129.
Pardoen, G.C., Kazanjy, R.P., Freund, E., Hamilton, C.H., Larsen, D., Shah, N. and
Smith, A. (2000). “Results from the City of Los Angeles-UC Irvine shear wall
test program.” Paper 1.1.1 on CD in Proc 6th World Conf on Timber Eng, 31
July to 3 Aug 2000, Whistler, BC.
Pei, S. (2007). “Loss analysis and loss based seismic design for woodframe
structures.” Ph.D. thesis, Department of Civil and Environmental Engineering,
Colorado State University, Fort Collins, CO.
Pei, S. and van de Lindt, J. W. (2007). “User’s Manual for SAPWood for Windows.”
<http://www.engr.colostate.edu/NEESWood/sapwood.shtml> (Dec. 10, 2007).
Pei, S. and van de Lindt, J.W. (2009). “Coupled shear-bending formulation for seismic
analysis of stacked wood shear wall systems.” Earthquake Engineering and
Structural Dynamics, 38(14), 1631-1647.
Pei, S., van de Lindt, J.W., Rosowsky, D.V. and Pang, W. (2006). “Next generation
hysteretic models for development of a performance-based seismic design
philosophy for woodframe construction.” 8th National Conference on
Earthquake Engineering, San Francisco, CA.
Schierle, G. G. (2003). “Northridge earthquake field investigations: Statistical analysis
of woodframe damage.” CUREE Publication No. W-09, Richmond, CA.
Somerville, P., Smith, N., Punyamurthula, S. and Sun, J. (1997). “Development of
Ground Motion Time Histories for Phase 2 of the FEMA/SAC Steel Project.”
Report No. SAC/BD-97/04, SAC Joint Venture for the Federal Emergency
Management Agency, Washington, D.C.
Tissell, J. R. (1993). “Wood Structural Panel Shear Walls.” Report 154, APA – The
Engineered Wood Association, Tacoma, WA.
U.S. Census Bureau, Population Division. (2009). “Population estimates-Vintage
2007 Archive.”
<http://www.census.gov/popest/archives/2000s/vintage_2007/> (Mar. 2,
2009).
109
van de Lindt, J. W., Pei, S., Liu, H. and Filiatrault, A. (2010). “Three-dimensional
seismic response of a full-scale light-frame wood building: Numerical
study.” Journal of Structural Engineering, 136(1), 56-65.
110
APPENDICES
111
Appendix A: Configuration summary for phase 1 study
Tables A1 to A5 summarize configuration details of all 151 case study models used in
phase 1 (Chapter 2). Plan shape parameters and notations refer to details described in
Figure 2.1.
Table A1 Configuration details for R-Shape
No.
R1
R2
R3
R4
Base Area
(sq.ft.)
1,500
1,500
1,500
1,500
Shape
Ratio
0.35
0.50
0.75
1.00
a (ft)
b (ft)
65.5
54.8
44.7
38.7
22.9
27.4
33.5
38.7
Table A2 Configuration details for L-Shape
No.
Base
Area
(sq.ft.)
Shape
Ratio
cutoff area
shape ratio
Percent
Cutoff
Area
a (ft)
b (ft)
c (ft)
d (ft)
L1
L2
L3
L4
L5
L6
L7
L8
L9
L10
L11
L12
L13
L14
L15
L16
L17
L18
L19
L20
L21
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
0.50
0.50
0.50
0.50
0.50
0.75
0.75
0.75
0.75
0.75
0.75
0.75
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.20
1.00
1.20
0.30
0.40
0.30
1.00
1.60
0.40
1.00
1.30
0.50
0.40
1.00
1.60
0.50
1.00
1.60
0.70
1.00
1.20
10
10
10
20
30
10
10
10
20
20
20
30
10
10
10
20
20
20
30
30
30
54.8
54.8
54.8
54.8
54.8
44.7
44.7
44.7
44.7
44.7
44.7
44.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
27.4
27.4
27.4
27.4
27.4
33.5
33.5
33.5
33.5
33.5
33.5
33.5
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
27.4
12.2
11.2
31.6
33.5
22.4
12.2
9.7
27.4
17.3
15.2
30.0
19.4
12.2
9.7
24.5
17.3
13.7
25.4
21.2
19.4
5.5
12.2
13.4
9.5
13.4
6.7
12.2
15.5
11.0
17.3
19.7
15.0
7.7
12.2
15.5
12.2
17.3
21.9
17.7
21.2
23.2
112
Table A3 Configuration details for T-Shape
No.
Base
Area
(sq.ft.)
Shape
Ratio
Percent
Cutoff
Area
Cutoff
Ratio
Rc1
d:f
a
(ft)
b
(ft)
c
(ft)
d
(ft)
e
(ft)
f
(ft)
T1
T2
T3
T4
T5
T6
T7
T8
T9
T10
T11
T12
T13
T14
T15
T16
T17
T18
T19
T20
T21
T22
T23
T24
T25
T26
T27
T28
T29
T30
T31
T32
T33
T34
T35
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.30
1.30
1.30
1.30
1.30
1.30
10
10
10
10
10
20
20
20
20
20
20
30
30
30
30
10
10
10
10
10
10
20
20
20
20
20
20
30
30
10
10
20
20
30
30
1.0
1.0
1.0
0.3
0.5
1.0
1.0
1.0
0.5
0.3
0.4
1.0
1.0
0.6
0.3
1.0
1.0
1.0
0.3
0.3
0.8
1.0
1.0
1.0
0.4
0.3
0.5
1.0
0.4
1.0
0.6
1.0
0.5
1.0
0.5
0.4
1.0
2.5
0.4
1.0
0.4
1.0
1.5
0.4
1.0
1.5
0.5
1.0
0.5
1.0
0.8
1.0
3.6
0.8
1.0
3.6
0.9
1.0
3.6
0.9
1.0
3.6
3.1
3.1
3.6
3.6
3.6
3.6
3.6
3.6
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
54.8
54.8
54.8
54.8
54.8
54.8
54.8
54.8
54.8
54.8
54.8
54.8
54.8
54.8
54.8
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
34.0
34.0
34.0
34.0
34.0
34.0
27.4
27.4
27.4
27.4
27.4
27.4
27.4
27.4
27.4
27.4
27.4
27.4
27.4
27.4
27.4
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
44.2
44.2
44.2
44.2
44.2
44.2
13.7
8.7
5.5
21.1
11.5
19.4
12.2
10.0
25.8
18.8
14.3
21.2
15.0
26.5
23.1
9.7
8.7
4.6
14.9
13.3
5.1
12.9
12.2
6.5
18.4
18.8
8.6
8.5
12.2
4.6
5.7
6.5
8.6
7.9
10.5
5.5
8.7
13.7
5.5
8.7
7.7
12.2
15.0
7.7
12.2
15.0
10.6
15.0
10.6
15.0
7.7
8.7
16.4
7.7
8.7
16.4
11.6
12.2
23.2
11.6
12.2
23.2
26.4
26.4
16.4
16.4
23.2
23.2
28.5
28.5
13.7
8.7
5.5
6.3
5.8
19.4
12.2
10.0
12.9
5.7
5.7
21.2
15.0
15.9
6.9
9.7
8.7
4.6
4.5
4.0
4.1
12.9
12.2
6.5
7.4
5.7
4.3
8.5
4.9
4.6
3.4
6.5
4.3
7.9
5.3
5.5
8.7
13.7
5.5
8.7
7.7
12.2
15.0
7.7
12.2
15.0
10.6
15.0
10.6
15.0
7.7
8.7
16.4
7.7
8.7
16.4
11.6
12.2
23.2
11.6
12.2
23.2
26.4
26.4
16.4
16.4
23.2
23.2
28.5
28.5
113
Table A4 Configuration details for U-Shape
No.
U1
U2
U3
U4
U5
U6
U7
U8
U9
U10
U11
U12
U13
U14
U15
U16
U17
U18
Base
Area
(sq.ft.)
Percent
Cutoff
Area
Shape
Ratio
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
5
5
5
10
10
10
15
15
5
5
5
10
10
10
15
5
10
15
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.30
1.30
1.30
h:e
f:d
a
(ft)
b
(ft)
c
(ft)
d
(ft)
e
(ft)
f (ft)
g
(ft)
0.4
1.0
54.8
27.4
27.4
24.6
1.0
1.0
54.8
27.4
27.4
23.1
2.3
1.0
54.8
27.4
27.4
0.7
1.0
54.8
27.4
27.4
1.0
1.0
54.8
27.4
2.3
1.0
54.8
1.0
1.0
54.8
2.1
1.0
0.3
h
(ft)
i
(ft)
13.7
24.6
13.7
5.5
0.0
8.7
23.1
8.7
8.7
0.0
20.8
5.7
20.8
5.7
13.1
0.0
22.3
14.6
22.3
14.6
10.2
0.0
27.4
21.3
12.2
21.3
12.2
12.2
0.0
27.4
27.4
18.1
8.1
18.1
8.1
18.6
0.0
27.4
27.4
19.9
15.0
19.9
15.0
15.0
0.0
54.8
27.4
27.4
16.5
10.4
16.5
10.4
21.7
0.0
1.0
38.7
38.7
38.7
17.0
15.8
17.0
15.8
4.7
0.0
1.0
1.0
38.7
38.7
38.7
15.0
8.7
15.0
8.7
8.7
0.0
1.2
1.0
38.7
38.7
38.7
14.6
7.9
14.6
7.9
9.5
0.0
0.3
1.0
38.7
38.7
38.7
16.0
22.4
16.0
22.4
6.7
0.0
1.0
1.0
38.7
38.7
38.7
13.2
12.2
13.2
12.2
12.2
0.0
1.4
1.0
38.7
38.7
38.7
12.1
10.4
12.1
10.4
14.5
0.0
0.5
1.0
38.7
38.7
38.7
14.1
21.2
14.1
21.2
10.6
0.0
0.3
1.0
34.0
44.2
44.2
14.6
15.8
14.6
15.8
4.7
0.0
0.3
1.0
34.0
44.2
44.2
13.6
22.4
13.6
22.4
6.7
0.0
0.4
1.0
34.0
44.2
44.2
12.2
23.7
12.2
23.7
9.5
0.0
114
Table A5 Configuration details for Z-Shape
No.
Z1
Z2
Z3
Z4
Z5
Z6
Z7
Z8
Z9
Z10
Z11
Z12
Z13
Z14
Z15
Z16
Z17
Z18
Z19
Z20
Z21
Z22
Z23
Z24
Z25
Z26
Z27
Z28
Z29
Z30
Z31
Z32
Z33
Z34
Z35
Z36
Z37
Z38
Z39
Z40
Z41
Base
Area
(sq.ft.)
Shape
Ratio
Percent
Cutoff
Area
Cutoff
Ratio
Rc1
(d:c)
Rc2
(f:e)
a
(ft)
b
(ft)
c
(ft)
d
(ft)
e
(ft)
f
(ft)
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
10
10
10
10
20
20
20
20
20
20
20
20
30
30
30
30
10
10
10
10
10
10
10
20
20
20
20
20
20
20
20
20
20
30
30
30
30
30
30
30
30
1.0
1.0
0.3
0.3
1.0
1.0
1.0
1.0
1.0
0.3
0.3
0.3
1.0
1.0
0.3
0.3
1.0
1.0
0.3
0.3
0.3
0.3
0.3
1.0
1.0
1.0
1.0
1.0
0.3
0.3
0.3
0.3
0.3
1.0
1.0
1.0
1.0
1.0
0.3
0.3
0.3
0.4
0.5
0.3
0.3
0.2
1.2
0.5
1.2
1.0
0.2
0.2
1.0
0.2
1.0
0.3
0.3
0.6
0.6
0.4
1.4
0.4
1.4
1.0
0.3
1.8
0.5
1.8
1.0
0.3
1.7
0.3
1.7
1.0
0.3
1.8
0.5
1.8
1.0
0.4
1.1
0.4
0.2
1.2
0.3
1.1
0.2
1.5
1.1
0.6
1.0
0.2
1.5
1.0
0.3
1.0
0.2
2.2
0.3
1.5
0.4
1.7
1.7
0.5
1.0
0.3
2.7
1.2
0.8
1.0
0.2
3.4
2.2
0.6
1.0
0.4
1.8
1.2
0.8
1.0
0.2
3.9
3.0
54.8
54.8
54.8
54.8
54.8
54.8
54.8
54.8
54.8
54.8
54.8
54.8
54.8
54.8
54.8
54.8
44.7
44.7
44.7
44.7
44.7
44.7
44.7
44.7
44.7
44.7
44.7
44.7
44.7
44.7
44.7
44.7
44.7
44.7
44.7
44.7
44.7
44.7
44.7
44.7
44.7
27.4
27.4
27.4
27.4
27.4
27.4
27.4
27.4
27.4
27.4
27.4
27.4
27.4
27.4
27.4
27.4
33.5
33.5
33.5
33.5
33.5
33.5
33.5
33.5
33.5
33.5
33.5
33.5
33.5
33.5
33.5
33.5
33.5
33.5
33.5
33.5
33.5
33.5
33.5
33.5
33.5
13.7
12.2
19.6
19.6
27.4
11.2
17.3
11.2
12.2
34.0
34.0
15.2
33.5
15.0
34.0
34.0
11.2
11.2
17.0
9.1
17.0
9.1
10.7
22.4
9.1
17.3
9.1
12.2
27.7
11.7
27.7
11.7
15.2
27.4
11.2
21.2
11.2
15.0
29.4
17.7
29.4
5.5
6.1
5.9
5.9
5.5
13.4
8.7
13.4
12.2
6.8
6.8
15.2
6.7
15.0
10.2
10.2
6.7
6.7
6.8
12.7
6.8
12.7
10.7
6.7
16.4
8.7
16.4
12.2
8.3
19.8
8.3
19.8
15.2
8.2
20.1
10.6
20.1
15.0
11.8
19.5
11.8
19.4
7.9
10.7
5.6
27.4
10.0
11.7
15.8
12.2
18.6
6.8
8.3
27.4
15.0
22.8
6.9
15.8
7.1
9.3
4.5
4.5
8.3
5.9
22.4
7.5
11.2
13.7
12.2
18.6
4.5
5.6
10.7
8.3
23.7
11.2
13.7
16.8
15.0
22.8
5.2
5.9
3.9
9.5
3.2
6.2
5.5
15.0
12.8
9.5
12.2
3.7
10.2
8.3
8.2
15.0
4.6
15.1
4.7
10.6
3.7
7.7
7.7
4.2
5.9
6.7
20.1
13.4
11.0
12.2
3.7
15.3
12.3
6.4
8.3
9.5
20.1
16.4
13.4
15.0
4.6
20.1
17.7
115
Table A5 (Continued) Configuration details for Z-Shape
No.
Base
Area
(sq.ft.)
Shape
Ratio
Percent
Cutoff
Area
Cutoff
Ratio
Rc1
(d:c)
Rc2
(f:e)
a
(ft)
b
(ft)
c
(ft)
d
(ft)
e
(ft)
f
(ft)
Z42
Z43
Z44
Z45
Z46
Z47
Z48
Z49
Z50
Z51
Z52
Z53
Z54
Z55
Z56
Z57
Z58
Z59
Z60
Z61
Z62
Z63
Z64
Z65
Z66
Z67
Z68
Z69
Z70
Z71
Z72
Z73
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
1,500
0.75
0.75
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
30
30
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
0.3
0.3
1.0
1.0
1.0
1.0
1.0
0.3
0.3
0.3
0.3
0.3
1.0
1.0
1.0
1.0
1.0
0.3
0.3
0.3
0.3
0.3
1.0
1.0
1.0
1.0
1.0
0.3
0.3
0.3
0.3
0.3
1.1
1.0
0.8
1.2
0.8
1.2
1.0
0.6
1.9
0.6
1.9
1.0
0.4
2.2
0.5
2.0
1.0
0.4
2.2
0.4
2.2
1.0
0.4
2.2
0.5
2.0
1.0
0.5
1.5
0.5
1.5
1.0
0.4
1.0
0.4
3.0
2.0
0.6
1.0
0.5
2.3
2.3
0.6
1.0
0.3
3.6
1.2
0.9
1.0
0.3
4.6
3.0
0.7
1.0
0.5
2.4
1.2
0.9
1.0
0.2
4.8
3.7
0.5
1.0
44.7
44.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
33.5
33.5
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
38.7
17.7
18.6
9.7
7.9
9.7
7.9
8.7
13.9
7.8
13.9
7.8
10.7
19.4
8.3
17.3
8.7
12.2
24.0
10.2
24.0
10.2
15.2
23.7
10.1
21.2
10.6
15.0
26.3
15.2
26.3
15.2
18.6
19.5
18.6
7.7
9.5
7.7
9.5
8.7
8.3
14.8
8.3
14.8
10.7
7.7
18.2
8.7
17.3
12.2
9.6
22.5
9.6
22.5
15.2
9.5
22.2
10.6
21.2
15.0
13.2
22.8
13.2
22.8
18.6
16.1
10.2
13.7
5.0
6.1
11.2
8.7
8.3
3.9
3.9
7.6
5.9
22.4
6.5
11.2
12.9
12.2
15.2
3.9
4.8
9.9
8.3
21.2
9.7
13.7
15.8
15.0
22.8
4.7
5.3
14.4
10.2
6.4
10.2
5.5
15.0
12.2
6.7
8.7
4.2
8.9
8.9
4.6
5.9
6.7
23.2
13.4
11.6
12.2
4.6
17.8
14.4
7.0
8.3
10.6
23.2
16.4
14.2
15.0
4.6
22.3
19.6
7.2
10.2
116
Appendix B: Median maximum drifts for phase 1 study
Tables B1 to B5 summarize the calculated median maximum drifts for all 151 case
study models in phase 1 (Chapter 2). All the calculated drifts that exceeded the 3%
drift limit (2.88 in, for this study) were shown as 2.88 inches in these tables since the
comparisons were made in terms of “number of drifts exceeding the 3% limit”. The
median maximum drifts for the target spectral acceleration of 1.4g to 2.0g were not
shown here since the median drifts for all models exceeded the 3% limit.
Table B1 Median maximum drifts (in.) for R-Shape
Model
R1
R2
R3
R4
0.1g
0.06
0.06
0.04
0.03
0.2g
0.14
0.11
0.09
0.08
0.3g
0.31
0.20
0.16
0.12
0.4g
0.46
0.37
0.24
0.19
Target Spectral Acceleration
0.5g
0.6g
0.7g
0.8g
0.9g
0.72
1.37
2.43
2.88
2.88
0.54
0.79
1.27
2.45
2.88
0.33
0.55
0.82
1.16
2.80
0.27
0.34
0.57
0.87
1.19
1.0g
2.88
2.88
2.88
2.77
1.1g
2.88
2.88
2.88
2.88
1.2g
2.88
2.88
2.88
2.88
1.3g
2.88
2.88
2.88
2.88
117
Table B2 Median maximum drifts (in.) for L-Shape
Model
L1
L2
L3
L4
L5
L6
L7
L8
L9
L10
L11
L12
L13
L14
L15
L16
L17
L18
L19
L20
L21
0.1g
0.05
0.05
0.05
0.05
0.04
0.04
0.04
0.04
0.04
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.2g
0.12
0.12
0.11
0.10
0.10
0.09
0.08
0.08
0.08
0.07
0.07
0.07
0.06
0.06
0.06
0.06
0.06
0.06
0.07
0.06
0.06
0.3g
0.19
0.18
0.18
0.19
0.18
0.13
0.13
0.13
0.14
0.13
0.13
0.13
0.12
0.11
0.12
0.10
0.10
0.10
0.10
0.10
0.10
0.4g
0.30
0.29
0.29
0.29
0.27
0.22
0.21
0.21
0.19
0.18
0.18
0.20
0.17
0.16
0.17
0.16
0.15
0.16
0.15
0.14
0.14
Target Spectral Acceleration
0.5g
0.6g
0.7g
0.8g
0.9g
0.51
0.73
1.08
2.31
2.88
0.48
0.69
1.07
2.63
2.88
0.48
0.69
1.06
2.17
2.88
0.43
0.73
1.03
1.39
2.43
0.40
0.59
0.93
1.24
1.72
0.31
0.44
0.69
1.06
1.40
0.30
0.42
0.69
0.98
1.42
0.30
0.41
0.68
0.97
1.42
0.31
0.41
0.59
0.95
1.25
0.28
0.38
0.53
0.84
1.17
0.27
0.37
0.51
0.87
1.16
0.27
0.40
0.52
0.73
1.11
0.25
0.34
0.43
0.69
1.13
0.25
0.34
0.42
0.71
1.05
0.25
0.34
0.42
0.71
1.04
0.23
0.32
0.44
0.57
0.92
0.22
0.30
0.43
0.54
0.87
0.23
0.31
0.43
0.55
0.91
0.21
0.30
0.40
0.54
0.66
0.20
0.28
0.38
0.53
0.64
0.20
0.29
0.38
0.53
0.65
1.0g
2.88
2.88
2.88
2.88
2.67
2.88
2.88
2.84
1.60
1.63
1.75
1.44
1.59
1.57
1.55
1.33
1.19
1.32
1.01
0.93
0.97
1.1g
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.84
2.88
1.84
2.88
2.88
2.88
1.96
1.58
1.89
1.36
1.19
1.43
1.2g
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.81
2.08
1.76
1.88
1.3g
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.49
2.40
2.45
118
Table B3 Median maximum drifts (in.) for T-Shape
Model
T1
T2
T3
T4
T5
T6
T7
T8
T9
T10
T11
T12
T13
T14
T15
T16
T17
T18
T19
T20
T21
T22
T23
T24
T25
T26
T27
T28
T29
T30
T31
T32
T33
T34
T35
0.1g
0.05
0.05
0.05
0.05
0.05
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.04
0.04
0.03
0.03
0.03
0.03
0.2g
0.11
0.11
0.11
0.12
0.11
0.09
0.09
0.09
0.09
0.09
0.09
0.08
0.08
0.09
0.09
0.06
0.06
0.06
0.06
0.06
0.06
0.05
0.05
0.06
0.06
0.06
0.06
0.06
0.06
0.08
0.08
0.07
0.07
0.07
0.07
0.3g
0.18
0.18
0.18
0.18
0.18
0.16
0.16
0.16
0.18
0.17
0.16
0.13
0.13
0.14
0.15
0.11
0.11
0.11
0.11
0.11
0.12
0.09
0.09
0.10
0.10
0.10
0.10
0.09
0.10
0.13
0.13
0.13
0.13
0.12
0.12
0.4g
0.28
0.28
0.29
0.29
0.28
0.24
0.25
0.25
0.26
0.24
0.25
0.21
0.22
0.23
0.23
0.16
0.16
0.16
0.16
0.16
0.17
0.14
0.14
0.16
0.15
0.15
0.16
0.14
0.14
0.21
0.21
0.19
0.19
0.19
0.20
Target Spectral Acceleration
0.5g
0.6g
0.7g
0.8g
0.9g
0.47
0.69
1.10
2.39
2.88
0.47
0.69
1.06
2.08
2.88
0.48
0.71
1.10
2.10
2.88
0.49
0.70
1.06
2.32
2.88
0.48
0.67
1.08
2.41
2.88
0.34
0.58
0.83
1.18
2.40
0.35
0.59
0.88
1.20
2.50
0.35
0.61
0.87
1.14
2.58
0.38
0.62
0.91
1.33
2.57
0.37
0.62
0.92
1.25
2.64
0.36
0.61
0.91
1.26
2.62
0.29
0.39
0.65
0.98
1.38
0.30
0.41
0.69
1.00
1.52
0.33
0.45
0.75
1.09
1.44
0.32
0.46
0.74
1.07
1.46
0.23
0.32
0.39
0.68
1.07
0.24
0.32
0.40
0.68
1.06
0.24
0.33
0.41
0.71
1.12
0.24
0.33
0.41
0.69
1.06
0.24
0.33
0.41
0.69
1.08
0.24
0.34
0.41
0.71
1.12
0.20
0.26
0.36
0.45
0.73
0.20
0.27
0.37
0.46
0.78
0.22
0.31
0.43
0.54
0.90
0.21
0.28
0.40
0.50
0.81
0.21
0.29
0.41
0.51
0.84
0.22
0.31
0.43
0.54
0.90
0.21
0.30
0.38
0.51
0.66
0.21
0.30
0.39
0.52
0.65
0.30
0.39
0.67
0.99
1.46
0.30
0.39
0.67
0.98
1.34
0.29
0.38
0.54
0.88
1.25
0.29
0.39
0.54
0.89
1.21
0.26
0.37
0.49
0.70
1.07
0.26
0.37
0.50
0.72
1.06
1.0g
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.64
2.80
2.88
1.52
1.48
1.66
1.57
1.47
1.60
1.12
1.09
1.31
1.18
1.22
1.35
1.01
1.01
2.88
2.82
1.62
1.59
1.42
1.41
1.1g
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
1.55
1.78
1.99
1.60
1.68
1.98
1.53
1.44
2.88
2.88
2.88
2.88
1.88
1.89
1.2g
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.21
2.19
2.88
2.88
2.88
2.88
2.60
2.59
1.3g
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.72
2.58
2.88
2.88
2.88
2.88
2.88
2.88
119
Table B4 Median maximum drifts (in.) for U-Shape
Model
U1
U2
U3
U4
U5
U6
U7
U8
U9
U10
U11
U12
U13
U14
U15
U16
U17
U18
0.1g
0.03
0.04
0.04
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.04
0.04
0.04
0.2g
0.06
0.08
0.09
0.06
0.06
0.08
0.05
0.06
0.08
0.07
0.07
0.07
0.06
0.06
0.06
0.09
0.09
0.08
0.3g
0.11
0.15
0.15
0.10
0.11
0.12
0.09
0.11
0.12
0.12
0.12
0.12
0.12
0.11
0.11
0.15
0.16
0.13
0.4g
0.16
0.20
0.23
0.17
0.16
0.20
0.14
0.16
0.18
0.17
0.17
0.17
0.16
0.16
0.17
0.22
0.22
0.22
Target Spectral Acceleration
0.5g
0.6g
0.7g
0.8g
0.9g
0.24
0.33
0.41
0.70
1.06
0.29
0.43
0.66
0.95
1.48
0.31
0.52
0.77
1.14
2.22
0.21
0.30
0.38
0.53
1.11
0.23
0.36
0.39
0.67
1.08
0.28
0.35
0.61
0.97
1.29
0.21
0.25
0.35
0.44
0.75
0.25
0.32
0.39
0.69
1.08
0.27
0.34
0.51
0.94
1.17
0.27
0.34
0.50
0.78
1.13
0.26
0.38
0.50
0.77
1.22
0.26
0.35
0.46
0.76
1.13
0.25
0.33
0.42
0.72
1.06
0.24
0.33
0.40
0.70
1.02
0.24
0.36
0.41
0.65
0.95
0.31
0.49
0.76
1.12
1.94
0.31
0.45
0.71
1.03
1.76
0.31
0.39
0.69
0.96
1.39
1.0g
1.42
2.88
2.88
1.30
1.44
2.59
1.13
1.43
1.86
1.63
1.56
1.74
1.53
1.54
1.33
2.88
2.81
2.71
1.1g
2.88
2.88
2.88
2.19
2.42
2.88
1.52
2.44
2.88
2.88
2.88
2.88
2.88
2.88
2.39
2.88
2.88
2.88
1.2g
2.88
2.88
2.88
2.88
2.88
2.88
2.62
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
1.3g
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
1.0g
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.58
2.73
2.60
2.79
2.71
2.87
2.88
2.73
2.87
2.83
1.47
1.1g
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
1.2g
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
1.3g
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
Table B5 Median maximum drifts (in.) for Z-Shape
Model
Z1
Z2
Z3
Z4
Z5
Z6
Z7
Z8
Z9
Z10
Z11
Z12
Z13
Z14
Z15
Z16
Z17
Z18
Z19
Z20
Z21
Z22
Z23
Z24
0.1g
0.05
0.05
0.05
0.05
0.04
0.04
0.04
0.04
0.04
0.05
0.05
0.04
0.04
0.03
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.03
0.2g
0.11
0.11
0.12
0.12
0.09
0.09
0.09
0.09
0.09
0.10
0.10
0.09
0.08
0.08
0.09
0.10
0.08
0.08
0.08
0.08
0.08
0.08
0.08
0.07
0.3g
0.18
0.18
0.18
0.18
0.16
0.16
0.17
0.17
0.16
0.18
0.18
0.17
0.13
0.13
0.16
0.16
0.13
0.13
0.13
0.13
0.13
0.13
0.13
0.12
0.4g
0.28
0.28
0.28
0.28
0.24
0.24
0.24
0.24
0.24
0.27
0.28
0.25
0.22
0.20
0.25
0.26
0.21
0.21
0.21
0.21
0.21
0.21
0.21
0.17
Target Spectral Acceleration
0.5g
0.6g
0.7g
0.8g
0.9g
0.47
0.68
1.07
2.36
2.88
0.47
0.68
1.03
2.36
2.88
0.48
0.70
1.07
2.33
2.88
0.49
0.70
1.05
2.34
2.88
0.34
0.57
0.82
1.18
2.45
0.34
0.57
0.83
1.19
2.38
0.34
0.58
0.87
1.20
2.56
0.35
0.58
0.85
1.17
2.88
0.34
0.57
0.82
1.18
2.40
0.41
0.66
0.96
1.38
2.40
0.41
0.68
0.96
1.36
2.45
0.36
0.59
0.86
1.24
2.63
0.31
0.41
0.71
1.01
1.39
0.29
0.38
0.64
0.94
1.29
0.36
0.51
0.82
1.17
1.59
0.38
0.54
0.85
1.16
1.61
0.29
0.40
0.66
0.96
1.35
0.29
0.40
0.65
0.96
1.42
0.30
0.41
0.69
1.02
1.35
0.29
0.40
0.67
1.00
1.44
0.30
0.42
0.68
1.01
1.39
0.29
0.40
0.66
1.01
1.44
0.29
0.40
0.66
1.01
1.38
0.25
0.33
0.45
0.73
1.08
120
Table B5 (Continued) Median maximum drifts (in.) for Z-Shape
Model
Z25
Z26
Z27
Z28
Z29
Z30
Z31
Z32
Z33
Z34
Z35
Z36
Z37
Z38
Z39
Z40
Z41
Z42
Z43
Z44
Z45
Z46
Z47
Z48
Z49
Z50
Z51
Z52
Z53
Z54
Z55
Z56
Z57
Z58
Z59
Z60
Z61
Z62
Z63
Z64
Z65
Z66
Z67
Z68
Z69
Z70
Z71
Z72
Z73
0.1g
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.2g
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.06
0.06
0.06
0.06
0.06
0.07
0.06
0.07
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.05
0.05
0.05
0.05
0.05
0.06
0.06
0.06
0.06
0.05
0.05
0.05
0.05
0.05
0.05
0.06
0.05
0.06
0.06
0.05
0.3g
0.12
0.12
0.12
0.12
0.13
0.12
0.13
0.12
0.12
0.09
0.09
0.10
0.10
0.09
0.11
0.10
0.11
0.10
0.10
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.09
0.09
0.09
0.09
0.09
0.10
0.10
0.10
0.10
0.09
0.08
0.08
0.08
0.08
0.08
0.08
0.08
0.09
0.08
0.08
0.4g
0.17
0.17
0.17
0.17
0.18
0.17
0.19
0.17
0.17
0.15
0.15
0.16
0.16
0.15
0.17
0.16
0.19
0.15
0.16
0.16
0.16
0.16
0.16
0.16
0.16
0.16
0.16
0.16
0.16
0.14
0.14
0.14
0.14
0.14
0.15
0.15
0.15
0.15
0.14
0.11
0.11
0.11
0.11
0.11
0.13
0.12
0.13
0.13
0.12
Target Spectral Acceleration
0.5g
0.6g
0.7g
0.8g
0.9g
0.26
0.34
0.46
0.74
1.08
0.26
0.35
0.47
0.77
1.09
0.26
0.34
0.47
0.74
1.09
0.26
0.33
0.47
0.73
1.06
0.28
0.37
0.53
0.89
1.22
0.26
0.33
0.46
0.78
1.18
0.29
0.38
0.55
0.86
1.24
0.26
0.34
0.47
0.78
1.18
0.26
0.34
0.47
0.79
1.14
0.20
0.29
0.38
0.50
0.82
0.19
0.27
0.36
0.47
0.77
0.21
0.30
0.39
0.51
0.85
0.21
0.29
0.38
0.50
0.83
0.19
0.27
0.36
0.47
0.77
0.23
0.33
0.44
0.62
0.99
0.21
0.30
0.39
0.48
0.83
0.25
0.36
0.47
0.67
1.03
0.21
0.29
0.37
0.48
0.87
0.21
0.30
0.38
0.48
0.86
0.23
0.32
0.39
0.67
1.04
0.23
0.32
0.39
0.67
1.03
0.23
0.32
0.39
0.67
1.02
0.23
0.32
0.39
0.67
1.03
0.23
0.32
0.38
0.66
1.04
0.23
0.32
0.39
0.68
1.06
0.23
0.32
0.39
0.68
1.08
0.23
0.32
0.40
0.68
1.09
0.23
0.32
0.40
0.68
1.05
0.23
0.32
0.39
0.67
1.04
0.19
0.26
0.35
0.43
0.74
0.20
0.26
0.36
0.44
0.76
0.20
0.27
0.37
0.45
0.74
0.20
0.26
0.37
0.45
0.74
0.19
0.25
0.35
0.42
0.70
0.21
0.28
0.39
0.49
0.83
0.21
0.28
0.38
0.48
0.83
0.21
0.29
0.41
0.51
0.84
0.21
0.29
0.40
0.49
0.84
0.20
0.26
0.35
0.43
0.74
0.16
0.22
0.28
0.36
0.46
0.15
0.22
0.27
0.35
0.45
0.16
0.24
0.31
0.41
0.51
0.16
0.24
0.31
0.40
0.51
0.15
0.22
0.27
0.35
0.44
0.18
0.26
0.32
0.43
0.54
0.17
0.24
0.29
0.38
0.50
0.19
0.27
0.36
0.47
0.59
0.18
0.26
0.33
0.43
0.54
0.17
0.24
0.29
0.37
0.49
1.0g
1.65
1.54
1.62
1.52
1.82
1.71
1.67
1.67
1.70
1.14
1.12
1.21
1.21
1.12
1.36
1.26
1.40
1.26
1.29
1.42
1.43
1.44
1.44
1.42
1.49
1.49
1.48
1.57
1.40
1.11
1.09
1.09
1.11
1.00
1.21
1.24
1.24
1.24
1.14
0.67
0.64
0.73
0.70
0.68
0.84
0.72
0.88
0.82
0.67
1.1g
2.88
2.84
2.86
2.88
2.88
2.88
2.88
2.88
2.88
1.66
1.63
1.57
1.70
1.61
1.83
1.76
1.84
1.74
1.93
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
1.45
1.51
1.50
1.46
1.44
1.77
1.92
1.73
1.83
1.57
1.06
1.05
1.09
1.09
1.03
1.26
1.13
1.28
1.24
1.11
1.2g
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.60
2.88
2.61
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.60
2.77
2.40
2.88
2.88
2.88
2.88
2.88
2.42
1.57
1.56
1.81
1.53
1.54
2.01
1.85
2.09
2.01
1.63
1.3g
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.88
2.30
2.33
2.48
2.46
2.73
2.72
2.35
2.44
2.42
2.49
121
Appendix C: Case study matrices for phase 2 study
Tables C1 to C10 summarize the case study matrices for all 480 representative models
analyzed in phase 2 (Chapter 3). The average seismic performance grades for each
model were also presented in these tables.
Table C1 Summary of 1-story rectangular shape models and their average seismic
performance grades
Base Area
(sq.ft.)
Shape
Ratio
Percent Opening (Long|Short)
Garage
Door
1R1
1R2
1R3
1R4
1R5
1R6
1R7
1R8
1R9
1R10
1R11
1R12
1R13
1R14
1R15
1R16
1R17
1R18
1R19
1R20
1R21
1R22
1R23
1R24
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30|0
30|15
30|30
60|0
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
0.167
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
60|30
60|60
1.0
0.5
3000
1500
Model
X
X
X
X
X
X
T arget Spectral
Acceleration (g)
X
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
0.5
3.4
3.2
3.7
3.5
3.8
3.2
4.0
3.6
3.2
3.2
4.0
3.9
3.2
3.2
3.2
3.2
3.2
3.2
3.4
3.2
3.2
3.2
3.4
3.2
1.0
2.9
2.0
3.0
2.9
3.1
2.7
3.2
3.0
2.4
1.8
3.2
3.1
1.8
1.3
2.3
1.8
2.5
1.9
2.9
2.4
1.5
1.1
2.9
2.5
1.5
1.1
0.6
1.2
1.1
1.4
1.2
2.2
1.2
0.8
0.7
2.3
1.5
0.5
0.3
0.9
0.6
1.0
0.6
1.2
0.8
0.3
0.2
1.2
1.1
122
1L1
1L2
1L3
1L4
1L5
1L6
1L7
1L8
1L9
1L10
1L11
1L12
1L13
1L14
1L15
1L16
1L17
1L18
1L19
1L20
1L21
1L22
1L23
1L24
1L25
1L26
1L27
1L28
1L29
1L30
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30|0
30|15
60|0
30|30
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
T arget Spectral
Acceleration (g)
0.167 0.5
X
X
X
X
X
X
X
X
X
X
X
X
X
Garage
Door
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
60|30
10
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Percent Opening
(Long|Short)
60|60
0.5
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30
%
Cutoff
Area
1.0
Overall
Shape
Ratio
3000
Model
Base
Area
(sq.ft.)
1500
Table C2 Summary of 1-story L-shape models and their average seismic performance
grades
X
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
3.6
3.2
3.6
3.6
4
3.5
4
3.9
4
3.3
4
3.6
4
3.7
4
3.9
3.2
3.2
4
4
3.7
3.4
4
4
3.2
3.2
3.2
3.2
3.2
3.2
1.0
3
2.1
3.2
2.9
3.2
2.9
3.2
3.1
3.1
2.4
3.2
2.9
3.2
3
3.2
3.1
2.5
2.2
3.2
3.2
3.1
2.8
3.2
3.2
1.9
1.3
2.6
2.3
2.5
2.2
1.5
1.1
0.8
1.9
1.3
2
1.2
2.4
1.7
1.8
1
2.6
1.4
2.6
1.7
3.1
1.9
1.1
0.7
2.6
2.3
1.2
1.1
3.1
2.8
0.6
0.5
1
0.8
1.2
0.8
123
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Garage
Door
30|0
30|15
30|30
60|0
60|30
Percent Opening
(Long|Short)
60|60
X
X
X
X
X
X
X
X
X
X
30
10
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
1.0
%
Cutoff
Area
0.5
1L31
1L32
1L33
1L34
1L35
1L36
1L37
1L38
1L39
1L40
1L41
1L42
1L43
1L44
1L45
1L46
1L47
1L48
Overall
Shape
Ratio
3000
Model
Base
Area
(sq.ft.)
1500
Table C2 (Continued) Summary of 1-story L-shape models and their average seismic
performance grades
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
0.167 0.5
X
X
X
X
X
X
X
X
X
T arget Spectral
Acceleration (g)
X
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
3.6
3.2
3.3
3.2
3.7
3.4
3.8
3.3
4
3.6
3.2
3.2
3.6
3.5
3.2
3.2
4
3.9
1.0
3
2.6
2.5
1.3
3
2.6
3.1
2.7
3.2
2.8
1.3
1.1
3
2.9
2.1
1.5
3.2
3.1
1.5
1.2
1
0.9
0.4
1.3
0.9
1.4
1
1.9
1.2
0.7
0.4
1.2
1
0.7
0.6
2
1.6
124
1T 1
1T 2
1T 3
1T 4
1T 5
1T 6
1T 7
1T 8
1T 9
1T 10
1T 11
1T 12
1T 13
1T 14
1T 15
1T 16
1T 17
1T 18
1T 19
1T 20
1T 21
1T 22
1T 23
1T 24
1T 25
1T 26
1T 27
1T 28
1T 29
1T 30
1T 31
1T 32
1T 33
1T 34
1T 35
1T 36
1T 37
1T 38
1T 39
1T 40
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Garage
Door
30|0
30|15
30|30
60|0
60|30
60|60
Percent Opening
(Long|Short)
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
T arget Spectral
Acceleration (g)
0.167 0.5
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30
%
Cutoff
Area
10
4500
3000
1500
Model
Overall
Shape
Ratio
1.0
Base Area
(sq.ft.)
0.5
Table C3 Summary of 1-story T-shape models and their average seismic performance
grades
X
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
3.6
3.2
3.9
3.7
4.0
3.5
4.0
3.9
4.0
3.6
4.0
3.9
4.0
3.9
4.0
4.0
3.2
3.2
4.0
4.0
3.7
3.4
4.0
4.0
3.2
3.2
3.2
3.2
3.2
3.2
3.6
3.2
3.4
3.2
3.7
3.5
3.9
3.4
4.0
3.8
1.0
3.0
2.4
3.2
3.1
3.2
2.9
3.2
3.1
3.2
2.8
3.2
3.1
3.2
3.1
3.2
3.2
2.6
2.2
3.2
3.2
3.1
2.8
3.2
3.2
2.1
1.4
2.6
2.4
2.5
2.2
3.0
2.7
2.7
2.0
3.0
2.9
3.1
2.7
3.2
3.0
1.5
1.2
0.8
1.9
1.3
2.0
1.1
2.6
1.7
2.1
1.3
2.9
2.0
3.0
1.8
3.1
2.4
1.1
0.7
2.6
2.3
1.2
1.2
3.1
2.8
0.8
0.4
1.1
0.8
1.2
0.8
1.2
1.0
1.1
0.7
1.3
1.2
1.4
1.0
2.1
1.6
125
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30|0
30|15
30|30
60|0
Garage
Door
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
T arget Spectral
Acceleration (g)
0.167 0.5
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
60|30
X
X
X
X
Percent Opening
(Long|Short)
60|60
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30
4500
%
Cutoff
Area
10
1T 41
1T 42
1T 43
1T 44
1T 45
1T 46
1T 47
1T 48
1T 49
1T 50
1T 51
1T 52
1T 53
1T 54
1T 55
1T 56
1T 57
1T 58
1T 59
1T 60
1T 61
1T 62
1T 63
1T 64
1T 65
1T 66
1T 67
1T 68
1T 69
1T 70
1T 71
1T 72
3000
1500
Model
Overall
Shape
Ratio
1.0
Base Area
(sq.ft.)
0.5
Table C3 (Continued) Summary of 1-story T-shape models and their average seismic
performance grades
X
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
3.2
3.2
3.6
3.5
3.2
3.2
4.0
3.9
3.2
2.9
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.3
3.2
3.7
3.2
3.2
3.0
3.2
3.2
3.2
3.2
3.6
3.4
1.0
1.5
1.1
3.0
2.9
2.1
1.7
3.2
3.1
1.3
1.0
1.8
1.3
2.0
1.3
2.5
1.6
2.0
1.1
2.5
1.8
2.8
1.9
3.0
2.2
1.2
0.9
2.5
2.2
1.3
1.0
3.1
2.7
1.5
0.7
0.3
1.2
1.1
0.7
0.6
2.0
1.6
0.5
0.2
0.7
0.4
0.7
0.4
1.2
0.6
0.8
0.3
1.2
0.7
1.2
0.6
1.3
0.9
0.2
0.2
1.1
0.7
0.4
0.2
1.2
1.1
126
Table C4 Summary of 1-story U-shape models and their average seismic performance
grades
1U1
1U2
1U3
1U4
1U5
1U6
1U7
1U8
1U9
1U10
1U11
1U12
1U13
1U14
1U15
1U16
1U17
1U18
1U19
1U20
1U21
1U22
1U23
1U24
1U25
1U26
1U27
1U28
1U29
1U30
1U31
1U32
1U33
1U34
1U35
1U36
1U37
1U38
1U39
1U40
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Garage
Door
30|0
30|15
30|30
60|0
60|30
60|60
15
Percent Opening
(Long|Short)
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
T arget Spectral
Acceleration (g)
0.167 0.5
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
%
Cutoff
Area
5
1.0
4500
3000
1500
Model
Overall
Shape
Ratio
1.3
Base Area
(sq.ft.)
X
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
3.5
4.0
4.0
4.0
4.0
4.0
4.0
4.0
3.9
4.0
4.0
4.0
4.0
4.0
4.0
3.2
3.2
4.0
3.9
3.2
3.2
4.0
4.0
3.2
3.2
3.2
3.2
3.6
3.3
4.0
3.7
3.5
3.2
3.8
3.7
3.9
3.5
4.0
3.9
1.0
3.2
3.0
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.1
3.2
3.2
3.2
3.2
3.2
3.2
2.4
2.0
3.2
3.2
2.6
2.4
3.2
3.2
2.5
2.2
2.5
2.5
3.0
2.6
3.2
3.0
2.9
2.6
3.1
3.1
3.1
2.9
3.2
3.1
1.5
2.0
1.3
1.9
2.0
2.6
2.2
3.1
2.5
2.3
1.6
3.0
2.8
3.0
2.3
3.2
3.0
1.1
0.7
2.5
1.9
1.1
0.8
2.6
2.4
1.1
0.7
1.2
1.2
1.2
1.2
2.0
1.3
1.1
1.1
1.3
1.2
1.6
1.1
2.3
1.8
127
Table C4 (Continued) Summary of 1-story U-shape models and their average seismic
performance grades
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30|0
30|15
30|30
60|0
Garage
Door
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
T arget Spectral
Acceleration (g)
0.167 0.5
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
60|30
X
X
X
X
Percent Opening
(Long|Short)
60|60
X
X
X
X
X
X
X
X
15
5
4500
X
X
X
X
X
X
X
X
%
Cutoff
Area
1.0
1U41
1U42
1U43
1U44
1U45
1U46
1U47
1U48
1U49
1U50
1U51
1U52
1U53
1U54
1U55
1U56
1U57
1U58
1U59
1U60
1U61
1U62
1U63
1U64
1U65
1U66
1U67
1U68
1U69
1U70
1U71
1U72
3000
1500
Model
Overall
Shape
Ratio
1.3
Base Area
(sq.ft.)
X
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
3.2
3.2
3.5
3.2
3.2
3.2
3.7
3.5
3.2
3.2
3.2
3.2
3.2
3.2
3.5
3.2
3.2
3.2
3.2
3.2
3.4
3.2
3.9
3.3
3.2
3.0
3.2
3.2
3.2
3.1
3.2
3.2
1.0
1.5
1.1
3.0
2.5
1.7
1.4
3.0
2.9
1.8
1.3
1.9
1.9
2.5
1.9
3.0
2.6
2.2
1.5
2.7
2.5
2.9
2.5
3.1
2.8
1.2
1.0
2.4
1.8
1.2
1.1
2.5
2.3
1.5
0.6
0.3
1.2
1.2
0.6
0.6
1.3
1.2
0.6
0.4
0.6
0.6
1.1
0.8
1.1
1.0
0.8
0.7
1.2
1.1
1.2
0.9
1.4
1.2
0.3
0.2
1.1
0.7
0.3
0.2
1.2
0.9
128
1Z1
1Z2
1Z3
1Z4
1Z5
1Z6
1Z7
1Z8
1Z9
1Z10
1Z11
1Z12
1Z13
1Z14
1Z15
1Z16
1Z17
1Z18
1Z19
1Z20
1Z21
1Z22
1Z23
1Z24
1Z25
1Z26
1Z27
1Z28
1Z29
1Z30
1Z31
1Z32
1Z33
1Z34
1Z35
1Z36
1Z37
1Z38
1Z39
1Z40
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30|0
30|15
30|30
60|0
Garage
Door
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
T arget Spectral
Acceleration (g)
0.167 0.5
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
60|30
10
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Percent Opening
(Long|Short)
60|60
0.5
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30
%
Cutoff
Area
1.0
Overall
Shape
Ratio
3000
Model
Base
Area
(sq.ft.)
1500
Table C5 Summary of 1-story Z-shape models and their average seismic performance
grades
X
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
3.7
3.2
3.9
3.6
4.0
3.5
4.0
3.9
4.0
3.3
4.0
3.9
4.0
3.9
4.0
4.0
3.2
3.2
4.0
4.0
3.6
3.4
4.0
4.0
3.2
3.2
3.2
3.2
3.2
3.2
3.6
3.2
3.3
3.2
3.7
3.5
3.8
3.3
4.0
3.6
1.0
3.0
2.5
3.2
3.1
3.2
2.9
3.2
3.1
3.2
2.7
3.2
3.1
3.2
3.1
3.2
3.1
2.6
2.2
3.2
3.2
3.1
2.8
3.2
3.2
2.1
1.4
2.6
2.4
2.5
2.2
3.0
2.7
2.7
1.9
3.0
2.7
3.0
2.7
3.2
3.0
1.5
1.2
1.0
1.9
1.2
2.0
1.1
2.6
1.6
2.0
1.2
3.0
1.6
2.6
2.0
3.1
2.2
1.2
0.9
2.7
2.3
1.2
1.2
3.1
3.0
0.9
0.4
1.0
0.9
1.2
0.8
1.2
1.1
1.0
0.6
1.3
1.1
1.4
1.2
2.0
1.3
129
X
X
30|0
Garage
Door
X
X
X
X
X
X
T arget Spectral
Acceleration (g)
0.167 0.5
X
X
X
X
X
X
X
30|15
30|30
60|0
60|30
10
X
X
X
X
Percent Opening
(Long|Short)
60|60
1.0
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30
%
Cutoff
Area
0.5
1Z41
1Z42
1Z43
1Z44
1Z45
1Z46
1Z47
1Z48
Overall
Shape
Ratio
3000
Model
Base
Area
(sq.ft.)
1500
Table C5 (Continued) Summary of 1-story Z-shape models and their average seismic
performance grades
X
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
3.2
3.2
3.6
3.5
3.2
3.2
4.0
3.9
1.0
1.6
1.1
3.0
2.9
2.2
1.8
3.2
3.1
1.5
0.6
0.3
1.2
1.2
0.7
0.6
2.1
1.7
130
Table C6 Summary of 2-story rectangular shape models and their average seismic
performance grades
Base Area
(sq.ft.)
Shape
Ratio
Percent Opening (Long|Short)
Garage
Door
2R1
2R2
2R3
2R4
2R5
2R6
2R7
2R8
2R9
2R10
2R11
2R12
2R13
2R14
2R15
2R16
2R17
2R18
2R19
2R20
2R21
2R22
2R23
2R24
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30|0
30|15
30|30
60|0
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
0.167
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
60|30
60|60
1.0
0.5
2x2500
2x1250
Model
X
X
X
X
X
X
T arget Spectral
Acceleration (g)
X
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
3.8
4.0
4.0
4.0
4.0
4.0
4.0
4.0
3.8
4.0
4.0
0.5
3.3
2.8
3.3
3.2
3.3
3.1
3.8
3.3
3.2
2.7
3.8
3.4
2.9
2.0
3.2
2.4
3.2
2.5
3.2
2.8
2.7
2.2
3.4
3.1
1.0
1.4
0.8
1.6
1.1
1.6
1.2
2.0
1.3
1.3
1.0
2.0
1.6
1.1
0.5
1.2
0.6
1.4
0.8
1.5
0.9
0.8
0.4
1.6
1.2
1.5
0.3
0.3
0.8
0.3
0.6
0.3
1.0
0.5
0.3
0.2
1.0
0.6
0.2
0.2
0.2
0.3
0.2
0.3
0.4
0.4
0.2
0.1
0.4
0.3
131
2L1
2L2
2L3
2L4
2L5
2L6
2L7
2L8
2L9
2L10
2L11
2L12
2L13
2L14
2L15
2L16
2L17
2L18
2L19
2L20
2L21
2L22
2L23
2L24
2L25
2L26
2L27
2L28
2L29
2L30
2L31
2L32
2L33
2L34
2L35
2L36
2L37
2L38
2L39
2L40
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30|0
30|15
30|30
60|0
Garage
Door
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
T arget Spectral
Acceleration (g)
0.167 0.5
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
60|30
10
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Percent Opening
(Long|Short)
60|60
0.5
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30
%
Cutoff
Area
1.0
Overall
Shape
Ratio
2x2500
Model
Base
Area
(sq.ft.)
2x1250
Table C7 Summary of 2-story L- shape models and their average seismic performance
grades
X
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
3.8
4.0
4.0
4.0
4.0
4.0
4.0
4.0
3.8
4.0
3.8
4.0
4.0
4.0
4.0
3.3
3.0
3.5
3.3
3.7
3.2
3.9
3.4
3.6
3.0
4.0
3.3
3.9
3.3
4.0
3.3
3.2
3.0
4.0
3.8
3.4
3.2
4.0
3.9
3.0
2.0
3.2
2.4
3.1
2.3
3.2
2.7
3.2
1.8
3.3
2.0
3.4
2.7
3.7
2.8
1.0
1.5
0.9
1.7
1.2
1.7
1.3
2.2
1.4
1.4
0.9
2.2
1.3
2.1
1.4
2.6
1.5
1.4
1.4
2.3
1.8
1.4
1.3
2.6
2.2
1.0
0.5
1.3
0.7
1.4
0.9
1.5
0.9
1.1
0.5
1.3
0.8
1.3
0.9
1.4
0.9
1.5
0.5
0.3
0.9
0.4
0.9
0.5
1.1
0.6
0.4
0.3
1.0
0.5
0.9
0.5
1.0
0.5
0.4
0.4
1.0
0.7
0.4
0.2
1.1
1.0
0.3
0.1
0.2
0.3
0.3
0.4
0.4
0.4
0.2
0.3
0.5
0.3
0.5
0.3
0.6
0.4
132
X
X
30|0
Garage
Door
X
X
X
X
X
X
T arget Spectral
Acceleration (g)
0.167 0.5
X
X
X
X
X
X
X
30|15
30|30
60|0
60|30
10
X
X
X
X
Percent Opening
(Long|Short)
60|60
1.0
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30
%
Cutoff
Area
0.5
2L41
2L42
2L43
2L44
2L45
2L46
2L47
2L48
Overall
Shape
Ratio
2x2500
Model
Base
Area
(sq.ft.)
2x1250
Table C7 (Continued) Summary of 2-story L- shape models and their average seismic
performance grades
X
4.0
4.0
4.0
4.0
4.0
3.6
4.0
4.0
2.8
2.4
3.3
3.1
3.1
2.5
3.7
3.3
1.0
0.9
0.5
1.4
1.2
1.2
0.7
1.7
1.3
1.5
0.4
0.2
0.5
0.2
0.4
0.3
0.7
0.5
133
2T 1
2T 2
2T 3
2T 4
2T 5
2T 6
2T 7
2T 8
2T 9
2T 10
2T 11
2T 12
2T 13
2T 14
2T 15
2T 16
2T 17
2T 18
2T 19
2T 20
2T 21
2T 22
2T 23
2T 24
2T 25
2T 26
2T 27
2T 28
2T 29
2T 30
2T 31
2T 32
2T 33
2T 34
2T 35
2T 36
2T 37
2T 38
2T 39
2T 40
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30|0
30|15
30|30
60|0
Garage
Door
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
T arget Spectral
Acceleration (g)
0.167 0.5
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
60|30
10
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Percent Opening
(Long|Short)
60|60
0.5
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30
%
Cutoff
Area
1.0
Overall
Shape
Ratio
2x2500
Model
Base
Area
(sq.ft.)
2x1250
Table C8 Summary of 2-story T- shape models and their average seismic performance
grades
X
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
3.9
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
3.3
3.2
3.5
3.3
3.7
3.2
4.0
3.4
3.8
3.3
4.0
3.7
4.0
3.2
4.0
3.8
3.2
3.0
4.0
3.8
3.4
3.2
4.0
3.9
3.1
2.1
3.2
2.5
3.2
2.4
3.2
2.6
3.2
2.3
3.3
3.0
3.4
2.9
3.8
3.2
1.0
1.5
1.1
1.7
1.3
1.7
1.4
2.2
1.3
1.8
1.2
2.3
1.5
2.3
1.5
2.6
1.7
1.3
1.3
2.3
1.9
1.4
1.3
2.5
2.3
1.3
0.5
1.2
0.7
1.5
0.9
1.5
0.9
1.2
0.7
1.5
0.9
1.5
0.9
1.7
1.1
1.5
0.6
0.3
0.9
0.4
1.1
0.5
1.1
0.5
0.8
0.4
0.9
0.7
1.0
0.6
1.1
0.7
0.4
0.3
1.0
0.9
0.4
0.2
1.0
0.9
0.2
0.2
0.2
0.3
0.3
0.3
0.5
0.4
0.2
0.3
0.6
0.3
0.5
0.4
0.6
0.5
134
X
X
30|0
Garage
Door
X
X
X
X
X
X
T arget Spectral
Acceleration (g)
0.167 0.5
X
X
X
X
X
X
X
30|15
30|30
60|0
60|30
10
X
X
X
X
Percent Opening
(Long|Short)
60|60
1.0
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30
%
Cutoff
Area
0.5
2T 41
2T 42
2T 43
2T 44
2T 45
2T 46
2T 47
2T 48
Overall
Shape
Ratio
2x2500
Model
Base
Area
(sq.ft.)
2x1250
Table C8 (Continued) Summary of 2-story T- shape models and their average seismic
performance grades
X
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
2.8
2.4
3.3
3.1
3.0
2.5
3.7
3.2
1.0
0.9
0.5
1.6
1.2
1.1
0.6
1.7
1.3
1.5
0.4
0.2
0.5
0.3
0.2
0.3
0.6
0.3
135
2U1
2U2
2U3
2U4
2U5
2U6
2U7
2U8
2U9
2U10
2U11
2U12
2U13
2U14
2U15
2U16
2U17
2U18
2U19
2U20
2U21
2U22
2U23
2U24
2U25
2U26
2U27
2U28
2U29
2U30
2U31
2U32
2U33
2U34
2U35
2U36
2U37
2U38
2U39
2U40
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Garage
Door
30|0
30|15
30|30
60|0
60|30
60|60
15
Percent Opening
(Long|Short)
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
T arget Spectral
Acceleration (g)
0.167 0.5
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
%
Cutoff
Area
5
1.3
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
1.0
Overall
Shape
Ratio
2x2500
Model
Base
Area
(sq.ft.)
2x1250
Table C9 Summary of 2-story U- shape models and their average seismic performance
grades
X
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
4.0
3.9
3.7
4.0
4.0
4.0
3.8
4.0
4.0
4.0
3.6
4.0
3.9
4.0
3.8
4.0
4.0
4.0
3.8
4.0
4.0
4.0
4.0
4.0
4.0
3.2
3.1
3.2
3.2
3.2
3.3
3.2
3.2
3.2
3.2
3.2
3.2
3.2
3.3
3.2
3.2
3.1
2.6
3.2
3.2
3.2
3.0
3.2
3.3
3.2
2.5
3.1
3.0
3.2
2.9
3.2
3.1
3.2
2.7
3.2
3.1
3.2
3.1
3.2
3.2
1.0
1.6
1.1
1.5
1.4
1.9
1.4
2.4
1.8
1.7
1.2
2.1
1.5
1.9
1.6
2.6
1.9
1.1
0.8
1.9
1.5
1.3
1.0
1.8
1.7
1.1
0.6
1.1
0.9
1.4
1.1
1.6
1.1
1.2
1.0
1.4
1.1
1.6
1.2
1.6
1.2
1.5
0.5
0.2
0.8
0.5
0.6
0.7
1.1
0.8
0.7
0.3
0.7
0.7
0.9
0.7
1.0
0.7
0.5
0.3
0.8
0.7
0.2
0.3
0.9
0.6
0.2
0.2
0.3
0.3
0.4
0.4
0.6
0.3
0.3
0.3
0.5
0.2
0.6
0.3
0.7
0.3
136
X
X
30|0
Garage
Door
X
X
X
X
X
X
T arget Spectral
Acceleration (g)
0.167 0.5
X
X
X
X
X
X
X
30|15
30|30
60|0
60|30
X
X
X
X
Percent Opening
(Long|Short)
60|60
X
X
X
X
X
X
X
X
15
5
1.3
X
X
X
X
X
X
X
X
%
Cutoff
Area
1.0
2U41
2U42
2U43
2U44
2U45
2U46
2U47
2U48
Overall
Shape
Ratio
2x2500
Model
Base
Area
(sq.ft.)
2x1250
Table C9 (Continued) Summary of 2-story U- shape models and their average seismic
performance grades
X
3.4
3.4
4.0
3.8
3.5
3.5
4.0
4.0
2.5
2.0
3.2
3.0
2.7
2.1
3.2
3.1
1.0
0.7
0.5
1.4
0.9
0.8
0.5
1.4
1.2
1.5
0.1
0.2
0.4
0.2
0.3
0.2
0.6
0.3
137
2Z1
2Z2
2Z3
2Z4
2Z5
2Z6
2Z7
2Z8
2Z9
2Z10
2Z11
2Z12
2Z13
2Z14
2Z15
2Z16
2Z17
2Z18
2Z19
2Z20
2Z21
2Z22
2Z23
2Z24
2Z25
2Z26
2Z27
2Z28
2Z29
2Z30
2Z31
2Z32
2Z33
2Z34
2Z35
2Z36
2Z37
2Z38
2Z39
2Z40
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30|0
30|15
30|30
60|0
Garage
Door
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
T arget Spectral
Acceleration (g)
0.167 0.5
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
60|30
10
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Percent Opening
(Long|Short)
60|60
0.5
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30
%
Cutoff
Area
1.0
Overall
Shape
Ratio
2x2500
Model
Base
Area
(sq.ft.)
2x1250
Table C10 Summary of 2-story Z- shape models and their average seismic
performance grades
X
4.0
3.9
4.0
4.0
4.0
4.0
4.0
4.0
4.0
3.9
4.0
4.0
4.0
4.0
4.0
4.0
4.0
3.8
4.0
4.0
4.0
4.0
4.0
4.0
3.9
3.6
4.0
3.7
4.0
3.7
4.0
3.9
4.0
3.6
4.0
3.6
4.0
3.8
4.0
3.9
3.2
3.0
3.3
3.1
3.2
3.1
3.2
3.2
3.2
3.0
3.2
3.1
3.4
3.2
3.5
3.3
3.2
2.8
3.2
3.3
3.2
3.1
3.2
3.2
3.1
1.9
3.2
2.5
3.2
2.6
3.2
2.7
3.1
2.0
3.2
2.4
3.2
2.7
3.2
2.8
1.0
1.4
1.0
1.5
1.3
1.7
1.4
2.2
1.3
1.5
1.0
1.9
1.2
2.2
1.4
2.4
1.5
1.1
0.8
1.9
1.6
1.4
1.2
2.6
2.2
0.9
0.5
1.0
0.6
1.3
0.7
1.4
0.8
1.0
0.6
1.2
0.7
1.3
0.8
1.6
0.8
1.5
0.5
0.2
0.6
0.2
0.7
0.4
1.0
0.3
0.4
0.4
0.7
0.4
1.0
0.4
1.1
0.7
0.2
0.5
0.8
0.7
0.2
0.3
1.1
0.9
0.2
0.1
0.2
0.2
0.2
0.3
0.3
0.3
0.3
0.2
0.3
0.4
0.3
0.3
0.7
0.4
138
X
X
30|0
Garage
Door
X
X
X
X
X
X
T arget Spectral
Acceleration (g)
0.167 0.5
X
X
X
X
X
X
X
30|15
30|30
60|0
60|30
10
X
X
X
X
Percent Opening
(Long|Short)
60|60
1.0
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
30
%
Cutoff
Area
0.5
2Z41
2Z42
2Z43
2Z44
2Z45
2Z46
2Z47
2Z48
Overall
Shape
Ratio
2x2500
Model
Base
Area
(sq.ft.)
2x1250
Table C10 (Continued) Summary of 2-story Z- shape models and their average
seismic performance grades
X
3.4
3.5
4.0
4.0
3.8
3.6
4.0
4.0
2.7
2.0
3.2
3.1
2.6
2.4
3.3
3.2
1.0
0.8
0.6
1.4
1.1
0.9
0.6
1.5
1.3
1.5
0.3
0.2
0.4
0.2
0.4
0.3
0.6
0.3
139
Appendix D: piRVS grading sheets developed in phase 2
140
Figure D1 Grading sheet for 1-story rectangular shape
141
Figure D2 Grading sheet for 1-story L, T, and Z shapes
142
Figure D3 Grading sheet for 1-story T-shape (for 4,500 sq.ft. base area)
143
Figure D4 Grading sheet for 1-story U-shape
144
Figure D5 Grading sheet for 1-story U-shape (for 4,500 sq.ft. base area)
145
Figure D6 Grading sheet for 2-story rectangular shape
146
Figure D7 Grading sheet for 2-story L, T, Z shapes
147
Figure D8 Grading sheet for 2-story U-shape
148
Appendix E: Configuration summary for phase 3 study
Tables E1 to E9 summarize configuration details for 95 one-story houses and 29 twostory houses used in phase 3 (Chapter 4). In these tables, “1G” and “2G” refer to
single-car garage doors (10 ft-wide) and double-car garage doors (18 ft-wide),
respectively. Wall number for each plan shape is illustrated in Figure E1.
Figure E1 Wall side notations for each plan shape (phase 3)
149
Table E1 Configuration details for 1-story rectangular shape samples
Sample
Code
Wall length (ft)
W1
W2
W3
Percent Openings
W4
W1
W2
W3
W4
C-R1
50
28
50
28
60
30
60
30
C-R2
38
36
38
36
60
25
60
25
C-R3
48
26
48
26 65 (1G)
40
65
40
C-R4
68
38
68
38 55 (2G)
30
55
30
C-R5
54
28
54
28 50 (1G)
40
50
40
C-R6
48
30
48
30 60 (1G)
25
60
25
C-R7
52
26
52
26 65 (1G)
0
65
0
C-R8
58
28
58
28 60 (1G)
0
60
0
C-R9
82
34
82
34 65 (2G)
35
65
35
C-R10
40
36
40
36
60
30
60
30
C-R11
70
30
70
30 50 (1G)
45
50
45
C-R12
32
30
32
30
45
40
45
40
C-R13
62
26
62
26 50 (1G)
0
50
0
C-R14
66
30
66
30 50 (2G)
20
50
20
C-R15
54
38
54
38 50 (2G)
20
50
20
C-R16
62
28
62
28 50 (2G)
0
50
0
C-R17
68
28
68
28 65 (2G)
0
65
0
C-R18
62
28
62
28 70 (2G)
0
70
0
C-R19
58
26
58
26 50 (1G)
0
50
0
C-R20
58
26
58
26 65 (1G)
0
65
0
150
Table E2 Configuration details for 1-story L-shape samples
Sample
Code
Wall length (ft)
W1
W2
W3
W4
Percent Openings
W5
W6
W1
W2
W3
W4
W5
W6
C-L1
38
30
12
4
26
34
65
20
0 (1G)
50
65
35
C-L2
54
28
14
22
40
50
32
0 (2G)
10
60
40
60
C-L3
66
28
20
4
46
32
44
0
50
80 40 (2G)
C-L4
70
30
40
16
30
46
46
C-L5
64
28
32
22
32
50 50 (2G)
C-L6
66
24
24
6
42
30
43
C-L7
50
30
24
14
26
44
60
C-L8
62
24
22
6
40
30
44
0
33 60 (2G)
40
35
30
40
46
40
40
40
0 (1G)
40
40
45
40
60
50
60
30 60 (1G)
0 (1G)
25
70
55
35
C-L9
58
28
30
8
28
36
72
20 75 (2G)
0
70
16
C-L10
56
28
34
18
22
46
55
25
55
22
55
20
C-L11
68
30
40
8
28
38
55
20 45 (1G)
0
65
16
C-L12
66
30
26
28
40
58 50 (2G)
50
16
50
25
C-L13
60
30
30
6
30
36
41
15 30 (2G)
15
45
15
C-L14
64
32
36
8
28
40
50
13 65 (2G)
0
40
15
C-L15
66
32
24
4
42
36
58
25
C-L16
66
26
34
28
32
54
33
33 40 (2G)
C-L17
66
46
42
4
24
50
50
23
50
C-L18
60
32
32
28
28
60
46
C-L19
70
26
38
16
32
42 60 (2G)
C-L20
72
30
46
8
26
C-L21
62
30
42
6
C-L22
30
26
14
4
C-L23
72
34
40
20
C-L24
66
32
18
6
C-L25
52
28
36
22
C-L26
54
26
36
8
C-L27
62
30
36
C-L28
64
34
40
C-L29
66
28
36
C-L30
68
34
22
6
46
40
60
20
C-L31
62
26
38
12
24
38
58
20 50 (2G)
0
65
20
C-L32
54
36
28
12
26
48
45
24
0
0 (2G)
30
C-L33
56
38
26
12
30
50
45
0
45
0
0 (2G)
20
C-L34
56
34
26
18
30
52
35
0 (2G)
20
45
30
45
C-L35
56
40
30
12
26
52 50 (2G)
0
50
0
50
0
C-L36
64
32
40
10
24
42
55
12
55
0
0 (2G)
15
C-L37
54
30
26
8
28
38
62
0 40 (1G)
0
75
0
C-L38
64
28
36
4
28
32
48
0 45 (2G)
11
50
20
C-L39
68
28
42
10
26
38
45
0
45
0
0 (2G)
0
C-L40
48
26
12
12
36
38
30
50
30
50
30
50
0
40
25 75 (2G)
25
30
30
35
0
0 (2G)
25
50
60 10 (1G)
30
36
30
60
30
60
30
38 50 (2G)
40
50
40
50
40
20
36
45
35
45
0
0 (1G)
35
16
30
34
30
50
0
20
26
32
54 55 (2G)
45
42
45
20
45
48
38
60
25
0 (2G)
70
60
25
16
50 55 (1G)
0
55
10
55
15
18
34
50
0
50
0
0 (1G)
0
22
26
52
35
15
15
15
10
24
44
45
0
45
0
0 (2G)
20
8
30
36
50
0 50 (2G)
8
50
15
20 60 (2G)
20
50 20 (2G)
60
45
151
Table E3 Configuration details for 1-story T-shape samples
Wall length (ft)
Sample
Code W1 W2 W3 W4 W5 W6 W7 W8
Percent Openings
W1
42
W2
65
W3
0 (2G)
W6
30
28
18
6
C-T 2
52
30
12
20
30
20
10
30 60 (1G)
20
70
65
60
35
50
40
C-T 3
52
30
16
18
30
18
6
30 65 (1G)
25
65
25
65
25
65
25
C-T 4
54
26
20
16
26
16
8
26 40 (1G)
25
40
25
40
25
40
25
C-T 5
48
28
8
32
30
16
10
44
25
55
0 25 (2G)
21
45
21
45
C-T 6
50
24
14
40
32
40
4
24
30
57
0
65
C-T 7
50
30
14
40
28
40
8
30
45
62
36
62
30 65 (2G)
0
60
C-T 8
30
10
6
25
20
20
4
15
20
17
39
17
0 30 (1G)
80
45
C-T 9
56
26
16
42
32
42
8
26
30
28
34
28
C-T 10
80
30
30
4
30
4
20
30
41
25 40 (2G)
30
45
30
35
40
C-T 11
64
30
28
26
30
26
6
30
50
35
43
35
30
0 (1G)
35
35
C-T 12
76
22
28
40
34
36
14
26
21
50
21
50
30
50
C-T 13
48
26
10
36
30
44
8
18
30
50
50 55 (2G)
25
31
52
31
C-T 14
50
28
12
34
30
42
8
20
15
65
30 30 (2G)
15
17
52
17
C-T 15
56
30
22
18
26
18
8
30 60 (1G)
60
0
60
0
C-T 16
52
16
14
44
26
36
12
56 30 (2G)
0
75
57
0
60
0
12
56
12
43
W8
14
17
25
W7
30
15
50
W5
48
24
60
W4
C-T 1
30
50
30
0 0 (2G)
50
0 0 (2G)
0 0 (2G)
Table E4 Configuration details for 1-story U-shape samples
Wall length (ft)
Sample
Code W1 W2 W3 W4 W5 W6 W7 W8
C-U1
56
38
16
12
C-U2
44
32
10
C-U3
60
34
22
C-U4
66
38
C-U5
60
50
C-U6
56
C-U7
62
30
Percent Openings
W1
W4
W5
W6
W7
W8
33
29
33
29
30
50
40
40
40
40
40
40
40
0
45
0
45
0
45
0
49
29
0 (2G)
0
55
0
40
35
50
0
0 (2G)
50
50
0
50
0
52
50
20
0 (2G)
28
47
15
40
40
40
40
15
0 (2G)
0
40
0
40
40
10
28
54 35 (1G)
6
8
26
26
52
40
8
16
8
22
34 45 (1G)
24
4
26
4
16
38
26
4
8
8
26
54
38
24
8
4
22
28
34
22
10
10
16
30
W2
0
W3
152
Table E5 Configuration details for 1-story Z-shape samples
Wall length (ft)
Sample
Code W1 W2 W3 W4 W5 W6 W7 W8 W1
C-Z1
38
24
20
30
48
C-Z2
32
10
28
34
C-Z3
48
20
24
30
C-Z4
20
12
54
40
C-Z5
36
20
20
30
C-Z6
26
6
42
C-Z7
36
20
C-Z8
44
10
C-Z9
22
8
C-Z10
24
8
42
C-Z11
32
18
24
C-Z12
28
20
38
36
Percent Openings
W2
W3
W4
W5
W6
W7
W8
28
10
26
20
60
25
60
35
60
0
0 (2G)
30
6
30
38
50
20
50
20
50
20 50 (2G)
66
14
6
36
35
60
35
60
35
60
35
24
8
50
44
54
46 55 (1G)
50
40
0
60
50
50
24
6
26
55
60
32
60
20
60
0
0 (2G)
40
28
4
40
42
50
9
50
10
50
0 50 (2G)
9
22
32
52
30
6
22
15
44
26
44
30
45
50 40 (1G)
20
24
46
6
18
28
55
25
0 (2G)
25
55
25
55
25
44
34
42
6
24
36
48
30
48
35 65 (2G)
0
30
30
32
48
14
18
26
65
16
65
16
65
45
0 (2G)
0
38
26
4
30
52
50
25
50
25
0 (2G)
25
50
25
26
8
40
48
50
20
50
20
0 (2G)
20
50
20
20
0 (1G)
153
Table E6 Configuration details for 2-story rectangular shape samples
Sample
Code
Wall length (ft)
Percent Openings
(1st fl.)
W1 W2 W3 W4 W1
W2
W3
Percent Openings
(2nd. fl.)
W4 W1 W2 W3 W4
S-R1
32
28
32
28
60
20
60
20
40
30
40
30
S-R2
34
34
34
34
40
40
40
40
30
30
30
30
S-R3
54
32
54
32
50
(2G)
20
50
20
50
30
50
30
S-R4
52
38
52
38
35
(2G)
0
35
0
35
25
35
25
S-R5
48
34
48
34
40
(2G)
0
40
20
40
25
40
25
S-R6
50
30
50
30
40
(2G)
0
40
0
40
0
40
25
S-R7
48
28
48
28
35
(2G)
35
35
35
40
35
40
35
S-R8
46
28
46
28
35
0
35
0
(1G)
35
20
35
0
S-R9
50
30
50
30
30
(2G)
35
30
35
40
30
40
30
S-R10
50
28
50
28
40
(2G)
25
40
25
40
0
40
20
S-R11
40
30
40
30
20
60
20
60
15
50
30
50
PDXR1
32
28
32
28
50
35
50
35
50
25
50
25
PDXR2
42
18
42
18
20
50
20
50
20
50
20
50
PDXR3
30
22
30
22
30
30
30
30
20
15
20
15
PDXR4
36
24
36
24
20
50
50
50
20
40
10
40
154
Table E7 Configuration details for 2-story L-shape samples
Sample
Code
Wall length (ft)
Percent Openings (1st fl.)
W1 W2 W3 W4 W5 W6 W1 W2
W3
W4
Percent Openings (2nd. fl.)
W5 W6 W1 W2 W3 W4 W5 W6
S-L1
50
36
26
14
24
50
25
0
25
0
0
(2G)
0
38
8
50
0
25
10
S-L2
42
24
20
8
22
32
30
20
0
(2G)
20
40
20
30
25
28
25
25
25
S-L3
34
28
12
4
22
32
60
27
0
(1G)
0
60
30
37
22
50
0
30
25
PDXL1
40
18
4
10
36
28
9
60
0
30
10
49
18
40
0
50
20
44
PDXL2
38
14
4
10
34
24
13
65
0
30
15
50
18
40
0
45
20
42
PDXL3
54
44
38
4
16
48
62
0
60
(2G)
0
65
0
54
14
50
0
65
15
PDXL4
42
16
12
10
30
26
40
50
0
0
(1G)
0
30
35
50
0
50
15
40
PDXL5
36
14
6
16
30
30
30
40
0
70
26
56
10
40
0
40
9
40
PDXL6
42
22
20
10
22
32
45
0
0
(2G)
0
45
0
23
20
20
0
25
14
PDXL7
40
24
8
14
32
38
8
0
(2G)
0
50
10
50
0
50
0
50
0
50
Table E8 Configuration details for 2-story T-shape samples
Sample
Code
Wall length (ft)
Percent Openings (1st fl.)
W1 W2 W3 W4 W5 W6 W7 W8 W1 W2 W3 W4
W5
Percent Openings (2nd. fl.)
W6 W7 W8 W1 W2 W3 W4 W5 W6 W7 W8
S-T 1
46
28
12
12
30
12
4
28
25
40
25
0
(1G)
25
40
25
40
14
20
0
40
20
26
14
26
PDXT1
54
34
10
10
40
20
4
24
30
65
25
65
20
65
0
0
(2G)
20
57
25
57
35
65
0
50
Table E9 Configuration details for 2-story Z-shape samples
Sample
Code
Wall length (ft)
Percent Openings (1st fl.)
W1 W2 W3 W4 W5 W6 W7 W8 W1 W2 W3 W4
W5
Percent Openings (2nd. fl.)
W6 W7 W8 W1 W2 W3 W4 W5 W6 W7 W8
PDXZ1
40
16
12
34
38
12
14
38
41
11
41
11
35
(2G)
0
50
15
45
11
45
11
50
0
30
15
PDXZ2
32
18
12
24
34
4
10
38
20
60
0
0
(2G)
15
60
15
60
0
50
0
40
15
44
7
44
155
Appendix F: Modified piRVS grading sheet for phase 3 study
156
Figure F1 Modified grading sheet for 1-story rectangular shape
157
Figure F2 Modified grading sheet for 1-story L, T, and Z shapes
158
Figure F3 Modified grading sheet for 1-story T-shape (3,751 to 5,000 sq.ft. base area)
159
Figure F4 Modified grading sheet for 1-story U-shape
160
Figure F5 Modified grading sheet for 1-story U-shape (3,751 to 5,000 sq.ft. base area)
161
Figure F6 Modified grading sheet for 2-story rectangular shape
162
Figure F7 Modified grading sheet for 2-story L, T, Z shapes
163
Figure F8 Modified grading sheet for 2-story U-shape
164
Appendix G: Summary of phase 3 analysis results
Tables G1 to G9 summarize phase 3 (Chapter 4) analysis results obtained from
SAPWood, piRVS, FEMA 154, and ASCE 31 Tier 1. For ASCE 31 Tier 1, the results
are shown in terms of maximum shear stress (plf) in shear walls calculated for
immediate occupancy limit, i.e. m= 4.0.
High 2
Low
Moderate
High 1
High 2
60
30
N
N
4.0
4.0
3.0
1.3
4.0
3.4
2.9
1.1
6.4
4.6
4.4
4.4
66 197 395
592
36
60
25
N
N
4.0
4.0
2.7
1.2
4.0
4.0
3.2
2.3
6.4
4.6
4.4
4.4
84 252 503
755
3
C-R3
48
26
65
40
Y
N
4.0
4.0
3.0
1.2
4.0
3.4
2.9
1.1
6.4
4.6
4.4
4.4
76 225 450
675
4
C-R4
68
38
55
30
Y
N
4.0
4.0
2.4
1.1
4.0
3.2
1.8
0.5
6.4
4.6
4.4
4.4
86 258 516
773
5
C-R5
54
28
50
40
Y
N
4.0
4.0
2.7
1.2
4.0
3.4
2.9
1.1
6.4
4.6
4.4
4.4
83 247 494
741
6
C-R6
48
30
60
25
Y
N
4.0
4.0
3.0
1.2
4.0
3.4
2.9
1.1
6.4
4.6
4.4
4.4
77 230 460
690
7
C-R7
52
26
65
0
Y
N
4.0
4.0
3.1
1.2
4.0
3.7
3.0
1.2
6.4
4.6
4.4
4.4
78 231 462
694
8
C-R8
58
28
60
0
Y
N
4.0
4.0
3.0
1.3
4.0
3.7
3.0
1.2
6.4
4.6
4.4
4.4
71 214 429
643
9
C-R9
82
34
65
35
Y
N
4.0
3.9
1.4
0.5
4.0
3.2
1.8
0.5
6.4
4.6
4.4
4.4 110 328 656
984
10
C-R10
40
36
60
30
N
N
4.0
4.0
2.7
1.2
4.0
4.0
3.2
2.3
6.4
4.6
4.4
4.4
747
11
C-R11
70
30
50
45
Y
N
4.0
3.6
1.5
0.8
4.0
3.4
2.9
1.1
6.4
4.6
4.4
4.4 114 343 686 1030
12
C-R12
32
30
45
40
N
N
4.0
4.0
4.0
2.6
4.0
4.0
3.2
2.3
6.4
4.6
4.4
4.4
13
C-R13
62
26
50
0
Y
N
4.0
4.0
3.8
2.2
4.0
3.7
3.0
1.2
6.4
4.6
4.4
4.4
59 176 352
529
14
C-R14
66
30
50
20
Y
N
4.0
4.0
2.9
1.1
4.0
3.8
3.1
1.4
6.4
4.6
4.4
4.4
75 225 451
676
15
C-R15
54
38
50
20
Y
N
4.0
4.0
2.6
1.2
4.0
3.8
3.1
1.4
6.4
4.6
4.4
4.4
83 249 498
747
16
C-R16
62
28
50
0
Y
N
4.0
4.0
3.6
1.9
4.0
3.7
3.0
1.2
6.4
4.6
4.4
4.4
61 184 368
553
17
C-R17
68
28
65
0
Y
N
4.0
4.0
2.5
1.2
4.0
3.7
3.0
1.2
6.4
4.6
4.4
4.4
84 250 501
751
18
C-R18
62
28
70
0
Y
N
4.0
4.0
2.2
0.9
4.0
3.7
3.0
1.2
6.4
4.6
4.4
4.4
99 296 593
889
19
C-R19
58
26
50
0
Y
N
4.0
4.0
4.0
2.2
4.0
3.7
3.0
1.2
6.4
4.6
4.4
4.4
55 166 332
498
20
C-R20
58
26
65
0
Y
N
4.0
4.0
3.1
1.2
4.0
3.7
3.0
1.2
6.4
4.6
4.4
4.4
76 226 452
678
83 249 498
53 158 316
High 2
High 1
28
38
High 1
Moderate
50
C-R2
Short
dir.
Moderate
Low
C-R1
2
Long
dir.
FEMA 154 final score
Low
High 2
1
No.
Sample code
High 1
ASCE 31 T ier1 max.
shear (plf) (m= 4)
Moderate
piRVS performance
score
Low
SAPWood
performance score
Garage door on
shorts direction
Average percent
openings
Garage door
Overall width (ft.)
Overall length (ft.)
Table G1 Summary of analysis results (phase 3) for 1-story rectangular shape
474
165
SAPWood
piRVS performance
performance score
score
FEMA 154 final
score
ASCE 31 T ier1 max.
shear (plf) (m= 4)
44
5
Y
N
4.0 4.0 3.5 1.7 4.0 4.0 3.2 2.4 5.6 4.1 3.9 3.9
63 187
374
560
4
C-L4
70
46
20
46
33
Y
N
4.0 4.0 2.7 1.0 4.0 3.2 1.9 0.6 5.6 4.1 3.9 3.9
76 226
453
679
5
C-L5
64
50
22
46
40
Y
N
4.0 4.0 2.8 1.1 4.0 3.3 2.5 0.9 5.6 4.1 3.9 3.9
76 227
453
680
6
C-L6
66
30
7
43
40
Y
Y
4.0 4.0 2.3 0.9 4.0 3.1 2.1 0.2 5.6 4.1 3.9 3.9
96 289
577
865
7
C-L7
50
44
15
50
60
Y
Y
4.0 3.9 1.9 1.0 4.0 3.2 2.2 0.7 5.6 4.1 3.9 3.9 107 318
636
954
8
C-L8
62
30
7
44
41
Y
Y
4.0 4.0 2.5 0.9 4.0 3.1 2.1 0.2 5.6 4.1 3.9 3.9
547
820
91 273
High 2
4
High 1
32
Moderate
66
Low
C-L3
High 2
3
High 1
849
997
Moderate
567
665
Low
94 283
4.0 3.9 1.6 0.7 4.0 3.1 1.1 0.3 5.6 4.1 3.9 3.9 111 333
High 2
4.0 4.0 2.5 0.9 4.0 4.0 3.2 2.6 5.6 4.1 3.9 3.9
Y
High 1
N
Y
Moderate
Y
60
Low
29
32
High 2
65
11
High 1
4
50
Short
dir.
Moderate
34
54
Long
dir.
Low
38
C-L2
Percent cutoff
area
C-L1
2
Overall length
(ft.)
1
No.
Sample code
Garage door on
shorts direction
Average percent
openings
Garage door
Overall width (ft.)
Table G2 Summary of analysis results (phase 3) for 1-story L-shape
9
C-L9
58
36
11
72
16
Y
N
4.0 3.7 1.5 0.8 4.0 4.0 3.2 2.0 5.6 4.1 3.9 3.9 120 361
722
1083
10
C-L10
56
46
24
55
22
N
N
4.0 4.0 3.1 1.3 4.0 3.8 3.0 1.4 5.6 4.1 3.9 3.9
73 218
436
654
11
C-L11
68
38
12
55
16
Y
N
4.0 4.0 3.0 1.2 4.0 3.2 2.5 1.2 5.6 4.1 3.9 3.9
73 218
435
652
12
C-L12
66
58
19
50
16
Y
N
4.0 4.0 2.2 1.0 4.0 3.6 3.0 1.2 5.6 4.1 3.9 3.9
99 295
590
885
13
C-L13
60
36
8
41
15
Y
N
4.0 4.0 3.5 1.8 4.0 4.0 3.2 2.0 5.6 4.1 3.9 3.9
61 184
367
551
14
C-L14
64
40
11
50
13
Y
N
4.0 4.0 3.0 1.2 4.0 3.2 2.5 1.2 5.6 4.1 3.9 3.9
76 226
453
680
15
C-L15
66
36
4
58
25
Y
N
4.0 4.0 2.6 1.1 4.0 3.2 1.9 0.6 5.6 4.1 3.9 3.9
85 254
508
762
16
C-L16
66
54
27
33
33
Y
N
4.0 4.0 3.0 1.3 4.0 3.3 2.5 0.9 5.6 4.1 3.9 3.9
67 200
400
600
17
C-L17
66
50
5
50
23
Y
N
4.0 4.0 2.5 1.0 4.0 3.2 1.9 0.6 5.6 4.1 3.9 3.9
93 278
556
835
18
C-L18
60
60
25
46
36
Y
Y
4.0 4.0 2.9 1.1 4.0 3.9 2.6 1.6 5.6 4.1 3.9 3.9
76 227
453
679
19
C-L19
70
42
21
60
30
Y
N
4.0 4.0 2.6 1.2 4.0 3.3 2.5 0.9 5.6 4.1 3.9 3.9
86 257
513
770
20
C-L20
72
38
13
50
40
Y
N
4.0 4.0 2.3 1.0 4.0 3.2 1.9 0.6 5.6 4.1 3.9 3.9
93 279
557
835
166
Garage door on
shorts direction
Y
N
4.0 4.0 2.9 1.2 4.0 3.6 3.0 1.1 5.6 4.1 3.9 3.9
30
6
34
26
N
N
4.0 4.0 4.0 3.4 4.0 4.0 3.2 2.6 5.6 4.1 3.9 3.9
44 131
262
393
54
21
42
45
Y
N
4.0 4.0 2.2 1.0 4.0 3.3 2.5 0.9 5.6 4.1 3.9 3.9
93 277
554
831
38
4
60
29
Y
N
4.0 4.0 2.3 0.8 4.0 3.2 1.9 0.6 5.6 4.1 3.9 3.9
90 269
537
806
50
30
55
10
Y
N
4.0 4.0 2.6 1.3 4.0 4.0 3.2 2.0 5.6 4.1 3.9 3.9
82 246
492
738
54
34
16
50
0
Y
N
4.0 4.0 4.0 2.4 4.0 3.6 3.2 1.9 5.6 4.1 3.9 3.9
57 170
340
509
C-L27
62
52
25
35
15
Y
Y
4.0 4.0 3.4 1.7 4.0 3.3 1.8 0.7 5.6 4.1 3.9 3.9
63 188
375
562
C-L28
64
44
14
45
10
Y
N
4.0 4.0 3.0 1.3 4.0 3.2 2.5 1.2 5.6 4.1 3.9 3.9
71 212
425
637
29
C-L29
66
36
12
50
8
Y
N
4.0 4.0 3.2 1.4 4.0 3.2 2.5 1.2 5.6 4.1 3.9 3.9
68 204
407
611
30
C-L30
68
40
5
60
20
Y
N
4.0 4.0 2.2 1.0 4.0 3.2 2.5 1.2 5.6 4.1 3.9 3.9
98 292
585
877
31
C-L31
62
38
19
58
17
Y
N
4.0 4.0 2.7 1.2 4.0 3.2 2.5 1.2 5.6 4.1 3.9 3.9
79 236
473
709
32
C-L32
54
48
13
45
24
Y
N
4.0 4.0 2.7 1.2 4.0 3.6 3.0 1.2 5.6 4.1 3.9 3.9
79 235
469
704
33
C-L33
56
50
11
45
10
Y
N
4.0 4.0 2.6 1.3 4.0 3.6 3.0 1.2 5.6 4.1 3.9 3.9
81 242
484
726
34
C-L34
56
52
16
30
45
Y
Y
4.0 4.0 2.6 1.2 4.0 3.5 2.8 0.9 5.6 4.1 3.9 3.9
82 246
493
739
35
C-L35
56
52
12
50
0
Y
N
4.0 4.0 2.1 1.0 4.0 3.6 3.0 1.2 5.6 4.1 3.9 3.9 101 302
604
905
36
C-L36
64
42
15
55
12
Y
N
4.0 4.0 2.7 1.3 4.0 3.2 2.5 1.2 5.6 4.1 3.9 3.9
80 238
476
714
37
C-L37
54
38
10
62
0
Y
N
4.0 4.0 2.5 1.1 4.0 3.6 3.2 1.9 5.6 4.1 3.9 3.9
93 278
555
832
38
C-L38
64
32
7
48
11
Y
N
4.0 4.0 3.4 1.7 4.0 4.0 3.2 2.0 5.6 4.1 3.9 3.9
62 185
370
555
39
C-L39
68
38
16
45
0
Y
N
4.0 4.0 3.8 2.0 4.0 3.6 3.0 1.2 5.6 4.1 3.9 3.9
60 179
357
536
40
C-L40
48
38
8
30
50
N
N
4.0 4.0 2.6 1.2 4.0 3.6 3.0 1.1 5.6 4.1 3.9 3.9
83 249
497
745
21
C-L21
62
36
22
C-L22
30
23
C-L23
72
24
C-L24
66
25
C-L25
52
26
C-L26
27
28
75 225
450
High 2
High 1
Moderate
ASCE 31 T ier1 max.
shear (plf) (m= 4)
Low
High 2
High 1
Moderate
FEMA 154 final
score
Low
High 2
High 1
Moderate
Low
High 2
Short
dir.
High 1
Long
dir.
SAPWood
piRVS performance
performance score
score
Moderate
Average percent
openings
Low
Percent cutoff
area
32
Overall width
(ft.)
45
Overall length
(ft.)
11
No.
Sample code
Garage door
Table G2 (Continued) Summary of analysis results (phase 3) for 1-story L-shape
675
167
Percent cutoff area
SAPWood
piRVS performance
performance score
score
FEMA 154 final
score
ASCE 31 T ier1 max.
shear (plf) (m= 4)
17
60
38
Y
N
4.0 4.0 2.0 1.0 4.0 3.6 3.0 1.2 5.6 4.1 3.9 3.9 104 310
620
929
48
16
65
25
Y
N
4.0 3.7 1.6 0.9 4.0 3.6 3.0 1.2 5.6 4.1 3.9 3.9 116 347
692
1039
4
C-T 4
54
42
20
40
25
Y
N
4.0 4.0 3.8 2.4 4.0 3.2 1.9 0.6 5.6 4.1 3.9 3.9
58 175
350
525
5
C-T 5
60
48
14
45
21
Y
N
4.0 4.0 2.7 1.1 4.0 3.2 2.5 1.2 5.6 4.1 3.9 3.9
81 241
483
724
6
C-T 6
64
50
23
57
17
Y
N
4.0 4.0 2.5 1.0 4.0 3.8 3.0 1.4 5.6 4.1 3.9 3.9
95 285
570
854
7
C-T 7
70
50
25
62
36
Y
N
4.0 4.0 2.1 0.9 4.0 3.3 2.5 0.9 5.6 4.1 3.9 3.9 100 301
603
904
8
C-T 8
35
30
22
39
17
Y
N
4.0 4.0 4.0 3.9 4.0 4.0 3.2 3.1 5.6 4.1 3.9 3.9
39 117
235
352
9
C-T 9
68
56
26
34
28
Y
N
4.0 4.0 3.0 1.4 4.0 3.3 2.5 0.9 5.6 4.1 3.9 3.9
66 199
397
595
10
C-T 10
80
34
7
41
32
Y
N
4.0 4.0 2.2 0.9 4.0 3.2 1.9 0.6 5.6 4.1 3.9 3.9 100 299
597
896
11
C-T 11
64
56
25
43
35
Y
Y
4.0 4.0 3.0 1.3 4.0 3.9 2.6 1.6 5.6 4.1 3.9 3.9
69 206
413
619
12
C-T 12
76
62
34
21
50
Y
Y
4.0 4.0 2.2 1.0 4.0 2.8 1.3 0.2 5.6 4.1 3.9 3.9 100 300
599
898
13
C-T 13
62
48
24
52
31
Y
N
4.0 4.0 3.2 1.3 4.0 3.3 2.5 0.9 5.6 4.1 3.9 3.9
65 196
392
588
14
C-T 14
62
50
24
52
17
Y
N
4.0 4.0 3.4 1.9 4.0 3.8 3.0 1.4 5.6 4.1 3.9 3.9
61 184
368
552
15
C-T 15
56
48
20
60
0
Y
N
4.0 4.0 2.2 0.9 4.0 3.6 3.0 1.2 5.6 4.1 3.9 3.9
99 296
592
888
16
C-T 16
60
52
34
56
12
Y
N
4.0 4.0 3.1 1.7 4.0 4.0 3.2 2.0 5.6 4.1 3.9 3.9
55 166
332
498
High 2
50
52
High 1
52
C-T 3
Moderate
C-T 2
3
Low
2
High 2
531
High 1
89 266
Moderate
4.0 4.0 2.3 1.0 4.0 3.2 1.9 0.6 5.6 4.1 3.9 3.9
Low
N
High 2
Y
High 1
50
Moderate
43
Low
18
High 2
48
High 1
60
Short
dir.
Moderate
C-T 1
Long
dir.
Low
1
No.
Sample code
Garage door on
shorts direction
Average percent
openings
Garage door
Overall width (ft.)
Overall length (ft.)
Table G3 Summary of analysis results (phase 3) for 1-story T-shape
797
168
Percent cutoff area
SAPWood
piRVS performance
performance score
score
FEMA 154 final
score
ASCE 31 T ier1 max.
shear (plf) (m= 4)
60
34
6
45
0
Y
N
4.0 4.0 3.7 2.2 4.0 4.0 3.2 3.1 5.6 4.1 3.9 3.9
61 183
366
548
4
C-U4
66
38
4
49
29
Y
N
4.0 4.0 3.0 1.2 4.0 3.2 2.5 1.1 5.6 4.1 3.9 3.9
73 219
437
656
5
C-U5
60
54
5
50
2
Y
N
4.0 4.0 2.1 0.9 4.0 3.2 2.5 1.2 5.6 4.1 3.9 3.9 102 307
614
921
6
C-U6
56
52
15
47
28
Y
N
4.0 4.0 2.5 1.2 4.0 3.5 2.9 1.1 5.6 4.1 3.9 3.9
87 260
520
779
7
C-U7
62
40
12
40
21
Y
N
4.0 4.0 3.5 1.9 4.0 3.9 3.1 1.6 5.6 4.1 3.9 3.9
63 190
380
569
High 2
C-U3
High 1
3
Moderate
604
Low
618
403
High 2
412
67 201
High 1
69 206
4.0 4.0 3.0 1.5 4.0 3.5 2.9 1.1 5.6 4.1 3.9 3.9
Moderate
4.0 4.0 3.0 1.3 4.0 3.5 2.9 1.1 5.6 4.1 3.9 3.9
N
Low
N
N
High 2
Y
40
High 1
29
40
Moderate
33
18
Low
18
44
High 2
54
52
High 1
56
C-U2
Short
dir.
Moderate
C-U1
2
Long
dir.
Low
1
No.
Sample code
Garage door on
shorts direction
Average percent
openings
Garage door
Overall width (ft.)
Overall length (ft.)
Table G4 Summary of analysis results (phase 3) for 1-story U-shape
169
Percent cutoff area
SAPWood
piRVS performance
performance score
score
FEMA 154 final
score
ASCE 31 T ier1 max.
shear (plf) (m= 4)
72
50
16
35
60
Y
Y
4.0 3.9 1.8 1.0 4.0 2.8 1.3 0.2 5.6 4.1 3.9 3.9 106 317
635
953
4
C-Z4
74
52
27
54
46
Y
N
4.0 4.0 2.5 0.9 4.0 3.3 2.5 0.9 5.6 4.1 3.9 3.9
88 264
528
792
5
C-Z5
56
50
19
32
60
Y
Y
4.0 3.9 1.7 0.9 4.0 3.1 1.1 0.3 5.6 4.1 3.9 3.9 109 326
652
977
6
C-Z6
68
46
13
50
9
Y
N
4.0 4.0 2.6 1.2 4.0 3.2 2.5 1.2 5.6 4.1 3.9 3.9
84 251
503
754
7
C-Z7
58
52
21
26
44
Y
Y
4.0 4.0 2.6 1.1 4.0 3.9 2.6 1.6 5.6 4.1 3.9 3.9
84 252
504
756
8
C-Z8
64
34
14
55
25
Y
N
4.0 4.0 3.0 1.3 4.0 3.6 3.0 1.1 5.6 4.1 3.9 3.9
68 203
405
608
High 2
C-Z3
High 1
3
Moderate
708
Low
472
High 2
958
79 236
High 1
639
4.0 4.0 2.7 1.3 4.0 3.2 2.5 1.2 5.6 4.1 3.9 3.9
Moderate
4.0 3.9 1.9 1.0 4.0 3.1 1.5 0.3 5.6 4.1 3.9 3.9 107 319
N
Low
Y
Y
High 2
Y
20
High 1
60
50
Moderate
25
17
Low
24
44
High 2
54
60
High 1
58
C-Z2
Short
dir.
Moderate
C-Z1
2
Long
dir.
Low
1
No.
Sample code
Garage door on
shorts direction
Average percent
openings
Garage door
Overall width (ft.)
Overall length (ft.)
Table G5 Summary of analysis results (phase 3) for 1-story Z-shape
9
C-Z9
66
42
18
48
30
Y
N
4.0 4.0 3.0 1.3 4.0 3.2 1.9 0.6 5.6 4.1 3.9 3.9
71 211
422
633
10
C-Z10
66
40
22
65
16
Y
N
4.0 4.0 2.2 0.9 4.0 3.8 3.0 1.4 5.6 4.1 3.9 3.9
90 267
535
802
11
C-Z11
56
56
18
50
25
Y
N
4.0 4.0 2.5 1.0 4.0 3.6 3.0 1.2 5.6 4.1 3.9 3.9
92 277
553
830
12
C-Z12
66
56
29
50
20
Y
N
4.0 4.0 2.7 1.1 4.0 3.8 3.0 1.4 5.6 4.1 3.9 3.9
79 237
474
711
170
Garage door on shorts
direction
Low
Moderate
High 1
High 2
Low
Moderate
High 1
High 2
Low
Moderate
High 1
High 2
32
28
60
20
N
N
4.0
3.3
1.6
0.5
4.0
3.8
2.0
1.0
6.4
4.6
4.4
4.4 113 340 680 1020
S-R2
34
34
40
40
N
N
4.0
3.7
1.8
1.0
4.0
3.8
2.0
1.0
6.4
4.6
4.4
4.4
3
S-R3
54
32
50
20
Y
N
4.0
3.2
1.3
0.4
4.0
3.3
1.6
0.6
6.4
4.6
4.4
4.4 116 348 696 1043
4
S-R4
52
38
35
0
Y
N
4.0
3.4
1.3
0.4
4.0
3.2
1.5
0.4
6.4
4.6
4.4
4.4 110 328 655
983
5
S-R5
48
34
40
10
Y
N
4.0
3.4
1.3
0.4
4.0
3.3
1.6
0.6
6.4
4.6
4.4
4.4 108 324 648
972
6
S-R6
50
30
40
0
Y
N
4.0
3.4
1.6
0.8
4.0
3.8
2.0
1.0
6.4
4.6
4.4
4.4
868
7
S-R7
48
28
35
35
Y
N
4.0
3.2
1.3
0.4
4.0
3.3
1.4
0.3
6.4
4.6
4.4
4.4 115 346 690 1036
8
S-R8
46
28
35
0
Y
Y
4.0
3.4
1.5
0.6
4.0
3.3
1.3
0.5
6.4
4.6
4.4
4.4
FEMA 154 final score
ASCE 31 T ier1 max.
shear (plf) (m= 4)
90 270 540
97 289 579
91 272 545
High 2
Short
dir.
piRVS performance
score
High 1
Long
dir.
SAPWood
performance score
Moderate
Average percent
openings
Low
Overall width (ft.)
S-R1
2
Overall length (ft.)
1
No.
Sample code
Garage door
Table G6 Summary of analysis results (phase 3) for 2-story rectangular shape
811
817
9
S-R9
50
30
30
35
Y
N
4.0
3.2
1.4
0.3
4.0
3.3
1.4
0.3
6.4
4.6
4.4
4.4 119 358 715 1072
10
S-R10
50
28
40
25
Y
N
4.0
3.4
1.5
0.6
4.0
3.3
1.4
0.3
6.4
4.6
4.4
4.4 105 316 630
11
S-R11
40
30
20
60
N
N
4.0
2.9
1.1
0.5
4.0
3.3
1.4
0.3
6.4
4.6
4.4
4.4 159 476 952 1428
12 PDX-R1
32
28
50
35
N
N
4.0
3.7
1.8
1.0
4.0
3.8
2.0
1.0
6.4
4.6
4.4
4.4
13 PDX-R2
42
18
20
50
N
N
4.0
3.2
1.3
0.6
4.0
3.3
1.4
0.3
6.4
4.6
4.4
4.4 147 439 879 1318
14 PDX-R3
30
22
30
30
N
N
4.0
4.0
2.4
1.1
4.0
3.3
1.4
0.3
6.4
4.6
4.4
4.4
15 PDX-R4
36
24
35
50
N
N
4.0
3.2
1.5
0.5
4.0
3.3
1.4
0.3
6.4
4.6
4.4
4.4 120 358 717 1074
90 270 539
76 228 455
946
809
683
171
25
0
4.0 3.4 1.3 0.4 4.0 3.2 1.4 0.4 5.6 4.1 3.9 3.9 108 323
645
High 2
High 1
Moderate
ASCE 31 T ier1 max.
shear (plf) (m= 4)
Low
High 2
High 1
Moderate
FEMA 154 final
score
Low
High 2
High 1
Moderate
Low
High 2
N
High 1
Y
Moderate
Short
dir.
SAPWood
piRVS performance
performance score
score
Low
Long
dir.
Garage door on
shorts direction
Average percent
openings
Garage door
Percent cutoff area
Overall width (ft.)
Overall length (ft.)
No.
Sample code
Table G7 Summary of analysis results (phase 3) for 2-story L-shape
1
S-L1
50
50
15
968
2
S-L2
42
32
12
33
20
Y
N
4.0 3.8 1.9 0.9 4.0 3.2 1.7 0.7 5.6 4.1 3.9 3.9
87 260
520
780
3
S-L3
34
32
4
60
27
Y
N
4.0 3.3 1.4 0.4 4.0 3.2 1.9 0.8 5.6 4.1 3.9 3.9 136 409
819
1228
4
PDX-L1
40
28
4
9
49
N
N
4.0 3.3 1.5 0.5 4.0 3.2 1.4 0.5 5.6 4.1 3.9 3.9 126 377
753
1130
5
PDX-L2
38
24
4
13
50
N
N
4.0 3.2 1.4 0.6 4.0 3.2 1.4 0.5 5.6 4.1 3.9 3.9 125 372
745
1117
6
PDX-L3
54
48
6
62
0
Y
N
3.9 2.4 0.8 0.2 4.0 3.2 1.4 0.4 5.6 4.1 3.9 3.9 215 643 1287
1929
7
PDX-L4
42
26
11
20
38
Y
Y
4.0 3.2 1.4 0.4 3.9 3.0 0.5 0.0 5.6 4.1 3.9 3.9 115 347
692
1039
8
PDX-L5
36
30
9
26
56
N
N
4.0 3.2 1.5 0.6 4.0 3.2 1.4 0.5 5.6 4.1 3.9 3.9 124 370
741
1111
9
PDX-L6
42
32
15
45
0
Y
N
4.0 3.4 1.7 0.8 4.0 3.2 2.2 1.0 5.6 4.1 3.9 3.9 103 309
618
926
10
PDX-L7
40
38
7
8
50
Y
Y
4.0 3.3 1.4 0.4 3.8 2.8 0.8 0.1 5.6 4.1 3.9 3.9 141 423
848
1271
172
High 1
High 2
Moderate
10
25
40
Y
Y
4.0 3.2 1.4 0.3 3.8 2.8 1.6 0.7 5.6 4.1 3.9 3.9 123 368
735
1103
44
8
25
65
Y
Y
3.8 2.3 0.6 0.2 3.6 1.9 0.3 0.1 5.6 4.1 3.9 3.9 232 693 1387
2080
Low
High 2
High 1
Moderate
40
54
Low
High 2
46
Low
S-T 1
PDX-T 1
Low
High 1
Moderate
ASCE 31 T ier1 max.
shear (plf) (m= 4)
2
Short
dir.
High 2
FEMA 154 final
score
1
Long
dir.
High 1
SAPWood
piRVS performance
performance score
score
Moderate
Garage door on
shorts direction
Average percent
openings
Garage door
Percent cutoff area
Overall width (ft.)
Overall length (ft.)
No.
Sample code
Table G8 Summary of analysis results (phase 3) for 2-story T-shape
Percent cutoff area
ASCE 31 T ier1 max.
shear (plf) (m= 4)
44
42
14
15
60
Y
Y
4.0 2.8 1.1 0.5 3.8 2.8 0.8 0.1 5.6 4.1 3.9 3.9 169 503 1007
1510
Moderate
PDX-Z2
Low
2
High 2
1226
High 1
817
Moderate
4.0 3.3 1.3 0.3 4.0 3.2 1.4 0.4 5.6 4.1 3.9 3.9 137 409
Low
N
High 2
Y
High 1
11
Moderate
41
Low
14
High 2
50
High 1
52
Short
dir.
Moderate
PDX-Z1
Long
dir.
Low
1
No.
Sample code
High 2
FEMA 154 final
score
High 1
SAPWood
piRVS performance
performance score
score
Garage door on
shorts direction
Average percent
openings
Garage door
Overall width (ft.)
Overall length (ft.)
Table G9 Summary of analysis results (phase 3) for 2-story Z-shape
173