AN ABSTRACT OF THE DISSERTATION OF
Jun Hee Kim for the degree of Doctor of Philosophy in Civil Engineering
presented on December 22, 2003.
Title: Performance-Based Seismic Design of Light-Frame Shearwalls
Abstract approved:
Redacted for privacy
David V. Rosowsky
Performance-based design has gained interest in recent years among
structural designers and researchers. Performance-based design includes selection
of appropriate building sites, structural systems and configurations, as well as
analytical procedures used in the design process, to confirm that the structure has
adequate strength, stiffness and energy dissipation capacity to respond to the
design loads without exceeding permissible damage states. Although performancebased seismic design has advanced for some materials and structural types, such as
steel and reinforced concrete buildings and bridges, its application to light-frame
structures remains largely unexplored.
The objective of this research was to explore the potential for the
application of performance-based engineering concepts to the design and
assessment of woodframe structures subject to earthquakes. Nonlinear dynamic
time-history analysis was used to predict the performance of shearwalls
considering a suite of scaled characteristic ordinary ground motions to represent
the seismic hazard. Sensitivity studies were performed to investigate the relative
effects of damping, sheathing properties, fastener type and spacing, panel layout,
and other properties on the performance of wood shearwalls. In addition, the
effects of uncertainty in ground motions and variability in sheathing-to-framing
connection hysteretic parameters were investigated. Issues such as the contribution
of nonstructural finish materials, different seismic hazard regions, and construction
quality also were investigated and modification factors to adjust peak displacement
distributions were developed. The peak displacement distributions were then used
to construct performance curves and design charts as a function of seismic weights
for two baseline walls. Finally, fragility curves were developed for the baseline
walls considering different nailing schedules, corresponding allowable seismic
weights, and various overstrength (R) factors.
©Copyright by Jun Hee Kim
December 22, 2003
All Rights Reserved
Performance-Based Seismic Design of Light-Frame Shearwalls
by
Jun Hee Kim
A DISSERTATION
submitted to
Oregon State University
In partial fulfillment of
the requirements for the
degree of
Doctor of Philosophy
Presented December 22, 2003
Commencement June 2004
Doctor of Philosophy dissertation of Jun Hee Kim
presented on December 22, 2003.
APPROVED:
Redacted for privacy
Major Professor, Civil Engineering
Redacted for privacy
Head of Department of Civil, Construction and Environmental Engineering
Redacted for privacy
Dean of thet-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.
Redacted for privacy
Jun Hee Kim, Authr
ACKNOWLEDGEMENTS
The research presented here was made possible largely through grants from
the CUREE-Caltech Woodframe Project and the National Science Foundation
through Grant No. CMS-0049038. This financial support from these organizations
is acknowledged.
I would like to express my sincere appreciation to Dr. David Rosowsky for
his advice, guidance, passion, patience, encouragement, and financial support
throughout my graduate work at Oregon State University. I also would like to
thank my graduate committee members: Dr. Solomon Yim, Dr. Robert Leichti, Dr.
Thomas Miller, and Dr. Bartelt Eleveld for their advice and help in completing my
graduate program. Special thanks are due to Dr. Brian Folz for his valuable
assistance with the computer programs CASHEW and SAWS.
Many thanks to the Structural Reliability Research Group members and the
staff in Civil Engineering for their assistance during the course of this research.
I would like to thank my sister, Mun Hee Kim, and brother-in-law, Dr.
Daniel Kim, for their love and support. Also, I would like to thank my father,
Dong Chan Kim, who passed away two months ago, and my mother, Jung Sook
Mm, for their love, encouragement, support, and prayer. And finally, I wish to
thank my wife, Mi Soon, and two lovely children, Gyu Yeun and Gyu Tae, for
their love, patience, prayer and support.
TABLE OF CONTENTS
1. INTRODUCTION ...................................................................................................... 1
1.1 General .................................................................................................................
1
1.2 Scope and objectives ............................................................................................ 4
2. BACKGROUND AND LITERATURE REVIEW .................................................... 6
3. NONLINEAR DYNAMIC TIME-HISTORY ANALYSIS .................................... 10
3.1 Computer programs ............................................................................................ 10
3.1.1 CASHEW .................................................................................................... 10
3.1.2SASH1 ........................................................................................................ 11
3.1.3SASHFIT .................................................................................................... 12
3.1.4 SAWS .......................................................................................................... 14
3.2 Ordinary ground motion records ........................................................................ 16
3.3 Distribution functions (exceedence probability curves) .................................... 17
4. ANALYSIS OF ISOLATED SHEARWALLS ....................................................... 22
4.1 Model configuration (isolated shearwall) .......................................................... 22
4.2 Sensitivity studies .............................................................................................. 26
4.2.1 Baseline sensitivity studies ......................................................................... 26
4.2.1.1 Ground motions .................................................................................... 27
4.2.1.2 Damping ............................................................................................... 28
4.2.1.3 Shear modulus of sheathing materials.................................................. 31
4.2.1.4 Fastener spacing ................................................................................... 32
4.2.1.5 Panel layout .......................................................................................... 35
4.2.1.6 Shake-table test walls ........................................................................... 35
4.2.1.7 Missing fasteners .................................................................................. 38
4.2.1.8 Model uncertainty ................................................................................. 40
4.2.2 Sheathing-to-framing connection hysteretic parameter variability ............. 47
4.2.3 Contribution of nonstructural finish materials ............................................ 55
4.2.3.1 Analysis of solidwall ........................................................................... 57
4.2.3.2 Analysis of walls with openings .......................................................... 62
4.2.4 Construction quality .................................................................................... 65
4.2.5 Effects of different seismic hazard regions ................................................. 73
TABLE OF CONTENTS (Continued)
4.3 Additional studies
.
84
4.3.1 Development of modification factors ......................................................... 84
4.3.1.1 Sheathing-to-framing connection hysteretic parameter variability ...... 84
4.3.1.2 Construction quality ............................................................................. 89
4.3.1.3 Contribution of nonstructural finish materials ..................................... 99
4.3.2 Construction of performance curves and design charts ............................ 107
4.3.2.1 Baseline walls .................................................................................... 107
4.3.2.1.1 Construction of performance curves ........................................... 108
4.3.2.1.2 Design charts ............................................................................... 111
4.3.2.2 Construction quality ........................................................................... 121
4.3.2.2.1 Construction of performance curves ........................................... 121
4.3.2.2.2 Design charts ............................................................................... 122
4.3.2.3 Effects of different seismic hazard regions ........................................ 130
4.4 Performance-based design ............................................................................... 136
4.4.1 Incremental dynamic analysis ...................................................................
4.4.2 Fragility curves .........................................................................................
4.4.2.1 Fragility curve based on peak displacement ......................................
4.4.2.2 Fragility curve based on ultimate force ..............................................
136
143
143
154
5. ANALYSIS OF SHEARWALLS IN COMPLETE STRUCTURES .................... 161
5.1 Model configuration......................................................................................... 161
5.1.1 Model configuration of one-story residential structure ............................. 162
5.1.2 Model configuration of two-story residential structure ............................ 165
5.2 Shearwall performance in complete structures ................................................ 167
5.2.1 One-story structure .................................................................................... 167
5.2.1.1 Performance of shearwalls with OSB only ........................................ 167
5.2.1.2 Performance of shearwalls with NSF materials ................................. 170
5.2.2 Two-story structure ................................................................................... 177
5.2.2.1 Performance of shearwalls with OSB only ........................................ 177
5.2.2.2 Performance of shearwalls with NSF materials ................................. 182
5.2.3 Additional studies ..................................................................................... 187
5.2.3.1 Interstory displacement ...................................................................... 187
5.2.3.2 Effect of partition walls ...................................................................... 192
TABLE OF CONTENTS (Continued)
gç
5.2.3.3 Performance comparison for isolated wall and wall in one-story
structure........................................................................................... 197
5.3 Performance-based design ............................................................................... 200
5.3.1 Incremental dynamic analysis ................................................................... 200
5.3.2 Fragility curves ......................................................................................... 203
5.3.2.1 Fragility curve for one-story structure ............................................... 203
5.3.2.2 Fragility curve for two-story structure ............................................... 206
6. CONCLUSIONS AND RECOMMENDATIONS ................................................ 214
6.1 Conclusions ...................................................................................................... 215
6.2 Recommendations ............................................................................................ 218
REFERENCES ........................................................................................................... 221
APPENDICES........................................................................................................... 230
LIST OF FIGURES
Figure
3.1 CASHEW modeling procedure ..............................................................................
11
3.2 Force-displacement response of a wood shearwall under cyclic loading.
Hysteretic model is fit to test data for an 8 ft x 8 ft shearwall with 3/8-in. thick
OSB sheathing panels (from: Durham, 1998) ...................................................... 13
3.3 Load-displacement curve using parameters determined by SASHFIT .................. 14
3.4 Code based target response spectra ........................................................................
1S
3.5 Development of probability-based design charts for shearwall selection .............. 21
3.6 Fitting a lognormal distribution to the sample CDF of peak displacements .......... 21
4.1 Components of typical woodframe shearwall ........................................................ 23
4.2 Detailed configurations of baseline solid wall (BW1) and walls with
openings(OWl and 0W2) .................................................................................. 25
4.3 Baseline wall sheathing configuration ................................................................... 27
4.4 Response (peak displacement) variability for the three limit states ....................... 29
4.5 Effects of viscous damping ratio () on peak displacement .................................. 31
4.6 Effect of assigned shear modulus (G) on peak displacement ................................ 33
4.7 Effect of fastener spacing on peak displacement (W
560 lbs/ft) ........................ 33
4.8 Effect of fastener spacing on peak displacement (W
840 lbs/ft) ........................ 34
4.9 Effect of fastener spacing on peak displacement (W = 1120 lbs/ft) ...................... 34
4.10 Effect of fastener spacing on peak displacement (W = 1400 lbs/ft) .................... 35
4.11 Effect of panel layout on peak displacement ....................................................... 36
4.12 Task 1.1.1 and task 1.1.2 walls ............................................................................ 37
LIST OF FIGURES (Continued)
Figure
4.13 Peak displacement distributions for task 1.1.1 and task 1.1.2 walls .................... 37
4.14 Effect of missing fasteners on peak displacement (10, 5 0/50) ............................ 39
4.15 Effect of missing fasteners on peak displacement (LS, 10/50) ............................ 39
4.16 Effect of missing fasteners on peak displacement (CP, 2/50) .............................. 40
4.17 Effect of model uncertainty on peak displacement distribution ........................... 43
4.18 Effect of model uncertainty on peak displacement (3"/6") .................................. 44
4.19 Effect of model uncertainty on peak displacement (3"/12") ................................ 44
4.20 Effect of model uncertainty on peak displacement (4"/12") ................................ 45
4.21 Effect of model uncertainty on peak displacement (6"/6") .................................. 45
4.22 Effect of model uncertainty on peak displacement (6"/12") ................................ 46
4.23 Comparison of peak displacement distributions for different nail parameters
(W=5601bs/ft) .................................................................................................... 50
4.24 Comparison of peak displacement distributions for different nail parameters
(W=8401bs/ft) .................................................................................................... 51
4.25 Comparison of peak displacement distributions for different nail parameters
(W=ll2Olbs/ft) .................................................................................................. 51
4.26 Comparison of peak displacement distributions for different nail parameters
(W= 1400 lbs/ft) .................................................................................................. 52
4.27 Effect of fastener parameter variability on peak displacement ............................ 54
4.28 Typical exterior wall cross-section ...................................................................... 56
4.29 Effect of nonstructural finish materials on peak displacement
(W 560 lbs/ft) ..................................................................................................... 59
LIST OF FIGURES (Continued)
Figure
4.30 Effect of nonstructural finish materials on peak displacement
(W= 840 lbs/fl) ..................................................................................................... 59
4.31 Effect of nonstructural finish materials on peak displacement
(W= 1120 lbs/ft) ................................................................................................... 60
4.32 Effect of nonstructural finish materials on peak displacement
(W 1400 lbs/ft) ................................................................................................... 60
4.33 Effect of nonstructural finish materials on peak displacement
(W= 840 lbs/ft) ..................................................................................................... 61
4.34 Effect of nonstructural finish materials on peak displacement
(W= 1400 lbs/fl) ................................................................................................... 61
4.35 Effect of nonstructural finish materials on peak displacement
(W=281 lbs/fl) ..................................................................................................... 63
4.36 Effect of nonstructural finish materials on peak displacement
(W= 703 lbs/ft) ..................................................................................................... 63
4.37 Effect of nonstructural finish materials on peak displacement
(W= 703 lbs/ft) ..................................................................................................... 64
4.38 Effect of nonstructural finish materials on peak displacement
(W 984 lbs/fl) ..................................................................................................... 64
4.39 Peak displacement distributions for construction qualities
(BW1, OSB only) ................................................................................................. 68
4.40 Peak displacement distributions for construction qualities
(BW1, OSB ± GWB) ........................................................................................... 69
4.41 Peak displacement distributions for construction qualities
(BW1, OSB + Stucco) .......................................................................................... 69
4.42 Peak displacement distributions for BW1 considering different
constructionqualities ........................................................................................... 70
LIST OF FIGURES (Continued)
Figure
4.43 Peak displacement distributions for OWl (OSB only) considering
different construction qualities ............................................................................. 70
4.44 Peak displacement distributions for OWl (OSB + GWB) considering
different construction qualities ............................................................................. 71
4.45 Peak displacement distributions for OWl (OSB + Stucco) considering
different construction qualities ............................................................................. 71
4.46 Peak displacement distributions for OWl (OSB + GWB + Stucco)
considering different construction qualities ......................................................... 72
4.47 Target response spectra for different seismic hazard regions .............................. 75
4.48 Comparison of earthquake record scaling to target response spectra .................. 76
4.49 Comparison of peak displacement between CCWP and SAC
earthquake records ............................................................................................... 80
4.50 Comparison of peak displacement between fault-normal and fault-parallel
earthquake records ............................................................................................... 81
4.51 Comparison of peak displacement for different seismic hazard regions
(@4"/12", W 1400 lbs/ft) ................................................................................. 82
4.52 Comparison of peak displacement for different seismic hazard regions
(@6"/12", W 1400 lbs/ft) ................................................................................. 82
4.53 Selection of median and target peak displacement distributions ......................... 86
4.54 Change of peak displacement considering various mean values of
modificationfactor ............................................................................................... 86
4.55 Change of peak displacement considering various COV values of
modification factor ............................................................................................... 87
4.56 Modification factors for sheathing-to-framing connection hysteretic
parameter variability ............................................................................................ 88
LIST OF FIGURES (Continued)
Figure
Page
4.57 Graphical method for determination of modification factors in
construction quality (BW1) ................................................................................... 91
4.58 Graphical method for determination of modification factors in
construction quality (OWl) .................................................................................. 91
4.59 Mean of modification factor for BW1 (OSB only) .............................................. 92
4.60 COV of modification factor for BW1 (OSB only) ............................................... 92
4.61 Mean of modification factor for BW1 (OSB + GWB) ........................................ 93
4.62 COV of modification factor for BW1 (OSB +GWB) .......................................... 93
4.63 Mean of modification factor for BW1 (OSB + Stucco) ....................................... 94
4.64 COy of modification factor for BW1 (OSB + Stucco) ....................................... 94
4.65 Mean of modification factor for OWl (OSB only) .............................................. 95
4.66 COV of modification factor for OWl (OSB only) .............................................. 95
4.67 Mean of modification factor for OWl (OSB + GWB) ........................................ 96
4.68 COy of modification factor for OWl (OSB + GWB) ......................................... 96
4.69 Mean of modification factor for OWl (OSB + Stucco) ....................................... 97
4.70 COV of modification factor for OWl (OSB + Stucco) ....................................... 97
4.71 Mean of modification factor for OWl (OSB + GWB + Stucco) ......................... 98
4.72 COV of modification factor for OWl (OSB + GWB + Stucco) .......................... 98
4.73 Graphical method to develop deterministic modification factors in
nonstructural finish materials effects (BW1) ..................................................... 103
4.74 Graphical method to develop deterministic modification factors in
nonstructural finish materials effects (0W2) ..................................................... 104
LIST OF FIGURES (Continued)
Figure
4.75 Mean of deterministic modification factor for BW1 (OSB sheathing) .............. 104
4.76 Mean of deterministic modification factor for BW1 (Plywood sheathing) ....... 105
4.77 Mean of deterministic modification factor for BW1 (Plywood sheathing) ....... 105
4.78 Mean of deterministic modification factor for OWl (OSB sheathing) .............. 106
4.79 Mean of deterministic modification factor for 0W2 (OSB sheathing) .............. 106
4.80 Performance curve for BW1, OSB (3/8-in.), @3"/6" ......................................... 112
4.81 Performance curve for BW1, OSB (3/8-in.), @4"/12" ....................................... 112
4.82 Performance curve for BW1, OSB (3/8-in.), @6"/6" ......................................... 113
4.83 Performance curve for BW1, OSB (3/s-in.), @6"/12" ....................................... 113
4.84 Performance curve for BW1, OSB (3/s-in.), @3"/6", axes switched ................. 114
4.85 Performance curve for BW1, PWD (3/8-in.), 8d@3"/6" .................................... 114
4.86 Performance curve for BW1, PWD (3/8-in.), 8d@4"/12" .................................. 115
4.87 Performance curve for OWl, OSB (3/8-in.), @3"/3" ......................................... 115
4.88 Performance curve for OWl, OSB (3/s-in.), @4"/4" ......................................... 116
4.89 Performance curve for OWl, OSB (3/8-in.), @6"/6" ......................................... 116
4.90 Performance curve for OWl, PWD (31'8-in.), 8d@4"/4" .................................... 117
4.91 Performance curve for OWL PWD (3/8-in.), 8d@6"/6" .................................... 117
4.92 Effect of model uncertainty on performance curve for BW1,
OSB(3/8-in.), @3"/6"......................................................................................... 118
4.93 95thPercentile design chart for BW1, JO (50/50) .............................................. 118
LIST OF FIGURES (Continued)
Figure
494 95thPercenti1e design chart for BW1, LS (10/50) ............................................. 119
495 95thPercentj1e design chart for OWl, JO (50/50) .............................................. 119
4.96 95thPercentile design chart for OWl, LS (50/50) ............................................. 120
4.97 Performance curve for BW1, OSB only ............................................................ 123
4.98 Performance curve for BW1, OSB + GWB ....................................................... 123
4.99 Performance curve for BW1, OSB + Stucco ..................................................... 124
4.100 Performance curve for OWl, OSB only .......................................................... 124
4.101 Performance curve for OWl, OSB + GWB ..................................................... 125
4.102 Performance curve for OWl, OSB + Stucco ................................................... 125
4.103 Performance curve for OWl, OSB + GWB + Stucco ...................................... 126
4.104 95thPercentile design chart for BW1, poor quality ......................................... 126
4.105 95thPercentile design chart for BW 1, typical quality ...................................... 127
4.106 95thPercentile design chart for OWl, poor quality ......................................... 127
4.107 95thPercentile design chart for OWl, typical quality...................................... 128
4.108 95t1'-Percentile design chart for BW1, (OSB + Stucco) ................................... 128
4.109 95tIiPercentile design chart for OWl, (OSB + GWB + Stucco) ..................... 129
4.110 Performance curve for BW1, seismic zone III (Seattle), @3"/12" .................. 131
4.111 Performance curve for BW1, seismic zone IV (LA), @3"/12" ....................... 131
4.112 Performance curve for BW1, seismic zone II (Boston), @4"/12" ................... 132
4.113 Performance curve for BW1, seismic zone III (Seattle), @4"/12" .................. 132
LIST OF FIGURES (Continued)
Figure
iEiig
4.114 Performance curve for BW1, seismic zone IV (LA), @4"/12" ....................... 133
4.115 Performance curve for BW1, seismic zone II (Boston), @6"/12" ................... 133
4.116 Performance curve for BW1, seismic zone III (Seattle), @6"112" .................. 134
4.117 Performance curve for BW1, seismic zone IV (LA), @6"/12" ....................... 134
4.118 95tlPercentile design chart for BW1, LS (10/50) ........................................... 135
4.119 Typical IDA curve ........................................................................................... 139
4.120 Estimated collapse points by tangent slope ...................................................... 139
4.121 Set of IDA curves (BW1, group 1) .................................................................. 140
4.122 Set of IDA curves (BW1, group 2) .................................................................. 140
4.123 Set of IDA curves (BW1, group 3) .................................................................. 141
4.124 Set of IDA curves (Owl, group 1) .................................................................. 141
4.125 Set of IDA curves (Owl, group 2) .................................................................. 142
4.126. Set of IDA curves (Owl, group 3) ................................................................. 142
4.127 Peak displacement distributions for different R factors (3"/12", 10) .............. 146
4.128 Peak displacement distributions for different R factors (3"/12", LS) .............. 146
4.129 Peak displacement distributions for different R factors (3"/12", CP) .............. 147
4.130 Fragility curves for three different hazard levels (2"/ 12") ............................... 148
4.13 1 Fragility curves for three different hazard levels (3"/12") ............................... 149
4.132 Fragility curves for three different hazard levels (4"! 12") ............................... 149
4.133 Fragility curves for three different hazard levels (6"/12") ............................... 150
LIST OF FIGURES (Continued)
Figure
4.134 Fragility curves considering R = 2.5 (LS, 10/50 hazard level) ........................ 151
4.135 Fragility curves considering R = 3.5 (LS, 10/50 hazard level) ........................ 152
4.136 Fragility curves considering R = 4.5 (LS, 10/50 hazard level) ........................ 152
4.137 Fragility curves considering R
5.5 (LS, 10/50 hazard level) ........................ 153
4.138 Single fragility curve considering R = 4.5 (LS, 10/50 hazard level) ............... 153
4.139 Fragility curves considering different assumed R factors (LS, 3"/12") ........... 154
4.140 CDF for ultimate force with various R factors (3"/12", JO) ............................ 156
4.141 CDF for ultimate force with various R factors (3"/12", LS) ............................ 156
4.142 CDF for ultimate force with various R factors (3"/12", CP) ........................... 157
4.143 Fragility curve for ultimate uplift force with various R factors
(3"/12", HTT 22) ................................................................................................ 158
4.144 Fragility curve for ultimate uplift force with various R factors
(3"/12", PHD2-SDS3) ........................................................................................ 158
4.145 Fragility curve for ultimate uplift force with various R factors
(4"/12", LTT 20B) ............................................................................................. 159
4.146 Hold-down fragility curve considering ultimate uplift capacity ...................... 160
5.1 Plan view and section view for the one-story house model ................................. 163
5.2 Detailed wall configurations for the one-story house model ............................... 164
5.3 Elevation and plan view for two-story house model
(from: Fischer et al., 2001) ................................................................................. 166
5.4 SAWS model of the one-story structure, OSB only ............................................ 168
LIST OF FIGURES (Continued)
Figure
5.5 Peak displacement distributions for shearwalls in one-story structure,
OSB only (JO, 50/50 hazard level) .................................................................... 169
5.6 Peak displacement distributions for shearwalls in one-story structure,
OSB only (LS, 10/50 hazard level) .................................................................... 169
5.7 Peak displacement distributions for shearwalls in one-story structure,
OSB only (CP, 2/50 hazard level) ...................................................................... 170
5.8 SAWS model of the one-story structure, OSB and NSF materials
(GWB and Stucco) ............................................................................................. 173
5.9 SAWS model of the one-story structure, OSB and GWB ................................... 173
5.10 Peak displacement distributions for shearwalls in one-story structure,
OSB + GWB (10, 50/50 hazard level) ............................................................... 174
5.11 Peak displacement distributions for shearwalls in one-story structure,
OSB + GWB (LS, 10/5 0 hazard level) .............................................................. 175
5.12 Peak displacement distributions for shearwalls in one-story structure,
OSB + GWB (CP, 2/50 hazard level) ................................................................ 175
5.13 Peak displacement distributions for shearwalls in one-story structure,
OSB + GWB + Stucco (10, 50/150 hazard level) ................................................ 176
5.14 Peak displacement distributions for shearwalls in one-story structure,
OSB + GWB + Stucco (LS, 10/50 hazard level) ............................................... 176
5.15 Peak displacement distributions for shearwalls in one-story structure,
OSB + GWB + Stucco (CP, 2/50 hazard level) ................................................. 177
5.16 SAWS model of the two-story structure, OSB only
(from: Folz and Filiatrault, 2002) ....................................................................... 180
5.17 Peak displacement (relative to ground) distributions for shearwalls
in two-story structure (JO, 50/50 hazard level) .................................................. 181
LIST OF FIGURES (Continued)
Figure
iag
5.18 Peak displacement (relative to ground) distributions for shearwalls
in two-story structure (LS, 10/50 hazard level) ................................................. 181
5.19 Peak displacement (relative to ground) distributions for shearwalls
in two-story structure (CP, 2/50 hazard level) ................................................... 182
5.20 SAWS model of the two-story Structure, OSB and NSF materials
(from: Folz and Filiatrault, 2002) ....................................................................... 185
5.21 Peak displacement (relative to ground) distributions for shearwalls
in two-story structure (10, 50/50 hazard level) .................................................. 186
5.22 Peak displacement (relative to ground) distributions for shearwalls
in two-story structure (LS, 10/50 hazard level) ................................................. 186
5.23 Peak displacement (relative to ground) distributions for shearwalls
in two-story structure (CP, 2/50 hazard level) ................................................... 187
5.24 Comparison of peak displacements at first and second stories,
OSB (JO, 50/50 hazard level) ............................................................................ 189
5.25 Comparison of peak displacements at first and second stories,
OSB (LS, 10/50 hazard level) ............................................................................ 189
5.26 Comparison of peak displacements at first and second stories,
OSB (CP, 2/50 hazard level) .............................................................................. 190
5.27 Comparison of peak displacements at first and second stories,
OSB + GWB ± Stucco (10, 50/50 hazard level) ................................................ 190
5.28 Comparison of peak displacements at first and second stories,
OSB + GWB + Stucco (LS, 10/50 hazard level) ............................................... 191
5.29. Comparison of peak displacements at first and second stories,
OSB + GWB + Stucco (CP, 2/50 hazard level) ................................................. 191
5.30 SAWS model of one-story structure without partition walls,
(OSB+GWB) .................................................................................................... 194
LIST OF FIGURES (Continued)
Figure
5.31 Peak displacement distributions for one-story structure,
OSB + GWB (without partition walls), 10 (50/50 hazard level) ....................... 194
5.32 Peak displacement distributions for one-story structure,
OSB + GWB (without partition walls), LS (10/50 hazard level) ....................... 195
5.33 Peak displacement distributions for one-story structure,
OSB + GWB (without partition walls), CP (2/50 hazard level) ........................ 195
5.34 Comparison of peak displacement distributions for the effect of
partition walls and NSF materials, (JO, 50/50 hazard level) .............................. 196
5.35 Comparison of peak displacement distributions for the effect of
partition walls and NSF materials, (LS, 5 0/50 hazard level) ............................. 196
5.36 Comparison of peak displacement distributions for the effect of
partition walls and NSF materials, (CP, 2/50 hazard level) ............................... 197
5.37 Comparison of peak displacement distributions for isolated shearwall and
shearwall in complete one-story structure (JO, 50/50 hazard level) .................. 199
5.38 Comparison of peak displacement distributions for isolated shearwall and
shearwall in complete one-story structure (LS, 10/50 hazard level) .................. 199
5.39 Set of IDA curves for selected OSB-only walls with garage door opening
(2EW) ................................................................................................................. 202
5.40 Set of IDA curves for selected OSB + NSF walls with pedestrian door
opening(2WW) .................................................................................................. 202
5.41 Fragility curves for the North wall (OSB only) in the one-story structure
(without partition walls) ..................................................................................... 204
5.42 Fragility curves for the North wall (OSB + GWB) in the
one-story structure (without partition walls) ...................................................... 205
5.43 Comparison of fragility curves for the North wall in the
one-story structure (JO, 50/50, 1% drift limit) ................................................... 205
LIST OF FIGURES (Continued)
Figure
5.44 Fragility curve for wall with garage door opening, max
(relative to ground) at first story ........................................................................ 207
5.45 Fragility curve for wall with garage door opening, interstory drift ................... 208
5.46 Fragility curve for wall with garage door opening, ömax
(relative to ground) at second story .................................................................... 208
5.47 Fragility curve for wall with pedestrian door opening, max
(relative to ground) at first story ........................................................................ 209
5.48 Fragility curve for wall with pedestrian door opening, 6max
(relative to ground) at second story .................................................................... 209
5.49 Comparison of fragility curves for shearwafl in two-story structure
(JO, 50/50, 1% drift limit) .................................................................................. 210
5.50 Comparison of fragility curves for shearwall in two-story structure
(LS, 10/50, 2% drift limit) ................................................................................. 210
5.51 Fragility curves for shearwall with NSF materials (2EW) in
two-story structure ............................................................................................. 212
5.52 Fragility curves for shearwall with NSF materials (2WW) in
two-story structure ............................................................................................. 212
5.53 Comparison of fragility curves showing contribution of NSF materials,
max (relative to ground) at first story ................................................................. 213
5.54 Comparison of fragility curves showing contribution of NSF materials,
ömax (relative to ground) at second story ............................................................ 213
LIST OF TABLES
Table
3.1 20 Ordinary ground motion records and PGA values ............................................ 19
3.2 Structural performance levels and requirements for woodframe walls
(from: Table C 1-3, FEMA 356) ........................................................................... 19
4.1 Sheathing-to-framing connection hysteretic parameters ........................................ 48
4.2 Comparable connection hysteretic parameters from other studies ........................ 49
4.3 Nail properties considered in this study ................................................................. 54
4.4 Matrix of walls used to investigate nonstructural finish material effects .............. 57
4.5 Definitions of three construction quality categories
(from: Isoda et al., 2002) ...................................................................................... 66
4.6 Developed deterministic modification factor for construction quality .................. 67
4.7 Target response spectra for different seismic hazard regions ................................ 75
4.8 20 Ordinary ground motion records and PGA values (seismic zone IV, LA) ....... 76
4.9 20 Ordinary ground motion records and PGA values
(seismic zone III, Seattle) ..................................................................................... 78
4.10 20 Ordinary ground motion records and PGA values
(seismic zone II, Boston) ...................................................................................... 79
4.11 Analysis matrix for effects of different seismic hazard regions .......................... 79
4.12 Summary of modification factors considering construction quality .................... 90
4.13 Developed deterministic modification factor (ty) for contribution of
nonstructural finish materials effects ................................................................. 103
4.14 Fastener parameters used to develop performance curves and
design charts for baseline walls ......................................................................... 108
LIST OF TABLES (Continued)
Table
4.15 Seismic weights calculated based on UBC '97 allowable unit shear values
(Table 23-TI-I-i) ................................................................................................. 145
4.16 Capacities of hold-downs considered in this study ............................................ 155
5.1 Hysteretic parameters for the shearwall spring elements in
one-story structure, OSB only ............................................................................ 167
5.2 Hysteretic parameters for the shearwall spring elements in
one-story structure, OSB and NSF materials ..................................................... 172
5.3 Hysteretic parameters for the shearwall spring elements,
OSB sheathing only (from: Folz and Filiatrault, 2002) ..................................... 179
5.4 Fitted hysteretic parameters for the SDOF shear element model of an
8 ft>< 8 ft shearwall with stucco and gypsum wallboard
(from: Folz and Filiatrault, 2002) ....................................................................... 183
5.5 Hysteretic parameters for the shearwall spring elements,
OSB and NSF materials (from: Folz and Filiatrault, 2002) ............................... 184
5.6 Estimated collapse limit (from IDA) for shearwall in the complete
two-story structure ............................................................................................. 201
LIST OF APPENDICES
Appendix
A. Example showing convolution of hazard curve and fragility curve ...................... 231
B. Deterministic modification factors for construction quality ................................. 233
C. Scaling earthquake records to response spectra considering different scaling
methods.............................................................................................................. 236
D. Earthquake records used in this study ................................................................... 239
E. Peak displacement distributions considering different R factors .......................... 244
F. Fragility curves for baseline wall (BW1) considering different hazard levels ...... 250
G. Fragility curves for baseline wall (BW1) considering different R factors
and nailing schedules ......................................................................................... 257
H. CDF for baseline wall (BW1) considering ultimate force with
variousR factors ................................................................................................ 262
LIST OF APPENDIX FIGURES
Figure
A.1 Convolution of hazard curve and fragility curve ................................................ 232
C. 1 20 0GM records (CUREE) scaled over the plateau region of the response
spectrum(LS, 10/50) .......................................................................................... 237
C.2 20 0GM records (CUREE) scaled at a period of 0.2 sec to the response
spectrum(LS, 10/50) .......................................................................................... 237
C.3 20 0GM records (CUREE) scaled at a period of 0.5 sec to the response
spectrum(LS, 10/50) .......................................................................................... 238
E. 1 Peak displacement distributions considering different R factors
(2"/12", JO) ........................................................................................................ 245
E.2 Peak displacement distributions considering different R factors
(2"/12", LS) ........................................................................................................ 245
E.3 Peak displacement distributions considering different R factors
(2"/12", CP) ....................................................................................................... 246
E.4 Peak displacement distributions considering different R factors
(4"/12", 10) ........................................................................................................ 246
E.5 Peak displacement distributions considering different R factors
(4"/12", LS) ........................................................................................................ 247
E.6 Peak displacement distributions considering different R factors
(4"/12", CP) ....................................................................................................... 247
E.7 Peak displacement distributions considering different R factors
(6"/12", 10) ........................................................................................................ 248
E.8 Peak displacement distributions considering different R factors
(6"/12", LS) ........................................................................................................ 248
E.9 Peak displacement distributions considering different R factors
(6"/12", CP) ....................................................................................................... 249
F.1 Fragility curves (R= 2.5, 2"/12") ........................................................................ 251
LIST OF APPENDIX FIGURES (Continued)
Figure
F.2 Fragility curves (R=2.5, 3"/12") ........................................................................ 251
F.3 Fragility curves (R = 2.5, 4"/12") ........................................................................ 252
F.4 Fragility curves (R = 2.5, 6"/12") ........................................................................ 252
F.5 Fragility curves (R
3.5, 2"/12") ........................................................................ 253
F.6 Fragility curves (R
3.5, 3"/12") ........................................................................ 253
F.7 Fragility curves (R = 3.5, 4"/12") ........................................................................ 254
F.8 Fragility curves (R = 3.5, 6"/12") ........................................................................ 254
F.9 Fragility curves (R = 4.5, 2"/12") ........................................................................ 255
F.10 Fragility curves (R
4.5, 3"/12") ...................................................................... 255
F. 11 Fragility curves (R = 4.5, 4"/12") ...................................................................... 256
F. 12 Fragility curves (R = 4.5, 6"/12") ...................................................................... 256
G.1 Fragility curves considering R = 2.5 (10, 50/50 hazard level) ............................ 258
G.2 Fragility curves considering R = 3.5 (10, 50/50 hazard level) ............................ 258
G.3 Fragility curves considering R = 4.5 (JO, 50/50 hazard level) ............................ 259
G.4 Fragility curves considering R = 5.5 (10, 50/50 hazard level) ............................ 259
G.5 Fragility curves considering R = 3.5 (CP, 2/50 hazard level) ............................. 260
G.6 Fragility curves considering R = 4.5 (CP, 2/50 hazard level) ............................. 260
G.7 Fragility curves considering R = 5.5 (CP, 2/50 hazard level) ............................. 261
H. 1 CDF for ultimate force with various R factors (2"/12", 10) ............................... 263
H.2 CDF for ultimate force with various R factors (2"/12", LS) ............................... 263
LIST OF APPENDIX FIGURES (Continued)
Figure
H.3 CDF for ultimate force with various R factors (2"/12", CP) .............................. 264
H.4 CDF for ultimate force with various R factors (4"/12", 10) ............................... 264
H.5 CDF for ultimate force with various R factors (4"/12", LS) ............................... 265
H.6 CDF for ultimate force with various R factors (4"/12", CP) .............................. 265
H.7 CDF for ultimate force with various R factors (6"/12", 10) ............................... 266
H.8 CDF for ultimate force with various R factors (6"/12", LS) ............................... 266
H.9 CDF for ultimate force with various R factors (6'712", CP) .............................. 267
LIST OF APPENDIX TABLES
Table
B. 1 Deterministic modification factors for construction quality ............................... 235
D.1 Set of LA ordinary ground motion records (CUREE project) ............................ 240
D.2 Set of LA earthquake ground motions with 10% probability of
exceedence in 50 years (SAC project) ............................................................... 241
D.3 Set of Seattle earthquake ground motions with 10% probability of
exceedence in 50 years (SAC project) ............................................................... 242
D.4 Set of Boston earthquake ground motions with 10% probability of
exceedence in 50 years (SAC project) ............................................................... 243
Performance-Based Seismic Design of Light-Frame Shearwalls
1. INTRODUCTION
1.1 General
Wood is the most common material used in one- and two-story residential
construction in the United States. Light-frame wood structures have a number of
advantages including aesthetics, beauty, construction cost and time, versatility,
flexibility in floor plans, and so forth. Most woodframe structures consist of floors,
walls, and roof systems tied together by fasteners. Shearwalls and diaphragms provide
the primary resistance to lateral forces in woodframe structures.
Light-frame wood structures generally have performed well with regard to life-
safety under natural hazard loadings such as earthquakes and hurricanes. Properly
built woodframe structures can withstand major earthquakes and hurricanes without
collapsing. However, costly damage (both nonstructural and secondary assemblies),
which can add significantly to the total economic loss in natural hazards, remains a
problem. Many woodframe structures designed to meet current standards (code
requirements) were damaged in recent natural disasters such as the Northridge
earthquake and hurricane Andrew [NAHB, 1993, 1994]. In the wake of these and
other events, the structural engineering community has come to recognize the
limitations of current design provisions, particularly with respect to damage
prevention. For example, current seismic design procedures for light-frame structures
[ICBO, 1997; AF&PA, 2001] require an estimate of the elastic fundamental period.
2
This may not be simple to estimate since woodframe buildings exhibit inelastic
response over the entire range of lateral deformation. Current strength-based code
procedures do not allow for a proper assessment of the safety of engineered buildings
considering the various limit states that these structures may have to meet during their
service-life. Therefore, the structural engineering community has started to embrace a
new design approach (termed "performance-based design") in order to address more
explicitly various performance requirements. Although performance-based seismic
design has advanced for some materials and structural types, such as steel and
reinforced concrete buildings and bridges [SAC, 1995; Wen and Foutch, 1997], its
application to light-frame structures remains largely unexplored.
In recent years, the concept of performance-based design has gained interest
among designers and researchers. Performance-based design includes selection of
appropriate building sites, structural systems and configurations, as well as analytical
procedures used in the design process, to confirm that the structure has adequate
strength, stiffness and energy dissipation capacity to respond to the design loads
without exceeding permissible damage states [SEAOC, 1999; FEMA, 2000 a,b; AISC,
2001]. The objective of performance-based design is to obtain a more reliable
prediction of structural behavior, quantifying and controlling the damage risk to an
acceptable level during the service-life of the structure [Moller et al., 2001].
Performance-based design has evident benefits. These benefits have to be made clear
in order for performance-based design to be an accepted alternative to present design
procedures.
3
Although performance-based design concepts are gaining acceptance in the
design community, these are a number of obstacles that must be overcome for
performance-based design to be widely accepted. Performance objectives (including
both performance levels and hazard levels) must be formulated in a probability-based
format to take proper account of the various sources of uncertainty. Uncertainties can
be classified as aleatory or epistemic. Aleatory uncertainties arise from inherent
variability in (e.g., material) properties, whereas epistemic uncertainties arise from a
deficiency in the knowledge base, including limited data or model uncertainties. In
design for natural hazards, the greatest source of uncertainty arises from the hazard
itself. For example, variability in the seismic hazard (as represented by a characteristic
suite of ground motions) contributes the greatest uncertainty to the predicted response
(peak displacement) of a woodframe shearwall. The ground motions are highly
variable in terms of peak ground acceleration, strong motion duration, frequency
content, and so forth. Other uncertainty sources could include the analytical models,
material and connection properties, construction materials, workmanship, and so on.
Efforts to develop performance-based design procedures must identify and quantify
sources of uncertainty to accurately evaluate the associated reliability (performance)
levels.
The objective of the proposed research is to explore the potential for the
application
of
performance-based engineering concepts to the design and
assessment of woodframe structures subject to earthquakes. To accomplish this, a
general methodology will be developed for assessing probabilistic response of
ru
woodframe structures. The eventual adoption of performance-based concepts in design
can lead to an improvement in performance, reduction in property destruction and
damage, improvement in durability, and reduction in maintenance costs of woodframe
structures. This research also can provide a technical basis for the development of
further performance-based design provisions for woodframe construction.
1.2 Scope and objectives
The focus of this research is on shearwalls in woodframe structures subject to
earthquake loading. The shearwalls are treated as isolated subassemblies (Chapter 4)
or as parts of complete systems (Chapter 5). Shearwalls comprise the vertical elements
in the lateral force resisting system of woodframe structures. They support the
horizontal diaphragms and transfer the lateral forces downward into the foundation. A
number of sheathing materials can be used to develop shearwall action in a light-frame
wall. These include wood structural panels such as OSB and plywood, gypsum
wallboard (interior finish material), and stucco (exterior finish material).
There are three main objectives in this research. The first is the development of
general methodology for assessing probabilistic response of wood shearwalls subject
to earthquake loading while considering the various parameters (ordinary ground
motion records, effects of nonstructural finish materials, construction quality, effects
of different seismic hazard regions, and sheathing-to-framing connection hysteretic
parameters) which affect shearwall performance. The shearwall response (peak
displacement) is obtained by nonlinear time history analysis using the analytical model
CASHEW and visually best-fit program, SASHFIT (detailed descriptions of both
programs are provided in Chapter 3). The second objective is the development of
probability-based (risk-consistent) design aids for woodframe shearwall design
(selection) in seismic regions. The resulting design aids (performance curves and
design charts) can be used in both design and evaluation applications. The third
objective is the application of fragility methodology, which can be used for design and
post-disaster condition assessment.
2. BACKGROUND AND LITERATURE REVIEW
In the early 1990's, several natural disasters struck opposite ends of the United
States. Hurricane Andrew struck the coast of Florida in 1992 and the Northridge
earthquake hit Southern California in 1994. These two large-scale natural hazards
caused tremendous damage to residential woodframe structures in these regions.
According to an NAHB survey, the main forms of damage to residential woodframe
structures were roof sheathing removal due to wind loading and damage to interior and
exterior finish materials due to earthquake loading [NAHB, 1993; 1994]. In seismic
events, shearwalls function mainly to resist lateral force, while in high-wind events,
roof systems function primarily as sheltering elements for the interior spaces of
buildings. In light of the costs of these recent natural disasters, many studies have
focused on mitigating damage through the development and implementation of
improved design procedures.
Wood shearwalls have been the subject of extensive investigation in recent
years. Numerous experimental tests have been conducted and both static and dynamic
analysis models have been developed to describe shearwall performance subject to
earthquake loading [Foschi, 1977; Tuomi and McCutcheon, 1978; McCutcheon, 1985;
Stewart, 1987; Cheung et al., 1988; Dolan, 1989; Filiatrault 1990; Dolan and Madsen,
1992; Durham, 1998; Dinehart and Shenton, 1998; Salenikovich, 2000; Dinehart and
Shenton, 2000; Folz and Filiatrault, 2000; 2001; 2002]. More recently, reliability
concepts have been applied to predicting shearwall performance under seismic
loading. Ceccotti and Foschi (1998) evaluated the earthquake design procedure for
7
woodframe shearwalls in the Canadian National Building Code using First-Order
Reliability Method (FORM) techniques. Paevere and Foliente (2000) investigated the
effect of hysteretic pinching and stiffness degradation on the peak displacement and
reliability of shearwalls using the Bouc-Wen-Baber-Noori (BWBN) model combined
with Monte Carlo Simulation. Rosowsky and Kim (2002a) proposed a risk-based
methodology for woodframe shearwall design considering a suite of earthquake
records and using a numerical model (CASHEW) and nonlinear dynamic time history
analysis. Another study by van de Lindt and Walz (2003) used a new hysteretic model
for dynamic analysis of wood shearwalls and fit the response to a Weibull distribution.
A large, multi-university project (the CUREE-Caltech Woodframe Project) with the
overall objective of developing improved analysis and design techniques for
woodframe structures is nearing completion at the time of this research. The project
included shake table tests of various woodframe assemblies and structures,
development of testing protocols, consideration of effects of anchorage and wall finish
materials, testing of nail and screw fastener connections, development of seismic
analysis software, reliability studies, and other aspects of woodframe structures
subject to earthquake loading [Camelo et al., 2002; Cobeen, 2001; Deierlein and
Kanvinde, 2003; Folz and Filiatrault, 2000; Fonseca et al., 2001; Isoda et al., 2001;
Krawinkler et al., 2000; Mahaney and Kehoe, 2002; McMullin and Merrick, 2001;
Rosowsky and Kim, 2002a]
As described above, many studies have focused on reducing the damage to
woodframe structures subject to natural hazards. Many of these are based on emerging
[I]
performance-based design concepts. The concept of performance-based design, in
actuality, is not new. The U.S. Department of Housing and Urban Development
experimented with what would later be known as performance-based design when
they sponsored a large research program ("Operation Breakthrough") to develop
criteria for design and evaluation of innovative housing systems [Performance, 1977].
This concept appeared again after the Northridge earthquake of 1994, where it became
apparent that buildings designed by code for life safety did not perform up to
performance expectations in other aspects.
Performance-based design, when implemented successfully, can contribute
effectively to the reduction of damage and associated losses, as well as improvement
in
the performance and safety of structures under natural hazard loadings.
Performance-based design requires, most importantly, a realistic model for the
structural behavior under appropriately described natural hazard loadings. In addition,
tools are needed for the evaluation of probabilistic assessment of the response in order
to quantify the exceedence probability for each of the relevant performance states.
Performance-based design consists of four key features: performance levels,
seismic hazard levels, performance objectives, and confidence levels. Performance
levels are a state of defined and observable damage in a structure or structural
component. The performance goals should be based on reliability and uncertainty
principles. In other words, they should be based on calculated responses associated
with observed behaviors, and the acceptable risks should be determined in relationship
to other societal risks. Seismic hazard levels are representations of variation in suitable
parameters of the annual probability of exceedence. Performance objectives are the
coupling of performance levels with hazard levels. Confidence levels that the building
will satisfy the design requirements must then determined. Performance objectives
must be translated into engineering quantities to establish acceptance criteria, defined
as limiting values in the response parameters that become targets for the design
[AISC, 2001]. The expression of performance requirements is one of the most
significant challenges in developing performance-based design concepts.
10
3. NONLINEAR DYNAMIC TIME-HISTORY ANALYSIS
3.1 Computer programs
3.1.1 CASHEW
The CASHEW (Cyclic Analysis of Shearwalls) program was used in this study
to evaluate the dynamic response of woodframe shearwalls (treated as isolated
subassemblies). Specifically, the response quantity of interest was peak displacement
(or "drift") at the top of the wall. CASHEW is a numerical model capable of
predicting the load-displacement response of wood shearwalls under quasi-static
cyclic loading, and was developed under Task 1.5.1 (Analysis Software) of the
CUREE-Caltech Woodframe Project {Folz and Filiatrault, 2000, 2001]. With
information on shearwall geometry, material properties, and the hysteretic behavior of
the individual fasteners, CASHEW can be used to calibrate the parameters of an
equivalent SDOF system (modified Stewart hysteretic model). This is done, for
example, using the CUREE-Calteeh loading protocol developed under Task 1.3.2 of
the CUREE-Caltech Woodframe Project. The equivalent SDOF hysteretic model can
then be used to predict the global cyclic response of a shearwall under arbitrary quasistatic cyclic loading or, using a nonlinear dynamic time-history analysis program, and
actual ground motion records. The CASHEW modeling procedure is illustrated in
Figure 3.1. Details of the numerical modeling procedure, the loading protocol, the
system identification procedure used to define the equivalent SDOF model parameters
is provided elsewhere [Folz and Filiatrault, 2000, 2001].
11
With assumed structural
and connection parameters
CUREE bas
ProtocJ
I
Single set of hysteretic
parameters for given wa/I
CASHE
Program
I
Equivalent
Nonlinear SOOF
llar
J
A
.
.
.
Ground
motion
Ordinary ground motions
characterizing seismic
hazard in southern CA
Scaling
Procedurej
UBC design spectrum
NEHRP guidelines
_____
Scaled
ground
moti
HI
Suite of 0GM records scaled
for specific performance level
(LS-10/50, 10-50/50)
Figure 3.1 CASHEW modeling procedure
3.1.2 SASH!
SASH 1 is a nonlinear dynamic time history analysis program used to analyze
shearwalls under actual earthquake ground motions. The shearwall is modeled as a
single degree-of-freedom nonlinear oscillator using a modified Stewart hysteretic
model. The global shearwall hysteretic parameters used as input to SASH 1 are
obtained from CASHEW or SASHFIT (described next). The mass and damping ratio
as a percentage of critical, along with the earthquake record scaled appropriately for
the target hazard levels, also are required input for SASH 1. The SASH 1 program then
performs a nonlinear dynamic time history analysis to predict the peak relative
displacement of shearwall. The program also generates peak relative acceleration,
peak relative velocity, peak absolute acceleration, and peak force at top of wall.
12
3.1.3 SASHFIT
SASHFIT is a spreadsheet program which can be used to develop a set of
hysteretic parameters for the behavior of a single fastener or an entire (isolated)
shearwall. It requires the complete cyclic test data (i.e., load-deformation curve) for
the particular fastener or assembly. SASHFIT is developed based on the following
equation [Foschi, 1977]:
sgn(8) (F0
F=
+
K0 S)x
[i
exp( K0 s)i F0
5j
(3.1)
sgn(8)xF+r2K0[8_sgn(s)x8J
0,
where, F = global force, 8 = deformation, 8u = deformation at ultimate load,
deformation at failure, F0 = force intercept of the asymptotic line, K0
Sp' =
initial
stiffness, rjK0 = asymptotic stiffness under monotonic load, F = ultimate load, and
r2K0 =
post ultimate strength stiffness under monotonic load. This equation was
developed based on monotonic loading, so further consideration of cyclic loading is
required. Figure 3.2 shows a load-deformation curve under an arbitrary cyclic loading.
In this figure, r3K0 = unloading stiffness, r4K0
degrading stiffness K = KO(6O/8m)a, 6m
stiffness degradation, and
re-loading pinched stiffness,
/38, a and /3 = hysteretic parameters for
= final unloading displacement.
13
30
-
(o,F)
lj
1rK
20 -
I
G
F0
K
z
U
-
E
14KO__
ci)
0
0
120- [Cyclic Loading Protocoj
LI
E80-
-10
400)
E
ci)
<-,
-20
0-
D
D
-30
1111111
-80
-80-
111111 I
-40
I
0
I 11111111 I III
40
I 1111111
80
120
Displacement,
(mm)
Figure 3.2 Force-displacement response of a wood shearwall under cyclic loading.
Hysteretic model is fit to test data for an 8 ft x 8 ft shearwall with 3/g-in. thick OSB
sheathing panels (from: Durham, 1998)
The hysteretic response of a typical shearwall exhibits the same defining
characteristics (pinched behavior, strength and stiffness degradation, etc.) as those of
the individual sheathing-to-framing connector under cyclic loading [Dolan and
Madsen, 1992]. Consequently, the hysteretic model presented here, which was used to
represent the hysteretic behavior of sheathing-to-framing connectors [Folz and
Filiatrault, 2001], also can be used to represent the global hysteretic response of a
shearwall under cyclic loading with appropriate model parameter values. The
spreadsheet application, SASHFIT, developed as part of this research, can be used to
identify the ten hysteretic parameters for the shearwall directly from full-scale cyclic
14
shearwall test data. Alternatively, SASHFIT can be used to identify the ten hysteretic
parameters of the individual fasteners, and CASHEW can be used to determine the
global hysteretic parameters of the overall shearwall. Figure 3.3 shows a comparison
of one example of the model based on the parameters determined by SASHFIT with
the original cyclic load-displacement curve.
1r\
a
C',
0
-J
Displacement (in.)
Figure 3.3 Load-displacement curve using parameters determined by SASHFIT
3.1.4 SAWS
The SAWS (Seismic Analysis of Woodframe Structures) program was
developed to predict the seismic response of a complete structure [Folz and Filiatrault,
2002]. In this model, the light-frame structure is composed of two primary
components: rigid horizontal diaphragms and nonlinear lateral load resisting shearwall
elements. In the modeling of the structure, it is assumed that both the floor and roof
15
elements have sufficiently high in-plane stiffness to be considered rigid elements. This
is expected to be a reasonable assumption for typically constructed diaphragms with a
planar aspect ratio on the order of 2:1, as supported by experimental results from full-
scale diaphragm tests [Philips et al., 1993]. The actual three-dimensional building is
degenerated into a two-dimensional planar model using zero-height shearwall spring
elements connected between the diaphragms and the foundation. All diaphragms in the
building model are assumed to have infinite in-plane stiffness [Folz and Filiatrault,
2002].
The SAWS program executes linear dynamic analysis, nonlinear dynamic
analysis, and quasi-static pushover analysis on the woodframe building model with
information of building configuration, masses of system, hysteretic wall parameters,
viscous damping parameters, and earthquake records. The program also can be used to
predict the response of structures consisting of shearwalls with nonstructural finish
materials such as stucco and gypsum wallboard. The hysteretic parameters for the
shearwalls in the structure can be obtained by CASHEW or SASHFIT. Selected
hysteretic parameters for nonstructural finish (NSF) materials are provided in the
SAWS report [Folz and Filiatrault, 2002], however they also can be developed using
SASHFIT if full-scale test data are available. The SAWS report only provided
hysteretic parameters for an 8 ft.
x
8 ft. wall with NSF materials (stucco and gypsum).
Therefore, these values must be adjusted for the length of the actual wall and for the
presence of door and window openings [Folz and Filiatrault, 2002].
16
3.2 Ordinary ground motion records
The ground motions considered in this research were obtained from Task 1.3.2
(Loading Protocol) of the CUREE-Caltech Woodframe Project (CCWP). The suite of
20 ordinary ground motion (0GM) records are assumed to be representative of the
10% in 50 years (10/50) hazard level for California conditions and formed the basis
for the development of the CUREE-Caltech loading protocol {Krawinkler et al., 2000;
Filiatrault and Folz, 2001]. Two limit states, life safety (LS) and immediate occupancy
(10), were the focus of this study. The life safety limit state is paired with the 10%
probability of exceedance in 50 years (10/50) hazard level, while the immediate
occupancy limit state is paired with the 50% probability of exceedance in 50 years
(50/50) hazard level [FEMA, 2000a,b]. For the life safety (LS, 10/50) limit state
analyses, each record was scaled such that its mean 5% damped spectral value
between periods of about 0.12 and 0.58 seconds matched the UBC design spectral
value of 1.lg for the same period range {ICBO, 1997]. For the immediate occupancy
(10, 50/50) limit state, the records were scaled according to the procedure
recommended in the NEHRP Guidelines [FEMA, 2000a,b]. Seismic zone 4 and soil
type D were assumed for most cases in this study. The code provided target response
spectra are shown in Figure 3.4 with three hazard levels (JO, LS, and CP). The scaled
peak ground accelerations for the 20 records are shown in Table 3.1.
The evaluation of the collapse prevention (CP, 2/50) limit state, which is
paired with the 2% probability of exceedance in 50 years (2/5 0) hazard level [FEMA,
2000a,b], is the subject of some discussion. While not considered as extensively as the
17
LS (10/50) and 10 (50/50) limit states here, the CP (2/50) limit state (generally
associated with a 2% in 50 years hazard level) was considered in selected stages of
this research. The peak ground accelerations for these records also are shown in Table
3.1. Again, the focus of this study was on the life safety (LS, 10/50) and immediate
occupancy (JO, 50/50) limit states.
3.3 Distribution functions (exceedence probability curves)
The greatest source of variability (or more specifically, the largest contribution
to the variability in peak response) arises from the ground motions themselves (i.e.,
the suite of 20 ordinary ground motion records characterizing the seismic environment
in California). It was therefore decided to present the peak displacements obtained
using each of the ground motions, scaled as appropriate for the limit state, in the form
of a sample cumulative distribution function (CDF). The relative contribution of the
ground motion variability to the overall response (drift) variability will be addressed in
the next section. These distribution functions provide a convenient method for
estimating probabilities of exceedence, or "non-performance." That is, one can quickly
evaluate the probability of the maximum shearwall drift exceeding (or not exceeding)
a prescribed level at the hazard level defined by the suite of ground motions. In this
study, the prescribed performance levels correspond to the FEMA 356 drift limits (see
Table 3.2). Once the peak displacement distributions are determined, they can be post-
processed into a form useful for design and/or assessment for given target
probabilities. This process is illustrated in Figure 3.5 and will be described later in
Section 4.3.2.
2
1.8
- - -
1.6
1.4
I
1.2
Collapse Prevention (2%/5oyrs)
0)
\
(I)
([
0.8
Life Safety (10%/50yrs)
Immediate Occupancy (50%I5Oyrs)
0.6
0.4
0.2
OL
0
0.5
1
1.5
2
Period (sec)
Figure 3.4 Code based target response spectra
2.5
3
3.5
4
Iv
EQ Event
File
&Year
Peak Ground Acceleration (g)
Raw
Scaled
Station
OG
North d
SUP1
SUP2
SUP3
NOR2
NOR3
Brawley
El Centro Imperial County Center
NOR4
NOR5
NOR6
NOR9
Glendale
NOR1O
LP1
LP2
LP3
LP4
LP5
LP6
CM1
CM2
Loma Prieta
(1989)
Cape Mendocino
(1992)
Landers
(1992)
LAN!
LAN2
PlasterCity
Beverly Hills 14145 Mulhol
CanogaPark-TopangaCanyon
Las Palmas
LA-Hollywood Storage
LA (North) Faring Road
NorthHollywood-Coldwater
Sunland-MtGleasonAve
Capitola
Gilroy Array #3
Gilroy Array #4
Gilroy Array #7
Hollister Differential Array
Saratoga West Valley
Fortuna Boulevard
Rio Dell Overpass
DesertHotSprings
1
10
(50/50)
LS
(10/50)
CP
(2/50)
0.264
0.255
0.174
0.205
0.261
0.206
0.210
0.266
0.212
0.206
0.185
0.206
0.227
0.179
0.604
0.584
0.398
0.470
0.599
0.472
0.482
0.609
0.485
0.472
0.423
0.473
0.520
0.410
0.415
0.600
0.530
0.532
0.542
0.399
0.985
0.973
0.643
0.759
0.967
0.762
0.778
0.984
0.783
0.762
0.683
0.764
0.840
0.662
0.670
0.969
0.856
0.859
0.875
0.644
0.116
0.258
0.186
0.416
0.356
0.357
0.231
0.273
0.271
0.157
0.529
0.555
0.417
0.226
0.279
0.332
0.116
0.3 85
0.154
0.152
Yermo Fire Station
0.181
0.262
0.231
0.232
0.237
0.174
Table 3.1 20 Ordinary ground motion records and PGA values
Structural Performance Levels
Elements
Type
j
]
Primary
Wood Stud
Walls
Secondary
Drift
Assumed hazard level and
mean return period
Collapse Prevention]
Connections loose,
Nails partially
withdrawn. Some
splitting of
members and
panels. Veneers
dislodged
Sheathing sheared
off Let-in braces
fractures and
buckled. Framing
split and fractured.
3% transient or
permanent.
2/50 (2% in
years),
2475 years
50
F
Life Safe
Moderate loosening
of connections and
minor splitting of
members
Connections loose,
Nails partially
withdrawn. Some
splitting of
members and
panels.
2% transient;
1% permanent
10/50 (10% in 50
years), 474 years
Immediate
Occupancy
Distributed minor
hairline cracking of
gypsum and plaster
veneers
Same as primary
1% transient;
0.25% permanent
50/50 (50% in 50
years), 72 years
Table 3.2 Structural performance levels and requirements for woodframe walls
Table C1-3, FEMA 356)
(from:
20
Figure 3.6 illustrates the construction of the sample cumulative distribution
function (CDF) and the fitted distribution function Fx(x) for the peak displacement of
one wall considering both the life safety (LS, 10/50) and immediate occupancy (JO,
50/50) limit states. Each point represents the peak drift obtained from a nonlinear
time-history analysis for a particular ground motion record. The results are then rankordered to construct the sample cumulative distribution function (CDF), which is then
fit to a lognormal (LN) distribution given by:
F(x)
(3.2)
where 'Do = standard normal cumulative distribution (CDF) function, X = logarithmic
mean, and
= logarithmic standard deviation. The LN parameters (X, ) are obtained
using a maximum likelihood procedure. In addition to providing a good fit, the LN
distribution is the most convenient distribution form for fragility analysis as well as
consideration of model uncertainty, as will be discussed later. Figure 3.6 can be used,
for example, to evaluate the probability that a wall of this type will exceed a certain
peak drift, again assuming California seismic hazard conditions. For example, the
probability that the peak drift will exceed the FEMA 356 drift limit for life safety (LS,
10/50) of 2% is about 0.03 (or a 97% non-exceedence probability). As can be seen
from this figure, the probability of non-performance of this wall considering the
immediate occupancy (JO, 50/50) limit state is very small. The JO (50/50) distribution
function is considerably below the 1% drift limit prescribed by FEMA 356.
21
Scaled
ground
motion
ds
SASH1
program
Peak
displacement
1
L
dtribution,Fx(x)
j
Nonlinear time-history analysis
Modified Stewart hysteretic model
Parameters from CASHEW
Seismic hazard
characterization
Response distribution for
given seismic weight
II
Performance
curves
(peak drift vs.
seismic weight)
Design charts for
shearwall selection
J
One set for each
non-exceedence
probability level
One set for each combination of
Structural parameters (sheathing,
Fastener type, fastener spacing)
Figure 3.5 Development of probability-based design charts for shearwall selection
0.9
+
*
+
0.8
*
IO(5lI50)
0.7
*
*
0.6
LS(10/50)
.
0.4
I
I
I
I
*
0.3
H
I8ft.
Ill+
8ft.
*
i
0.2
I
C'4
*
d
+
0.1
BW (8 >< 8), 8d3"I6,
OSB(3/8"),ED= /8',
f
ii
+
G =l8Oksi,ç=2%,
*
+
W = 1400 lbs/ft (50 kN total)
C)
0
0.5
1
1.5
2
2.5
3
6max (in.)
Figure 3.6 Fitting a lognormal distribution to the sample CDF of peak displacements
22
4. ANALYSIS OF ISOLATED SHEARWALLS
4.1 Model configuration (isolated shearwall)
The focus of this chapter is on the performance of shearwalls in woodframe
structures under real earthquake loading. These shearwalls are treated as isolated
subassemblies in this chapter. Shearwalls acting as part of a complete structure are
discussed in Chapter 5.
Woodframe shearwalls typically have three major components: dimension
lumber framing, sheathing panels, and fasteners. The dimension lumber framing
elements generally are nominal 2 in.
x
4 in. or nominal 2 in. x 6 in. sawn lumber
pieces. These are oriented horizontally (plates and sills) and vertically (studs) with
only nominal nailing to hold the framework together. The top plate and end studs
generally consist of double members, while the sole plate and the interior studs are
single members. Studs are generally spaced at 16 in. or 24 in. on center. Hold-downs
are used to prevent overturning of the wall and ensure a racking mode of deformation.
For exterior sheathing, structural panels such as oriented strand board (OSB) and
plywood are most commonly used. Gypsum wallboard is most commonly used for
interior sheathing and stucco is a widely used finishing material, particularly in
California. Sheathing panel thicknesses vary, but 3/8-in., 15/32-in., and 7/16-in. are the
most common in typical lightframe shearwall construction. Sheathing panels are
usually 4 ft. x 8 ft. in size and are installed either vertically or horizontally. Blocking
is often used when panels are installed horizontally. The sheathing is attached to the
framing with dowel-type fasteners such as nails (most common), screws, or staples,
23
although adhesives sometimes are used. These fasteners are typically spaced at regular
intervals with fastener lines around the perimeter of the sheathing panels more densely
spaced than throughout the sheathing panel interior. Figure 4.1 depicts the components
of typical woodframe shearwall.
Top-plate
Sheathing-to-framing connector
i:rnr.r.r
Sill
Sheathing material
Figure 4.1 Components of typical woodframe shearwall
Three (typical) shearwall configurations were considered in this study. The
first baseline wall (BW1) was a solid 8 ft. x 8 ft. wall built with 2 in. x 4 in. nominal
lumber, 4 ft. x 8 ft. OSB sheathing materials (3/8-in. thicimess) oriented vertically and
various nailing schedules (3"/12", 4"/12", and 6"112"). Double top plate and end studs
were assumed with single sole plate and interior studs. The stud spacing was 16 in.
and properly installed hold-downs were assumed to be present. The second baseline
24
wall (OW!) was a long wall with a 16 ft. garage door opening (see Figure 4.2) This
wall was built with 2 in. x 4 in. nominal framing lumber, vertically oriented OSB
sheathing (3/8-in. thickness) at the wall ends, a solid header over the opening, and
various nailing schedules. Hold-down anchorage was assumed to be present and
properly installed. The third baseline wall (0W2) was a 16 ft. long wall with a
pedestrian door opening (see Figure 4.2). The construction parameters were similar to
those of OWl.
25
- - - ----11-.
S
I
I
II
II
I
I
II
.
I
II
I
II
II
.
I
II
BV\/1
II
II
II
I
I
i
S
I
II
II
S
S
S
11l
I
II
I
II
S
II
.
S
S
II
II
.
II
II
_11___
I
I
S
I
4ft.
4ft.
8ft.
.
S
S
S
:
:
.
owl
I
.
I
S
I
I
S
S
I
4-
-----Il----
3ft.
3ft.
loft.
16 ft.
-1
.
S
I
I
I
II
I
I
I
S.
S
es
S
II
I
I
II
I
I
I
I
S
II
I
I
..
S
S
0W2
:
3ft.
3.5 ft.
3ft.
:
3.5 ft.
.:
.
3ft.
16 ft.
Figure 4.2 Detailed configurations of baseline solid wall (BW1) and walls with
openings (OWl and 0W2)
26
4.2 Sensitivity studies
4.2.1 Baseline sensitivity studies
Sensitivity studies were performed to investigate the relative contribution of
both aleatory (inherent) and epistemic (knowledge-based) uncertainties to the
estimation of shearwall peak displacement. Some factors affecting performance of
wood structures are inherently random (aleatory) in nature, and thus are irreducible at
the current level of engineering analysis {Ellingwood et al., 2003]. Examples would
include strength of wood in tension or in compression parallel-to-grain, shear modulus
values for sheathing materials and fastener hysteretic parameters. Others arise from
the assumptions made in the analysis of the system and from limitations in the
supporting databases. In contrast to the aleatory uncertainties, these knowledge-based
(epistemic) uncertainties depend on the quality of the analysis supporting databases,
and generally can be reduced, at the expenses of more comprehensive (and costly)
analysis. Sources of epistemic uncertainty in light-frame wood construction include
modeling error (CASHEW), two-dimensional models of three-dimensional buildings,
seismic mass, and probabilistic models of uncertainty estimated from small data
samples. The effects of these sources of uncertainty (variability) on shearwall response
(peak displacement) are described in the following sections. The four solid walls (all 8
ft. x 8 ft.) considered in the sensitivity studies are shown in Figure 4.3. The baseline
wall used for most comparisons is the 8 ft. < 8 ft. solid wall with two sheathing panels
oriented vertically, designated BW1.
27
-
II
I
II
I
II
I
II
I
II
I
II
I
II
I
II
I
II
II
I
II
II
II
II
II
II
II
II
4ft.
II
II
II
II
II
II
I
I
I
I
II
I
I
II
I
I
II
I
I
II
I
I
II
I
I
II
I
18 ft.
8
-
II
I
I
I
I
I
I
II
II
II
II
II
II
II
II
II
II
II
I
I
I
I
I
I
I
II
I
I
I
II
I
II
I
II
4ft
I
II
I
II
I
I
II
I
I
4ft.
- - -
4ft.
8ft.
8 ft.
Baseline Wall 1 (BW1)
Baseline Wall 2 (BW2)
-4ft.
ir-II
II
II
II
4ft.
8
-
rt.
III
III
8 ft.
I
il
--
I
II
-
4ft.
Baseline Wall 3 (BW3)
4ft.
8 ft.
Baseline Wall 4 (BW4)
Figure 4.3 Baseline wall sheathing configuration
4.2.1.1 Ground motions
The greatest contributor to response variability is expected to be the ground
motions. The 20 ground motions taken to be representative of the seismic hazard in
southern California are highly variable (in terms of spectral acceleration, strong
motion duration, frequency content, etc.). Figure 4.4 shows the variability of relative
!41
response (peak displacement) obtained using the CASHEW modeling procedure
described in Section 3.1.1 for one given wall configuration, assuming the Durham nail
hysteretic parameters (described in Section 4.2.2), and considering the three limit
states: life safety (LS, 10/50), immediate occupancy (JO, 50/50), and collapse
prevention (CP, 2/50). The distributions shown for 10 (50/50), LS (10/50), and CP
(2/50) are obtained using the 20 ordinary ground motion records scaled to the
appropriate UBC design spectral values (1.1 g) and NEHRP guidelines {TCBO, 1997;
FEMA, 2000a, b]. The distribution for CP_NF is obtained using the six near-fault
records also identified as part of the CCWP. These near-fault records were not scaled
because insufficient knowledge exists at this time to scale near-fault records to return
period specific hazard levels [Krawinkler et al., 2000]. The FEMA 356 drift limits are
shown for comparison. The response variability clearly increases at higher hazard
levels. The evaluation of the CP (2/50) limit state is the subject of some debate, and
the focus of this study is on the LS (10/50) and JO (50/50) limit states.
4.2.1.2 Damping
Damping ratios for woodframe structures are often presumed to be in the range
of 2% to 8%. Fischer et al. (2001) performed shake-table tests of full-scale woodframe
structures as part of Task 1.1.1 of the CUREE-Caltech Woodframe Project (CCWP)
and found equivalent viscous damping ratios of 3.1% at ambient levels, increasing to
12% at PGA = 0.22g shaking, and decreasing to about 6% at PGA
0.5g shaking.
As part of CCWP Task 1.3.3 (Dynamic Characteristics of Woodframe
Structures), damping ratios were determined to be in the range of 2.6% to 17.3%, with
an average of 7.2% [Camelo et al., 2001]. However, much of this is likely to be
hysteretic damping, which is accounted for directly in the hysteretic model.
I
0.9
IO(50/50)
0.8
LS(10/50)
0.7
0.6
--
I-
KCPNF (2/50)
CP (2/50)
/
0.5
/
LL
0.4
0.3
0.2
Bft.
0.1
,'
/
BWI (8' x 8'), 8d3"/6", OSB(3/8"),
ED = I8", G = 180 ksi, ç = 2%,
W=1400 lbs/ft (50 kN total)
0
0
2
4
6
8
10
6max
12
14
16
18
20
(in.)
Figure 4.4 Response (peak displacement) variability for the three limit states
The damping parameter in the nonlinear time-history analysis program is the
nominal viscous damping value, as a percent of critical. This is why measured
damping values are often in excess of 15%, while most people assume about 2%
(viscous) damping in their models [Foliente, 1995]. In fact, the viscous damping is
thought by some to be much less, perhaps effectively zero, in woodframe shearwalls,
particularly at high peak ground acceleration (PGA) values. Some people use 0.1%
(for example) to avoid singularity problems in the analyses.
Discussion among Element 1 researchers in the CCWP suggested it may be
appropriate to use different damping values for different ground motion intensities.
For example, the full-scale building tests at University of California at San Diego
suggest viscous damping levels of about 7% for low-intensity shaking, and close to
zero for strong shaking. Using BW1 (and considering both JO, 50/50 and LS, 10/50),
three different approaches to the assignment of viscous damping are considered: (1)
constant damping, 0%, 1% and 2%, is assumed for all cases; (2) 7% is assumed for the
records scaled for 10 (50/50) and 0.1% is assumed for the records scaled for LS
(10/50) and (3) damping is assumed to vary linearly from 0.1% to 7%, inversely
proportional to the PGA of the scaled record. The effect of these damping assumptions
on the peak displacement distribution is shown in Figure 4.5 for the two different
performance levels. For the development of performance curves and design charts,
described later in this dissertation, a single damping value of 2% of critical is
assumed. However, based on the results shown in Figure 4.5, it may be conservative in
future studies to assume a lower value of damping for higher intensity ground motions
(i.e., records scaled for LS, 10/50).
31
17/
/Z'
0.9
/f :LL"
0.8
ç = 0% l0, 50/50) /,,"
= 0% (LS, 10/50)
= 1% (10, 50/50) //'/
= 0.1% (LS, 10/50)
= 2% (l$D, 5O/5O),i-c.:
0.7
Variable
(10,
5oI1'J
,,N
0.5
1"
1'I
LL
(LS, 10/50)
2% (LS, 10/50)
= 7% (10] 50/50)""
1x
= 1% (LS, 10/50)
Variable
I
0.4
I;,,;
0.3
8ft
0.2
8ft.
II
Ii
BW1 (8' >< 8'), 8d@3"/6",
0.1
OSB(3/8"), G = 180 ksi,
W = 1400 lbs/ft (50 kN total)
01
0
iii
0.5
1
1.5
2
2.5
3
max (in.)
Figure 4.5 Effects of viscous damping ratio () on peak displacement
4.2.1.3 Shear modulus of sheathing materials
The assigned shear modulus (G) for wood sheathing panels ranges from about
60
90 ksi (0.41
0.62 GPa) for plywood, and about 180 - 290 ksi (1.24 - 2.00 GPa)
for OSB [Plywood, 1998; Wood Handbook, 1999]. The shear modulus increases with
panel thickness. It was shown that the variability in shear modulus (G) contributes
very little to the variability in response (peak displacement), and hence, shear modulus
can be treated as a deterministic quantity. A sensitivity study can be performed to
evaluate the effect of shear modulus on peak displacement, however it must be
recognized that in addition to changing shear modulus, the change in thickness and
sheathing material will affect the fastener hysteretic parameters. Since only the
Durham (1998) nail data (see Section 4.2.2) is used for this part of study, only the
32
shear modulus is changed for the purposes of this comparison. Figure 4.6 shows the
effect of assigned shear modulus on the peak displacement distribution, considering
baseline wall BW1 and the life safety (LS, 10/50) limit state. The effect of shear
modulus, considering sheathing thickness varying from
/8
/8
in., is seen to be
relatively small; however, to properly investigate its effect will require the appropriate
fastener hysteretic parameters. From this point forward, the shear modulus (G) is
assumed to be deterministic with values of 60 ksi for plywood and 180 ksi for OSB.
42.l.4 Fastener spacing
The number of fasteners is clearly one of the most significant factors affecting
shearwall performance under earthquake loading. The arrangement (spacing) of
fasteners also is important. These factors influence specific fastener failure modes
(i.e., which fasteners are worked hardest) as well as the overall energy dissipating
characteristics of the shearwall. Figures 4.7 through 4.10 show the effect of fastener
spacing on peak displacement with various assumed seismic weights, considering
BW1 and the life safety (LS, 1 0/5 0) limit state. A practical drift limit of 4 in. also is
shown on these figures. Based on the comparison of 6"/6" and 6"/12" nailing
schedules, field nailing schedule has little effect on the performance of shearwalls
compared to the effect of edge nailing schedule, particularly at higher values of
seismic weight (see Figures 4.7 through 4.10). Fastener spacing obviously is a
significant design parameter for woodframe shearwalis and will be treated as such in
the design charts developed in Section 4.3.2.
33
0.9
G
290
0.8
G=235ksL
';;/
0.7
G = 218 ksi
G=180ksN//
0.6
0.5
U-
______
7/
0.4
/1
0.3
________8ff
8ff.
//
0.2
BW1 (8 x 8), 8d3'I6",
OSB(3/8"),ED= /8",
/1
0.1
0
W5OkN,ç=2%,
/
[S (10/50)
n
0
0.5
2
1.5
1
2.5
3
(in)
Figure 4.6 Effect of assigned shear modulus (G) on peak displacement
S.
8d@4"/l
/
5;
I
I
8d@3"/12" ...
0.7
8d6"I6"
'
/
I
8d@6"/12"
I
0.6
:
'
/
0.5
//
0/
Lii
1i
0.4
/
0/I
I
0.3
/
I
0.2
,'o /
/
1
0.1
/
/
_J
It
0
0.2
8ff.
/
'>i
8ff.
BW1 (8' x 8'), OSB (/"), ED =
/
G=180ksi,=2%,LS(10/50),
',/
0
/
0.4
0.6
W = 560 lbs/ft (20 kN total)
0.8
1
1.2
1.4
1.6
ömax (in.)
Figure 4.7 Effect of fastener spacing on peak displacement (W = 560 lbs/fl)
34
0.9
8d©4"/12"
/
0.8
,, I
0.7
8d@fi2"
///
0.6
8d@3flhlr
0.5
0.4
I
0.3
/
0.2
/
0.1
8ft._Oft.
/ ,'//
,/
/
/
/
BW1 (8
8'), OSB
(3/),
ED =/8",
G=l8Oksi,ç=2%,LS(10/50),
W = 840 lbs/ft (30 kN total)
n
0
0.5
1.5
1
2
ömax
2.5
3
4
3.5
(in.)
Figure 4.8 Effect of fastener spacing on peak displacement (W = 840 lbs/ft)
/
0.9
8d@4"/12"
--
V
I
-
/
-
-.
I
-
--
0.8
8d©3"/12"
xr8d@6"/6"
0.7
0.6
/
0.5
U0.4
11/
0.3
j
II
/ /
0.1
,/
8ft.
,'/
I
/
0.2
,'g
/
'
V
BW1 (8' x 8'), OSB (/"), ED =
G = 180 ksi, = 2%, LS (10/50),
W = 1120 lbs/ft (40 kN total)
U
0
0.5
1
1.5
2
2.5
3max
3
3.5
4
4.5
5
(in.)
Figure 4.9 Effect of fastener spacing on peak displacement (W
1120 lbs/ft)
35
7
0.9
8d@4"/12"
0.8
/
8d@3"/12"/
0.7
0.6
Th'-i,/'
'1
/
/
I
0.5
U-
I
/
/
0.4
/
/
0.3
8d@6"/12"
//
'
,,
HI
// 1
0.2
__8ft.
f
,r /
/ / ,,
0.1
,
BW1 (8' x 8'), OSB (/8"), ED
G
/
180 ksi,
/8,
= 2%, LS (1 0/50),
W = 1400 lbs/ft (50 kN total)
-
n
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
6max (in.)
Figure 4.10 Effect of fastener spacing on peak displacement (W = 1400 lbs/fl)
4.2.1.5 Panel layout
Figure 4.11 shows the effect of sheathing arrangement on the peak
displacement distribution. The horizontal panel arrangement (with blocking) performs
better than the vertical panel arrangement. Despite having more fasteners, BW4
performs the least well because of the additional discontinuity in the sheathing and
hence reduced overall rigidity of the wall.
4.2.1.6 Shake-table test walls
The procedure described in Section 3.1 also can be used to construct peak
displacement distributions for walls that have been tested on a shake-table. This can
serve a number of purposes, among them (1) to validate the CASHEW model, and (2)
36
to provide information on expected shearwall response under dynamic loading. The
full-scale walls considered in Task 1.1.1 (UCSD) and Task 1.1.2 (UC- Berkeley) were
analyzed using this procedure. These walls were designed and built specifically for
shake-table testing under specific ground motions (and with specific seismic weights).
Figure 4.12 shows the three walls with the panel layouts. Figure 4.13 shows the peak
displacement distributions determined using the CASHEW modeling procedure for the
east and west walls tested in Task 1.1.1 and the rear wall tested in Task 1.1.2 (for two
different seismic masses, the smaller value corresponding to a post-retrofit condition).
The performance of the Task 1.1.2 rear wall (with retrofit) exhibits significantly lower
peak displacements, in part due to the reduction in seismic weight.
1
BW4
BW3
BW1
BW2
BW1
,
88.
8ft.
0.5
1/
U-
/1
7/
0.4
/
8ff.
8ff.
BW3
BW4
88.
8ft.
0.3
0.2
8d©3"16", OSB (I8"), ED =18',
G = 180 ksi, ç = 2%, LS(10150),
I/,,L
0.1
W = 840 lbs/ft (30 kN total)
0
0
0.5
1
1.5
2
2.5
ömax (in.)
Figure 4.11 Effect of panel layout on peak displacement
3
3.5
4
37
96n.
in
32in. 46in.
36in.
46in.
32in.
192 in.
I 03r\,
I. I.
Task 1.1.1 West Wall
I L.QL VVGIII
in.
I
asK 1.1.2 Kear Wall (Norm Wan)
Figure 4.12 Task 1.1.1 and task 1.1.2 walls
0.9
/
0.8
I
0.7
/
Task 1.l.1 west Wall
W = 82(t) lsIft (58.4 kN tota9-4
OSB, G
,V
-
180 ksi,
/ task 1.1.1 East Wall
/ / W = 856 lbs/ft (58.4 kN total)
/
/
lbs/ft (1 7.8kN tl)
/
__Task 1.1. Rear Wll
O.5
w = ii od
OSB, G = 180 ksi, 8d@3"/12"
PWD,GF6Oksl,8d 4I1,
0.4
With Retfofit
,'
0.3
/ / Task 1.1.2 Rear Wall
// /
/
W=22171bs/ft(315.SkNtotal)
PWD, G
60 ksi, 8d@4"/12"
0.2
/
0.1
-
7"
ED
C'
3/,
/8, t
= 2%, LS (10/50)
-
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
max (in.)
Figure 4.13 Peak displacement distributions for task 1.1.1 and task 1.1.2 walls
4.2.1.7 Missing fasteners
As a preliminary study to investigate the effect of construction tolerances
(errors), the effect of missing fasteners was investigated using the CASHEW modeling
procedure. Such issues of construction quality are thought by some to significantly
affect the performance of woodframe assemblies, particularly under dynamic loading
[Seible et al., 1999]. Using BW3, the effect of missing fasteners or fastener lines in
critical locations is investigated. The results are shown in Figures 4.14 through 4.16
for the three limit states (immediate occupancy, life safety and collapse prevention),
respectively. While certainly not a comprehensive study, the results in these figures
provide some indication of the relative importance of ensuring the design fastener
schedule on the shearwall performance. Notice that while the nail along the sole plate
has a significant effect on performance, the fact that overturning anchors are present
reduces the effect of missing nails since the sole plate nails only resist wall racking
forces. Further discussion of construction tolerance issues is provided in Section 4.2.4.
39
1
0.9
d@3"16" [2M]
8c3 '/6" [4M]
8d3"/6" [3M]
8d©/6 MM]
0.7
/
8d©3"/è"
/
0.6
0.5
3/6" baseline wall nail pattern
ElM] missing left side vertical nail line in S1
[2M] missing horizontal blocking at mid-height
[3M] missing every other nail along sole plate
[4M] missing entire nail line along sole plate
,'
//
I-I-
/
0.4
Iii
1s21s31
,"
0.3
J
/
SI
(0
0)
,,
0.2
I
I
86.
II
III
0.1
/
BW3 (8'
I
0
'
ED=3/8"
8'), 8d@3"/6", OSB
x
(/8"),
G=180ksi,=2%, 10(50/50),
W = 1400 lbs/ft (50 kN total)
nt
0
0.5
2
1.5
1
max
(in.)
Figure 4.14 Effect of missing fasteners on peak displacement (JO, 50/50)
-- --------"0.9
-
8d©3"/6" [2M]
8d@3"16" [4M}
0.8
-,
8d@3"/6" [3M]
0.7
8d@3"/6" MM]
8d@3"16"
0.6
k, I
/
/
L"/6" baseline wall nail pattern
[1 M] missing left side vertical nail line in S1
[2M] missing horizontal blocking at mid-height
I[3M] missing every other nail along sole plate
missing entire nail line along sole plate
0.5
I
U-
0.4
I
0.3
Is3
I
I
I//'
0.2
s
186.
ci
I
Si
I
I
I
I
811.
0.1
BW3 (8' < 8'), 8d@3'/6", OSB (3/s),
ED = /8", G = 180 ksi, = 2%, LS (10/50),
W = 1400 lbs/ft (50 kN total)
0
U
0
0.5
1
1.5
2
ömax
2.5
3
3.5
(in.)
Figure 4.15 Effect of missing fasteners on peak displacement (LS, 10/50)
4
1
0.9
8d@3"16" [2M
0.8
/
8d©3"/6" [4M]
8d@3"/6" [1M]
0.7
8d©3"16"
//
0.6
8d©3"/6" [3M]
0.5
/
// /
U-
/
0.4
/
36",taseline wall nail pattern
,,11M missing left side vertical nail line in S1
[2MJ missing horizontal blocking at mid-height
J1M] missing every other nail along sole plate
, [4M] missing entire nail line along sole plate
r
//,','
//
0.3
S2S3
8ft.
S1
//
0.2
/ // -/
0.1
0
0.5
1
1.5
'
BW3 (8 > 8), 8d@3"16", OSB (3/),
G = 180 ksi, ç = 2%, CP (2/50),
ED =
W 1400 lbs/ft (50 kN total)
2
2.5
3
3.5
4
4.5
5
5.5
6
max (in.)
Figure 4.16 Effect of missing fasteners on peak displacement (CP, 2/50)
4.2.1.8 Model uncertainty
The numerical model (CASHEW) contributes to the epistemic uncertainty in
the analysis. This uncertainty arises from modeling assumptions and simplifications,
either idealizations or approximations. One example is the assumption in CASHEW of
rigid tie-downs. Model uncertainty should therefore account for variations in (or
perhaps lack of) anchorage. While it is expected that this uncertainty and its effect on
dynamic response would be greater than some of the physical parameters such as
fastener hysteretic parameters and sheathing properties, it is not obvious how it would
compare to the effect of variability in the ground motions (seismic hazard). Model
uncertainty often is taken into account using an error term (s), such that X* =
where X = model predicted response (a random variable) and X = the random
41
response taking into account model uncertainty. The model error term, s, can be
modeled as a random variable. (If both and X are lognormal variables, then X also is
lognormal.)
In order to determine moments of the model error term, it is necessary to have
a series of full-scale test results to which model predictions can be compared. (Note
that additional uncertainty is introduced in moving from actual field construction to
laboratory test conditions). Only limited full-scale test results are presently available
for which direct comparisons can be made to model predictions using CASHEW.
However, since the Durham fastener parameters for the spiral nail (see Section 4.2.2)
were used in this part of the study, the model predictions obtained using CASHEW
can be compared with the full-scale wall tests conducted by Durham (1998). Folz et al.
(2001) presented a comparison of these results considering peak displacement under
both a cyclic loading protocol and the Landers earthquake. The results suggest an
"error" term having a mean of about 1.0 and a COV between 15% and 30%,
depending on how many peaks in the Landers analysis are used in the comparison
[Rosowsky and Kim, 2002]. Lognormal parameters (2w, ) can be determined using the
method of moments.
To examine the effect of model uncertainty on the dynamic response, one
could compare peak displacement distributions, as done previously. The relative
contribution of the model error also could be evaluated by considering its effect on the
peak displacement distribution parameters. Since a lognormal distribution is fit to the
peak displacements obtained using a suite of 20 scaled ordinary ground motion
42
records, the modified distribution, taking into account the model error term, is given
by F (4= s x F (4. The lognormal parameters (2, ) for the modified distribution
F; (x) are given by:
=
+
(4.1)
(4.2)
Figure 4.17 shows the effect of model uncertainty on the peak displacement
distribution for BW1, for LS (10/50) and Figures 4.18 through 4.22 show the effect of
including these error terms on the peak displacement distributions for various nail
spacings and two seismic weights. The effect of including the model uncertainty
(error) diminishes as the response variability increases, e.g., for large nail spacings
(see Figures 4.21 and 4.22). In that case, the response variability is completely
dominated by the variability in the seismic hazard (i.e., the suite of ground motion
records). The model error may be significant, however, for peak displacement
distributions having less variability, such as those with tighter nail spacings. Note that
these steeper distributions (lower variability) are typically seen at lower values of peak
displacement, i.e., for walls that would meet the FEMA 356 peak drift criteria with
high probability. In these cases, the uncertainty introduced by model error may be on
the same order of magnitude as the response variability arising from the suite of
ground motions.
The effect of model error associated with the CASHEW program may be
significant. The model error also may not be uniform over all displacement ranges
(i.e., degree of nonlinearity). This is a potentially significant source of uncertainty and
43
should be studied further, prior to the development of final design recommendations.
This will require additional comparisons between full-scale tests and CASHEW model
predictions. Results from tests such as those conducted at UCSD (Task 1.3.1) and UC-
Irvine (Task 1.4.4) could be useful in this regard. Consideration also could be given to
the differences between laboratory tests and actual field conditions. This also could be
taken into account through a model error term.
1
S.
8d@3"/6" (COV=0%)
0.8
8d@3"16" (COV=15%)
fN
0.7
8d@3"16" (COV=30%)
[SIr
0.5
U-
0.4
8ff.
0.2
BW (8 x 8'), 8d@36", OSB (3/.),
0.1
ED = /8, G = 180 ksi,
= 2%,
W = 1400 lbs/ft (50 kN total), LS (10/50)
0
0.5
1
1.5
2
2.5
3
3.5
ömax (in.)
Figure 4.17 Effect of model uncertainty on peak displacement distribution
4
0.9
:IT2lbS/ft (40 kN total)
0.8
8d3"/6" (COV=0%)
8d©3"/6' (COV=15%)
8d@3"/6" (COV=30%)
0.7
0.6
W = 560 lbs/ft (20 lN total)
8d@3"/G" (COV=0°(o)
8d@3"/6" (COV=15%)
8d@3"/6" (COV=30%)
LL
0.4
0.3
811.
C)
0.2
811.
OW (8'>< 8'), 8d@3'I6",
0.1
OSB(3/e"),ED=3/8",=2%,
G = 180 ksi, LS (10150)
n
0.5
0
1.5
1
max
2.5
2
3
(in.)
Figure 4.18 Effect of model uncertainty on peak displacement (3"/6")
0.9
//YN
II'
1/"
0.8
I;
'N
0.7
8d@3"/1" (COV=0%)
8d@3"/1" (COV=15%)
//'
8dQ3"/1"
N.J'
0.6
W = 1120 lbs/ft (40 kN total)
,TN W = 560 lbs/ft (20 N total)
0.5
8d@3"/12" (COV=Ø%)
8d©3"/12" (COV=15%)
'J
"I
0.4
8d@3"/12" (COV=0%)
0.3
_8ft.
0.2
0.1
,'
'
/1
OW (8' x 8'), 8d@3"112",
OSB(3/8"),ED=3/8",=2%,
/
= 180 ksi, LS (10/50)
-
0
0
0.5
1
1.5
max
2
2.5
(in.)
Figure 4.19 Effect of model uncertainty on peak displacement (3"/12")
3
45
1'
0.9
W=ll2Olbs/ft(4okNtotal)
,//'
0.8
8d©4"/12"(COV=0%)
8d@4"/12" (C0V15%)
8d@4"/12" (C0V30%)
/'
II:
0.7
W = 560 IbIft(20 kN1 total)
0.6
8d@4"/l 2'COV=0°/)
8d©4"/12Y(COV=15%)
(COV=30/0)
8d@4"f
o.5
:1
0.4
0.3
8ft.
0.2
j
0.1
/
BW (8' x 8), 8d©4"/12", OSB (/8")
ED = /8, G = 180 ks
= 2%, LS (1 0/50)
1)
0
0.5
1.5
1
2.5
2
max
3.5
3
4
(in.)
Figure 4.20 Effect of model uncertainty on peak displacement (4"/12")
0.9
(//
0.8
W=5601bs/ft(20kNtotal)
8d@6"I6" (COV=0%)
8d©6"/6" (COV=15%)
8d@6"/6"
1120 lbs/ft (40 kN total)
0.7
0.6
0.5
0.4
0.3
811.
0.2
8L
0.1
BW (8' x 8'), 8d@6"/6", OSB (3/),
ED = /8", G = 180 ksi,
= 2°I, LS (10/50)
r)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
6max (in.)
Figure 4.21 Effect of model uncertainty on peak displacement (6"/o")
5
- - -
0.9
'VV = 560 lbs/ft (20 kN total)
/,' 8d@6"12" (COV=0%)
8d@6"/12"
0.8
8d©6"12" (COW39%'o) W =
0.7
/
/
0.6
1120 lbs/ft (40 kN total)
8d@6"/12" (COV=0%)
8d@6"/12" (COV=15%)
8d©6"/12" (COV=30%)
0.5
HY
0.4
0.3
0.2
8ft.1
0.1
BW (8 x 8), 8d©6"/12", OSE (/8"),
ED = '8, G = 180 ks,
= 2%, LS (10/50)
n
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
max (in.)
Figure 4.22 Effect of model uncertainty on peak displacement (6"/12")
6
47
4.2.2 Sheathing-to-framing connection hysteretic parameter variability
As part of Task 1.4.8.1 of the CUREE-Caltech Woodframe Project (CCWP), a
database of sheathing-to-framing connection hysteretic properties was developed for a
wide range of fastener types, sheathing materials, and boundary conditions. Once
validated, this database can provide valuable information for the development of
performance curves and design charts (discussed later in Section 4.3.2) for a broad
range of structural types. For the purposes of this study, however, the fastener
parameters (see Table 4.1) provided by Durham (1998) for an spiral nail and by Folz
(2001) for an 8d box nail were used. (Additional parameters from Dolan (1989) also
will be used later.)
The Durham parameters were obtained from tests of 3/8-In. OSB sheathing,
having an assigned shear modulus of 218 ksi, attached to nominal 2 in. x 4 in. framing
members with pneumatically-driven 2 in. long spiral nails. The Folz parameters were
obtained from tests of 3/8-in. OSB sheathing, attached to nominal 2 in.
x
4 in. framing
members with pneumatically-driven 8d box gun nails. Table 4.1 shows the sheathingto-framing connection hysteretic parameters obtained from the experimental studies by
Durham (1998) and Folz (2001). Further information on these hysteretic model
parameters may be found elsewhere [Durham, 1998; Fischer et al., 2001; Folz and
Filiatrault, 2000, 2001].
Nail
K0
r2
r1
r3
r4
F0
a
F1
J
DurhamW
spiral
Folz°
8d box
gun
I
I
3.203
kips/in
4.87
kips/in
I
0.061
-0.078
I
1.40
I
0.049
-0.049
0.143
I
1.40
0.015
0.169
kips
0.180
kips
I
I
0.032
kips
0.042
kips
0.492
I
I
in.
0.50
in.
0.8
1.1
0.8
1.1
I
Table 4.1 Sheathing-to-framing connection hysteretic parameters
(1)
Values obtained by Durham (1998). Fasteners were 2 in. long, power-driven spiral nails attaching iin. OSB to framing members.
(2)
Values obtained by Folz (2001). Fasteners were 8d box gun nails attaching 3/8-in. OSB to framing
members.
(3)
Protocol did not include cyclic behavior near the ultimate capacity of the wall, resulting in
unrealistically high values of r4 compared to other studies. Therefore, the value of r4 was changed in this
study to 0.05 (see Folz and Filiatrault, 2000).
Selected data from other studies were considered in order to investigate the
contribution of fastener parameter variability on performance (peak displacement) of
shearwalls. First, a comparison was made between results obtained using the Durham
and Folz nail data and comparable sets of parameters developed in the CCWP Task
1.4.8.1
(see Table 4.2). Fonseca
et al.
(2002) obtained sheathing-to-framing
connection hysteretic parameters for numerous connection types and compiled a
database. This database was used in the sensitivity studies to investigate the variability
of sheathing-to-framing connection hysteretic parameters. Several parameters were
considered in that study such as sheathing types and nail types, sheathing panel
direction (perpendicular and parallel), edge distances, and the effect of overdriven
nails; however only Douglas Fir-Larch (DF-L) framing lumber was used. Testing was
conducted using the simplified basic loading history developed in Task 1.3.2 of
CCWP [Krawinkler et al., 2000]. Ten specimens were tested for each combination of
parameters. Sampling was done at a rate of 20 points per second, and ten hysteretic
parameters (for use in CASHEW) were determined for each specimen tested. Also
shown in this table are the parameters obtained by Dolan (1989) for a comparable
plywood product.
Institutions
Parameter
K0
Units
lups
'In
r1
r2
Durham'
Folz2
IJBC
IJCSD
/8" OSB
/8" OSB
'8 OSB
3.2034
4.8700
2.9746
3.5898
4.0341
5.1791
0,0610
-0.0780
0,0490
-0.0490
1.4000
0.0150
0.0150
0.1800
0.0420
0.5000
0.8000
1.1000
0.0740
-0.0774
2.4933
0.0724
0.0724
0.1344
0.0418
0.2502
0.6000
1.1000
0.1099
-0.1459
1.6240
0.1363
0.0500
0.1229
0.0431
0.1385
0.6000
0.1220
-0.0753
1.3495
0.1334
0.0700
0.1318
0.0442
0.1573
0.6000
1.1000
0.0496
0.0595
1.4000
0.0265
0.0265
r3
1.4000
r4
0.1430
0.0500
0.1688
0.0317
r4
F0
F1
jp_
kips
in
a
0.4921
0.8000
1.1000
Task 1.4.8.1 (Fonseca et. al.,)3
BYU
3/8"OSB
3/8"OSB
Dolan4
UBC
Plywood
1.1000
0.2271
0.0409
0.3150
0.8000
1.1000
Table 4.2 Comparable connection hysteretic parameters from other studies
Values obtained by Durham (1998). Fasteners were 2 in. long, power-driven spiral nails attaching iin. OSB to SPF framing members.
2)
Values obtained by Folz (2001). Fasteners were 8d box gun nails attaching 3/8-in. OSB to framing
members.
Fastener hysteretic parameters (average values shown) obtained by Fonseca (2001). Fasteners were
8d common nails attaching 3/3-in. OSB to DFL framing members. Loading was perpendicular to the
grain. Three different OSB manufacturers were considered.
(4)
Fastener hysteretic parameters (average values shown) determined using results obtained by Dolan
(1989). Fasteners were 8d common nails attaching 3/g-in. plywood to SPF framing member, 3/8-in, edge
distance, loading perpendicular to grain.
Values of r4 changed per Note 3 in Table 4.1.
3)
Figures 4.23 through 4.26 present a comparison of peak displacement
distributions for the Durham OSB data set (spiral nail), the Folz OSB data set (8d box
gun nail) and the three BYU (Task 1.4.8.1) OSB data sets (8d cooler nail) with various
assumed seismic weights and considering the life safety (10/50) hazard level. The
baseline 8 ft. x 8 ft. solid wall (BW1) with two sheathing panels oriented vertically
and a 3"/l 2" (edge/field) fastener schedule was considered. The sample distribution
functions in these figures provide some indication as to the relative sensitivity of
50
results to assumed fastener parameters, which increases dramatically for larger
demands (seismic weights). The peak displacement curve developed using the Durham
nail parameters (spiral nail) generally is close to the median of the peak displacement
distributions throughout the range of seismic weights considered. This median peak
displacement curve will be used to develop a modification factor for sheathing-toframing connection hysteretic parameter variability in Section 4.3.1.1.
/,
1
8d cooler nail_3
8d box nail
'
/
/'/
I
/:
/
/'
,,
/
/
8d cooler nail_i
8d cooler nail 2
8d spiral nail
/
0.5
!,," // /
0.4
// // /
0.3
0.2
8ft
/,," // /
,/'//
0.1
8 ft.
BW(8'
8'), 8d©3"/12", OSB (/"),
ED318",G
l8Oksi,ç2%,
W = 560 lbs/ft (20 kN total), LS (10/50)
ii
0
x
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
6max (in.)
Figure 4.23 Comparison of peak displacement distributions for different nail
parameters (W = 560 lbs/ft)
51
-
/7,',
0.9
8d cooler nail 3
0.8
/ ,'
,7'
8d box nail
8d cooler nail_i
8d cooler nail 2
8d spiral nail
// /
/
/
0.7
0.6
,f/
/ //
0.5
LL
/ //
0.4
///
':
0.3
18ft
0.2
/ //
!'
//
/,'
0.1
8ft.
//
/
BW (8
x
8'), 8d@3"/12", OSB (/"),
ED=3/8",G=l8oksi,ç=2%,
W = 840 ibs/ft (30 kN totai), [S (10/50)
n
0
0.3
0.9
0.6
max
1.2
1.5
(in.)
Figure 4.24 Comparison of peak displacement distributions for different nail
parameters (W = 840 lbs/ft)
0.9
0.8
/,7
8d spiral nail
8d cooler nail 3
8d box nail
0.7
/7
/
//
8d cooler nail_i
8d cooler nail 2
//
0.6
H,
0.5
U-
0.4
/
/
0.3
/
8ft.
0.2
BW (8
x
8), 8d3"/12",
OSB(3/8"),ED= /8',
0.1
/,,
G=180ksi,=2%,
/I//
W = 1120 ibs/ft (40 kN totai),
LS(10/50
n
0
0.5
1
1.5
6max (in.)
2
2.5
3
Figure 4.25 Comparison of peak displacement distributions for different nail
parameters (W = 1120 lb s/ft)
52
1
0.9 8d cooler nail 3
0.8
8d box nail
8d cooler naiL 2
0.7
I
8d spiral nail
0.5
U-
0.4
0.3
/
8ft.
,,///
0.2
8L.
BW1 8' x 8'), 8d@3'/12", OSB (/"),
0.1
ED = /", G = 180 ksi. LS (10/50),
W1400 lbs/ft (50 kN total),
0.5
1
1.5
2
2.5
3
3.5
= 2%
4
max (in.)
Figure 4.26 Comparison of peak displacement distributions for different nail
parameters (1N = 1400 lb s/ft)
Next, variability among parameter sets was investigated. Since many of the
fastener hysteretic parameters are strongly correlated, it is not possible to explicitly
consider the effect of individual parameter variability on the predicted shearwall
response. Instead, the results from the individual connection tests are considered as
sets of parameters. That is, rather than using the average values (obtained by averaging
the results from 10 individual tests per series), the hysteretic parameters fit to each
individual connection specimen are considered. The peak displacement distribution
results can be compared to those obtained using the average values, thereby providing
some indication of the relative contribution of fastener parameter variability. This was
done using the 3/g-in. OSB MFG1 data set from Task 1.4.8.1 (see Table 4.2). The
results are shown in Figure 4.27 for the LS (10/50) limit state, and assuming 4496 lbs,
53
6744 ibs, and 8992 lbs seismic weights. Note that only five curves are shown (in
addition to curve obtained using the average values) for each seismic weight.
CASHEW could not provide a convergent solution for the other five sets of
parameters. Whether this suggests a lack of robustness of the CASHEW program or a
problem fitting the test data obtained in Task 1.4.8.1 (there are still questions
regarding edge distance effects in this data, for example) remains to be determined.
Still, the limited results shown in Figure 4.27 provide some insight into the relative
contribution of fastener parameter variability to the predicted response. The peak
displacement distribution could be modified by a factor to account for fastener
parameter variability. For example, one could apply a factor to the logarithmic mean
value, denoted by 2, to adjust the median response. Alternatively, a positive factor
could be applied to the logarithmic standard deviation, denoted by E, to adjust the
uncertainty in the response. This is conceptually similar to the treatment of model
error, which is discussed in Section 4.2.1.8.
For the remainder of this study, the sheathing-to-framing connection hysteretic
parameter sets obtained by Durham and Folz for 3/8-in. OSB, and determined from
data obtained by Dolan for 3/8-in. plywood, are used without further consideration of
fastener parameter variability. (Note that the fasteners are different; see Table 4.3.)
54
Nail type
8d box gun nail
Spiral nail
8d cooler nail
8d common nail
Test location (investigator)
UCSD (Folz)
UBC (Durham)
BYU (Fonseca et al.)
Length (in.)
Shank diameter (in.)
21/2
0.113
2
0.105
2/
0.113
2'/2
0.131
UBC(Dolan)
'lable 4.3 Nail properties considered in this study
1
[ /
/(
0.9
0.8
0.7
W=1120 lbs/ft
I//I
W= 840 lbs/ft
total)
(30
0.5
/1!
U-
W = 560 lbJ/ft.
(20 kN
0.4
total?
0.3
I//I '.
0.2
8 ft.
/
88.
0.1
J
n
0
BW1 (8 >< 8), 8d@3 /6, OSB
/,.'
0.5
1
1.5
(/8
ED=318",G=l8Oksi,1=2%,LS(1O/50)
CN
2.5
2
max
3
3.5
(in.)
Figure 4.27 Effect of fastener parameter variability on peak displacement
4
4.2.3 Contribution of nonstructural finish materials
Woodframe structures are built with a wide variety of architectural finishes on
the walls. Two of the most common wall finishes in woodframe structures are gypsum
wallboard and stucco (Portland cement plaster). Modern structures usually rely upon
OSB or plywood shearwalls for lateral strength. They are seldom the final surface of
the wall and are usually covered with either gypsum wallboard or stucco (Portland
cement), for both appearance and fire resistance [McMullin and Merrick, 2001].
Finish materials such as stucco or gypsum wallboard usually are not
considered to have significant structural capacities and thus are neglected in design.
However, results from both the shearwall tests and the full-scale shake-table tests
conducted as part of Element 1 of the CUREE-Caltech Woodframe Project (CCWP)
suggest the presence of stucco, albeit under fairly ideal conditions (i.e., well applied,
uncracked, undamaged by moisture or other environmental actions), may be beneficial
from the standpoint of performance (drift). In the case of shearwalls, a well applied
stucco layer has the effect of making the sheathing panels perform as a single rigid
body. In the case of the full-scale structures, the stucco has the additional effect of
providing shell action around corners. The result in both cases is substantially reduced
drifts. Recent studies also indicate that the presence of finish materials in shearwalls
decreases deflection capacity and increases strength and initial stiffness [Gatto and
Uang, 2002]. Also, stucco applied to the sheathing panel appears to restrain sheathing
nail withdrawal and partially restrain nail head rotation [Cobeen, 2001]. This further
suggests the effect of finish materials such as gypsum wallboard and stucco may
56
indeed be significant and should be considered in developing performance-based
design guidelines. A cross-section of a typical wood shearwall with nonstructural
finish (NSF) materials is shown in Figure 4.28.
Gypsum wallboard
Framing member
OSB or Plywood
Stucco
Figure 4.28 Typical exterior wall cross-section
It is difficult to use CASHEW to account directly for the behavior of
nonstructural finish materials such as stucco and gypsum wallboard since it may not
be possible to determine a particular nailing schedule and shear modulus that can
capture the performance of the nonstructural finish materials. Therefore, the results of
three recent experimental tests of wall with nonstructural finish materials were used to
investigate this issue using SASHFJT rather than the CASHEW modeling procedure.
The three experimental testing programs were taken from: (1) CCWP Task 1.3.1, (2)
CCWP Task 1.4.4, and (3) the CoLA test program [Gatto and Uang, 2002; Pardoen
57
et.al., 2001, 2002]. These tests results were used to capture the global shearwall
hysteretic parameters using the visual best-fit program SASHFIT. The material
combinations and test programs considered are summarized in Table 4.4.
Project
CUREE
1.3.1
Sheathing materials + NSF
OSB (3/)
OSB (I8") +
OSB (/8") +
PWD (15/)
PWD (15/)
(15/)
PWD
GWB ('/2")
Stucco (/8")
1.4.4
CoLA
OSB (/8")+ Stucco ("8")
OSB (3/8")+GWB ('/2") + Stucco (/8")
OSB (3/)
OSB (/8") + Stucco (/8")
OSB (/8") + GWB ('/2") + Stucco (/8")
PWD (3 ,' )
PWD (/8") + GWB ('/2")
PWD (/8") + GWB ('/2", 2 sides)
Loading
protocol
solid wall
(8 ft. x 8 ft.)
+ GWB ('/")
+ Stucco (/8")
_OSB (/8")
CUREE
Shearwall
wall with garage
door opening
(16 ft. x 8 ft.)
wall with pedestrian
door opening
(16 ft. x 8 ft.)
solid wall
(8 ft. x 8 ft.)
CUREE
SPD'
Table 4.4 Matrix of walls used to investigate nonstructural finish material effects
(1)
Sequential phased displacement loading protocol
4.2.3.1 Analysis of solid wall
Results from two experimental test programs (CUREE Task 1.3.1 and CoLA)
were used to investigate the performance of an 8 ft.
x
8 ft. solid shearwall with
nonstructural finish materials. The test programs considered the same shearwall
configuration, nailing schedule, and sheathing materials. The test data were obtained
from the CUREE (Task 1.3.1) and CoLA testing program. Each shearwall
configuration was tested two or three times in these programs. Only the worst case
results for each shearwall configuration were selected to study NSF materials effects
on the performance of the isolated solid baseline shearwall, BW1 (8 ft. x 8 ft.). Two
sheathing material types, 3/g-in. OSB and 15/32-in. plywood, were used in Task 1.3.1
and
3/8-In.
plywood was used
in
the CoLA tests. The fastener schedules were 4"112"
(edges/field) with a double row at the end studs for the Task 1.3.1 and 4"/12" for the
CoLA tests. Both tests had the same thickness of nonstructural materials: Y2-in.
gypsum wallboard and 7/8-in, stucco. The material properties of the stucco and gypsum
wallboard are found elsewhere [Gatto and Uang, 2002; SEAOSC, 2001].
The peak displacement curves showing the effects of NSF materials are shown
in Figures 4.29 through 4.32 for various assumed seismic weights. As expected, NSF
materials greatly enhance the performance of shearwalls. In particular, the presence of
stucco serves to greatly reduce peak wall displacement. Figures 4.33 and 4.34 also
show the effect of two-sided gypsum wallboard on shearwall behavior. The use of
gypsum wallboard on both sides of the wall, as is done for interior partition walls, is
considerably more effective than one-sided GWB.
59
0.9
0.8
PWD+Stucco1
OSB
PWD
,
OSB+GWB
,'
OSB + Stucco
--/
0.7
PWD + GWB
/
0.6
0.5
LL
/
I
0.4
/
/
0.3
/
/.
0.2
/
BW (8'
0
0.2
8', 8d@4"/12",
2%,
GWB (/2'), Stucco (I8"),
W = 560 lbs/ft (20 kN total), LS (10/50)
/_,' /
0.1
OSB (/"), PWD
0.4
(15/..)
0.6
max
0.8
(in.)
Figure 4.29 Effect of nonstructural finish materials on peak displacement (W 560
lbs/fl)
-----
:
0.9
0.8
n:::::
0.7
OSB + Stucco
*EX
,:'T T,/<: + GWB
OSB
0.6
0.5
0.4
/
0.3
/1//
0.2
,' :,/
/
/
/
,'/ /
/1
8ft.
8ft.
,/
/
0.1
',,
n
0
0.2
0.4
0.6
BW (8' x 8'), 8d@4"/12", = 2%,
(3/),
OSB
PWD (/32"), GWB (l/2) Stucco
W = 840 lbs/ft (30 kN total), LS (1 0/50)
0.8
1
1.2
(7/),
1.4
1.6
6max (in.)
Figure 4.30 Effect of nonstructural finish materials on peak displacement
lhs/ft)
(W=1
840
0.9
OSB+GWB-
..,
0.8 PWD + Stucco
0.7
PWDGWB
OSB + Stucco
PWD
OSB
1/
0.6
/i
0.5
0.4
;':/°
8ft
4I
0.3
8ft.
0.2
*
BW (8 x 8), 8d@4"/12",
OSB (/8"), PWD (15/32),
GWB (/2"), Stucco (/8"),
= 2%, LS (10/50),
W = 1120 lbs/ft (40 kN total)
0.1
it
0.5
0
1.5
1
2.5
2
3
ömax (in.)
Figure 4.31 Effect of nonstructural finish materials on peak displacement (W= 1120
lbs/ft)
OSB+GWB/ ,,'
0.9
0.8 PWD+Stucco
OSB+Stucco'
0.7
PWD+GWB
4'-'
k
0.6
0.5
0.4
//,,,,, //
0.3
8 ft.
0.2
I,
0.1
I,
'/ //
= 2%,, LS (10/50)
OSB (3/), PWD (15/32W), GWB (1/2)
BW (8 x 8), 8d@4'112",
/,,./
Stucco (7/), W = 1400 lbs/ft (50 kN total)
It
0
0.5
1
1.5
2
2.5
3
3.5
4
6max (in.)
Figure 4.32 Effect of nonstructural finish materials on peak displacement (W= 1400
lbs/ft)
61
1
0.9
:/
0.8
0.7
PWD
PWD+GWB
7
0.6
PWD GWB (both sides)
I.
0.5
0.4
0.3
0.2
//
7
0.1
,'
_J'
C)
0
0.1
0.2
0.3
0.4
SW (8' x 8), 8d@4"/1 2",
= 2%,
PWD (/"), GWB (1/2), LS (10/50)
W = 840 lbs/ft (30 kN total)
0.5
0.7
0.6
0.8
0.9
1
ömax (in.)
Figure 4.33 Effect of nonstructural finish materials on peak displacement (W= 840
lbs/ft)
0.9
0.8
/PWD
0.7
PWD+WB
0.6
/
0.5
U-
PWD + GWB (both sides)
0.4
/
0.3
0.2
'
/
/
/
80.
BW (8' x 8'), 8d@4'/12",
/
0.1
)=2%, LS(10/50)
W = 1400 lbs/ft (50 kN total)
1)
0
0.5
1
1.5
max
2
2.5
3
(in.)
Figure 4.34 Effect of nonstructural finish materials on peak displacement (W= 1400
lbs/ft)
62
4.2.3.2 Analysis of walls with openings
Two types of shearwalls with openings were considered, both 8 ft. high
x
16 ft.
long, one having a garage door opening and the other having a pedestrian door
opening. Both walls had vertically oriented sheathing at the ends and a solid header
over the opening, and were tested under Task 1.4.4 of the CUREE-Caltech
Woodframe Project (CCWP). As before, only the worst case results for each shearwall
configuration were selected from the CUREE Task 1.4.4 experimental test results to
investigate the contributions of NSF materials for walls with openings. The walls had
3/8-in. OSB, ½-in, gypsum wallboard, and 7/8-in. stucco. The nailing schedules
(edge/field) were 3"/12" for the wall with the garage door opening and 6"/12" for the
wall with the pedestrian door opening. The material properties of the stucco and
gypsum wallboard are given by Pardoen et al. (2003).
Figures 4.35 and 4.36 show the NSF material effects on the performance of the
wall with the large garage door opening for various assumed seismic weights. As with
the solid wall, NSF materials are seen to contribute significantly to shearwall
performance. The effects of NSF materials on peak displacement of the wall with the
pedestrian door opening are shown in Figures 4.37 and 4.38. As was seen in the wall
with the large garage door opening, NSF materials serve to reduce the peak wall
displacement.
63
/*
/x
0.9
OSB
/
i/i
/
0.8
OSB + Stucco
/
0.7
OSB + GWB + Stucco
0.6
/ ,/
0.5
U-
I
0.4
0.3
H8ft
H
0.2
OW(i36X8adq/122
0.1
W = 281 lbs/ft (20 kN total),LS (10/50)
U
0
0.2
0.6
0.4
0.8
1
max (in.)
Figure 4.35 Effect of nonstructural finish materials on peak displacement (W= 281
lbs/ft)
0.9
OSB
0.8
OSB + Stucco
0.7
OSB + GWB + Stucco
/(
0.6
0.5
0.4
A' /
0.3
H16 ft.
-
0.2
H
8 ft.
OW (16 x 8'), 8d@3"/12",
=2%,LS(10I50)
OSB (/8"), GWB (1/2)
Stucco (/8),
W = 703 lbs/ft (50 kN total)
0.1
(1
0
0.5
1
1.5
2
2.5
3
max (in.)
Figure 4.36 Effect of nonstructural finish materials on peak displacement (W= 703
lbs/ft)
0.9
/
OSB+Stucco
0.8
,'QSB + GWB + Stucc
OSB
0.7
0.6
/
0.5
U-
/
0.4
0.3
0.2
+
I'
0.1
OW (16' x 8'), 8d6"/12", ç = 2%,
/
OSS (/"), GWB (/2), Stucco
(/8"),
W = 703 lbs/ft (50 kN total),LS (10/50)
('I
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
6max (in.)
Figure 4.37 Effect of nonstructural finish materials on peak displacement (W= 703
lbs/ft)
0.9
OSB + Stucco
/bSB + GWB
0.8
0.7
OSB
0.6
0.5
U-
0.4
0.3
H H
0.2
H8ft.
16ff.
OW (16' x 8'), 8d6"/12", ç = 2%,
0.1
OSB (/8"), GWB (/2"),
Stucco (/"),
W = 984 lbs/ft (70 kN total),LS (10/50)
n
0
0.5
1
1.5
2
2.5
3
3.5
4
ömax (in.)
Figure 4.38 Effect of nonstructural finish materials on peak displacement (W 984
lbs/ft)
65
4.2.4 Construction quality
While construction quality issues (specifically, missing fasteners) were
addressed in a very cursory way in the sensitivity studies in Section 4.2.1.7, there are a
number of other construction quality issues which could significantly influence overall
shearwall behavior. Among these are missing or misplaced fasteners and anchors,
deterioration of structural and nonstructural finish materials, improper selection of
fasteners, under-driven or over-driven fasteners, missing blocking, the use of smaller
panel segments, cutouts in framing members (e.g., for installation of conduit), and so
forth. Wood structures may deteriorate with time. In addition to natural aging, walls in
woodframe structures may be subject to severe environmental conditions such as
moisture absorption and fungus attack. A number of such durability issues could
significantly impact the dynamic behavior of fasteners and woodframe assemblies.
Isoda et al. (2002) developed numerical models for deterministic nonlinear
time-history analyses of four index woodframe buildings (small house, large house,
small town house, and apartment building). The required input parameters for the
shearwalls in the index buildings were developed using the CASHEW program and
available experimental test data [Folz and Filiatrault, 2000; SEAOSC, 2001]. The
walls in the four woodframe buildings included nonstructural finish materials such as
gypsum wallboard and stucco. Three categories of construction quality were
considered for each of the index woodframe buildings: superior quality, typical
quality, and poor quality. These are described in Table 4.5. A nonlinear dynamic time
history analysis was conducted to investigate the effects of construction quality using
the global hysteretic parameters and the three construction quality categories.
Superior Quality
Good nailing of diaphragms.
100% of stiffness and strength
from high-quality laboratory
tests.
Typical Quality
Good nailing of diaphragms.
90% of stiffness and strength
from high-quality laboratory
tests,
Good nailing of shearwalls.
100% of stiffness and strength
from high-quality laboratory
tests.
Average nailing of shearwalls.
5% greater nail spacing.
Good connections between
structural elements,
100% of stiffness and strength
from high-quality laboratory
tests.
Typical connections between
structural elements.
10% reduction of stiffness and
strength in shearwalls from highquality laboratory tests.
Good quality stucco.
100% of stiffness and strength
from high-quality laboratory
tests.
Superior nailing of interior
gypsum wallboard.
100% of stiffness and strength
from high-quality laboratory
tests.
Average quality stucco.
90% of stiffness and strength
from high-quality laboratory
tests,
Good nailing of interior gypsum
wallboard,
85% of stiffness and strength
from high-quality laboratory
tests,
Poor Quality
Poor nailing of
diaphragms.
80% of stiffness and
strength from high-quality
laboratory tests.
Poor nailing of shearwalls.
20% greater nail spacing.
5% reduction stiffness and
strength due to water
damage.
Poor connections between
structural elements.
20% reduction of stiffness
and strength in shearwalls
from high-quality
laboratory tests.
Poor quality stucco.
70% of stiffness and
strength from high-quality
laboratory tests.
Poor nailing of interior
gypsum wallboard.
75% of stiffness and
strength from high-quality
laboratory tests.
Table 4.5 Definitions of three construction quality categories (from: Isoda et al., 2002)
The global hysteretic parameters developed to correspond to each of the cases
are similar in form to those considered in the nonlinear time history analyses
performed in the CCWP Task 1.5.3 and described earlier in this dissertation. A
sensitivity study was performed to investigate the construction quality on performance
of shearwalls. Deterministic modification factors (relating back to superior quality)
were then developed for each hysteretic parameter. Table 4.6 shows the deterministic
modification factors for the different construction quality levels. These factors are
67
used to modify the original hysteretic parameters, assumed to correspond to superior
quality, to obtain the global hysteretic parameters of shearwalls of poor or typical
construction quality. Complete results of this sensitivity study are presented in
Appendix B.
Quality
TYP.
Sheathing
OSB
OSB+NSF
OSB
POOR
OSB+NSF
OSB + NSF
(GWB)
K0
a
1.00
F
0.85
0.86
0.63
0.66
F
0.85
0.86
0.63
0.67
0.85
0.87
0.61
0.66
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.69
0.69
0.69
1.00
1.00
r1
r2
r3
0.86
0.87
0.61
0.66
0.99
0.99
0.99
1.00
1.00
1.00
0.99
0.99
0.97
0.98
0.69
1.00
0.98
F0
]
1.01
lable 4.6 Developed deterministic modification factor for construction quality
(1)
r4
is assumed to be 1.00
for
all cases.
The peak displacement curves were constructed using the modified global
hysteretic parameters (i.e, global hysteretic parameters obtained from experimental
test x modification factor) and the CCWP Task 1.3.1 shearwall test results. Various
assumed seismic weights were considered to construct peak displacement distributions
for shearwalls with different sheathing combinations (i.e, OSB only, OSB + GWB,
and OSB + Stucco). These results can be used to develop performance curves and
design charts (discussed later in Chapter 4.3.2.2) considering different construction
quality. Figures 4.39 through 4.41 show comparisons of peak displacements for
different combinations of sheathing materials and nonstructural finish materials. The
seismic weights in these figures were selected such that the majority of peak
displacements of the poor quality shearwalls were below a practical drift limit of four
inches. As another comparison, Figure 4.42 shows the peak displacements for the
L!I
different combinations of sheathing materials with one value of seismic weight (W
840 lbs/ft) for all shearwalls with or without nonstructural finish materials. The NSF
materials significantly improve the shearwall performance at all quality levels. Similar
analyses were performed for a shearwall with a large garage door opening using the
modified hysteretic parameters and the CCWP Task 1.4.4 test results. The results are
shown in Figures 4.43 through 4.46.
>-0.9
TYP.
0.8
SUP.
IPOOR
0.7
0.6
0.5
/*
0.4
0.3
//
8ft.
0?
0.2
8ft
0.1
BW (8' x 8'), 8d@4"/12, OSB (/"), ç = 2%,
W = 840 lbs/ft (30 kN total), LS (10/50)
ni
0
0.5
1
1.5
2
2.5
3
3.5
4
6max (in.)
Figure 4.39 Peak displacement distributions for construction qualities (BW1, OSB
only)
0.9
0.8
/
0.6
/
0.5
/
//
U-
POOR
-.
0.7
,H
0.4
0.3
8ft
0.2
8ft.
1/
0.1
7'
-
= 2%,
LS (10/50),
W = 1350 lbs/ft (48 kN total)
BW (8
n
0
0.5
1
2
1.5
8'), 8d@4"/1 2",
OSB (I') GWB (1/)
9
-
x
max
3
2.5
3.5
4
(in.)
Figure 4.40 Peak displacement distributions for construction qualities (BW1, OSB +
GWB)
SUPIYP.TT
0.9
0.8
///
0.7
POOR
0.6
// H-:
//
0.4
0.3
8ft.
0.2
/
0.1
0
0.5
8L.
/
1
8W (8'
8'), 8d4"/12',
= 2%,
(7/),
LS (10/50),
Stucco
W = 1690 lbs/ft (60 kN total)
OSB
1.5
2
6max
x
(/8") +
2.5
3
3.5
4
(in.)
Figure 4.41 Peak displacement distributions for construction qualities (BW1, OSB +
Stucco)
70
0.9
"-.-- OSB only
0.8
(SUP., TYP., POOR)
OSB+GWB
0.7
(SUP., TYP., POOR)
0.6
I:!
//
OSB + Stucco
(SUP., TYP., POOR)
0.5
U-
I
II,'!
0.4
j:
:/
0.3
8ft
/:7/
/
0.2
0.1
8L.
BW (8'
2%,
8'), 8d@4"/12",
OSS (/"). GWB (1/2), Stucco (7/),
W = 840 lbs/ft (30 kN total), LS (10/50)
x
n
0
0.5
1
2
1.5
2.5
3
4
3.5
ömax (in.)
Figure 4.42 Peak displacement distributions for BW1 considering different
construction qualities
0.9
0.8
0.7
POOR
0.6
/ 1
0.5
0.4
0.3
0.2
H
/ /
//
/
0.1
0
0.5
16ft.
OW (16' x 8'), 8d©3"/12", = 2%,
OSB (3/), LS (10/50),
W = 562 lbs/ft (40 kN total)
P
n
H8ft
(,J
1
1.5
2
ömax
2.5
3
3.5
4
(in.)
Figure 4.43 Peak displacement distributions for OWl (OSB only) considering
different construction qualities
71
//v7
0.9
TYP./i
0.8
SUP
0.7
POOR
if H
0.6
0.5
/e
LL
0.4
/1 :"
0.3
//
0.2
H
"
/
// /
0.1
-
0
0.5
l6ft.
OW (16' x 8'), 8d3"I12', = 2%,
OSB (3/), GWB (/2), LS (10/50),
W = 562 lbs/ft (40 kN total)
2
1.5
1
3
2.5
3.5
4
(in.)
max
Figure 4.44 Peak displacement distributions for OWl (OSB + GWB) considering
different construction qualities
0.9
TYP.
/
-
0.8
POOR
sup.
0.7
,,-'
0.6
/ I
0.5
/
I
0.4
I
0.3
H8ft
H
,/
/ /
0.2
I /
I
0.1
/
/
OW (16'>< 8'), 8d3"I12", ç = 2%,
(7/),
(3/5),
0
-
OSB
Stucco
LS (10/50),
W = 562 lbs/ft (40 kN total)
ft
0
0.5
1
1.5
2
max
2.5
3
3.5
4
(in.)
Figure 4.45 Peak displacement distributions for OWl (OSB + Stucco) considering
different construction qualities
72
7I
1
0.9
TYP.
0.8
SUP.
POOR
7/
0.7
1/
LL
0.4
//
0.3
0.2
/
H
I
/ /
0.1
8ft
16f1.
OW (16'>< 8'), 8dc3"/12",
0
I
= 2%,
OSB (3/), GWB (/2"), Stucco (p18").
W = 562 lbs/ft (40 kN total), LS (10/50)
0
0
0.5
1
1.5
2
2.5
3
3.5
4
6max (in.)
Figure 4.46 Peak displacement distributions for OWl (OSB + GWB + Stucco)
considering different construction qualities
73
4.2.5 Effects of different seismic hazard regions
Previous studies (see Section 4.2.1.1) have shown that the greatest source of
uncertainty arises from the characterization of the seismic hazard. Thus, the inherent
variability in the ordinary ground motion records contribute significantly to the
variability in performance (peak displacement) of a shearwall. The CUREE-Caltech
Woodframe Project (CCWP) Task 1.5.3 was conducted using a suite of ordinary
ground motion records selected to characterize the seismic hazard in California
(seismic zone IV). These ground motions were recorded far enough from the rupture
to be free of typical near-fault pulse characteristics, and therefore near-fault ground
motions were not included. Furthermore, seismic zone IV and soil type D were
assumed when scaling to match the design spectrum. As such, it is unlikely the
performance curves and design charts developed in the CCWP Task 1.5.3 are
applicable to other seismic regions. The procedure developed in CCWP Task 1.5.3 is
sufficiently modular to allow a different suite of ground motion records (and hence
regions of seismic hazard) to be considered. Seismic zone II and III were considered to
investigate this issue. Much of the Pacific Northwest, including parts of Washington
and Oregon, has been designated seismic zone III [ICBO, 1997; FEMA, 2000 a,b].
Many woodframe buildings were damaged in the recent Nisqually earthquake, which
occurred in February, 2001 [Filiatrault et al., 2001]. The Northwest (seismic zone III)
earthquakes are characterized by long duration, subduction zone or interplate seismic
source, long hypocentral depth, and little aftershock activity. Earthquakes in Southern
74
California (seismic zone IV), on the other hand, are characterized by short duration,
shallow crustal seismic source, short hypocentral depth, and many aftershocks.
Three suites of ordinary ground motion records (20 records from LA, 20
records from Seattle, and 20 records from Boston) obtained from SAC Joint Venture
Project [Somerville et al., 1997] were used to generalize the methodology for
shearwall design (selection) for different seismic hazard regions (seismic zone II, III
and IV) and soil profile types (soil type B and D). Each ordinary ground motion record
was scaled independently for the appropriate performance level (e.g., life safety, 10%
probability of exceedance in 50 years) over the period range of interest. This was done
according to the procedures given by UBC '97 and the NEHRP guidelines [ICBO,
1997; FEMA, 2000a, b], as described previously. Figure 4.47 shows the target
response spectra for different seismic hazard regions according to UBC '97.
Information about the target response spectra for the different seismic regions is
shown in Table 4.7. The analysis of peak displacements was conducted as described
previously (see Section 3.3). The scaled peak ground accelerations for the 20 records
in the three different seismic zones are shown in Tables 4.8 through 4.10.
The method used for scaling earthquake records also was investigated. Three
cases are examined: scaling over the plateau region (presumed to be the period range
into which most woodframe structures fall), scaling to match at a period of 0.2 secs,
and scaling to match at a period of 0.5 secs. Figure 4.48 presents the peak
displacement distributions for the three different scaling methods for one given wall
configuration (BW 1), assuming the Durham nail hysteretic parameters, a 3 "/12"
75
nailing schedule, and the life safety (LS, 10/50) hazard level. When earthquake
records are scaled to target periods (0.2 sec or 0.5 sec), the displacement distribution
exhibits greater variability than when the earthquake records are scaled over the
plateau region. However, the median displacement values are similar. This is similar
to the results obtained by Shome (1999).
The performance levels and drifts limits are adopted from FEMA 356 [FEMA,
2000a, b], as was done previously. Details about the earthquake records used in this
study are provided in Appendix D.
1''
I
I
-
Typical period range of interest (0.1 sec
for woodframe structure
I
0.6 sec)
0
SI5
0)
6j
Region), SD
Seismic Zone II (Boston Region), SD
(I)
\
04
Zone fl (SeaU
Seismic Zone II (Boston Region), SB
1:
S
___5___
-
_SS___
0 2
-
0
0
0.5
1.5
1
2.5
2
3.5
3
4
Period (sec)
Figure 4.47 Target response spectra for different seismic hazard regions
Seismic zone
Soil profile type
]
IV (LA)
III (Seattle)
II (Boston)
D
D
B
D
Period of interest
(plateau region)
1
j
Spectral acceleration
at plateau region,
0.12 sec 0.58 sec
0.12 sec 0.60 sec
0.08 sec
0.40 sec
0.12 sec 0.58 sec
lable 4.7 Target response spectra for different seismic hazard regions
Sa
1.lg
0.9g
0.375g
0.55g
76
0.9
/
0.8
Plateau Region
0.2sec
0.5sec
0.7
0.6
0.4
0.3
0.2
8ft._8ft.
SW (8' x 8'), @3"/12", OSB (/8"),
/
0.1
>
ED
/
,',
/8, G = 184 ksi, ç = 2%,
0
W = 843 lbs/ft (30 kN total), LS (10/50)
(1
0
0.5
1.5
1
max
2
(in.)
Figure 4.48 Comparison of earthquake record scaling to target response spectra
EQ Event &
Year
Imperial Valley
(1940)
Imperial Valley
(1979)
Landers (1992)
Loma Prieta
(1989)
Northridge
(1994)
N. Palm Springs
(1986)
File
Station
LAOI
LAO2
LAO3
LAO4
Imperial Valley, El Centro
Imperial Valley, El Centro
Imperial Valley, Array #5
Imperial Valley, Array #5
Imperial Valley, Array #6
Imperial Valley, Array #6
Landers, Barstow
Landers Barstow
Landers, Yermo
Landers, Yermo
Loma Prieta, Gilroy
LomaPrieta, Gilroy
Loma Prieta, Newhall
Loma Prieta, Newhall
Northridge, Rinaldi RS
Northridge, Rinaldi RS
Northridge, Sylmar
Northridge, Sylmar
North Palm Springs
North Palm Springs
LAOS
LAO6
LAO7
LAO8
LAO9
LA1O
LA1 1
LA12
LA13
LA14
LA15
LA16
LA17
LA18
LA19
LA2O
Peak Ground Acceleration (g)
Unsealed
Scaled
0GM
LS (10/50)
0.229
0.498
0.336
0.527
0.390
0.460
0.483
0.509
0.359
0.603
0.279
0.440
0.132
0.677
0.133
0.638
0.240
0.597
0.166
0.429
0.372
0.464
0.542
0,430
0.658
0.430
0.63 8
0.479
0.675
0.5 14
0.734
0.555
0.575
0.691
0.825
0.480
0.343
0.497
0.332
0.43 1
I able 4. 20 Ordinary ground motion records and PGA values (seismic zone IV, LA)
77
While using the SAC-Joint Venture earthquake records to consider other
seismic regions in this study, it was decided to compare the results obtained using the
CCWP and the SAC earthquake records for seismic zone IV (LA region). It was
presumed that the results would be similar. The nonlinear dynamic time history
analysis described previously was performed to investigate this issue. Both sets of
earthquake records were scaled to the same target response spectra and assumed soil
types
D (SD).
Figure 4.49 shows a comparison of peak displacements for both sets of
earthquake records with various assumed seismic weights. As expected, no significant
difference was observed. Therefore, it was decided that the 20 earthquake records
developed by CCWP would be used for all further analysis considering the LA
(California) hazard in this study. Table 4.11 summarizes the ground motions used to
evaluate shearwall response in different seismic hazard regions.
EQ Event &
Year
Imperial Valley
(1979)
Morgan Hill
(1984)
Olympia
(1949)
File
Station
SEO1
SEO2
SEO3
Long Beach, Vermon CMD Bldg
Long Beach, Vermon CMD Bldg
Morgan Hill, Gilroy
Morgan Hill, Gilroy
West Washington, Olympia
West Washington, Olympia
West Washington,
Seattle Army B
West Washington,
Seattle Army B
North Palm Springs
North Palm Springs
Puget Sound, WA, Olympia,
Puget Sound, WA, Olympia,
Puget Sound, WA,
Federal OFC B
Puget Sound, WA,
Federal OFC B
Eastern WA, Tacoma County
Eastern WA, Tacoma County
Llolleo, Chile
Llolleo, Chile
Vinadel Mar, Chile
Vinadel Mar, Chile
SEO4
SEO5
SEO6
SEO7
SEO8
N. Palm Springs
(1986)
SEO9
SE1O
SEll
SE12
Seattle
(1949)
Valparaiso
(1985)
SE13
SE 14
5E15
SE16
SE17
SE18
SE19
SE2O
Peak Ground Acceleration (g)
Unsealed
Scaled
0GM
LS (10/50)
0.3 55
0.492
0.276
0.362
0.136
0.371
0.233
0.495
0.206
0.361
0.189
0.345
0.055
0.360
0.073
0.474
0.344
0.333
0.175
0.139
0.4 12
0.3 56
0.070
0.308
0.057
0.343
0.033
0.066
0.563
0.541
0.320
0.227
0.392
0.423
0.382
0.49 1
0.385
0.401
0.432
0.430
Table 4.9 20 Ordinary ground motion records and PGA values (seismic zone III,
Seattle)
79
EQ Event &
Year
Reverse 1
Reverse 2
New Hampshire
(1982)
Nahanni
(1985)
Saguenay
(1988)
File
Peak Ground Acceleration (g)
Unscaled
Scaled
Station
BOO!
Simulation, Hanging Wall
Simulation, Hanging Wall
Simulation Foot Wall
Simulation, Foot Wall
New Hampshire
New Hampshire
Nahanni
Nahanni
Nahanni
B002
B003
B004
B005
B006
B007
B008
BOO9
ianni
BOlO
B011
B012
B013
B014
B015
B016
B017
B018
B019
B020
Nahanni
Nahanni
Saguenay
Saguenay
Saguenay
Saguenay
Saguenay
Saguenay
Saguenay
Saguenay
0GM
LS(l0/50)
0.319
0.191
0.267
0.207
0.054
0.029
0.978
0.920
0.303
0.368
0.145
0.148
0.128
0.174
0.163
0.077
0.056
0.070
0.053
0.082
0.279
0.217
0.282
0.270
0.4 14
0.306
0.329
0.417
0.385
0.371
0.493
0.535
0.252
0.261
0.319
0.432
0.246
0.220
0.266
0.288
Table 4.10 20 Ordinary ground motion records and PGA values (seismic zone II,
Boston)
Seismic Hazard
Region
Seismic Zone IV
jon)
Seismic Zone III
(Seattle Region)
Seismic Zone jj
(Boston Region)
Soil
Type
Performance
Level
D
LS (10/50)
B
Records
20 0GM from
LA region
20 0GM from
Seattle region
20 0GM from
Boston region
D
Source
CUREE-Caltech
Woodframe Project
SAC Joint Venture
[
Table 4.11 Analysis matrix for effects of different seismic hazard regions
c
0.9
CCWP (30 kN)
/1
SAC (30 kN)'
0.8
//
/1
CCWP (40 kN)
/
0.7
SAC (40 kN)
/
/
0.6
/i
/
ii
V
CCWP(5OkN)
SAC (50 kN)
0.5
0.4
0.3
0.2
0.1
/
I
I //
_8ft.
Bft.
BW (8 x 8), @4"/12", OSB (3/)
ED
/8, G = 180 ksi, ç = 2%, LS (10/50)
n
0
0.5
1
1.5
2
2.5
3
3.5
4
ömax (in.)
Figure 4.49 Comparison of peak displacement between CCWP and SAC earthquake
records
The two sets of 20 SAC earthquake records for seismic zone III (Seattle
region) and seismic zone II (Boston region) each contain 10 fault-normal and 10 faultparallel earthquake records. Figure 4.50 shows the peak displacement distributions for
the 10 fault-normal earthquake records and the 10 fault-parallel earthquake records for
each seismic region and for a given seismic weight. This figure also shows the peak
shearwall response for the 20 combined earthquake records (i.e., 10 fault-normal and
10 fault-parallel earthquake records). No significant difference was observed between
the fault-normal and fault-parallel earthquake records. Therefore, it was decided to use
the combined of 20 earthquake records (i.e., 10 fault-normal plus 10 fault-parallel
earthquake records) for the purpose of investigating the effects of different seismic
hazards on shearwall performance.
E:JI
1
-
/7'
(LA)
(Boston) //'iii (Seattle)
1/:-
Fault_Nor'l
/- Combineçt/'
Ii
- Fault_Pllel - Fault Pp.1l'el
- Fault_Normal
- Combined
- Fault_Parallel
//'
/
U-
FaultjNormaj.<'
CombineØ"/'
0.4
/A
/1
0.3
0.2
/
1' i"
J_y
//'
/
0.1
)
n
0
0.5
1
BW (8' x 8'), @6/12', OSB (/8"),
9
ED =
G = 180 ksi,
= 2%,
W = 1400 lbs/ft (50 kN total), LS (10/50)
1.5
2
2.5
3
3.5
4
6max (in.)
Figure 4.50 Comparison of peak displacement between fault-normal and fault-parallel
earthquake records
The effect of soil profile types also was considered. Soil profile type D
(SD)
would be a relatively common (and conservative) design assumption for seismic zone
IV (LA) and III (Seattle). However, soil profile types for seismic zone II (Boston) are
difficult to determine (widely varying, highly localized conditions). Based on
consultation with a geotechnical engineer [Home, 20021, the representative soil profile
types for Boston region were determined. Thus, soil profile type D
(SD)
for seismic zone IV (LA) and III (Seattle), and soil profile type B
was assumed
(SB)
and D
(SD)
were assumed for seismic zone II (Boston). Figures 4.51 and 4.52 show a comparison
of peak displacement distributions for these seismic regions considering two typical
nailing schedules and one value of seismic weight.
7
0.9
--
-
C
iioston
0.8
eattie D
I
/
+
0.7
"'
I
,,
/
/
I
0.6
(LA)D
/C
/
H
0.5
U-
0.4
0.3
88.
0.2
/
I
0.1
I
I
fl
/
1
BW (8' x 8'), @4/12", OSB (/8"),
-'
ksi, = 2%,
W = 1400 lbs/ft (50 kN total), [S (10/50)
ED = J8", G = 180
/
C)
0.5
0
1.5
1
2.5
2
max
3.5
3
4
(in.)
Figure 4.51 Comparison of peak displacement for different seismic hazard regions
(@4"/12", W 1400 lbs/fl)
0.9
/
\)7'
0.7
/
II (Bostn)_D
0.5
III (SeatUey6
0.4
iv
(LA)_D
L-
/C
,-H
/
I
LL
-
/
II
0.6
-
'II (Boston)_B
/
1/
0.8
II
0.3
88
0.2
1/
0.1
BW (8'x 8'), @6/12", OSB (3/),
/
I
/
JJ
n
0
- -
0.5
1
- 2%,
ED = /8", G = 180 ksi,
'
W = 1400 lbs/ft (50 kN total), LS (10/50)
1.5
2
2.5
3
3.5
4
4.5
5
6max (in.)
Figure 4.52 Comparison of peak displacement for different seismic hazard regions
(@6"/12", W = 1400 lbs/ft)
Clearly, the shearwalls in seismic zone IV (LA) perform the worst because of
the higher peak ground accelerations. These figures illustrate the need to specifically
consider seismic hazard when specifying design requirements, i.e., selection of dense
nailing schedules, use of thicker sheathing materials, and so forth. In the case of
seismic zone II (Boston), shearwalls built in soil profile type B
better than those in soil profile type D
(SD,
stiff soil).
(SB,
rock) perform
4.3 Additional studies
4.3.1 Development of modification factors
4.3.1.1 Sheathing-to-framing connection hysteretic parameter variability
It is important to understand the extent to which sheathing-to-framing
connection hysteretic parameter variability influences the predicted response (peak
displacement) of the shearwall. Significant variability was observed in the fastener
data obtained under Task 1.4.8.1 of CUREE-Caltech Woodframe Project [see Figures
4.23 through 4.27]. Careful consideration must be given to how best utilize the data
obtained in CCWP Task 1.4.8.1. This is a potentially valuable database; however
some additional post-processing and evaluation of the data still may be needed to
develop design recommendations using a model-based procedure. Once done, it
should be possible to evaluate an appropriate modification factor to account for
fastener parameter variability.
The sheathing-to-framing connection hysteretic parameter variability can be
handled similar to the treatment of model uncertainty in Section 4.2.1.8, i.e., in the
form of modification factors (with parameters Xy, y) applied to the peak displacement
distribution. The lognormal parameters (Xz, z) for the worst-case (target) peak
displacement distribution and lognormal parameters (2x, Ex) for the median peak
displacement distribution can be obtained by the method of maximum likelihood.
Figure 4.53 illustrates the example for selection of median and target peak
displacement distributions for a particular set of wall parameters. The parameters of
these distributions are given by:
(4.3)
z
=k +
(4.4)
where, Xz and z = lognormal parameters for target peak displacement distribution, Xx
and
x = lognormal parameters for median peak displacement distribution, Xy =
logarithmic mean of modification factor, and y = logarithmic standard deviation of
modification factor, respectively. The lognormal parameters Xy and
can be obtained
by solving eqs. 4.3 and 4.4. Once they are determined, the statistical moments (mean
t
and standard deviation ) for the modification factors (Xy, y) can be determined by:
=e
a
(Y+)
e')
(4.5)
(4.6)
where, ty and Jy are the mean and standard deviation of the modification factor,
respectively.
To illustrate the effect of choice of moments for the modification factors, the
mean was varied while holding the COy constant. This is shown Figure 4.54. Next,
the COy was varied while holding the mean constant. This is shown in Figure 4.55.
0.9
Target (worst-case)
0.8
Median
0.7
/
0.6
0.5
U-
0.4
,// /
'I,,,
0.3
// // /
0.2
0.1
8ft._8ft.
/ / /
,'
ED
/
/
,
BW (8' x 8'), 8d©3"112", OSE (3/3),
= 2%,
G = 180 ksi,
W = 560 lbs/ft (20 kN total), LS (10/50)
n
0
0.1
0.2
0.3
0.5
0.4
ömax
0.6
0.7
0.8
0.9
(in.)
Figure 4.53 Selection of median and target peak displacement distributions
0.9
Median
0.8
Target
w=l.00,Vy=0.20
0.7
/
0.6
0.5
/
yl.2O, Vy0.2O
j.tyl.4O, Vy0.20
1=1.50,V=0.20
/
/
/
Ly=1.60,Vy=0.20
jiyl.7O, Vy0.20
/
U-
0.4
0.3
0.2
//////1
0.1
BW (8'
ED=3/5",G=180ksil2%,
W = 1400 lbs/ft (50 kN total), [S (10/50)
n
0
0.5
1
1.5
2
2.5
ömax
3
3.5
4
4.5
5
(in.)
Figure 4.54 Change of peak displacement considering various mean values of
modification factor
0.9
Median
0.8
ty=1.00,Vy=0.20
iy=l.00, Vy0.40
0.7
jy=l.00, Vy=0.50
ty=l.00, Vy0.60
j.ty=l.00, Vy0.70
0.6
iy=l.00, Vy0.80
0.5
Target
0.4
/
0.3
S
8ft.
I
I
0.2
I
I
I
I
I
8ft.
II
I
BW (8' x 8'), 8d@3"/12", OSB
0.1
(3/),
ED=3/6",G=l8Oksi,ç2%,
W = 1400 lbs/ft (50 kN total), LS (10/50)
n
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
6max (in.)
Figure 4.55 Change of peak displacement considering various COy values of
modification factor
The baseline solid wall, BW1 (8 ft. x 8 ft.) with two sheathing panels oriented
vertically and a 3"/12" fastener schedule was considered when developing the
modification factors for sheathing-to-framing connection hysteretic parameter
variability. Only the life safety (10/50) limit state was considered. Five sets of nail
parameters (Durham, Folz and 3 BYU) were used. Also, the range of seismic weight
considered was 560 lbs/ft to 2530 lbs/ft. The average values for the mean and COV of
the modification factor (see Figure 4.56) for sheathing-to-framing connection
hysteretic parameter variability were 1.295 and 0.2 13, respectively.
[SIb]
1.6
1.4
Y,Avg
.295
1.2
>-
>
0
coy
0.6
0.4
-
0.2
01
500
1000
1500
2000
2500
3000
Seismic Weight (Ibs/ft)
Figure 4.56 Modification factors for sheathing-to-framing connection hysteretic
parameter variability
4.3.1.2 Construction quality
Significant differences were observed in shearwall performance (peak
displacement) considering different levels of construction quality (see Section 4.2.4).
Modification factors to account for construction quality can be obtained using the
procedure described in the previous section. The modification factor is intended here
to adjust the peak displacement distribution for a wall having superior quality to walls
having either typical or poor qaulity. Therefore, in eqs 4.3 and 4.4, Xz and z =
lognormal parameters for peak displacement distribution of typical or poor quality
walls, ?x and E = lognormal parameters for a peak displacement distribution of
superior quality wall, ?y and y = logarithmic mean and logarithmic standard
deviation of the construction quality modification factor, respectively.
Figure 4.57 shows the peak displacement distributions for BW1 assuming
superior, typical and poor quality. Modification factors are sought to predict the peak
displacement of shearwalls built with typical or poor quality, in relation to the superior
quality case. While these factors apply only to the wall being considered here, the
approach can be generalized for other wall configurations and/or definitions of
construction qaulity. As another example, Figure 4.58 shows the peak displacement
distribution for the wall with a large opening including nonstructural finish materials.
Two types of shearwalls, the baseline solid wall, BW1 (8 ft.
x
8 ft.) with
sheathing panels oriented vertically, and the wall with a garage door opening, OWl
(16 ft. x
8 ft.), are considered to develop modification factors to account for effects of
construction quality. The life safety (10/50) limit state and various assumed seismic
weights are considered. Using the same procedure described in Section 4.3.1.1,
modification factors were developed for different values of seismic weight, and
different sheathing materials and shearwall types. Figures 4.59 through 4.64 show the
statistical moments of the modification factors for baseline wall BW1 as a function of
seismic weight. The mean modification factor remains relatively consistent,
particularly when the effects of nonstructural finish materials are not considered.
However, the COV tends to increase at high demands (large seismic weights). Figures
4.65 through 4.72 show the same results for the wall with a garage door opening.
Similar trends (consistent mean modification factor and increasing COV as a function
of seismic weight) were observed. Table 4.12 summarizes the moments of the
modification factors developed in this section.
Wall type
Baseline solid wall (BW1)
OSB+
OSB+
GWB
Stucco
Sheathing
OSB
1.251
1.238
1.243
COVTYP
0.136
2.081
0.242
0.178
1.827
0.287
0.134
k'OOR
COVPOOR
1.775
0.238
Wall with a garage door opening (OW 1)
OSB +
OSB+
OSB+
OSB
GWB+
GWB
Stucco
Stucco
1.268
0.125
2.173
0.226
1.253
1.281
0.152
1.750
0.207
0.093
2.074
0.269
Table 4.12 Summary of modification factors considering construction quality
1.242
0.133
1.840
0.254
91
0.9
0.8
0.7
0.6
0.5
U-
0.4
0.3
0.2
0.1
0
-
= 2%,
BW (8' x 8'), 8d@4"/12", OSB (/8"),
W = 843 lbs/ft (30 kN total), LS (10/50)
n
0
0.5
1
1.5
2
3
2.5
ömax
3.5
4
5
4.5
(in.)
Figure 4.57 Graphical method for determination of modification factors in
construction quality (BW1)
0.9
SUP
0.8
0.7
TYP.
0.6
0.5
0.4
0.3
118
0.2
ft
6 ft
OW (16'
0.1
x 8'), 8d3"/12",
OSB (/"), GWB (/2"), Stucco
2%,
(/8")
W = 422 lbs/ft (3) kN total),LS (10/50)
n
0
0.5
1.5
1
6max
2
2.5
(in.)
Figure 4.58 Graphical method for determination of modification factors in
construction quality (OWl)
92
2.5
POOR
Y,AVQ
2.081
2
1.5
>-
1
0.5
0'
200
I
300
400
500
600
700
800
900
1000
Seismic Weight (Ibs/ft)
Figure 4.59 Mean of modification factor for BW1 (OSB only)
0.4
POOR
0.3
>
COVAvg = 0.242
0
0
0.2
/
0.1
TYP.
n
200
300
400
500
600
700
800
Seismic Weight (ibs/ft)
Figure 4.60 COV of modification factor for BW1 (OSB only)
900
1000
93
2.5
POOR
2
Y,Avg
1.827
.tY,Avg
1.238
1.5
>-
1
TYP.
0.5
0'
I
200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400
Seismic Weight (Ibs/ft)
Figure 4.61 Mean of modification factor for BW1 (OSB + GWB)
0.5
0.4
0.3
COVAvg = 0.287
0.2
COVAvg = 0.178
>
0
0
0.1
TYP.
200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400
Seismic Weight (Ibs/ft)
Figure 4.62 COV of modification factor for BW1 (OSB +GWB)
2.5
POOR
2
,Avg
1.775
1.5
lY,Avg = 1.243
>-
:1
I
TYP.
0.5
0'
200
I
400
600
800
1000
1200
1400
1600
1800
Seismic Weight (Ibs/ft)
Figure 4.63 Mean of modification factor for BW1 (OSB + Stucco)
0.5
0.4
POOR
0.3
>
0
0
COVAvg0238,'
0.2
COVAVg = 0.134
0.1
TYP.
0'
200
I
400
600
800
1000
1200
1400
1600
Seismic Weight (Ibs/ft)
Figure 4.64 COV of modification factor for BW1 (OSB + Stucco)
1800
2.5
-
A2.173
_!
2
POOR
1.5
_±'_=
>-
- -..
1.
,iii:;1
I
TYP.
0.5
0'
100
I
200
300
400
500
600
Seismic Weight (Ibs/ft)
Figure 4.65 Mean of modification factor for OWl (OSB only)
>
0
0
0
100
200
300
400
Seismic Weight (Ibs/ft)
Figure 4.66 COY of modification factor for OWl (OSB only
500
600
2.5
POOR
2
-Y,=
1.5
-
LY,Avg = 1.253
>-
1
TYP.
0.5
0'
100
200
400
300
500
Seismic Weight (Ibs/ft)
Figure 4.67 Mean of modification factor for OWl (OSB + GWB)
C
0.4
POOR
0.3
>
TYP.
0
0
COVAvg = 0.207
0.2
COVAVg = 0.152
0.1
0'
100
200
300
400
500
Seismic Weight (lbs/ft)
Figure 4.68 COV of modification factor for OWl (OSB + GWB)
97
2.5
tY,Avg = 2.074
2
1.5
JiY,Avg
1.281
TYP.
0.5
UI
400
600
500
700
Seismic Weight (Ibs/ft)
Figure 4.69 Mean of modification factor for OWl (OSB + Stucco)
[II
POOR
0.3
COV=ft26:
>
0
0
0.2
0.1
CoVAv90oN
rir
400
500
600
Seismic Weight (Ibs/ft)
Figure 4.70 coy of modification factor for OWl (OSB + Stucco)
700
2.5
POOR
2
.tY,Avg =
1.840
U
1.5
l-Y,Avg =
>
1.242
0.5
0'
100
200
300
400
500
600
700
800
Seismic Weight (Ibs/ft)
Figure 4.71 Mean of modification factor for OWl (OSB + GWB + Stucco)
>
0
0
0
100
200
300
400
500
600
700
800
Seismic Weight (tbs/ft)
Figure 4.72 COY of modification factor for OWl (OSB + GWB + Stucco)
4.3.1.3 Contribution of nonstructural finish materials
In Section 4.2.3, it was shown that the presence of stucco and/or gypsum
wallboard would result in significantly reduced peak drifts, particularly at high
demands. Many of the walls considered previously (particularly those without
nonstructural finish materials) were generally well behaved (i.e., low COV's in peak
displacement distribution) at lower values of seismic weight, but frequently exhibited
very large (and highly variable) drifts at larger seismic weights. (This also relates to
the geometric instability concept described in the Incremental Dynamic Analysis
section, see Section 4.4.1.) The result is often a poorer fit to the peak displacement
cumulative distribution function (CDF), in particular over the upper tail, which forms
the basis for the performance curves, design charts, and fragility curves. Simply put,
the more well behaved the shearwall response (i.e., the lower the variability in peak
displacement, by avoiding geometric instabilities), the more robust the procedure
developed in this study becomes. By taking proper account of the finish materials, not
only will the peak drifts be reduced, but also it is likely that the variability in peak
displacements can be maintained at relatively low levels over a wider range of seismic
weights.
The theory of products of statistically independent lognormal variables was
used to develop the modification factors for sheathing-to-framing connection
hysteretic parameter variability (Section 4.3.1.1) and construction quality (Section
4.3.1.2). However, that procedure cannot be used when developing modification
factors to account for nonstructural finish material effects because the COV's in peak
100
displacement of walls with nonstructural finish materials generally are lower than
those without nonstructural finish materials (i.e., OSB sheathing only). Since
=
+
,
then the logarithmic standard deviation (,y) for the modification factor is
obtained from the following equation;
Y
where,
z
='J
(4.7)
logarithmic standard deviation for the target peak displacement
distribution (wall with NSF materials), x = logarithmic standard deviation for the
median peak displacement distribution (wall built with OSB only), and
y
logarithmic standard deviation of the modification factor. The expression under the
square root must be positive for a real solution. However, in many cases, this value is
negative because the value of z is smaller than Ex (i.e., the value of COV in peak
displacement distribution considering OSB and NSF materials is lower than the COV
considering OSB only). Therefore, it was decided to develop a deterministic
modification factor to match the 90tlpercentile values of peak displacement for
shearwalls built with nonstructural finish materials. The deterministic modification
factor (i.e., logarithmic mean, ?y) can be obtained by varying the logarithmic mean
(?y) to visually match the 90thpercentile value of target peak displacement
distribution (OSB + NSF materials). Figures 4.73 and 4.74 graphically illustrate this
approach for the baseline solid shearwall and the large wall with a pedestrian door
opening, respectively. Alternatively, the deterministic modification factor can be
obtained directly using the lognormal distribution:
101
(4.8)
F(z)
where cI?(.) is CDF of the standard normal distribution,
is the logarithmic mean,
and z is the logarithmic standard deviation. The distribution parameters (X,
) are
obtained using a maximum likelihood procedure. Once the lognormal parameters (?z
z) for the target displacement distribution are determined (i.e., peak displacement
distribution including the effects of nonstructural finish materials), the 90thpercentile
value can be estimated knowing the lognormal parameters by solving the following
equation for lnZ.
(lnZ
in which, Xz and
= 0.90 =
(1.28)
(4.9)
are the lognormal parameters of peak displacement considering
the wall with NSF materials. Once lnZ is obtained from eqn. 4.9, it can be used in the
following equation:
jlnz(2 +%)',J=0.9o=(1.28)
(
+)
(4.10)
where, ?x and x are the lognormal parameters of peak displacement considering the
wall with OSB only, 2y is the logarithmic mean of modification factor, and y is the
logarithmic standard deviation of modification factor. It is assumed that the
logarithmic standard deviation (y) is nearly zero because the value of x is generally
larger than
z. Finally, the deterministic logarithmic mean (Xy) can be obtained
solving eqn. 4.10.
102
The resulting mean modification factor to account for the effects of
nonstructural finish materials, considering the baseline solid wall (BW1) sheathed
with OSB, are shown in Figure 4.75. The result in Figure 4.75 suggest that adding
stucco results in a greater reduction in peak displacement than only adding gypsum
wallboard, and this effect increases with increasing seismic weight. This is also seen in
Figure 4.76, which considered the shearwall sheathed with plywood. A shearwall with
two-sided gypsum wallboard (GWB) also was considered (Figure 4.77). The mean
modification factor for the two-sided GWB wall was about 1.5 times greater than that
wall with one-sided gypsum wallboard (see Table 4.13).
In the case of the wall with a large garage door opening, attaching stucco to the
outside and gypsum wallboard to the inside significantly decreases the peak
displacements. The mean modification factors as a function of seismic weight for
OWl are shown in Figure 4.78. Unlike the wall with the garage door opening, the use
of gypsum wallboard (in addition to stucco) does not significantly improve the
performance of the large wall with a pedestrian door opening. This can be seen in
Figure 4.79 which shows that the mean modification factors as a function of seismic
weight are nearly the same. Table 4.13 summarizes the deterministic modification
factors to account for the contribution of nonstructural finish materials.
103
Wall type
Baseline wall
OSB+GWB
0.548
0.470
N/A
0.827
OSB + Stucco
OSB + GWB + Stucco
PWD + GWB
PWD + GWB (2 sidL
PWD + Stucco
Wall with Qpening
Garage door
Pedestrian door
N/A
N/A
0.904
0.450
0.770
0.450
N/A
N/A
N/A
N/A
N/A
N/A
0.42 1
0.632
Table 4.13 Developed deterministic modification factor
nonstructural finish materials effects
(JLy)
for contribution of
90t5 Percenthe
0.9
0.8
0.7
11 1/
1x
OSB only
/ /1/
OSB + Stucco
0.5
0.4
'1/
'I
0.3
III
I
/ 11/
II
0.2
I
I
I
18ff.
8ff
/ /1/
0.1
I
BW(8 x 8'), 8d@4"/12", OSB (3/),
0
GWB (/2"), Stucco (/8"),
= 2%,
= 1400 lbs/ft (50 kN total), LS (10/50)
I
OL
0
0.5
1
1.5
2
2.5
3
3.5
4
6max (in.)
Figure 4.73 Graphical method to develop deterministic modification factors in
nonstructural finish materials effects (BW1)
104
9ot0percenthe
0.9
OSB only
0.8
OSB + Stucco
OSB+GWB
kg
0.7
OSB + Stuc
'I/
0.6
I l/I
0.5
Il/I
/
0.4
li/i
0.3
I'll,'
:,'
ii
0.2
i/i
0.1
__8ft.
I,
OW (16' x 8'), 8d@6"/12", OSB (3/),
GWB (1/2), Stucco (7/), = 2%,
/
W = 703 lbs/ft (50 kN total), LS (10/50)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
max (in.)
Figure 4.74 Graphical method to develop deterministic modification factors in
nonstructural finish materials effects (0W2)
0.9
0.8
0.7
OSB + Stucco
0.6
>-
---- - - -
l.tg
0.4
OSB + GWB
0,3
0.2
0.1
n
200
400
600
800
1000
1200
1400
1600
1800
2000
Seismic Weight (Ibs/ft)
Figure 4.75 Mean of deterministic modification factor for BW1 (OSB sheathing)
105
0.9
0.8
PWD + GWB
- -
vg0.8vg.87__
0.7
0.6
>-
:1
PWD + Stucco
0.4
0.3
0.2
0.1
n
200
400
600
800
1000
1200
1400
1600
1800
2000
Seismic Weight (lbs/ft)
Figure 4.76 Mean of deterministic modification factor for BW1 (Plywood sheathing)
09
PWD + GWB
0.8
0.7
0.6
>-
:1
0.4
0.3
0.2
0.1
C)
200
400
600
800
1000
1200
1400
1600
1800
2000
Seismic Weight (lbs/fl)
Figure 4.77 Mean of deterministic modification factor for BW1 (Plywood sheathing)
106
= 0.904
0.9
0.8
0.7
0.6
OSB + Stucco
>-
0.4
0.3
0.2
0.1
(1
100
200
300
400
500
600
700
800
900
1000
Seismic Weight (Ibs/ft)
Figure 4.78 Mean of deterministic modification factor for OWl (OSB sheathing)
1
0.9
0.8
0.7
OSB + Stucco + GWB
OSB + Stucco
0.4
0.3
0.2
0.1
n
100 200 300 400 500 600 700 800 900 1000 1100 1200 1300
Seismic Weight (Ibslft)
Figure 4.79 Mean of deterministic modification factor for 0W2 (OSB sheathing)
107
4.3.2 Construction of performance curves and design charts
4.3.2.1 Baseline walls
The sensitivity studies described previously (Section 4.2.1) were used to
establish appropriate ranges of system parameters to consider in developing
performance curves and design charts. Two baseline wall types were considered: an 8
ft. x 8 ft. solid wall with two sheathing panels oriented vertically, and a 8 ft.
x
16 ft.
long wall with a large garage door opening, vertically oriented sheathing at the ends,
and a solid header over the opening. Two sheathing types were considered, OSB and
plywood, both 3/s-in. thick. The assumed deterministic fastener hysteretic parameters
(power-driven spiral nail for the OSB and 8d common nail for the plywood; i.e., the
Durham and Dolan parameters) are shown in Table 4.14. Fastener schedules
(edge/field) ranging from 3"/3" to 6"/12" were considered. The suite of 20 ordinary
ground motion records developed for the CUREE-Caltech Woodframe Project
(CCWP) was used, scaled for the LS (10/50) and JO (50/50) limit states, with 2%
damping ratio assumed. No additional account was taken of model uncertainty or
fastener hysteretic parameter variability. Full overturning anchorage and all fasteners
were assumed to be properly installed.
Values obtained by Durham (1998). Fasteners were 2 in. (50mm) long, power-driven spiral nails
attaching 3/8-in. (9.5mm) OSB to SPF framing members.
r4W
K0
r1
r2
r3
F0
F1
A
_ç
3.203
0.169
0.032
0.492
us
0.061
-0.078
1.40
0.143
0.8
kip/in
kips
in
kips
0.561
0.061
-0.078
1.40
kN/mm
Values otr4 changed per note 3 in Table 4.1.
0.143
0.751
0.141
12.5
kN
kN
mm
0.8
J_
1.1
1.1
Fastener hysteretic parameters (average values shown) determined using results obtained by Dolan
(1989). Fasteners were 8d common nails attaching 318-in. (9.5mm) Plywood to SPF framing member,
3/8-in, edge distance, loading perpendicular to grain.
K0
r1
r2
F0
r32
r4
F1
a
0.227
0.041
0.315
US
0.050
-0060
1.40
0.027
1.1
0.8
kip/m
kips
in
kips
0.907
1.010
0.182
8.0
0.050
-0.060
1.40
0.027
1.1
0.8
kN!mm
kN
mm
kN
Value of r3 was assumed.
1
Table 4.14 Fastener parameters used to develop performance curves and design charts
for baseline walls
4.3.2.L1 Construction of performance curves
The information presented in the peak displacement distributions can be post-
processed into a more useful form for engineering designlassessment, using seismic
weight as the dependent variable (design parameter). This is not dissimilar from the
approach taken by researchers in New Zealand in which walls are rated using
sustainable seismic mass as the primary design parameter [Deam, 1997, 2000]. For the
present study, the range of seismic weight was determined from engineering design
calculations for selected woodframe structural configurations. For example, using
0.138g, unit shears were found to range from 23 lbs/ft to 200 lbs/ft in the second floor,
and 47 lbs/ft to 492 lbs/ft in the first floor of a two-story house. This corresponds to a
maximum seismic weight of 3565 lbs/ft. (A practical limit on mid-range demand
commonly seen in one- and two-family detached dwellings was suggested [Cobeen,
2000] to be about 3000 lbs/ft.) Performance curves can be constructed, using the
lognormal parameters for the appropriate peak displacement distributions, for
increasing values of seismic weight and for a set of structural parameters. Each
performance curve therefore corresponds to a particular limit state (JO, 50/50 or LS,
10/50) and non-exceedence probability (i.e., 50%, 84%, 90%, 95%, and 99%). Design
charts (described in next section) can then be constructed using the information in the
performance curves. These charts allow selection of a particular sheathing type and
fastener spacing (e.g.), for a given seismic weight, at a particular performance level or
non-exceedence probability. The quantities shown on the axes in both cases
(performance curves and design charts) are peak displacement and seismic weight.
The performance curves, as defined above, for baseline wall (BW1) with 3/8-in.
OSB, assuming the Durham fastener parameters and considering four different
fastener spacings, are shown in Figures 4.80 through 4.83. Each figure shows the 99%,
95%, 90%, 84%, and 50% non-exceedence curves, for both the life safety (LS, 10/50)
and immediate occupancy (JO, 50/50) limit states. Also shown are the FEMA 356 drift
limits, 2% for life safety (LS, 10/50) and 1% for immediate occupancy (JO, 50/50). A
slightly more restrictive JO (50/50) drift limit of 0.75% also is shown. Figure 4.83
presents the same performance curve information as shown in Figure 4.80, but with
the axes switched. Performance curves presented using either format
weight, or seismic weight vs.
ömax)
(6max
vs. seismic
can be used as design aids for shearwall selection.
For example, considering Figure 4.80 or Figure 4.84, and assuming a target peak drift
110
non-exceedence probability of 95%, the wall having parameters shown in the figure
can sustain about 1450 lbs/ft , limited by drift limit of 2% for LS (10/50).
Figures 4.85 and 4.86 present performance curves for 3/8-in. plywood,
assuming the Dolan fastener parameters and two different spacings. Note that in
addition to the different assumed fastener hysteretic parameters, the plywood has a
significantly lower shear modulus than the OSB. While not a complete range of
fastener spacings, these cases are presented for comparative purposes. Notice that this
wall can sustain significantly higher seismic weights than the wall with 3/8-in. OSB
due to differences in the fasteners and the sheathing material.
The performance curves for baseline wall (OWl) are shown in Figures 4.87
through 4.89 (OSB, three different fastener spacings) and Figures 4.90 and 4.91
(plywood, two different fastener spacings). As with the BW1 performance curves, each
figure shows the 99%, 95%, 90%, 84% and 50% non-exceedence curves, for both the
life safety (LS, 10/50) and immediate occupancy (JO, 50/50) limit states, and the
corresponding drift limits. Notice again the increased allowable seismic weight, due to
the use of larger nails and plywood (vs. OSB), evident when comparing Figure 4.87
and 4.89.
Figure 4.92 shows the effect of including model uncertainty on the LS (10/50)
performance curves for BW1 (cf. Figure 4.79). Values of COV in the model error term
of 0%, 15%, and 30% are considered. The effect is seen to be relatively small at low
seismic weights, but can become significant at higher weights. Note that model
111
uncertainty is not explicitly considered in developing the performance curves and
design charts in this dissertation.
4.3.2.1.2 Design charts
Design charts are constructed using the information in the performance curves.
Specifically, one design chart (i.e., set of selection curves) is developed for each of the
two performance limit states (LS, 10/50 and JO, 50/50) at a given percentile value, or
non-exceedence probability. The design chart can thus be used to select a particular
sheathing type and fastener spacing for a given seismic weight to ensure that the wall
performs within the specified drift limit. The performance curves presented previously
(see Figures 4.80 through 4.91) are used to construct examples of these design charts.
Design charts for baseline wall BW1 (8 ft.
x
8 ft. solid wall) are shown in Figures 4.92
and 4.93 for the JO (50/50) and LS (10/50) limit states, respectively. Design charts for
baseline wall OWl (16 ft.
x
8 ft. wall with a large garage door opening) are shown in
Figures 4.95 and 4.96, for the same two performance limit states.
112
3.5
/
/ 99% (LS)
8ff
3.0
/
8ff
2.5
BW (8
ED
8'), @3/6", OSB (/"),
x
'8,
G = 180 ksi,
= 2%
/ 90% (LS)
/ , a,
777
,' ./._' 84% (LS)
2%Drift=1.92in.
2.0
/ 95% (LS)
><
E
ro
.-- 50% (LS)
1.5
1% Drift= 096 in.
1.0
99% (10)
0.75%Drift=072ui.
95%(l0)
0.5
0.0
400
600
800
1000
1200
1600
1400
2000
1800
Seismic Weight (Ibs/ft)
Figure 4.80 Performance curve for BW1, OSB (3/8-in.), @3"/6"
5
99% (LS)
88.
4
88.
BW (8'
x
8'), @4"/12", OSB
95% (LS)
(/8"),
ED3/8", G180ks1, =2%
90% (LS)
3
84% (LS)
/
E
02
2%Drift=1.92jn.
1% Drift = 0.96 in.
9s
1
400
600
800
1000
1200
1400
1600
Seismic Weight (Ibs/ft)
Figure 481 Performance curve for BW1, OSB (3/8-in.), @4"/12"
1800
0
2000
113
6.5
6.0
/ 99% (LS)
8 ft.
5.5
5.0
8 ft.
4.5
SW (8' x 8'), @6"/6", os ç3i"),
ED = /8", G = 180 ksi, = 2%
4.0
95% (LS)
90% (LS)
3.5
.
/
84% (LS)
J3.0
2.5
50% (LS)
2% Drift = 1.92 in
2.0
99% (tO)
1.5
1.0
0.5
0.0
400
600
800
1000
1400
1200
1800
1600
2000
Seismic Weight (Ibs/ft)
Figure 4.82 Performance curve for BW1, OSB (3/8-in.), @6"/6"
3.5
99% (LS)
8ft.
3.0
8 ft.
95% (LS)
2.5
BW (8'>< 8'), @6/12",
OSB(3/8"), ED=3/8",
G = 180 ksi, = 2%
, 99% (10)
90% (LS)
84% (LS)
2.0
E
I
2%Drift=1
95% (10)
90% (10)
/,2'
1.5
1.0
/
V
50% (LS)
::--
84% (10)
1% Drift = 0.96 in.
0 75% DrIft2_
0.5
0.0
400
600
800
1000
1200
1400
1600
Seismic Weight (Ibs/ft)
Figure 4.83 Performance curve for BW1, OSB (3/8-in.), @6"/12"
1800
2000
114
2000
1800
84% 90% 95% 99% (LS)
50%
50, 84, 90, 95, 99% (tO)
1600
E
(I,
. 1400
0)
1200
0
E 1000
C/)
ii:'
a)
i
800
Ij
!!
:iiii
I
/ ,/
/,?,'
i'l
.
8 ft.
:'.
8ft
a
BW (8'
x
8'), @3/6", OSB
(3/),
ED=3/8",G=l8oksi,ç=2%
400
0.0
0.5
1.0
2.5
2.0
1.5
3.0
3.5
max (in.)
Figure 4.84 Performance curve for BW1, OSB (3/8-in.), @3"/6", axes switched
99% (LS)
8 ft.
3.0
/
8ft.
2.5
1 0
BW (8'
x
I'
8'), 8d@3"/6", PWD (/")
G=60 ksi
2/o
95% (LS)
1/ Drift = 096 in
j90%(IO)
0.5
84% (tO)
50% (tO)
0.0
400
600
800
1000
1200
1400
1600
Seismic Weight (Ibs/ft)
Figure 4.85 Performance curve for BW1, PWD (3/8-in.), 8d@3"/6"
1800
2000
115
6
8ft.
/
5
99%(LS)
/
8ft.
BW (8' x 8'), 8d@4"/12", PWD (3/J
4
ED
/8, G = 60 ksi, ç = 2% I"
/
/
/
c
7
/
/
/ 95% (LS)
,.
90%(LS)
/ /, 84%(LS)
E
2
1
;
0
400
600
800
1000
1200
1600
1400
1800
2000
Seismic Weight (Ibs/ft)
Figure 4.86 Performance curve for BW1, PWD (3/8-in.), 8d@4"/12"
9
99% (LS)
8
7
H
H96mn
184 in.
OW (16' x 8), @3/3", OSB (/8"),
6
ED=3/8",G=l8Oksi,ç=2%,
5
/
95% (LS)
90% (LS)
7/ 84% (LS)
'8
E4
3
100
300
500
700
900
1100
Seismic Weight (Ibs/ft)
Figure 4.87 Performance curve for OWl, OSB (3/8-in.), @3"/3"
1300
1500
116
8
199%(LS)
I
I
7
96 in.
184 in.
6
OW (16'
95% (LS)
8'), @4"14", OSB (/'),
ED=3/8", G= 180 ksi,ç=2%,
5
E
e.o
3
i;
2
0
100
300
500
900
700
1100
1300
1500
Seismic Weight (Ibs/ft)
Figure 4.88 Performance curve for OWl, OSB (3/8-in.), @4"/4"
9
8
[J96in
99% (10)1
L__J
7
184 in.
OW (16'x 8'), @6/6", OSB (/8").
6
95% (LS) ED =
G
90% (LS)
95% (10)
x
E4
84% (LS)
90% (10)
84% (10)
3
2
0
100
300
500
700
900
1100
Seismic Weight (lbs/fl)
Figure 4.89 Performance curve for OWl, OSB (3/8-in.), @6"/6"
1300
1500
117
6
96 in.
H
5
/
184 in.
/
OW (16 x 8'), 8d©4"/4", PWD (/a")/
4
99% (LS)
ED = '8, 0 = 180 ksi,
= 2%,
/
/
C
8<3
j
95% (LS)
90% (LS)
::::
84% (LS)
99%
95%
90%
84%
E
2
L
(10)
(10)
(10)
(10)
3.
1
0
300
100
500
700
900
1100
1300
1500
Seismic Weight (Ibs/ft)
Figure 4.90 Performance curve for OWl, PWD (3/8-in.), 8d@4"/4"
6
I
I
99%(l0)
I
96 in.
5
OW (16' >< 8'), 8d@6"16", PWD (/8"),
ED=3/<",G=l8Oksi,ç=2%,
184 in.
99/o(LS)
,,
4
I
950/0 '10
1
/95%(LS)
/ 90% (LS)
3
90% (10)
84%(LS)
/,//
84% (10)
TI!' Tr;O;I
100
300
500
700
900
1100
1300
Seismic Weight (Ibs/ft)
Figure 4.91 Performance curve for OWl, PWD (3/8-in.), 8d@6"/6"
1500
118
3.5
8 ft.
3.0
/ 95% (COV=30%)
/, 95% (COV=15%)
/ 95% (COV=0%)
784% (COV=30%)
8ft.
2.5
8W (8 x 8'), ©3"/6", OSB (/8"),
ED3/8",G180ksi,?=2%
84% (COV=15%)
84% (COV=0%)
2% Drift= 1.92 in.
><
cE 1.5
1.0
0.5
0.0200
400
600
800
1000
1200
1400
1600
1800
2000
2200
Seismic Weight (Ibs/ft)
Figure 4.92 Effect of model uncertainty on performance curve for BW1, OSB (3/8-in.),
@3"/6"
2.0
PWD (4/12")
j OSB (6/12")
1.8
1.6
8ft.
1.4
f,
BW (8 x 8), ED /" = 2%,
G08 = 180 ksi, GPWD = 60 ksi, 10(50/50)
1.2
C
./
,v
1.0
1% Drift = 0.96 in.
0.8
0.75% Drift = 0.72 in.
/
OSB (6/6")
OSB(4"i12")
E
..V
OSB (3/6")
PWD(3"/6')
0.6
0.4
0.2
0.0
400
600
800
1000
1200
1400
1600
Seismic Weight (Ibs!ft)
Figure 4.93 95t11-Percentile design chart for BW1, TO (50/50)
1800
2000
119
6
8 ft.
5
8 ft.
OSB (6/6")
BW(8'x8'), ED3/5",=2%,
4
G055 = 180 ksi, GFWD = 60 ksi,
LS (10/50)
PWD (4/12")
OSB (4/12")
PWD (4/12")
PWD (3/6')
E
2
2% Drift
0-!
400
600
800
1000
1200
1400
1600
1800
2000
Seismic Weight (Ibs/ft)
Figure 4.94 95t''-Percenti1e design chart for BW1, LS (10/50)
5
OSB (6/6"
V
Li 96 in.
4
L__j
184 in.
)ND (6/6"
BW(16' x 8'), ED = '8,
= 2%,
G0s8 = 180 ksi, GPWD
60 ksi,
0DB (4"/4"
10 (50/50)
3
C
B (3/3")
E
'D (4/4"
2
1
0-!
100
300
500
700
900
1100
Seismic Weight (!bs/ft)
Figure 495 95thPercenti1e design chart for OWl, JO (50/50)
1300
1500
120
7
L_J 96 in.
6
OSB (6/6")
L_i
OSB (4"/4")
184 in.
5
8W (16 x 8), ED
3/a",
/
= 2%,
GOSB = 180 ksi, GPWD = 60 ksi,
LS (10/50)
PWD (4"/4")
PWD
9
.c3
2
1 2% Drift= 1.92 i
1
0!
100
200
300
400
500
600
700
Seismic Weight (Ibs/ft)
Figure 4.96 95t1'-Percentile design chart for OW!, LS (50/50)
800
121
4.3.2.2 Construction quality
4.3.2.2.1 Construction of performance curves
The peak displacement distributions for the three different construction
qualities (superior, typical, and poor) were compared in Section 4.2.4. Significant
differences were observed among walls built with different construction quality levels.
The post-processing procedure described in Section 4.3.2.1 also was used to construct
performance curves considering different construction quality levels.
Performance curves for BW1, assuming 3/8-in. OSB, 4"/12" nailing schedule
with two rows of nails along the sides of the wall (as was tested in CUREE Task
1.3.1), were developed considering the three different levels of construction quality
defined in Table 4.5. These are shown in Figures 4.97 through 4.99. Each figure shows
the 95% and 84% non-exceedence curves, for the life safety (LS, 10/50) limit states.
Also shown is the FEMA 356 drift limit of 2% for life safety (LS, 10/50). Considering
Figure 4.99, and assuming a target peak drift non-exceedence probability of 95% and a
drift limit of 2% for LS (10/50), the wall built with superior quality and having
parameters shown in the figure can sustain about 1700 lbs/fl, the wall built with
typical quality can sustain about 1450 lbs/ft, and the wall built with poor quality can
sustain about 1030 lbs/ft.
Performance curves for OWl, assuming 3/8-in. OSB and a 3"/12" nailing
schedule, are shown in Figures 4.100 through 4.103. As with the BW1 performance
curves, each figure shows the 95% and 84% non-exceedence curves, for the life safety
(LS, 10/50) limit state and the corresponding drift limit. Note that model uncertainty
122
and sheathing-toframing hysteretic parameter variability are not explicitly considered
in developing the performance curves and design charts in this section since the
shearwall global hysteretic parameters were obtained directly the experimental test
results (see Section 4.2.4).
4.3.2.2.2 Design charts
Design charts are constructed using the information in the performance curves.
As an example, design charts (i.e., sets of selection curves) are developed for the LS
(10/50) performance limit state at a given percentile value, or non-exceedence
probability. The design chart can thus be used to select a particular sheathing type and
nonstructural finish material combination (with consideration of construction quality)
for a given seismic weight. The performance curves presented previously (see Figures
4.97 through 4.103) are used to construct examples of these design charts. Design
charts for BW1 (8 ft.
x
8 ft. solid wall) are shown in Figures 4.104 and 4.105 for
typical and poor quality, respectively. Design charts for OWl (16 ft. wall with a large
garage door opening) are shown in Figures 4.106 and 4.107, again for the two
construction quality levels. Figures 4.108 and 4.109 present design charts for the two
different walls (BW1 with OSB + Stucco, and OWl with OSB + GWB + Stucco)
considering the three different levels of quality. Note that CUREE Task 1.3.1 did not
consider walls sheathed with OSB and both GWB and stucco.
123
4.5
4.0
95% (POOR)
8ff
88
BW (8' x 8), 8d@4"/12" (2 rows),
3.0
OSB (/8"),
= 2%, [S (1 0/50),
84% (POOR)
OSB only
2.5
j2.0
95%(TYP.)
2% Drift = 1.92 in.
84%(TYP.)
1.5
95% (SUP.)
84% (SUP.)
1.0
200
400
800
600
1000
1200
Seismic Weight (Ibs/ft)
Figure 4.97 Performance curve for BW1, OSB only
4.0
95% (POOR)
8ff.
3.5
3.0
84% (POOR)
BW (8' x 8'), 8d©4"/12" (2 rows),
OSB (3/), ç = 2%, LS (10/50),
2.5
OSB+GWB
95% (TYP.)
29
84% (TYP.)
95% (SUP.)
84% (SUP.)
1.0
0.5
200
400
600
800
1000
1200
Seismic Weight (Ibs/ft)
Figure 4.98 Performance curve for BW1, OSB + GWB
1400
1600
1800
124
5.0
/
4.5
8 ft.
95% (POOR)
4.0
/
8 ft.
3.5
BW (8' x 8'), 8d@4"/12" (2 rows),
OSB (/"), = 2%, LS (10/50),
3.0
OSB+Stucco
,..
84% (POOR)
95%(TYP.)
2.5
E
84% (TYP.)
95% (SUP.)
84% (SUP.)
2
2.0
1.5
1.0
0.5
0.0
200
700
2200
1700
1200
Seismic Weight (Ibs/ft)
Figure 4.99 Performance curve for BW1, OSB + Stucco
4.0
I
95% (POOR)
I
L_i
3.0
16ft.
84% (POOR)
OW (16' x 8'), 8d@3"/12", OSB (/"),
ç = 2%, LS (10/50), OSB only
C
2% Drift= 1.92 in.
2.0
1.5
95% (TYP.)
84% (TYP.)
95% (SUP.)
84% (SUP.)
,,./_
..-
1.0 -
...___.,_'
0.5
o.oi
100
200
300
400
500
Seismic Weight (Ibs/ft)
Figure 4.100 Performance curve for OWl, OSB only
600
700
800
125
/
H
3.0
95% (POOR)
1186
16ft.
84% (POOR)
OW (16' < 8'), 8d@3"/12", OSB (/8"),
= 2%, LS(10/50), OSB + GWB
2 5
C
95%
84%
95%
84%
2°A
(TYP.)
(TYP.)
(SUP.)
(SUP.)
1.0:
0.5
0.0 mrr
100
200
300
400
500
600
700
800
Seismic Weight (Ibs/ft)
Figure 4.101 Performance curve for OWl, OSB + GWB
95% (POOR)
:
H
3.0
1186.
l6ft.
84% (POOR)
OW (16' < 8'), 8d©3"/12", OSB (/8"),
ç = 2%, LS (1 0/50), OSB + Stucco
2.5
C
2%Drjftl.921n.
95%
84%
95%
84%
(TYP.)
(TYP.)
(SUP.)
(SUP.)
H
0.0
100
200
300
400
500
Seismic Weight (Ibs/ft)
Figure 4.102 Performance curve for OWl, OSB + Stucco
600
700
800
126
4.0
95% (POOR)
H
3.0
H8ft
16 ft.
./
OW (16 x 8), 8d©3/12", OSB (/"),
= 2%, LS (10/50),
OSB + GWB + Stucco
2 5
2%Drrft=1.92in.
2.0
./
//
/
/
/
/
/
/ 95% (TYP.)
/ V/ // ,,
./
E
..
84% (POOR)
84% (TYP.)
95%(SUP.)
,./ 84% (SUP.)
1.5
1.0
::
100
300
500
700
900
Seismic Weight (lbs/ft)
Figure 4.103 Performance curve for Owl, OSB + GWB + Stucco
5.0
OSB + Stucco
4.5
4.0
3.5
3.0
2.5
E
2.0
2% Drift = 1.92 in.
//
8 ft.
2" (2 rows),
(10/50),
Poor Quality
200
700
1200
1700
Seismic Weight (Ibs/ft)
Figure 4.104 95thPercentile design chart for BW1, poor quality
2200
127
3.0
OSB + Stucco
2.5
OSB+GWB
/
OSB only
220
1921fl1
Typical Quality
0.0
200
700
2200
1700
1200
Seismic Weight (lbs/ft)
Figure 4.105 95thPercentile design chart for BW1, typical quality
4.0
OSB + GWB + Stucco
3.5
OSB + Stucco
/
,1
-//
,)&
/
I
//
/
3.0
OSB+GWBIII1uI'I?"
2.5
OSB only
2
/ //
,/
2%Drift=1.921n.
2.0
i
/
/
..
H
::
0.5
118ff
16ff.
OW (16 >< 8'), 8d@3"/12",
-'
OSB (I8"),
= 2%, LS (10/50).
Poor Quality
0.0
100
300
500
700
Seismic Weight (lbslft)
Figure 4.106 95thPercentile design chart for OWl, poor quality
900
2.5
2.0
2% Drift
1.92
/
in.
OSB + GWB + Stucco
1.5
OSB + Stucco
OSB only
H8tt
H
166.
OW (16 x 8'), 8d@3"/12",
OSB
(/8),
= 2%, LS (10/50),
Typical Quality
0.0
100
500
300
700
900
Seismic Weight (lbslft)
Figure
4.107
95th1Percenti1e design chart for OWl, typical quality
5.0
4.5
/
/
8ft.
401
8 ft.
POOR
BW (8'>< 8'), 8d@4"/12" (2 rows),
OSB (I"), = 2%, LS (10/50),
3.5
OSB+Stucco
3.0
10
200
700
1200
1700
Seismic Weight (lbs/ft)
Figure
4.108
95thPercentile design chart for BW1, (OSB + Stucco)
2200
129
:,
3.0
POOR
H
l6ft
OW (16 x 8'), 8d@3"/12', OSB (/8"),
ç = 2%, LS (10/50),
2.5
OSB + GWB + Stucco
C
TYP.
sup.
1.0
0.5
0.0
100
300
500
700
Seismic Weight (lbs/It)
Figure 4.109 95thPercenti1e design chart for OWl, (OSB + GWB + Stucco)
900
130
4.3.2.3 Effects of different seismic hazard regions
In Section 4.2.5, shearwall performance was compared for three different
hazard regions (LA, Seattle, and Boston). Different suites of earthquake records,
characterizing each of the three regions, were used to develop peak displacement
distributions. Again using the post-processing procedure described in Section 4.3.2.1,
performance curves were developed for one wall configuration (BW1) for each of the
three different seismic hazard regions.
Performance curves for BW1, assuming 3/8-in. OSB, Durham fastener
parameters, and three different fastener spacings are shown in Figures 4.110 through
4.117. Considering Figures 4.115 through 4.117, assuming a drift limit of 2% for LS
(10/50) and a target peak drift non-exceedence probability of 95%, the wall having the
parameters shown in the figure can sustain about 1900 lbs/ft in seismic zone II
(Boston), 920 lbs/ft in seismic zone III (Seattle), and 700 lbs/ft in seismic zone IV
(LA). Design charts (see Section 4.3.1) were constructed using the information in the
performance curves. The design charts for the baseline solid wall BW1 (8 ft.
x
8 ft.),
considering the life safety (10/50) limit state, is shown in Figures 4.118. Since Boston
(seismic zone II) is a relatively low seismic hazard region, the 3"/12" nailing schedule
was not considered. Note also that only OSB sheathing materials were considered.
131
4.0
/99%
8ft.
3.5
8ft.
3Q
95%
2.5
BW (8 x 8'), @3"/12", OSB (/8"),
ED = '8, G = 180 ksi, ç 2%,
Seismic Zone Ill (Seattle), LS (10/50)
2.0
2% Drift = 1.92 in.
/
,'
9Q%
// 84%
," //
/
-,.
1
"
," ..-."
1 .5
50%
.-'
_-.9
1.0
_-.._.--
0.5
0.0
I
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
Seismic Weight (Ibs/ft)
Figure 4.110 Performance curve for BW1, seismic zone III (Seattle), @3"/12"
7.0
/
/99%
8ft.
6.0
8ft.
// /
5.0
BW(8'x8'),@3"/12",OSB(3/8"),
. 95%
G = 180 ksi, ç = 2%,
ED =
Seismic Zone IV (LA), LS (10/50)
4.0
:::
3.0
50%
2% Drift = 1.92 in.
0.0
200
r-rrTJ-r--r---r--rJ--r---1
400
600
800
I
1000
!!IrrIrI!!rrIr
1200
1400
1600
1800
2000
Seismic Weight (bs!ft)
Figure 4.111 Performance curve for BW1, seismic zone IV (LA), @3"/12"
2200
132
7.0
8ft.
6.0
8 ft.
5.0
BW(8
ED =
x
8), @4"112", OSB (I"),
G = 180 ksi, ç= 2%,
/8.
Seismic Zone II (Boston), LS (10/50)
4.0
95%
2% Drift= 1.92 in.
50%
1.0
I
0.0
0
C
I
500
1000
1500
2000
2500
I
3000
3500
4000
Seismic Weight (lbs/fl)
Figure 4.112 Performance curve for BW1, seismic zone II (Boston), @4"/12"
4.0
99%
3.5
8ff.
8ft.
3.0
2.5
BW (8' x 8'), @4/12", OSB (/").
ED
G = 180 ksi, = 2%,
Seismic Zone III (Seattle), LS (10/50)
2.0
2%Driftl.92jn.
//
/
95%
90%
84%
1.5
50%
0.0
200
400
600
800
1000
1200
1400
1600
1800
2000
Seismic Weight (lbs/ft)
Figure 4.113 Performance curve for BW1, seismic zone III (Seattle), @4"/12"
133
99%
8ft.
L8L
3.5
BW (8'
x
95%
8'), @4/12", OSB (/8"),
ED=3/8",G=l8oksi,ç=2%,
90%
Seismic Zone IV (LA), LS (1 0/50)
84%
2.5
0
2% Drift = 1.92 in.
2.0
50%
0.0
400
200
600
1200
1000
800
1600
1400
Seismic Weight (Ibs/ft)
Figure 4.114 Performance curve for BW1, seismic zone IV (LA), @4"/12"
6.0
/ 99%
1
8ft.
5.0
8 ft.
BW (8'
4.0
x
8'), @6/12" OSB (/8"),
ED-3/8",G- l8Oksi,ç2%,
Seismic Zone II (Boston), LS (10/50)
95%
3.0
90%
E
84%
2.0
-
2% Drift = 1.92 in.
50%
1.0
0.0
0
500
1000
1500
2000
2500
3000
Seismic Weight (Ibs/ft)
Figure 4.115 Performance curve for BW1, seismic zone II (Boston), @6"/12"
134
_18ft
8W (8'
40
x
/L%
8'), @6/12", OSB (/"),
ED3/8",G180ksi,1=2%,
Seismic Zone Ill (Seattle), LS (10/50)
95%
90%
:.z
3.0
84%!
2°/ Drift = 1 92 in
2 0
."
-- - -
50%
1.0
0 J
-] ..............
200
400
T---r----r--
600
!I!!--------r--------r
800
F
1000
1200
Seismic Weight (Ibs!ft)
Figure 4.116 Performance curve for BW1, seismic zone III (Seattle), @6"/12"
3.5
99%
8ft.
3.0
8 ft.
2.5
BW (8'
x
8'), @6/12", OSB
(/8"),
ED3/e",Gl8Oksi,/=2%,
Seismic Zone IV (LA), LS (10150)
2.0
2% Drift= 1.92 in.
><
E
.c
1.5
0.0
200
300
400
500
600
700
800
Seismic Weight (Ibs/ft)
Figure 4.117 Performance curve for BW1, seismic zone IV (LA), @6"/12"
900
135
5.0
LA (3/12")
4.5
4.0
BOS (4/12")
LA (4/12")
(6/12")
3.5
3.0
LA (6/1 2")
SEA(3"
/
(4/112")
/
D=2
2.0
0
500
/SEA(
1000
1500
2000
2500
3000
Seismic Weight (lbslft)
Figure 4.118 95th..percentile design chart for BW1, LS (10/50)
3500
4000
136
4.4 Performance-based design
4.4.1 Incremental dynamic analysis
Development and implementation of performance-based design requires
translating performance requirements into structural checking equations for use by
design engineers. This is not always straightforward and may present considerable
challenges to codes and standards committees. Even among CCWP Element 1
researchers, and the broader community of earthquake engineers in general, the three
performance levels and corresponding drift limits specified in FEMA 356 (e.g.) have
raised questions. The limit state associated with structural collapse is well understood
by structural engineers. Performance limit states associated with life safety (LS, 10/50)
(access/egress) and immediate occupancy (JO, 50/50) are less well defined and less
well understood. The FEMA 356 drift limits for woodframe shearwalls were adopted
in this study, and no further statement is made about their suitability as a basis for
performance-based design.
It may be possible to use nonlinear analysis models (such as CASHEW and
SASH1) to evaluate appropriate definitions for the collapse prevention (e.g., CP, 2/50)
limit state. This approach, called an Incremental Dynamic Analysis (IDA), has been
applied to nonlinear MDOF systems [Cornell, 2000]. Incremental dynamic analysis
(IDA) is a new analysis method that involves performing nonlinear dynamic analyses
of the structural model under a suite of earthquake ground motion records, each scaled
to several intensity levels designed to force the structure all the way from elasticity to
final global dynamic instability [Vamvatsikos, 2002].
137
In an IDA, given record is scaled incrementally and the nonlinear response
(peak displacement) is evaluated. Thus, for each record considered, a curve of spectral
acceleration
(Sa) vs. peak displacement is obtained. Among the characteristics of these
curves is often a point at which the "slope" reduces dramatically, indicating a
Sa
value
above which the displacement increases very quickly. This is analogous to the
buckling response one sees in an imperfect column. If such a point can be evaluated
for a range of structural configurations and ground motion records, for example, it
may be possible to suggest a physically-based drift limit associated with impending
collapse. This concept is briefly explored here using the CASHEW modeling
procedure, BW1, and the ordinary ground motion records used in this study. The suite
of 20 ordinary ground motion records was divided into three groups because it was too
crowded to show all results on one figure. Two types of baseline shearwalls were
considered, BW1 and OWl. Figure 4.119 shows a typical IDA curve obtained from
nonlinear dynamic time history analysis with increasing spectral acceleration. The
IDA curve usually starts linearly in the elastic range, however, it becomes highly
nonlinear after it reaches the break point with a dramatic change in slope. (A
phenomenon, termed structural resurrection, has been observed in which a system is
pushed all the way to global collapse at some intensity measure, only to "reappear" as
non-collapsing at a higher intensity level [Vamvatsikos, 2002J.) One method for
estimating the collapse prevention point is shown in Figure 4.120. For comparison, the
collapse prevention (CP) 3% drift limit provided by FEMA 356 also is shown.
138
Figures 4.121 through 4.123 show Sa vs. peak displacement for baseline wall
BW1. Also shown are the tangents defining the apparent break points for those points.
A characteristic value could be selected as the design drift limit for collapse
prevention (CP, 2/50). For this particular example, the mean value corresponds to a
peak displacement of 3.04 in., or about 3.17% of the wall height. (Note that the FEMA
356 drift limit for collapse prevention (CP, 2/50) is 3% for wood shearwalls.) Figures
4.124 through 4.126 show Sa vs. peak displacement for the baseline wall with the large
opening. Also shown are the tangents defining the apparent break points for those
points. A characteristic value could be selected as the design drift limit for collapse
prevention (CP, 2/50). In this example, the mean value corresponds to a peak
displacement of 3.70 in., or about 3.86% of the wall height. This approach to limit
state identification appears to have merit and may be worth further study. The IDA
approach is expected to be more appropriate, however, for the analysis of entire
buildings rather than individual subassemblies.
139
1.2
1.0
0.8
0.6
C,)
0.4
0.2
0.0
0.0
10.0
20.0
40.0
30.0
6max
50.0
60.0
70.0
(in.)
Figure 4.119 Typical IDA curve
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
2.0
4.0
6.0
max (in.)
Figure 4.120 Estimated collapse points by tangent slope
8.0
10.0
140
1.0
0.9
0.8
0.7
0.6
a,
0.5
(I)
0.4
0.3
0.2
0.1
0.0
0
1
2
3
4
5
max
6
7
8
9
10
6
7
8
9
10
(in.)
Figure 4.12 1 Set of IDA curves (BW1, group 1)
1.5
1.2
0.9
a)
(I)
0.6
0.3
0.0
0
1
2
3
4
5
6max (in1)
Figure 4.122 Set of IDA curves (BW1, group 2)
141
1.2
1.0
0)
0.6
C,)
0.4
0.2
0.0
0
1
2
3
4
5
6
7
8
9
10
6
7
8
9
10
ömax (im)
Figure 4.123 Set of IDA curves (BW1, group 3)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0
1
2
3
4
5
ömax (in.)
Figure 4.124 Set of IDA curves (Owl, group 1)
142
2.0
1.8
1.6
1.4
1.2
C)
1.0
(I)
0.8
0.6
0.4
0.2
0.0
0
1
2
3
4
5
6
7
8
9
10
6
7
8
9
10
max (in.)
Figure 4.125 Set of IDA curves (OWl, group 2)
1.0
0.8
C)
0.6
0)
0.4
0.2
0.0
0
1
2
3
4
5
max 011)
Figure 4.126. Set of IDA curves (Owl, group 3)
143
4.4.2
Fragility curves
While performance curves are constructed as a function of seismic weight,
fragility curves can be develop as a function of hazard level (e.g., spectral
acceleration, Sa). This fragility approach has a number of potential advantages,
particularly when considering multiple damage states. Such an approach also may be
useful for performing loss estimation studies. A fragility methodology may have
applications to design and post-earthquake condition assessment {Rosowsky and
Ellingwood, 2001].
The fragility of a structural system commonly is modeled by a lognormal
distribution function (CDF). The lognormal CDF is given by:
FR(y)=
[ln(Y/mR)
(4.11)
where 1(.) = standard normal distribution function, mR = median capacity and R =
logarithmic standard deviation of capacity, approximately equal to the coefficient of
variation (COy),
4.4.2.1
VR,
when VR<O.3.
Fragility curve based on peak displacement
The baseline solid shearwall BW1 (8 ft.
x
8 ft.), with two OSB sheathing
panels oriented vertically, was used to develop illustrative fragility curves. The Folz
nail parameters were used to develop the global hysteretic parameters of the shearwall
using CASHEW. Various nailing schedules
(2"112", 3"/12", 4"/12",
and
6"/12")
and
the corresponding allowable seismic weights (back-calculated from the UBC '97
144
allowable unit shear values) were considered. Since the UBC '97 allowable unit shear
values include nonstructural finish material contribution and assume the wall is acting
as part of an entire woodframe building, it is necessary to consider the appropriate
overstrength factor (R) when converting allowable unit shears to seismic weights.
Since the assembly considered here is an isolated shearwall, values of R factor ranging
from 2.5 to 5.5 were considered when developing the fragility curves.
The total horizontal base shear, V, can be derived using the following equation:
F=ma=[Ja=[JW
in which, F = force, m
(4.12)
mass, a = acceleration, and g = acceleration due to gravity.
The UBC '97 form of this expression is somewhat modified. The (a/g) term is
replaced by a "seismic base shear coefficient". The UBC '97 base shear formula for a
the main lateral force resisting system is given by:
=
v
CI
2.5C1
RT
R
W
25"wo.l1c
1W
R
2.5CI
w
(4.13)
O.8ZCI w (for seismic zone 4
where V = base shear, W = weight of structure, CVI/RT = velocity-based seismic base
shear coefficient, 2.5CaI/R = acceleration-based seismic base shear coefficient, Z
seismic zone factor, I = occupancy importance factor, Ca and C
spectrum) coefficients, and T =
C1(h)213 =
==
seismic (response
structure period [ICBO, 1997; Breyer et.
al., 1998]. The acceleration-based seismic base shear coefficient (2.5CaI/R) usually
governs for buildings with short fundamental periods, and most woodframe structures
145
fall into this category. Therefore, using eqs. 4.12 and 4.13, and the allowable unit
shear values from UBC '97 Table IT-I-i, the seismic weight can be obtained. These
values are shown in Table 4.15 for the cases considered here (importance factor of 1.0,
seismic zone 4, soil profile type D, and various overstrength factors). Only unit shear
values considering 3/8-in. thick sheathing panel and 8d nails are used to calculate
seismic weights from allowable unit shear values in Table 23-IT-I-i in the UBC '97.
Panel
grade
Structurall
Minimum
nominal
panel
thickness
Minimum
nail
penetration
in framing
/8
l'/2
Overstrength factor
(R)
2.5
3.5
4.5
5.5
Panel applied directly to framing
Nail spacing at panel edges
Nail size
8d
Seismic base
shear coefficient
0.440
0.314
0.244
0.200
(in).
6
4
3
2
230
360
460
610
Weight (lb.)
5854.5
8203.8
10557.4
12880.0
I
9163.6
12840.8
16524.6
20160.0
I
11709.1
16407.6
21114.8
25760.0
I
15527.3
21758.0
28000.0
34160.0
Table 4.15 Seismic weights calculated based on UBC '97 allowable unit shear values
(Table 23-TI-I-i)
The peak displacement curves were next developed for the different nailing
schedules and R factors. Figures 4.127 through 4.129 show the sample CDF's
assuming a 3"/12" nailing schedule, various R factors, and the three different hazard
levels (JO, LS, CP). As expected, as the R factor increases, the allowable seismic
weight increases, and hence shearwall peak displacement increases. Peak displacement
curves for the other nailing schedules are provided in Appendix E.
0.9
V
/
0.8
R=2.5, W=1464 lbs/ft
R=3.5, W=2051 lbs/ft
0.7
W=2639 lbs/ft
0.6
/
0.5
R5.5, W=3229 lbs/ft
U-
0.4
0.3
//
;1
0.2
0.1
/
___
88.
88.
/
0
BW (8' x 8), 8d@3/12", OSB (/8"),
ED=3/5',G=200ksi,ç2%, 10 (50/50)
n
0
0.2
0.4
0.6
0.8
1.2
1
1.4
1.6
2
1.8
ömax (in.)
Figure 4.127 Peak displacement distributions for different R factors (3"/12", JO)
--
-
0.9
---
/
0.8
/
/
/
0.7
0.6
/
0.5
/
R=3.5, W=2051 lbs/ft
/
R=4.5, W=2639 lbs/ft
/
I
0.4
/
R=2.5, W1464 lbs/ft
V
U-
0.3
,'
R5.5, W=3229 lbs/ft
/
/
8ft.
0.2
1/:'
0.1
88.
0
8W (8' x 8'), 8d©3 /12 , OSB (I8"),
ED
- -
n
0
0.5
1
1.5
2
2.5
3
3.5
G = 200 ksi,ç = 2%, LS (10/50)
4
4.5
5
5.5
6
ömax (in.)
Figure 4.128 Peak displacement distributions for different R factors (3"/12", LS)
147
0.9
R=2.5, W=1464 lbs/ft
0.8
R=3.5, W=2051 lbs/ft
0.7
R=4.5, W=2639 lbs/ft
0.6
R=5.5, W=3229 lbs/ft
0.5
U-
,,
0.4
0.3
fl8ft.
0.2
/,/
0.1
-.
n
0
0.5
1
1.5
2
BW (8 < 8), 8d@3"/12", OSB (/8'),
G = 200 ksi, ç = 2%, CP (2/50)
ED =
-
2.5
3
max
3.5
4
4.5
5
5.5
6
(in.)
Figure 4.129 Peak displacement distributions for different R factors (3"/12", CP)
By changing the spectral acceleration for the 20 earthquake records, a peak
displacement CDF can be developed for each level of scaling. The probability of
failure can be determined non-parametrically as the relative frequency of the peak
displacement exceeding the specified drift limits. If this probability of failure is
conditioned on a given value of spectral acceleration, this becomes one point on the
fragility curve. This has the advantage of not requiring that a particular distribution be
fit to the peak displacements. The records were scaled to five different hazard levels:
50% in
50
years (72-year mean return period or MRI), 20% in
50
years (225-year
MRI), 10% in 50 years (474-year MRI), 5% in 50 years (975-year MRI) and 2% in 50
years (2475-year Mifi).
Figures 4.130 through 4.133 present fragility curves for a baseline solid wall (8
ft.
x
8 ft.) with two full sizes OSB sheathing panels oriented vertically, and four
different nailing schedules. The wall is assumed to be fully anchored. The effective
seismic weight acting on the wall was determined based on the allowable unit shear
values in the UBC '97, as described previously. An overstrength factor (R) of 5.5 was
assumed and drift limits of 1%, 2% and 3% were considered. The seismic demand
(interface) variable is spectral acceleration, Sa. Fragility curves of this type can be
used either as design aids or to assess risk consistency in current design provisions.
The fragility curves for other overstrength factors (2.5, 3.5 and 4.5) are provided in
Appendix F.
1
70.9
/
8ft.
0.8
/,,
/
8ft.
BW (8' x 8'), 8d@2"112", OSB (/"), /"-
0.7
ED=318",G= 185ksi,=2%, R=.5
W = 4271 lbs/ft (152.0 kN total)
/
0.6
0 (50/50)
/
0.5
/
/
0.4
/ /
0.3
,'
//
0.2
0.1
Ii
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Sa(g)
Figure 4.130 Fragility curves for three different hazard levels (2"/12")
2
149
1
- -
0.9
0.8
10 (50/50)
/
0.7
/
/
0.6
/,",
/
0.4
,'
/
/
//,,,,
0.3
/ / ,/
0.2
8ft.
8W (8'
/ 1/
0.1
x
8'), 8d@3"/12", OSB (I")
ED=3/8",G=200ksi,ç=2%, R=5.5
--
W = 3220 lbs/ft (114.6 kN total)
-
C)
0
0.5
2
1.5
1
2.5
S5(g)
Figure 4.131 Fragility curves for three different hazard levels (3"/12")
1
- - -
0.9
0.8
I0 (50/50)
0.7
0.6
CP (2/50)
'
/
//,,,,,
0.4
//,,,,
0.3
/ /
// //
0.2
0.1
8ft.
'
x 8'), 8d@4"/l 2", OSB
ED = /8, G = 180 ksi, = 2%, R = 5.5
W = 2521 lbs/ft (89.7 kN total)
BW (8
--
(1
0
0.5
1.5
1
2
Sa(g)
Figure 4.132 Fragility curves for three different hazard levels (4"/12")
2.5
150
0.9
0.8
/
0.7
0.6
a
/
0 (50/50)
/,,,
0.5
//,,,,,
0.4
//:"
0.3
0.2
/,,'
BW (8 x 8), 8d@6112", OSB (/8"),
/'
0.1
ED=3/5",G=185ksi,=2%,R=5.5
W = 1610 lbs/ft (57.3 kN total)
QL
0
0.5
1.5
1
2
2.5
Sa(g)
Figure 4.133 Fragility curves for three different hazard levels (6"/12")
Figures 4.134 through 4.137 show the resulting fragility curves for the baseline
solid shearwall (8 ft. x 8 ft.) with various nailing schedules (2"/12", 3"/12", 4"/12",
and 6"/12") considering life safety (LS, 10/50), for R factors ranging from 2.5 to 5.5.
The UBC walls provided relatively consistent levels of safety, as evidenced by the fact
that the resulting fragility curves were quite close for all nailing schedules. That is, the
allowable seismic weights provided in the UBC '97 for the different nailing schedules
resulted in comparable levels of performance. This permit the results for the different
nailing schedules to be combined to construct a single fragility curve for a given R-
factor (see Figure 4.138). Complete fragility curves for various R factors and
considering different seismic hazard levels (TO and CP) are provided in Appendix G.
Figure 4.139 shows the fragility curves for different assumed R factors considering the
151
baseline solid shearwall (8 ft. x 8 ft.), a 3"/12" nailing schedule, and the life safety
(10/50) hazard level. As expected, the failure probability of the shearwall increases as
the overstrength factor (R) increases.
I
0.9
0.8
/ /
8d@3"/12", W=1464 lbs/ft
8d@4"/12", W=1147 lbs/ft
0.7
/
/
//
8d@2"/12", W=1940 lbs/ft
0.6
8d@6"/12", W=730 lbs/ft
0.5
0.4
/1
0.3
0.2
///
0.1
BW (8 x 8'), oSB (3/5), ED =
-
= 2%, R = 2.5, LS (10/50)
0
0
0.5
1.5
1
2
2.5
Sa(g)
Figure 4.134 Fragility curves considering R = 2.5 (LS, 10/50 hazard level)
152
1
0.9
0.8
0.7
/
_8ft.
BW (8 x 8'), OSB (/8"), ED = /8",
/'!'
ç = 2%, R = 3.5, LS (10/50)
/8d@6"/12" W1026 lbs/ft
0.6
0.5
/'//
8d@2"/12", W=2720 lbs/ft
///8d@3"/12", W=2051 lbs/ft
8d@4"/12", W=1605 lbs/ft
/ //
0.4
0.3
0.2
/,//I
0.1
0
0.5
0
1.5
1
2.5
2
Sa(g)
Figure 4.135 Fragility curves considering R = 3.5 (LS, 10/50 hazard level)
1
0.9
7/
0.8
8 ft.
BW (8' x 8'), OSB (I") ED = /8,
0.7
= 2%, R = 4.5, LS (10/50)
0.6
o
0.5
8d©6"/12", W=1321 lbs/ft
/
0.4
8d©2"/12", W3500 lbs/ft
/' /
0.3
8d(4"/12", W=2065 lbs/ft
'I,'
8d@3"/12", W=2639 lbs/ft
0.2
0.1
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Sa(g)
Figure 4.136 Fragility curves considering R = 4.5 (LS, 10/50 hazard level)
2
153
1
0.9
88.
0.8
L8fl.
BW (8' x 8'), OSB (/8"), ED =
0.7
ç = 2%, R = 5.5, LS(1O/50)
/rd©I
0.6
W=4270 lbs/ft
8d©3"/12", W=3220 lbs/ft
8d)4"/12", W=2521 lbs/ft
1/
//
0.5
//
0.4
//
8d@6"/12", W=1610 lbs/ft
//
0.3
0.2
0.1
0
0
0.2
0.4
0.6
0.8
1.2
1
1.4
1.6
1.8
2
Sa(g)
Figure 4.137 Fragility curves considering R = 5.5 (LS, 10/50 hazard level)
1
0.9
88.
0.8
88.
BW (8' x 8'), OSB ( /"), ED = '8,
0.7
'
/
= 2%, R = 4.5, LS (10/50)
0.6
Single Average Fragility
0.5
/
18d©6"/12", W=1321 lbs/ft
8d@2"/12", W=3500 lbs/ft
0.4
0.3
: ::::
0.2
0.1
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Sa(g)
Figure 4.138 Single fragility curve considering R = 4.5 (LS, 10/50 hazard level)
154
1
_-
7 7
8ft.
8ft.
BW (8' x 8), 8d©3"/12", OSB (/")
0.7
ED
G = 200 ksi,
-
/
= 2%
/,/
//
0.6
R=2.5
0.4
R=3.5
/
0.3
/;' /
0.2
R=4.5
R=5.5
/,,' /
0.1
/,'/
Ill
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Sa(g)
Figure 4.139 Fragility curves considering different assumed R factors (LS, 3"/12")
4.4.2.2 Fragility curve based on ultimate force
In this section, the fragility curve concept is extended to the issue of shearwall
anchorage. Fragility curves can provide a useful tool for the selection of seismic holddowns making some assumptions about the amount of force being transferred from the
top of the wall down to the wall corner being anchored. By statics, the horizontal force
acting on top of the wall is equal to uplift load in the bottom plate if the dimension of
shearwall is square. Three types of hold-down anchors (Simpson HTT 22, LTT 20B,
and PHD2-SDS3) were considered. The hold-down ultimate tension capacities were
assumed to be Normally distributed with mean values taken then average ultimate
tension capacities obtained from the Simpson Strong-Tie catalogue and assumed
COV's of 0.2. With this information, the Sthpercentile value for capacity of each hold-
155
down was determined and was treated as a capacity limit. (This is similar to the drift
limit used when considering peak displacements.) These are shown in Table 4.16.
Hold-down type
1
HTT22(16)
LTT 20B
PHD2-SDS3
Average ultimate tension capacity
(from Simpson Catalogue)
13150 lbs.
8733 lbs.
12520 lbs.
Design value
(5thpercentile)
8824 lbs.
5860 lbs.
8401 lbs.
Table 4.16 Capacities of hold-downs considered in this study
Baseline wall BW1 (solid shearwall, 8 ft. x 8 ft., two OSB sheathing panels
oriented vertically) was used to develop illustrative fragility curves for anchorage
selection considering uplift capacity. The CASHEW program and the Folz nail
parameters were used to develop the global shearwall hysteretic parameters. Different
nailing schedules (2"/12", 3"/12", 4"/12", and 6"/12") were considered along with the
corresponding allowable seismic weights back-figured from the UBC '97 allowable
unit shear values (described in Section 4.4.2.1). Various R factors (2.5, 3.5, 4.5, and
5.5) also were considered.
The peak displacement distributions were then developed for the different
nailing schedules and R factors. Figures 4.140 through 4.142 show the sample CDF's
assuming a 3"/12" nailing schedule, various R factors, and the three different hazard
levels (JO, LS, and CP). As expected, as the R factor increases, the allowable seismic
weight increases, and hence shearwall peak displacement increases. Peak displacement
curves for the other nailing schedules are provided in Appendix H.
156
0.9
FT't
0.8
0.7
::::
;tLL
I
R=5.5
0.6
0.5
U-
I
_____
:1
0.4
8ft.
0.3
I
i;
0.2
Bft.
cI
II
BW (8' x 8), 8d@3"/12",
/
ii
II
/
0.1
,
/
0_I
n
0
2000
4000
6000
8000
OSB(318"),ED-3/8',
= 2%,
G = 200 ksi,
0 (50/50)
10000
12000
14000
Fmax (lbs.)
Figure 4.140 CDF for ultimate force with various R factors (3"/12", TO)
0.9
0.8
0.7
0.6
0.5
LL
0.4
0.3
.4'
0.2
_______8ft.
,'/
8,,
0.1
BW(8 x8) 8d@3/12 OSB(/8)
ED
G 200 ksi ç 2% LS (10/50)
/8
n
4000
6000
8000
10000
12000
14000
Fmax (lbs.)
Figure 4.141 CDF for ultimate force with various R factors (3"/12", LS)
157
0.9
/
0.8
8ff.
BW (8 x 8), 8d@3"/1 2", OS
0.7
/
('/8"),
ED = /8, G = 200 ksl, ç = 2°h, CP (2/50)
0.6
0.5
0.4
0.3
0.2
E
0.1
c!1C1
0
/1
R=5.5
n
6000
8000
10000
12000
14000
Fmax (lbs.)
Figure 4.142 CDF for ultimate force with various R factors (3"/12", CP)
The same method used to develop the fragility curves for peak displacement
was used to develop fragilities for uplift force of shearwall, i.e., time-history analysis
using a suite of 20 ordinary ground motions scaled to different hazard levels. Using
the same baseline solid shearwall (8 ft.
x
8 ft.), and considering three different hold-
downs (Simpson HTT 22, PHD2-SDS3, and LTT 20B), fragility curves for ultimate
uplift force were constructed for differing nailing schedules and assuming different R
factors from 2.5 to 5.5. Figures 4.143 through 4.145 present the fragility curves for the
baseline solid shearwall (8 ft. x 8 ft.) for each of the three different hold-downs
(considering one particular nailing schedule for each case). As the overstrength factor
(R) increases, the failure probability of each of the shearwalls increase.
158
1
0.9
0.8
0.7
1/
8ft.
8 ft.
BW (8 x 8'), 8d©3"112", OSB
ED
/8, G200ks1, ç=2%,
(/8"),
/
HTT22(16),'
0.6
(
0.5
,"
0.4
R=4.5
/
0.3
/
0.2
R=3.5
/
0.1
n
0
0.2
0.4
0.6
0.8
1.4
1.2
1
1.6
1.8
2
Sa(g)
Figure 4.143 Fragility curve for ultimate uplift force with various R factors (3 "/12",
HTT 22)
///
/7/
0.9
0.8
8ft.
BW (8'
0.7
x
8'), 8d@3"112", OSB
el8'),
/
/
ED318", G=2OOksi,2%,PHD2
0.6
/
I/I
/
0.4
0.3
::::
0.2
R=2.5
/
0.1
n
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Sa(g)
Figure 4.144 Fragility curve for ultimate uplift force with various R factors (3"/12",
PHD2-SDS3)
159
0.9
0.8
/
0.7
R = 5.5
/
R = 3.5
1
0.6
R = 2.5
//
a
o.
/
'I
0.4
0.3
'I
/
1/
0.2
8 ft.
8 ft.
0.1
BW (8' >< 8), 8d©4"1l2", OSB (I8'),
ED=3/8", G = 180 ksi,
0
0.2
0.4
0.6
0.8
1
1.2
1.4
=2%, LTT2OB
1.6
1.8
2
Sa(g)
Figure 4.145 Fragility curve for ultimate uplift force with various R factors (4"/12",
LTT 20B)
The fragilities for each of the three hold-downs, considering a single nailing
schedule and overstrength factor, also can be shown on the same figure. One example
is shown in Figure 4.146 for a 3"/12" nailing schedule and assuming R = 3.5. Again,
the effective seismic weight acting on the wall was determined based on the allowable
unit shear values in the UBC '97. The seismic demand (interface) variable is the
spectral acceleration, Sa. Fragility curves of this type can be used either as design aids
(selection of hold-downs) or to assess risk consistency in current design provision.
160
0.9
0.8
//
88.
BW (8' x 8'), 8d©3"/12",
0.7
OSBeI8"), ED =18,
LTT2OB
G=2OOksi,=2%,R=3.5
0.6
/
ci
0.5
/
0.4
/
0.3
/
0.2
0.1
C)
0
0.4
0.8
1.2
1.6
2
Sa(g)
Figure 4.146 Hold-down fragility curve considering ultimate uplift capacity
161
5. ANALYSIS OF SHEARWALLS IN COMPLETE STRUCTURES
5.1 Model configuration
This chapter presents the results from studies of shearwalls acting as part of
complete woodframe structures. As with the isolated shearwalls analyzed in the
previous chapter, the shearwalls are subjected to a suite of earthquake records, scaled
appropriately to specified hazard levels.
For more than 40 years, researchers have been conducting full-scale
experimental tests to investigate the performance of woodframe structures and
assemblies under wind, snow and earthquake loading [e.g., Dorey and Schriever,
1957; Hurst, 1965; Yokel et al., 1973; Tuomi and McCutcheon, 1974; Stewart et al.,
1988; Sugiyama et al., 1988; Phillips et al., 1993; Ohashi et al., 1998; Seo et al., 1999;
Paevere et al., 2003]. As part of CUREE-Caltech Woodframe Project (CCWP), the
seismic response of two and three-story woodframe structures were tested on large
shake tables [Fischer et al., 2001; Mosalam et al., 2002]. 'While tested at full-scale, the
overall size of these test structures was slightly scaled-down due to size (footprint)
limitations of the shake tables. The results were used to validate a numerical model
used to predict the seismic performance of complete woodframe structures [Folz and
Filiatrault, 2002]. The model can then be used to evaluate performance of structures
having other configurations.
The numerical model, SAWS (Seismic Analysis of Woodframe Structures),
developed as part of the CCWP, was used in this study to investigate the performance
of shearwalls in complete structures. The SAWS program was described in Chapter 3.
162
Nonlinear dynamic time-history analysis was conducted using the SAWS program and
the suite of 20 ordinary ground motion records, as was used previously. Two structural
configurations were considered, a one-story and a two-story structure. These two
structures are described in the following sections.
5.1.1 Model configuration of one-story residential structure
The model of the one-story single-family residential structure was developed
to be representative of typical southern California construction (i.e., a "bungalow"
style house). The plan of this structure was 32 ft. x 20 ft. and the structure had
openings for pedestrian doors and windows. The shearwalls in the structure were built
using 3/8-in. OSB, attached to the framing using the Durham spiral nail (2 in. long x
0.105 in. diameter). In most cases, a 6"/12" nailing schedules was used. The top-plate
and end studs were double members, while the sole-plate and the interior studs were
single members. The framing members were nominal 2 in.
x
4 in. spaced (in most
cases) at 24 in. on-center. Properly installed hold-downs were assumed to be present.
Nonstructural finish materials (1/2-in. gypsum wallboard and 7/8-in. stucco) were
assumed to be properly attached. The plan and section views are shown in Figure 5.1.
Figure 5.2 presents elevation views of each exterior wall in the one-story structure.
The information in this figure was used to develop the global hysteretic parameters for
each shearwall using CASHEW and the Durham nail parameters (see Table 4.1).
163
H'
4ft.
6ft.
ft
4ft.
4ft.
4ft.
8ft.
rhroom
Kitchen
Bedroom
4 ft.
4ft
20ft. 4ft.
4 ft.
3 ft.
4 ft.
Li
2 ft.
Living Room
Bedroom
I
4ft.
4
8ft.
20ft.
3ft.
4ft.
4
IIJ
444
3ft. 3ft.
8ft.
3 ft.
ft
32 ft.
4
Roofing (3-ply with gravel)
/8" Plywood
2x6 ©l6in o.c
51/
L
1/2"
12
4
Fiberglass Loose Insulation
Gypsum Wallboard
Stucco
OSB
2x4 @24in o.c
1/2" Gypsum
Wallboard
/8
/8"
32ft.
Figure 5.1 Plan view and section view for the one-story house model
8ft.
164
ft,
ft.
4ft.
8ft.
4ft.
3ft.
3ft.
2ft.
8ft.
*-4---ø
32ft.
East Wall (EW)
1.3 ft
4 ft.
ft.
ii
1
2ft
4fL
6ft.
4ft.
4ft
8ft.
4ft.
3ft.
%AI.._LlAI....II/AflAI\
VVOL VV4II
VVVVJ
1.311
4ft
ft.
2.7
4ft.
4ft.
4ft.
4ft.
ft.
4ft.
-4
I
20ft.
C'..... ..L
.J'.JL.1 LI I
AI._.II I('lAI'..
V V
V VJ
II
1.3ft
4ft
ft.
===
2.7
2ft
4ft.
3ft.
'I
*-3ft.
-
2ft
-4-pI
3ft.
ft.
3ft.
-p *-*
20ft.
KI.-....4L
AI....II 11.IIAI\
I'l'.JILII VVQIIkINVV1
Figure 5.2 Detailed wall configurations for the one-story house model
11.
165
5.1.2 Model configuration of two-story residential structure
The model of the two-story single-family residential structure was based on the
model in Task 1.1.1 of the CCWP [Fischer et al., 2001]. The structure has plan
dimensions of 20 ft.
x
16 ft. and has various openings for a garage door, a pedestrian
door, and windows. The shearwalls in the structure were built using 3/8-in. OSB,
attached to the framing using 8d box nails (2.5 in. long
x
0.113 in. diameter) at 6"/12"
(edge/field). A 3"/12" nailing schedule was used for the shearwalls on either side of
the garage door opening. Hold-downs were assumed to be properly installed.
Nonstructural finish materials (1/2-in. gypsum wallboard and 7/8-in. stucco) also were
assumed to be properly attached. The elevation and plan views are shown in Figure
5.3. This structure was design according to UBC '94 following typical construction
practices in California. A more detailed description of this structure can be found
elsewhere [Fischer et al., 2001].
166
9.5 mm(in)
1F
'I
/
I
L
OSB sheathing
with 8db @
150mm (6 in)
9.5 mm ( in)
OSB sheathing
9.5 mm (l in)
OSB sheathing
with 8db@
75 mm (3 in)
with8db@
lSOmm(6in)
4
'4.9m1
North -a------\XTZ+ Ai,ii
ni+;,,
HTT22 holdowns typ. at
shearwall element ends
/
rat ui,it
North
12.7 mm ( in) CDX plywood roof
sheathing with 8db @ 150mm (6 in)
in) OSB sheathing
with 8db @150mm (6 in)
9.5 mm
ISNW
6.lm (20 F)
North and South Wall Elevations
4.9 m (16 ft)
80 man x 305 n
(3 in x 12 in)
Roof trusses
@ 610mm
(24 in) o.c.
Interior bearint
wall
H(2 x 10) floor joists
38 mm x 235 mm
0
_
\
__
ii
@406mm (16 in)
_____
GLB & bearing wall _ \
o.c. lapped over
North
\
Floor sheathed with 19.0mm ( in) T & G
plywood with 10db @ 150mm (6 in)
0.9 m (3 ft) pedestrian door
North
Plan View
)
/
/\
_
/ \
/
i
/_/\
/11
Floor opening
below
Interior partition walls, typ.
2nd Story Plan View
Figure 5.3 Elevation and plan view for two-story house model (from: Fischer et al.,
2001)
167
5.2 Shearwall performance in complete structures
5.2.1 One-story structure
5.2.1.1 Performance of shearwalls with OSB only
The performance of shearwalls in a one-story structure was investigated using
the model described in Section 5.1.1. Based on assumed weight tributary to the roof
diaphragm and wall dead load, a calculated total seismic weight of 15040 lb. was
assigned at the roof level and an equivalent viscous damping of 1% of critical was
assumed.
The CASHEW program was used to develop global hysteretic parameters for
each shearwall assuming the Durham nail parameters and considering each specific
wall configuration. Table 5.1 presents the resulting hysteretic parameters for each
shearwall (OSB only) in the one-story structure. As done previously, seismic zone IV
(LA) and soil profile type D
(SD)
were assumed. Figure 5.4 presents the SAWS model
for this one-story structure (OSB only) composed of four zero-height nonlinear
shearwall spring elements.
Spring
Element
K0
II
ii
East_Wall
West_Wall
sy'
South_Wall
North_Wall
F0
F1
(kips)
(kips)
(in.)
0.066
7.35
1.51
2.32
0.76
1.10
1.297
0.066
8.36
1.74
2.32
0.75
1.10
-0.079
1.285
0.068
5.61
1.19
2.32
0.73
1.09
-0.046
1.383
0.068
5.56
1.00
2.92
1.00
1.12
(kips/
in.)
r1
r2
r3
r4
18.52
0.079
-0.031
1.298
21.52
0.080
-0.046
15.58
0.083
10.63
0.051
a
Table 5.1 Hysteretic parameters for the shearwall spring elements in one-Story
structure, OSB only
It,rsl
Figure 5.4 SAWS model of the one-story structure, OSB only
The peak displacement distributions for each shearwall are shown in Figures
5.5 through 5.7 for the three hazard levels (JO, LS, and CP). The performance of all
shearwalls is well below the drift limit at the low hazard level (JO, 50/50), however
the South wall (SW) and North wall (NW) performed less well inthe high hazard level
(CP, 2/50) because of the many openings and the relatively small number of fasteners
(6"/12" nailing schedule). The East wall (EW) and West wall (WW) performed well at
all hazard levels.
169
1
0.9
WW//
0.8
EW
SW
0.7
J+
NW
'
0.6
!/
01
0.5
Ii'
0.4
//
J"
0.3
'o
//
<
/
/
0.2
Structure Type: One Story (32 >< 20')
Nailing Schedule: 8d©6"-12"
Sheathing: OSB (/8")
Shearwall HP: Durham + CASHEW
NSF: None
Damping: 1%
Hazard Level: 10 (50%I5Oyrs)
o
[I
II
(
0.1
/
-
n
0
/o
W15040 lb. total
-
0.2
0.1
0.3
0.5
0.4
0.7
0.6
0.8
max (in.)
Figure 5.5 Peak displacement distributions for shearwalls in one-story structure, OSB
only (10, 50/50 hazard level)
--;--
EW
0.9
SW
0.8
/NW
0.7
0.6
/°
0.5
0.4
0.3
IStructure Type: One Story (32'
Nailing Schedule: 8d@6"-12"
I
0.1
4/
Shearwall HP: Durham + CASHEW
NSF: None
Damping: 1%
Hazard Level: LS (10%I5Oyrs)
W = 15040 lb. total
0/
0
: /
/
4/
-
n
0
0.2
0.4
0.6
0.8
20')
Sheathing: OSB (I")
/
0.2
x
1
1.2
1.4
1.6
1.8
2
ömax (in.)
Figure
5.6
Peak displacement distributions for shearwalls in one-story structure, OSB
hazard level)
only (LS, 10/50
170
1
0.9
EW
0.8
ww
0.7
0.6
//
0.5
U0.4
0.3
Structure Type: One Story (32 >< 20)
Nailing Schedule: 8d@6"-12"
Sheathing: OSB (/8')
Shearwall HP: Durham + CASHEW
NSF: NOne
Damping: 1%
Hazard Level: CP (2%I5Oyrs)
4/
0.2
//
i/
p
0.1
I
/
/
9
W= 15040 lb. total
0
0
1
2
3
4
5
6
6max (in.)
Figure 5.7 Peak displacement distributions for shearwalls in one-story structure, OSB
only (CP, 2/50 hazard level)
5.2.1.2 Performance of shearwalls with NSF materials
The performance of shearwalls with nonstructural finish materials (stucco and
gypsum wallboard) in the one-story structure also was investigated. Two cases were
considered: (1) walls with OSB and gypsum wallboard, and (2) walls with OSB,
gypsum wallboard and stucco. Based on calculation, and assuming weight tributary to
the roof diaphragm and wall dead load, a total seismic weight of 16793 lb. was
estimated for the structure with OSB and gypsum walls, while a total seismic weight
of 20952 lb. was estimated for the structure with OSB, gypsum wallboard, and stucco.
(Stucco was assumed to have a weight of 10 psf.) Equivalent viscous damping of 1%
of critical was assumed in both cases.
171
The hysteretic parameters for the stucco and gypsum wallboard were based on
available experimental test data and were adjusted for the length of the wall. In the
case of the partition walls, gypsum wallboard was attached on both sides, and it was
assumed that the stiffness and strength was twice that of a single side of gypsum
wallboard [Folz and Filiatrault, 2002]. The resulting hysteretic parameters for each
shearwall (with NSF materials) in the one-story structure are shown in Table 5.2. The
hysteretic parameters for the OSB-only shearwall (Table 5.1) can be used for the
OSB-only walls use in Table 5.2. Each subscript number corresponds to a layer in the
shearwall and subscripts x and y indicate a direction. If only gypsum wallboard is
considered (i.e., OSB + GWB), the hysteretic parameters for stucco
Sy9)
(Sx1, SX8,
Sy, and
in Table 5.2 are eliminated. The SAWS model for the one-story structure (with
NSF materials) is shown in Figure 5.8. This structure is composed of 17 zero-height
nonlinear shear spring elements, one each for: four OSB only layers, four stucco
layers, and nine gypsum wallboard layers. If only the gypsum NSF materials are
considered, the four stucco layers are removed. Figure 5.9 shows the SAWS model
considering the gypsum NSF materials only (note fewer springs).
172
K0
r
Spring
Element
Wall Type
& Location
(ks/
r1
r2
r3
r4
SXI
Stucco
East Wall
46.39
0.058
-0.050
1.000
0.020
2.92
S>2
OSB
East Wall
18.52
0.079
-0.031
1.298
0.066
24.13
0.029
-0.017
1.000
44.54
0.029
-0.017
29.69
0.029
25.98
GWB (I Side)
East_Wall
GWB (2 Sides)
Partition_Wall
GWB (2 Sides)
Partition_Wall
GWB (I Side)
SX7
SX8
5Y1
SY2
West_Wall
OSB
West Wall
Stucco
West Wall
Stucco
South Wall
OSB
South Wall
GWB (1 Side)
South_Wall
Sy4
& Sy
GWB (2 Sides)
Partition Wall
GWB (2 Sides)
Partition_Wall
GWB (1 Side)
S\8
North_Wall
OSB
North Wall
Stucco
North_Wall
AU
(in.)
a
13
0.44
0.96
0.60
1.10
7.35
1.51
2.32
0.76
1.10
0.005
1.30
0.29
1.54
0.80
1.10
1.000
0.005
2.40
0.54
2.83
0.80
1.10
-0.017
1.000
0.005
1.60
0.36
1.89
0.80
1.10
0.029
-0.017
1.000
0.005
1.40
0.31
1.65
0.80
1.10
21.52
0.080
-0.046
1.297
0.066
8.36
1.74
2.32
0.75
1.10
49.96
0.058
-0.050
1.000
0.020
3.15
0.47
1.03
0.60
1.10
42.83
0.058
-0.050
1.000
0.020
2.70
0.40
0.89
0.60
1.10
15.58
0.083
-0.079
1.285
0.068
5.61
1.19
2.32
0.73
1.09
22.27
0.029
-0.017
1.000
0.005
1.20
0.27
1.42
0.80
1.10
25.98
0.029
-0.017
1.000
0.005
1.40
0.31
1.65
0.80
1.10
37.12
0.029
-0.017
1.000
0.005
2.00
0.45
2.36
0.80
1.10
20.41
0.029
-0.017
1.000
0.005
1.10
0.25
1.30
0.80
1.10
10.63
0.051
-0.046
1.383
0.068
5.56
1.00
2.92
1.00
1.12
39.26
0.058
-0.050
1.000
0.020
2.47
0.37
0.81
0.60
1.10
(kips)
(kip
Table 5.2 Hysteretic parameters for the shearwall spring elements in one-story
structure, OSB and NSF materials
173
'X6
sx7
i
I
I
I
I
V
__________
Exterior sheanivall (OSB, GWB, stucco)
Window or doqr
Interior partitio wall (GWB on both sides)
s3
VVVS1
sY2
SY4
S6
SY5
Sy8
Sy9
$y3
Figure 5.8 SAWS model of the one-story structure, OSB and NSF materials (GWB
and Stucco)
Sx6
I
I
V
------
Exterior shear'vall (OSB, GWB)
Window or dock
Interior partitio1 wall (GWB on both sides)
4.
sY1
sY2
sY3
sY4
sY5
Figure 5.9 SAWS model of the one-story structure, OSB and GWB
sY6
sY7
174
Figures 5.10 through 5.12 present the peak displacement distributions for each
shearwall (OSB + gypsum wallboard) for the three different hazard levels (TO, LS, and
CO). The distributions for the wall with NSF materials (i.e., OSB + gypsum wallboard
+ stucco) are shown in Figures 5.13 through 5.15. As expected, the performance of the
shearwalls with NSF materials is better than OSB-only walls at all hazard levels. The
addition of stucco dramatically improves the shearwall performance. This also was
noted in Section 4.2.3, considering isolated shearwalls. This is especially evident at
the highest seismic hazard level.
-
1
0.9
0.8
0.7
SW
/
0.6
.1
05
U-
NW
i/i!
0.4
0.3
Structure Type: One Story (32' x 20')
Nailing Schedule: 8d@6"-12"
Sheathing: OSB (3/..)
Shearwall HP: Durham + CASHEW
NSF: GWB
Damping 1%
Hazard Level: 10 (50%/5Oyrs)
W = 16793 lb. total
j I
//
/
/
/
/
0.2
rI
1/
0.1
J
/
/
/
n
0
0.05
0.1
0.15
6max
0.2
0.25
0.3
(in.)
Figure 5.10 Peak displacement distributions for shearwalls in one-story structure, OSB
+ GWB (TO, 50/50 hazard level)
175
:
0.9
0.8
0.7
SW
NW
0.6
/
0.5
U0.4
0.3
Structure Type. One Story (32 x 20)
Nailing Schedule: 8d@6"-12"
Sheathing: OSB (/")
Shearwall HP: Durham + CASHEW
NSF:GWB
Damping: 1%
Hazard Level: LS (10%/5oyrs)
W = 16793 lb. total
Li.. /
0.2
/
I ?
/
fJ
0.1
1
hi
n
0
0.1
0.2
0.3
0.4
6max
0.6
0.5
0.7
0.8
(in.)
Figure 5.11 Peak displacement distributions for shearwalls in one-story structure, OSB
+ GWB (LS, 10/50 hazard level)
0.9
0.8
SW
0.7
NW
/
0.6
I
0.5
II
J1
0.4
0.3
Structure Type: One Story (32' x 20)
Nailing Schedule: 8d@6"-12"
Sheathing: OSB (/8")
Shearwall HP: Durham + CASHEW
NSF: GWB
Damping: 1%
Hazard Level: CP (2%I5Oyrs)
W= 16793 lb. total
ft
/
1/
II
/
0.2
/1
0.1
/
--
n
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
max (in.)
Figure 5.12 Peak displacement distributions for shearwalls in one-story structure, OSB
+ GWB (CP, 2/50 hazard level)
176
0.9
0.8
0.7
0.6
1/ /
NW
U-
i/i'
0.4
0.3
Structure Type. One Story (32
Nailing Schedule: 8d©6-1 2
/ I,
If
/
Shearwall HP: Durham + CASHEW
NSF: GWB + Stucco
Damping: 1%
Hazard Level: 10 (50%/5oyrs)
W = 20952 lb. total
/
/
0.1
n
0
20)
Sheathing: OSB ('")
/
0.2
x
0.04
0.12
0.08
6max
0.16
0.2
(in.)
Figure 5.13 Peak displacement distributions for shearwalls in one-story structure, OSB
+ GWB + Stucco (JO, 50/50 hazard level)
0.9
:
0.8
/NW
0.7
0.6
0.5
U-
r:/
0.4
q: /
0.3
//
0.2
A.
/
/ ;
7/,
/1
Structure Type: One Story (32 x 20)
Nailing Schedule: 8d@6"-12"
Sheathing: OSB (/8")
Shearwall HP: Durham + CASHEW
NSF: GWB + Stucco
Damping: 1%
Hazard Level: LS (10%/S0yrs)
W = 20952 lb. total
x
/
/
0.1
/
/
()
0
0.1
0.2
0.3
0.4
0.5
0.6
6max (in.)
Figure 5.14 Peak displacement distributions for shearwalls in one-story structure, OSB
+ GWB + Stucco (LS, 10/50 hazard level)
177
H
0.9
:
0.8
0.7
0.6
/
NW
0.5
/
4
0.4
II
Ii
0.3
/
.'
Structure Type: One Stery (32
Nailing Schedule: 8d@6-12"
//
/
I!
0.2
*1I
/
0.1
ff
x
20)
Sheathing: OSB (I")
Shearwall HP: Durham + CASHEW
NSF: GWB + Stucco
Damping: 1%
Hazard Level. CP (2 /ol50yrs)
x'
W 20952 lb. total
C)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
max (in.)
Figure 5.15 Peak displacement distributions for shearwalls in one-story structure, OSB
+ GWB + Stucco (CP, 2/50 hazard level)
5.2.2 Two-story structure
5.2.2.1 Performance of shearwalls with OSB only
The SAWS program was used to investigate the performance (peak
displacement) of shearwalls in a two-story structure under actual earthquake loading,
using a suite of 20 ordinary ground motions to characterize the seismic hazard. A total
seismic weight acting on this structure of 24730 lbs. was estimated, with 13938 lbs.
applied to the second floor diaphragm and 10792 lbs. applied to the roof diaphragm.
Equivalent viscous damping of 1% of critical in the first and second modes of
vibration was assumed. This value of viscous damping is consistent with other studies
[Foliente, 1995; Folz and Filiatrault, 2002].
178
As described
in Chapter 3, the SAWS program requires several input
parameters including the global hysteretic parameters for each shearwall, seismic
weights, viscous damping parameters, integration time-step, and input ground
acceleration parameters. The CASHEW program was used to determine the global
hysteretic parameters for each shearwall, using the Durham nail parameters. The
resulting sets of hysteretic parameters for each shearwall in the two-story structure are
shown in Table 5.3 [from: Folz and Filiatrault, 2002].
The peak displacements of each shearwall in complete structure were obtained
using SAWS program. In the discussion of the results in this section, peak
displacements are measured from the bottom of the first-story wall either to the top of
the first-story wall or to the top the second-story wall. Three hazard levels (JO, LS,
and CP) were considered, and seismic zone IV (LA) and soil profile type D (SD) were
assumed. Figure 5.16 illustrated the SAWS model for this structure (with OSB only).
This structure is composed of eight zero-height nonlinear shearwall spring elements
and two rigid diaphragms: one for the second floor and one at the roof level.
The resulting peak displacement distributions (peak displacement measured
relative to ground) for each shearwall are shown in Figures 5.17 through 5.19 for the
three different hazard levels (JO, LS and CP). Since the South and North shearwalls
(both 1SNW and 2SNW) have the same configuration for both stories, their
performance was identical. The performance (peak drift relative to ground level) of the
East shearwall (2EW) in the complete structure, located above the wall with the
garage door opening, performs the worst. However, as seismic demand increases, the
179
peak displacement distribution for the East wall (2EW) and West wall (2WW) in the
complete structure show more similar performance (see Figure 5.19).
Spring
Element
S1 Level 1
East_Wall
Sx2 Level 1
West_Wall
Sy1 Level 1
South_Wall
Sy Level 1
NorthWall
Sx3Level2
East_Wall
S4 Level 2
West_Wall
Sy3 Level 2
South_Wall
Level 2
North_Wall
Sy4
K0
(kips/
J in.)
i
r1
r2
r3
r4
F0
I
F
(kips)
(kips)
(in.)
a
I
I
16.73
0.083
-0.088
1.00
0.030
8.23
1.88
3.44
0.79
1.07
22.21
0.064
-0.056
1.07
0.030
8.25
1.98
2.28
0.87
1.11
32.49
0.065
-0.074
1.10
0.030
10.88
2.43
2.39
0.81
1.09
32.49
0.065
-0.074
1.10
0.030
10.88
2.43
2.39
0.81
1.09
11.99
0.069
-0.038
1.16
0.020
4.41
1.07
3.02
0.77
1.10
11.99
0.069
-0.038
1.16
0.020
4.41
1.07
3.02
0.77
1.10
19.13
0.054
-0.060
1.10
0.030
7.94
2.90
2.91
0.84
1.09
19.13
0.054
-0.060
1.10
0.030
7.94
2.90
2.91
0.84
1.09
Table 5.3 Hysteretic parameters for the shearwall spring elements, OSB sheathing
only (from: Folz and Filiatrault, 2002)
Exterior shearwall (OSB)
Window or door
secono uoor oiapnragm
Exterior shearwall (OSB)
Window or door
Figure 5.16 SAWS model of the two-story structure, OSB only (from: Folz and
Filiatrault, 2002)
181
/
0.9
I.L
/
0.8
0.7
1EW/,2W
/
1
ii
0.5
2EW
2SNW
II
0.6
:x
1SNW
1WW
a
I
III,
LL
0.4
/x'
I
0.3
x 16)
Nailing Schedule: 8d@6"/2" and 3/12"
Sheathing: OSB (/")
Structure Type: Two Story (20
/ /
/
S
/
0.2
/
/
J
0.1
Shearwall HP: Durham + ASHEW
NSF:None
Damping: 1%
Hazard Level: 10 (50%/50 rs)
W = 24730 lb. total
/
/ /
/
I,'
/
II
(1
0
0.2
0.6
0.4
0.8
1.2
1
max (in.)
Figure 5.17 Peak displacement (relative to ground) distributions for shearwalls in twostory structure (TO, 50/50 hazard level)
0.9
1SNW
0.8
1EW
0.7
:1
1WW
,
0.6
2SN!'
/,
LL
/
I;
/1'
0.4
II)
//:x
0.3
/
I'
/i
y}
0.1
0
0.5
Structure Type: Two Story (20 x 16)
Nailing Schedule: 8d@6"/12" and 3/12'
Sheathing: OSB (/8")
Shearwall HP: Durham + CASHEW
NSF: None
Damping: 1%
Hazard Level: [S (10%/5oyrs)
W = 24730 lb. total
.
I
//
0.2
ii
I'j<
//
/'
1
1.5
2
6max
2.5
3
3.5
4
(in.)
Figure 5.18 Peak displacement (relative to ground) distributions for shearwalls in twostory structure (LS, 10/50 hazard level)
182
1
I SNW
0.9
0.8
1 WW
0.7
2 EW
1EW /"
/
2WW
0.6
/'
IA:
0.5
U0.4
/
JR
[
q
ff
0.3
./
//
// /
/
/
0.2
7/
7/
I/
0.1
0
1
Shearwall HP: Durham CASHEW
7
1
/
/
J' _/_.
0
Structure Type: Two Story (20' x 16)
Nailing Schedule: 8d@6Y12" end 3/12"
Sheathing: OSB (/8")
NSF: None
Damping: 1%
Hazard Level: CP (2%/5pyrs)
W = 24730 lb. total
2
3
4
5
6
7
8
max (in.)
Figure 5.19 Peak displacement (relative to ground) distributions for shearwalls in twostory structure (CP, 2/50 hazard level)
5.2.2.2 Performance of shearwalls with NSF materials
The performance of shearwalls with nonstructural finish (NSF) materials such
as stucco and gypsum wallboard also was investigated using the SAWS program.
Hysteretic parameters for stucco and gypsum wallboard developed by Folz and
Filiatrault (2002) were used; these are shown in Table 5.4. These parameters were
developed from experimental test data obtained as part of the CCWP and CoLA
project [Gatto and Uang, 2002; Pardoen, 2001], and have been adjusted for the length
of the walls and presence of door and window openings in the two-story structure
considered in this study. Gypsum wallboard is assumed to be attached to the interior of
the wall, while stucco was assumed to be applied to the exterior. The case of an
interior partition wall with gypsum wallboard on both sides also was considered. In
183
that case, it was assumed that the two layers of gypsum wallboard have twice the
strength and stiffness of one layer of gypsum wallboard. The hysteretic parameters for
the OSB sheathing are the same as those shown in Table 5.3 [Folz and Filiatrault,
2002].
Hysteretic
Parameters
Stucco
GWB
K0
(kips/in.)
5.00
2.60
F0
r1
r2
r3
r4
0.058
0.029
-0.050
-0.017
1.00
1.00
0.020
0.005
.
(kips)
8.00
3.56
F1
A
(kips)
(in.)
15.0
24.0
1.20
0.80
a
0.60
0.80
1.10
1.10
Table 5.4 Fitted hysteretic parameters for the SDOF shear element model of an 8 ft. x
8 ft. shearwall with stucco and gypsum wallboard (from: Folz and Filiatrault, 2002)
The hysteretic parameter sets for each of the shearwalls having NSF materials
(for use in the analysis of the complete structure) are shown in Table 5.5. Again, in
this Table, subscripts x and y indicate the direction while the subscript number
indicates a given layer in the shearwall. Figure 5.20 presents the SAWS model
composed of 27 zero-height nonlinear shear spring elements corresponding to the
eight OSB layers, eight stucco layers, and eleven gypsum wallboard layers.
Figures 5.21 through 5.23 present the peak displacement distributions for each
of the shearwalls with the NSF materials for the three different hazard levels (10, LS,
and CP). Again, the performance of South and North shearwalls (both stories) is
identical since they have the same configuration. The performance of the East
shearwall second story (2EW), which is located above the wall with the large garage
door, exhibits the worst performance. This result was also observed in the previous
section (considering walls with OSB only). As expected, the shearwalls with the NSF
materials acting as part of the complete structure perform very well relative to the bare
shearwall. Comparing Figures 5.19 and 5.23 (CP, 2/50 hazard level), one sees that the
performance of walls with NSF materials is much better than that of walls with OSB
only.
Spring
Element
Wall Type
& Location
Stucco
Level_I_(EW)
OSB
SX2
SX4
S5
5X6
SX7
Sy1
& Sv
SY2
& SY5
Sy3
& Svo
Sxs
& SXI3
Level I (EW)
GWB (1 Side)
Level_l(EW)
GWB (2 Sides)
Levell(PW)
Stucco
Level 1 (WW)
OSB
Level I (WW)
GWB (1 Side)
Level 1 (WW)
Stucco
Level I (SNW)
OSB
Level 1 (SW)
GWB (1 Side)
Level 1 (SNW)
Stucco
Level 2 (EVoW)
SX9
OSB
& SX14
Level 2 (EW)
GWB (I Side)
Level 2 (E\VW)
GWB (2 Sides)
Level 2 (PW)
Stucco
Level 2 (SNW)
SXIO
& SX15
Sxi
&
SXI2
& Sy
Sy
OSB
& Sy11
Level 2 (SW)
GWB (I Side)
Level 2 (SNW)
Sy
&Syu
K0
(kips
I
r
r1
r2
r3
r4
r
F0
F1
A,,
(kips)
(kips)
(in.)
I
I
21.41
0.058
-0.050
1.00
0.030
1.35
0.22
0.44
0.60
1.10
16.73
0.083
-0.088
1.00
0.030
8.23
1.88
3.44
0.79
1.07
11.13
0.029
-0.017
1.00
0.005
0.60
0.13
0.72
0.80
1.10
22.27
0.029
-0.017
1.00
0.005
1.20
0.27
1.45
0.80
1.10
46.42
0.058
-0.050
1.00
0.030
2.92
0.44
0.96
0.60
1.10
22.21
0.064
-0.056
1.07
0.030
8.25
1.98
2.28
0.87
1.11
24.15
0.029
-0.017
1.00
0.005
1.30
0.29
1.54
0.80
1.10
49.96
0.058
-0.050
1.00
0.030
3.15
0.47
1.04
0.60
1.10
32.49
0.065
-0.074
1.10
0.030
10.88
2.43
2.39
0.81
1.09
25.98
0.029
-0.017
1.00
0.005
1.40
0.31
1.65
0.80
1.10
25.01
0.058
-0.050
1.00
0.030
1.57
0.24
0.52
0.60
1.10
11.99
0.069
-0038
1.16
0.020
4.41
1.07
3.02
0.77
1.10
13.02
0.029
-0.017
1.00
0.005
0.70
0.16
0.83
0.80
1.10
49.39
0.029
-0.017
1.00
0.005
2.65
0.60
3.15
0.80
1.10
42.83
0.058
-0.050
1.00
0.030
2.70
0.40
0.89
0.60
1.10
19.13
0.054
-0.060
1.10
0.030
7.94
2.90
2.91
0.84
1.09
22.27
0.029
-0.017
1.00
0.005
1.20
0.27
1.42
0.80
1.10
Table 5.5 Hysteretic parameters for the shearwall spring elements, OSB and NSF
materials (from: Folz and Filiatrault, 2002)
185
sx13
sx14
I
I
Exterior shearwall (OSB, GWB, stucco)
sx15
sx12
Window or door
r
-
Interior partition wall (GWB on both sides)
Partition Wall
I
L
Roof Diaphragm
sx8
sx9
sx10
sylo
sY7
sy8
sY9
syll
sY12
Connection to second __,,/
floor diaphragm
L...:.:.:.:>
sx6
sx7
N
Exterior shearwall (OSB, GWB, stucco)
Window or door
S4
I4
Partition Wall
Interior partition wall (GWB on both sides)
Second Floor Diaphragm
sx1
sx2
sx3
syl
sY4
sY2
sY5
sY6
sY3
Fixed support -/
Figure 5.20 SAWS model of the two-story Structure, OSB and NSF materials (from:
Folz and Filiatrault, 2002)
I,1
- -
/
0.9
/
0.8
1 WW
7/
0.7
/
/ ''
0.6
2SNW
/
IEW
/
0.5
U-
I
2WW
/ /7
/
0.4
2EW
/ J //'
"
0.3
Structure Type: Two Story (20 x 16')
Nailing Schedule: 8d@6"/12" and 3/12"
Sheathing: OSB (/8")
Shearwall HP: Durham + CASHEW
NSF: GWB + Stucco
Damping: lob
Hazard Level: 10 (50%/5oyrs)
W = 24730 lb. total
'
I
/
"
/
/
0.2
/
'
<
/1
1/
/
/7
/
/
0.1
i
/ /
'
/1
4
/
L
>
-
0
0
0.05
0.15
0.1
0.25
0.2
0.3
0.35
0.4
max (in.)
Figure 5.21 Peak displacement (relative to ground) distributions for shearwalls in twostory structure (JO, 50/50 hazard level)
0.9
/
0.8
1SNW
//x'
0.7
///-
/1WW
/
0.6
/
0.5
U-
1 EW
/
/
0.4
ti //
0.3
;2WW
/
/ /
I
2EW
,'
/
I
/.
/
0.2
0.1
/
/
// //
'j / /
'
L
/
Structure Type: Two Story (20 x 16')
Nailing Schedule: 8d@6"/12" and 3/12"
Sheathing: OSB (3/..)
Shearwall HP: Durham + CASHEW
NSF: GWB + Stucco
Damping: 1%
Hazard Level: LS (10%/5oyrs)
j1
I
I'
'
/
'
,
} _/_____'
n
0
0.2
0.4
2SNW
W=24730 lb. total
0.6
0.8
1
1.2
1.4
max (in.)
Figure 5.22 Peak displacement (relative to ground) distributions for shearwalls in twostory structure (LS, 10/50 hazard level)
187
0.9
0.8
1SNW
/
/i
0.7
/
1ww
/
0.6
://
7
1 EW
!
40.5
/
/
0.4
/1
/
0.3
/
/
0.2
/
,
/
/
/
/
/
/
/
0.1
,/
0
/
t
I / /
/
_:::i-__-' -
0
0.5
1
Structure Type: Two Story (20 16)
Nailing Schedule: 8d@6"/12" and 3/12"
Sheathing: OSB (3/)
Shearwall HP: Durham + CASHEW
NSF: GWB + Stucco
Damping: 1%
Hazard Level. CP (2/o/5oyrs)
W = 24730 lb. total
<
1.5
2
2.5
3
6max (in.)
Figure 5.23 Peak displacement (relative to ground) distributions for shearwalls in twostory structure (CP, 2/50 hazard level)
5.2.3 Additional studies
5.2.3.1 Interstory displacement
The performance of shearwalls acting as assemblies in complete structures was
investigated in Section 5.2. In addition to peak displacement (e.g., total drift at the top
of a multistory structure), interstory drift also is a criterion used to evaluate structural
performance under lateral loading. In this section, the interstory drift in the two-story
structure was separated out from the total drift at the first and second stories. Because
all displacements are functions of time, and the structure may deflect according to its
first or second mode at any given time, the peak interstory drift does not necessary
correspond to the difference between the peak drifts at the first and second stories. The
two-story structure is the same as the structure described in Section 5.1.2, and effects
188
of NSF materials also were considered. Only the wall having the worst performance at
each story (i.e., both 1EW and 2EW) was considered in the comparisons made in this
section.
Figures 5.24 through 5.26 present the distributions for peak displacement at the
top of the first-story wall, peak displacement at the top of the second-story wall, and
the interstory displacement, for the three different hazard levels (JO, LS, and CP),
respectively. Since the interstory drift is the absolute value of displacement difference
between the second-story and the first-story at any given time in the displacement
time-history, similar relative displacement behavior is observed at all hazard levels.
Figures 5.27 through 5.29 present the different peak displacement distributions
for the three different hazard levels (JO, LS, and CP) for a structure built with NSF
materials (stucco and gypsum wallboard). The peak displacement is significantly
reduced by adding NSF materials to the OSB-only walls, and the effect is more
pronounced at the higher hazard levels. (This also was seen in Section 5.2.2.2.)
However, the relative magnitude of interstoiy drift is different from that seen with the
OSB-only walls. (Specifically, the interstory displacement distribution is lower than
that of the first-story shearwall.) This might be the effect of the gypsum wallboard and
stucco, providing additional stiffness as well as connection between the first and
second stories. (The stucco layer also serves to restrain sheathing nail head rotation
under cyclic (dynamic) loading.) The application of NSF materials to shearwalls
improves the overall performance of shearwall, as shown previously.
189
0.9
0.8
0.7
first story
max
0.6
Interstory drift
0.5
ömax
0.4
t second story
x'
0.3
0.2
Structure Type: Two Story (20 x 16')
Nailing Sche1uIe: 8d@6"/12" and 3/12"
Sheathing: OSB (I8")
Shearwall HF?: Durham + CASHEW
NSF: None
Damping: 1%
Hazard Level: 0 (50%/50yrs)
L
0.1
}
0
W = 24730 l. total
--
0.2
0.4
0.8
0.6
1.2
1
1.4
max (in.)
Figure 5.24 Comparison of peak displacements at first and second stories, OSB (JO,
50/50 hazard level)
0.9
0.8
'
/
T/
Interstory drift
-I
I
0.6
J--
IA
0.7
6rnax at first story
x,'
I
max
at second story
/
0.5
/
/
0.4
0.3
t
/
i
I
/
/
I
0.2
I.
I
,
Structure Type. Two Story (20 x 16)
Nailing Schedule: 8d@6"112" and 3/12'
Sheathing: OSB (3I")
Shearwall HP: Durham + CASHEW
NSF: None
Damping: 1%
Hazard Level: LS (10%/50yrs)
W = 24730 lb. total
'
,'
II
/ /
0.1
//
n
0
0.5
-1
1.5
2
2.5
3
3.5
4
6max (in.)
Figure 5.25 Comparison of peak displacements at first and second stories, OSB (LS,
10/50 hazard level)
190
// H
0.9
0.8
0.7
0.6
max
40.5
U-
Interstry drift
/
0.4
max
/
/
0.3
/
Shearwall HP: Durha + CASHEW
NSF: None
Damping: 1%
Hazard Level: CP (2%I5Oyrs)
W = 24730 lb. total
X
0.1
-
--
C)
0
2
1
at second story
Structure Type: Two tory (20 x 16')
Nailing Schedule: 6d6"/12" and 3/12"
Sheathing: OSB (/")
':
/
/
0.2
at first stow
4
3
5
6
8
7
5max (in.)
Figure 5.26 Comparison of peak displacements at first and second stories, OSB (CP,
2/50 hazard level)
0.9
0.8
/-/
I
0.7
Interstory drift:
0.6
::: :
/
40.5
0.4
/Structure
0.3
Type: Two Story (20' x 16')
Nailing Schedule: 8d@6"/12" and 3/12"
Sheathing: OSB (/8")
Shearwall HP: Durham + CASHEW
NSF: GWB + Stucco
Damping: 1%
Hazard Level: 10 (50%/50yrs)
W = 24730 lb. total
L
/
0.2
/
/
0.1
/
J
(1
0
0.05
/
/
/
'
-
-
0.1
0.15
0.2
max
0.25
0.3
0.35
0.4
(in.)
Figure 5.27 Comparison of peak displacements at first and second stories, OSB +
GWB + Stucco (JO, 50/50 hazard level)
191
0.9
0.8
Interstory drift
0.7
6max at first story
/
0.6
0.5
0.4
x
max
0.3
/
/
0.2
Structure Type: Two Story (20 x 16)
Nailing Schedule: 8d©6"/12" and 3/12"
Sheathing: OSB (/8")
Shearwall HP: Durham + CASHEW
NSF: GWB + Stucco
Damping: 1%
Hazard Level: LS (10%I5Oyrs)
>
f
/
/
I
0.1
,
>
W=247301b. total
--
n
0
0.2
at second story
0.8
0.6
0.4
1
1.2
1.4
6max (in.)
Figure 5.28 Comparison of peak displacements at first and second stories, OSB +
GWB + Stucco (LS, 10/50 hazard level)
0.9
*
/_
7
/+
t
0.8
,'<
Interstory drift
0.7
6max at first story
0.6
0.5
U-
0.4
0.3
:
/
/
/
/
0.2
Structure Type: Two Story (20 x 16)
Nailing Schedule: 8d@6"/12" and 3/12"
Sheathing: OSB (/8")
Shearwall HP: Durham + CASHEW
NSF: GWB + Stucco
Damping: 1%
Hazard Level: CF (2%/5Oyrs)
,<
'
/
0.1
"
,
+
W 24730 lb. total
--
n
0
0.5
6max at second story
1
1.5
2
2.5
3
ömax (in.)
Figure 5.29. Comparison of peak displacements at first and second stories, OSB +
GWB + Stucco (CP, 2/50 hazard level)
192
5.2.3.2 Effect of partition walls
Gypsum wallboard is a common material used to sheath partition walls that
divide space in a building. Typical partition walls are constructed with gypsum
wallboard attached to both sides of the wall framing using mechanical fasteners
(drywall screws). The partition walls usually are treated as nonstructural elements in a
building (i.e., they are excluded in a structural analysis or in the design of the primary
shearwalls), however they may contribute to the overall structural performance. This
was investigated using the SAWS model of the one-story structure described in
Section 5.2.1.
The SAWS model of the one-story structure without partition walls is shown in
Figure 5.30. The dimensions of this structure are the same as shown in Figure 5.1.
This structure is composed of eight zero-height nonlinear shearwall spring elements
(shown), one for each wall layer. Gypsum wallboard was assumed to be used an all
interior walls.
Nonlinear dynamic time-history analysis was performed using the SAWS
model to investigate the contribution of the partition walls to peak displacement. The
peak displacement distributions of the structure without partition walls are shown in
Figures 5.31 through 5.33 for the three hazard levels (TO, LS, and CP), respectively.
Comparing these results with these shown in Figures 5.10 through 5.12 (with partition
walls), one sees that the partition walls significantly influence the shearwall
performance at all hazard levels. The results in Figures 5.10 through 5.12 are also
shown as light lines in Figures 5.31 through 5.33 to allow for easy comparison. While
193
the displacements of the North wall (NW) in the one-story structure with partition
walls are well below the drift limit, those for the same wall without partition walls are
above the drift limit. This also can be seen in Figures 5.34 through 5.36 which show
comparisons of peak displacement distributions considering different NSF materials
and the effect of partition walls for the North wall (NW). As expected, the OSB-only
shearwalls (without partition walls) exhibited the worst performance, while the
shearwalls with NSF materials (stucco and gypsum wallboard, and with partition
walls) performed considerably better. The worst-case wall performance was improved
even further when the partition walls were considered. All shearwalls (with or without
NSF materials) analyzed with consideration of partition walls perform well below the
drift limit at JO (50/50) and LS (10/50) hazard levels. Also, the variability in peak wall
displacement is reduced when the effect of partition walls is considered in the
analysis. This was observed at all hazard levels.
194
Figure 5.30 SAWS model of one-story structure without partition walls, (OSB +
GWB)
1
///
I.
/
/7/
-
/
sw
NW
/
0.5
itonWL
with
0.4
Ii!!
/
I!
//
0.3
/ /
0.2
//
/
I
1/
/
Structure Type: One Stow (32 20)
Nailing Schedule: 8d@6'-12"
Sheathing: OSB (3//)
Shearwall HP: Durham + CASHEW
NSF: GWB (without Partition Wall)
Damping: 1%
Hazard Level: 10 (50%ISOyrs)
/
/
/
/ /
/7
/
/ /
0.1
/7
'
/
/
0
0.05
/
,/
/
-,
ru
/
1/
-..-
/
--.---'
0.1
W16793 lb. total
/
0.15
.-___
0.2
0.25
0.3
____
0.35
0.4
max (in.)
Figure 5.31 Peak displacement distributions for one-story structure, OSB + GWB
(without partition walls), JO (50/50 hazard level)
195
/7
0.9
0.8
0.7
//iI
0.6
Sw
/
0.5
WW
NW
/
/
0.4
/
with t'arti'tiondias
0.3
ii
0.2
/
//
0.1
/
II
/
/7
///
n
//
/
/
/
0
-
0.2
//
0.4
x
20)
Sheathing: OSB (/")
I
I
/
Structure Type: One Story (32
Nailing Schedule: 8d@6"-12"
/
//
/
Shearwall HP: Durham + CASHEW
NSF: GWB (without Partition Wall)
Damping: 1%
Hazard Level: LS (10%/5oyrs)
W = 16793 lb. total
/
0.6
0.8
max
1.2
1
1.4
(in.)
Figure 5.32 Peak displacement distributions for one-story structure, OSB + GWB
(without partition walls), LS (10/50 hazard level)
0.9
/7/7
0.8
//Ew
//
0.7
WW,''
//
:
0.6
1:11
/1
NW
.
0.5
U0.4
,"1
0.3
,"/ /
aitiQ WaHs
with
//
//
/
0.2
//
/
//
0.1
I
/1
/
/
J /J/
n
0
0.5
/
Structure Type: One Story (32' x 20')
Nailing Schedule: 8d@6"-12"
Sheathing: OSB (/8")
Shearwall HP: Durham + CASHEW
NSF: GWB (without Partition Wall)
Damping: 1%
Hazard Level: CP (2%I5Oyrs)
//
W=167931b.total
1
1.5
2
max
2.5
3
3.5
4
(in.)
Figure 5.33 Peak displacement distributions for one-story structure, OSB + GWB
(without partition walls), CP (2/50 hazard level)
196
I
0.9
I OSB,'+ GWB + StØ'cco
(with Partition Walls)
SB only
(without Partition Walls)
0.7
OSB + GVB
(with Partition Walls)
0.6
I:
0.5
U-
0.4
/ OSBG\)
/ (without P
0.3
/
/
0.2
on Walls)
0.1
ii
0
0.2
0.1
Structure Type: One Story (32' x 20')
Nailing Schedule: 8d@6'-12"
Shearwall HP: Durham + CASHEW
Damping: 1%
Hazard Level: 10 (50%I5Oyrs)
Wall: North Wall (NW)
0.4
0.3
0.5
0.6
max (in.)
Figure 5.34 Comparison of peak displacement distributions for the effect of partition
walls and NSF materials, (JO, 50/50 hazard level)
I
S.
I;
OB+GWB+Stuc
o
(with Partition Wall)
II
0.7
0.6
I
/
OSB+GWB
(without Partition Walls
OSB+GWB/
OSB only
(without Partition Wa Is
(with Partiti n Walls)
0.5
0.4
0.3
0.2
0.1
0
0
0.4
Structure Type: One StoW (32' x 20')
Nailing Schedule: 8d@6"-12"
Shearwall HP: Durham + CASHEW
Damping: 1%
Hazard Level: LS (1 0%I50rs)
Wall: North Wall (NW)
0.8
1.2
1.6
2
6max (in.)
Figure 5.35 Comparison of peak displacement distributions for the effect of partition
walls and NSF materials, (LS, 50/50 hazard level)
197
1
0.9
+ GWB + S/cco
1(with Partition Walls)
0.8
0.7
/
0.6
/
OSB + GWB
(without Partition WaIIs
OSB only
(without Partition Walls)
/
/
OSB+GW
(with Parti(on Wa,}(s)
0.5
Li
/
I:
0.4
//
//
I:
/:
0.3
/
0.2
Structure Type: One Story (32' x 20')
Nailing Schedule: 8d@6'-12"
Shearwall HP: Durham + CASHEW
Damping: 1%
Hazard Level: CF (2%/5oyrs)
Wall: North Wall
0.1
0
0
1
2
4
3
max
5
6
(in.)
Figure 5.36 Comparison of peak displacement distributions for the effect of partition
walls and NSF materials, (CP, 2/50 hazard level)
5.2.3.3 Performance comparison for isolated wall and wall in one-story structure
Most experimental tests of wood shearwalls are performed on isolated
shearwall assemblies (with or without NSF materials), with solid walls (no openings)
being the most common assembly tested. Although some shake table tests of full-scale
structures have been performed recently, isolated shearwall assemblies remain the
most common test configuration used to evaluate the performance of wood shearwalls
under seismic loading.
Using the north wall (NW) in the model of the one-story structure (see Figure
5.1), the difference between performance of an isolated shearwall and the same
shearwall acting as part of a one-story structure was investigated. The seismic weight
acting on the isolated shearwall was assumed to be one-half of that on the full-scale
structure used in the Section 5.1.1. As described previously in Section 5.2.1.1, a set of
ten hysteretic parameters for the north wall in a one-story structure was obtained using
the CASHEW program and assuming the Durham nail parameters. The peak
displacement distributions were obtained using SASH! for the isolated wall and using
SAWS for the wall in the complete one-story structure.
Figures 5.37 and 5.38 present comparisons of the peak displacement
distributions for the isolated wall and the wall in the complete one-story structure for
the 10 and LS hazard levels, respectively. Only the wall having the worst performance
(North wall, NW) is considered here. The difference in peak displacement
distributions is relatively small at the JO hazard level, however increases as the hazard
level increases to the LS hazard level. (At the CP hazard level, most of the peak
displacements exceeded the drift limit of 3%, and so that figure is not included here.)
This suggests that consideration of the performance of the complete structure system
should be included in the design of wood shearwall assemblies, particularly at high
hazard level events. This might be able to be accomplished using a modification factor
(applied to peak drift, e.g.), however this factor may be very structure-dependent.
199
2;
0.9
0.8
Wall in System
0.7
Isolated Wall
0.6
0.5
0.4
0.3
Structure Type: One Story House (32 x 20)
Nailing Schedule: 8d@6"-12°
Shearwall HP: Durham + CASHEW
Damping: 1%
Hazard Level: 10 (50%/50yrs)
0.2
0.1
n
0
0.2
0.1
0.3
0.4
0.6
0.5
0.7
0.8
6max (in.)
Figure 5.37 Comparison of peak displacement distributions for isolated shearwall and
shearwall in complete one-story structure (10, 50/50 hazard level)
/
Structure Type: One Story (32' x 20)
Nailing Schedule: 8d@6"-12"
Shearwall HP: Durham + CASHEW
Damping: 1%
Hazard Level: LS (10%I5Oyrs)
0.9
0.8
Wall in system
0.7
Isolated wall
/
0.6
0.5
/
0.4
/
0.3
/
0.2
/
0.1
n
0
0.5
1
1.5
2
2.5
3
ömax (in.)
Figure 5.38 Comparison of peak displacement distributions for isolated shearwall and
shearwall in complete one-story structure (LS, 10/50 hazard level)
200
5.3 Performance-based design
5.3.1 Incremental dynamic analysis
Incremental dynamic analysis (IDA) was performed on isolated shearwalls
with and without openings in Section 4.4.1. The results could be used to help define
appropriate collapse limit state definitions. The same methodology is used in this
section to develop IDA curves for shearwalls in a two-story structure. The same suite
of 20 ordinary ground motion records was used as input to the nonlinear dynamic
time-history analysis. Seismic zone IV (LA) and soil profile type D
(SD)
were
assumed.
IDA curves were developed specifically for the East wall 2EW in the two-story
structure. This was the shearwall exhibiting the largest displacements (see Section
5.2.2). The suite of 20 ordinary ground motion records was divided into three groups
to make it easier to show the resulting IDA curves on a single figure. Only one set
(seven records) is shown here, however the results are representative.
Figure 5.39 shows Sa vs. peak displacement for shearwall 2EW in the twostory structure. Also shown are the tangents defining the apparent break points and an
estimated mean value for those break points. A characteristic value could be used to
define the design drift limit for collapse prevention (CP, 2/50). The mean value of this
break point corresponds to a peak displacement of 5.56 in. or about 2.7% of the total
wall height. (Note that the FEMA 356 drift limit for collapse prevention (CP, 2/50) is
3% of the total wall height for wood shearwalls.) If NSF materials are considered
201
(Figure
5.40),
the mean value of the IDA break point decreases to
4.01
in., or about
1.9% of the total wall height.
Similar analyses were performed for the wall with a pedestrian door opening
(2WW). There was no significant difference in the estimated collapse limit (IDA break
point) between wall 2EW with the garage door opening and wall 2WW with the
pedestrian door opening. The 3% drift limit suggested by FEMA
356
appears to
correlate well with the collapse limit determined by IDA for the wall without NSF
materials. However, if walls are built with NSF materials, the estimated collapse limit
decreases. Table
5.6
summarizes the estimated collapse limit (mean value) for the
shearwalls considered in this study.
IDA Set
1
2
3
4
Sheathing
OSB
OSB
OSB + Stucco + GWB
OSB + Stucco + GWB
Shearwall
2EW
2WW
2EW
2WW
Mean, t
5.56
5.63
4.05
4.15
in.
in.
in.
in.
lable 5.6 Estimated collapse limit (from IDA) for shearwall in the complete two-story
structure
202
2.0
1.5
c,)
1.0
C')
0.5
0.0
0
1
2
3
4
5
6
7
8
10
9
Smax (h.)
Figure 5.39 Set of IDA curves for selected OSB-only walls with garage door opening
(2EW)
2.0-
1.5
0)
1.0
C')
0.5
0.0
r
0
1
2
3
4
5
6
7
8
9
10
max (1)
Figure 5.40 Set of IDA curves for selected OSB + NSF walls with pedestrian door
opening (2WW)
203
5.3.2 Fragility curves
Fragility curves which could be used for design as well as for post-disaster
condition assessments were developed for an isolated shearwall (BW1) in Section
4.4.2. In this section, fragility curves for shearwalls in representative one and twostory residential structures are developed. The seismic demand (interface) variable is
the spectral acceleration, 5a Fragility curves of this type can be used either as design
aids or to assess risk consistency in current design provision.
5.3.2.1 Fragility curve for one-story structure
Fragility curves were developed for the North wall (NW) of the one-story
structure, which has a pedestrian door and windows as shown in Figure 5.1. The North
wall (NW) exhibited the worst displacement performance in the one-story structure
(see Figures 5.5 through 5.7). As in the previous section, the records were scaled to six
different hazard levels: 50% in 50 years (72-year MRI), 20% in 50 years (225-year
MRT), 10% in 50 years (474-year MRI), 5% in 50 years (975-year Mifi), 2% in 50
years (2475-year MRI), and 1% in 50 years (4795-year MRI). The procedure for
constructing the fragility curves is the same as was described in the previous section
(Section 4.4.2).
The fragility curves for the North wall (NW) sheathed with OSB only, are
shown in Figure 5.41. Drift limits of 1%, 2% and 3% of the total wall height were
considered. Figure 5.42 presents a comparison of fragility curves for the North wall
constructed with gypsum wallboard, but without consideration of interior partition
204
walls. Figure 5.43 presents the fragility curves for the North wall (NW) with different
combinations of finish materials, and with and without consideration of the partition
walls. As before, only the JO (50/50, 1% drift limit) performance level is shown here
since the other performance levels (LS, CP) result in very low failure probabilities for
the walls built with NSF materials. Figure 5.43 confirms that NSF materials (stucco
and gypsum wallboard) contribute significantly to the performance of shearwalls
acting as part of complete structures under earthquake loading. It also shows that
partition walls significantly influence the performance of shearwalls acting as part of a
complete structure and subject to earthquake loading.
0.9
0.8
/,"3%
0.7
/
0.6
d
/
/
0.5
/
/
0.4
1/:"
/
0.3
'
/
0.2
//
0.1
'
'
W=150401b.total
-- -
n
0
0.5
1
Structure Type: One Story (32' >< 20')
Nailing Schedule: 8d@6"-12"
Sheathing: OSB (/8")
Shearwall HP: Durham + CASHEW
NSF: None
Damping: 1%
1.5
2
2.5
3
Sa(g)
Figure 5.41 Fragility curves for the North wall (OSB only) in the one-story structure
(without partition walls)
205
1
Structure Type: One Story (32
Nailing Schedule: 8d@6-12"
0.9
20)
x
[
/
Sheathing: OSB (I)
Shearwall HP: Durham + CASHEW /
NSF: GWB (without Partition Walls)/
Damping: 1%
W = 16793 lb. total
0.8
0.7
I
/
/0
/
/
/
0.6
Q:
/
L /0
"...
3%
I
0.5
/,,,,
0.4
/"
0.3
I
0.2
I
/
0.1
0
0.5
1
2
1.5
2.5
3
Sa(g)
Figure 5.42 Fragility curves for the North wall (OSB + GWB) in the one-story
structure (without partition walls)
I
0.9
0.8
OSB only
(without Partition Wall
/
0.7
0.6
0
B + GW + Stucco
1(th Partition Walls)
OSB + GWB
(without Partition Wa ls)
o.s
OSB+GWB
I
/
0.4
/
(with Partition Walls)
/
0.3
/
/
0.2
0.1
//
n
0
0.5
1
1.5
x 20)
Niling Schedule: 8d@d"-12"
(3/5)
sheathing: OSB
Shearwall HP: Durham + CASHEW
Stvucture Type: One Story (32
/ NSF: GWB + Stucco
/ Damping: 1%
Hazard Level: 10 (50%I0yrs)
2
2.5
3
Sa(g)
Figure 5.43 Comparison of fragility curves for the North wali in the one-story
structure (JO, 50/50, 1% drift limit)
206
5.3.2.2 Fragility curve for two-story structure
Fragility curves were developed for the East wall (2EW) and West wall
(2WW) with a garage door and pedestrian door opening, respectively, in the two-story
structure described in Figure 5.3. Peak displacement distributions were obtained for
each hazard level and the probability of failure was determined non-parametrically as
the relative frequency of the peak displacement exceeding specified drift limits. The
records were scaled to six different hazard levels: 50% in 50 years (72-year mean
return period, or MRI), 20% in 50 years (225-year MRI), 10% in 50 years (474-year
Mifi), 5% in 50 years (975-year MRI), 2% in 50 years (2475-year MRI), and 1% in 50
years (4975-year MRT).
Figures 5.44 through 5.46 show the fragility curves for the East wall (2EW)
considering three different peak displacements:
interstory drift, and
max
3max
at first story (relative to ground),
at second story (relative to ground). Drift limits of 1%, 2%
and 3% of the relevant wall height were considered. The first story has a height of 8 ft.
1 in., and the second story has a (total) height of 17 ft. 2 in. Considering the life safety
drift limit (2% of total wall height), the limit for the first story is 1.94 in., the limit for
the second story is 4.12 in., and the drift limit considering interstory drift is 1.94 in.
Figures 5.47 and 5.48 show the fragility curves for the West wall (2WW) in
the two-story structure considering two different peak displacements
story and
max
@max
at the first
at the second story). Drift limits of 1%, 2% and 3% of the wall height
were considered.
207
All of the fragility curves for the two walls with openings (garage door and
pedestrian door) in the two-story structure are shown for comparison in Figures 5.49
and 5.50 assuming the FEMA 356 drift limit (1%, and 2% for JO and LS,
respectively). In the plateau region of the response spectrum considering seismic zone
IV (LA) and
SD
soil profile type, the spectral acceleration
occupancy (TO, 50/50) and
Sa
= 0.633g for immediate
= 1.lg for life safety (LS, 10/50). In this example, the
Sa
fragility curves indicate very low probabilities of failure for these performance levels,
with the exception of interstory drift. Thus, interstory drift might be the most
appropriate (conservative) displacement criteria to consider in design.
1
0.9
1%
0.8
1/
0.7
2%'
3%
0.6
/
/
0.5
/
/
0.4
/
/
0.3
I
/
I
0.2
I
/
/
0.1
.// .../-/
n
0
0.5
1
Structure Type: Two Story (20 x 16)
Nailing Schedule: 8d@6Il:2" and 3/12"
Sheathing: OSB (/8")
Shearwall HP: Durham + CASHEW
NSF: None
Damping: 1%
W = 24730 lb. total
I
/
/
'
I
-
1.5
2
2.5
3
3.5
4
4.5
5
Sa(g)
Figure 5.44 Fragility curve for wall with garage door opening,
ground) at first story
max
(relative to
------
1
0.9
0.8
0.7
/
,,3%
/
0.6
o
/
0.5
/
/,,,,
0.4
/
0.3
:'
/
/
0.2
/
0.1
/
,'
/
Structure Type: Two Story(20' x 16)
Nailing Schedule: 8d©6"/12" and 3/12'
Sheathing: OSB (/8")
Shearwall HP: Durham + CASHEW
'
,
'
'
/
NSF: None
Damping: 1%
W = 24730 lb. total
-
- -
ft
0
0.5
2
1.5
1
2.5
3
Sa(g)
Figure
5.45
Fragility curve for wall with garage door opening, interstory drift
1/o/
1
0.9
/
2%
0.8
3%
0.7
0.6
ci
/
0.5
/,','
/
/
0.4
/,"
/
0.3
/
/
/
/
0.2
/
0.1
._-'
'-I
0
0.5
_..._1
/
/
/
--
/
/
-
Structure Type: Two Story (20' x 16')
Na/lIng Schedule: 8d@6"/12' and 3/12"
Sheathing: OSB (/8')
Shearwall HP: Durham + CASHEW
'NSF: None
Damping: 1%
W = 24730 lb. total
1.5
2
2.5
3
Sa(g)
Figure 5.46 Fragility curve for wall with garage door opening, ömax (relative to
ground) at second story
//
1
10
0.9
2%
0.8
/
'.) /0
0.7
209
-
0.6
d
/
0.5
/
/
/
0.4
/
/
/
0.3
/
/
/
/
0.1
"
n
0
0.5
_.-
/
/
/
x 16)
Nailing Schedule: 8d@6'/12 and 3/12"
Sheathing: OSB (/a)
Structure Type: Two Story (20
/
/
0.2
'
"
Shearwall HP: Durham + CASHEW
NSF: None
Damping: 1%
W= 24730 lb. total
'
3
2.5
2
1.5
1
3.5
Sa(g)
Figure 5.47 Fragility curve for wall with pedestrian door opening,
ground) at first story
max
(relative to
1
Structure Type: Two Story (20 x 16)
Nailing Schedule: 8d@6"/12" and 3/12"
0.9
Sheathing: OSB (I)
Shearwall HP: Durham + CASHEW
NSF: None
Damping: 1%
W = 24730 lb total
0.8
0.7
0.6
0.5
0.4
0.3
/
0.2
/
/
/
0.1
n
0
0.5
1
1.5
2
2.5
3
Sa(g)
Figure 5.48 Fragility curve for wall with pedestrian door opening,
ground) at second story
6max
(relative to
210
0.9
""
/
0.8
0.7
2' Story (GD)
/
0.6
Interstory (GD)
2
I
Story (PD)
1' Story (GD)
/
1S Story (PD)
/
0.4
/
0.3
Structure Type: Two Story (20 x 16')
Nailing Schedule: 8d@6"/12" and 3/12"
Sheathing: OSB (/8")
Shearwall HP: Durham + CASHEW
NSF: None
Damping: 1%
Hazard Level: 10 (50%/50yrs)
W = 24730 lb. total
/
0.2
0.1
(1
0
0.5
2.5
2
1.5
1
Sa(g)
Figure 5.49 Comparison of fragility curves for shearwall in two-story structure (JO,
50/50, 1% drift limit)
--
1
0.9
Interstory(GD)
0.8
2nd Story (PD)
0.7
1st Story (GD)
nd
1st
0.6
0
'_,/"
Story (PD)
0.5
//
0.4
/7
/
0.3
//
0.2
//-
0.1
/
/ Structure Type: Two Story (20
/
,i
16')
Nailing Schedule: 8d@6"/12" and 3/12"
Sheathing: OSB (/8")
Shearwall HP: Durham + CASHEW
NSF: None
Damping: 1%
Hazard Level: LS (10%/5oyrs)
W = 24730 lb. total
(1
0
0.5
1
1.5
2
2.5
3
Sa(g)
Figure 5.50 Comparison of fragility curves for shearwall in two-story structure (LS,
10/50, 2% drift limit)
211
Figures 5.51 and 5.52 present the fragility curves for the East wall (2EW) and
West wall (2WW), built with nonstructural finish materials (stucco and gypsum
wallboard), with partition walls and considering the JO (50/50) performance level (1%
drift limit). As noted earlier, NSF materials significantly improve the displacement
performance of wood shearwalls. For this wall, only the immediate occupancy (with
JO, 50/50) with the 1% drift limit case could be considered since very low failure
probabilities were obtained for the LS and CP performance levels when NSF materials
were included. The fragility curves in Figures 5.53 and 5.54 show that wall
constructed with NSF materials (with partition walls) can sustain higher seismic
demand than walls sheathed with OSB only (without partition walls). For example, if
the seismic demand variable
(Sa)
is 1.5g, the probability of failure of wall 1WW
considering NSF materials and partition walls is about 10%, versus about 80% for the
equivalent bare wall. Similarly, the probability of failure for wall 2WW is about 3%
considering NSF materials and partition walls, versus about 85% for the bare wall.
212
Structure Type: Two Story (20 x 16)
Nailing Schedule: 8d@6"/12" and 3/12'
0.9
Sheathing: OSB (/")
Shearwall HP: Durham + CASHEW
NSF: GWB + Stucco
Damping: 1%
Hazard Level: ID (50%/50yrs)
W = 24730 lb. total
0.8
0.7
/:
0.6
o.5
First story
(with Partition Walls)
0.4
0.3
/ Second story
0.2
(with Partition Walls)
0.1
0
0.5
1
2.5
2
1.5
3
Sa(g)
Figure 5.51 Fragility curves for shearwall with NSF materials (2EW) in two-story
structure
//
Structure Type: Two Story (20 x 16')
Nailing Schedule: 8d@6"/12" and 3/12"
(3/.)
Sheathing: OSB
Shearwall HP: Durham + CASHEW
NSF: GWB + Stucco
Damping: 1%
Hazard Level: 10 (50%/5oyrs)
W = 24730 lb. total
0.9
0.8
0.7
o
/
/
0.6
0.5
First story
/
(with Partition Walls)
0.4
/
/
0.3
/
0.2
Second story
(with Partition Walls)
/
0.1
A
0
0.5
1
1.5
2
2.5
3
Sa(g)
Figure 5.52 Fragility curves for shearwall with NSF materials (2WW) in two-story
structure
213
1
Structure Type: Two Story (20 x 16)
Nailing Schedule: 8d@6'112" and 3/12"
0.9
/
Sheathing: OSB (/)
/
Shearwall HP: Durham + CASHEW
NSF: GWB + Stucco
Damping: 1%
Hazard Level: 10 (50%I5Oyrs)
W = 24730 lb. total
0.8
0.7
/
,
,'
0.6
o
Bare wall (GD)
(without Partition Walls
Bare wall (PD)
(without Partition Walls)
0.5
/
0.4
NSF wall (GD)
/,,(with Partition Walls')
0.3
/
0.2
NSF wall (PD)
(with Partition Walls')
/
0.1
0
0.5
2
1.5
1
2.5
3
Sa(g)
Figure 5.53 Comparison of fragility curves showing contribution of NSF materials,
max (relative to ground) at first story
// .'
Structure Type: Two Story (20' x 16')
Nailing Schedule: 8d@6'/12" and 3/12"
0.9
Sheathing: 058 (/')
Shearwall HP: Durham + CASHEW
NSF: GWB + Stucco
Damping: 1%
Hazard Level: 10 (50%/5Oyrs)
W = 24730 lb. total
0.8
0.7
/
/
//
/
I
//
//
/
0.6
I
ci
/
/ NSF Wall (GD)
/ NSF Wall (PD)
(with Partition Walls
0.5
//
/
0.4
/1
0.3
Bare wall (GD) /
(without Parti7n Walls)
0.2
Bare wall (PD)1'
(without Partjyon Walls)
0.1
n
0
0.5
1
1.5
2
2.5
3
Sa(g)
Figure 5.54 Comparison of fragility curves showing contribution of NSF materials,
ömax (relative to ground) at second story
214
6. CONCLUSIONS AND RECOMMENDATIONS
Wood is the most common material used in low-rise construction in the United
States. Light-frame wood structures have a number of advantages including aesthetics,
beauty, construction cost and time, versatility, flexibility in floor plans, and so forth.
Most woodframe structures consist of floors, walls, and roof systems tied together by
fasteners. Shearwalls provide the primary resistance to lateral forces (along with
diaphragms), such as these arising from earthquake loading, in most woodframe
structures.
The objective of this research was to explore the potential for the application of
performance-based engineering concepts to the design and assessment of woodframe
structures subject to earthquakes. To accomplish this, shearwalls either were treated as
isolated subassemblies or were assumed to act as part of complete structure. Nonlinear
dynamic time-history analysis was used to predict the performance of shearwalls
considering a suite of suitably scaled characteristic ordinary ground motions to
represent the seismic hazard.
Sensitivity studies were performed to investigate the relative effects of
damping, sheathing properties, fastener type and spacing, panel layout. and other
properties on the performance of wood shearwalls. In addition, the effects of
uncertainty in ground motions and variability in sheathing-to-framing connection
hysteretic parameters were investigated. Issues such as the contribution of
nonstructural finish materials, different seismic hazard regions, and construction
quality also were investigated and modification factors to adjust peak displacement
215
distributions were developed. The peak displacement distributions were then used to
construct performance curves and design charts as a function of seismic weights for
two baseline walls (BW1 and Owl), considering different levels of construction
quality, and different seismic hazard regions. In the consideration of shearwalls acting
as part of a complete structure, interstory drift and the effects of considering partition
walls also were investigated.
Incremental dynamic analysis (IDA) using baseline isolated shearwall and the
worst performance wall in two-story structure was performed in efforts to quantify an
approach drift limit for collapse prevention. In most cases considered, this value was
close to the drift limit specified by FEMA 356. Examples of fragility curves
(considering both peak displacement and ultimate uplift force) were developed. The
shearwalls to construct fragility curves were designed by considering different nailing
schedules (2"/12", 3"/12", 4"/12", and 6"/12"), corresponding allowable seismic
weights (back-calculated from the UBC '97 allowable unit shear values), and various
overstrength (R) factors.
6.1 Conclusions
The following conclusions were drawn from the results of this research:
1.
Performance-based design concepts can be applied to the design and
assessment of woodframe structure and can provide valuable information for
understanding the performance of shearwalls subject to earthquake loading.
216
2. The greatest contributors to variability in predicted shearwall response are the
ground motions. Therefore, caution must be used when specifying the seismic
hazard used to develop performance-based design requirements. Other
uncertainties contributing variability in shearwall response are model
uncertainty, sheathing-to-framing connection hysteretic parameters, and
construction quality.
3.
The contributions of nonstructural finish materials to the performance of
woodframe shearwalls may be significant, especially at large demands, and
therefore should be considered when developing performance-based design
guidelines. In particular, the application of stucco serves to greatly reduce peak
shearwall displacements.
4.
Construction quality issues such as missing or misplaced fasteners, overall
levels of construction quality, and quality of NSF material application can
significantly influence shearwall performance under earthquake loading.
5.
Different earthquake scaling methods will result in different predicted
shearwall performance. However, the median displacement values are similar.
6.
Simple deterministic modification factors can be developed to account for
variation in sheathing to-framing connection hysteretic parameters, effects of
different levels of construction quality, and contributions of nonstructural
finish materials. These factors can be used to adjust peak displacement
distributions obtained by nonlinear dynamic time-history analysis.
217
7.
Performance curves and design charts can be developed using seismic weight
as the design variable. These permit selection of a particular sheathing type and
fastener spacing for a given seismic weight to meet specific performance
objectives at different hazard levels. The procedure to develop performance
curves and design charts is sufficiently modular to allow different information
on shearwall properties, seismic hazard, and so forth to be included.
8.
Incremental dynamic analysis (IDA) can be used to quantify appropriate drift
limits for collapse prevention. In most cases considered in this study, this value
was close to the drift limit specified by FEMA
9.
356.
The shearwalls designed using UBC '97 allowable unit shear values provide
relatively consistent levels of safety, as evidenced by the fact that the resulting
fragility curves were quite close for all nailing schedules. Thus, a single
fragility curve can be constructed for a given R factor.
10. Interstory drift may be used the most appropriate (conservative) displacement
criteria to consider in displacement-based design of woodframe structures.
11. The performance of a shearwall acting as part of a one- or two-story structure
is quite different from a shearwall acting as an isolated assembly. The
difference in peak displacement distributions is relatively small at the 10
hazard level, however increases as the hazard level increases. It therefore may
be appropriate to modify isolated shearwall performance to take into account
overall system performance of a woodframe structure, particularly for high
hazard levels. This modification, however, may be structure-dependent. In both
218
cases (isolated shearwall and wall acting as part of a complete structure),
however, peak displacements are significantly reduced with the addition of
NSF materials.
12. Partition walls have a significant effect on the performance of shearwalls at all
hazard levels. Also, the variability in peak wall displacement is reduced when
the effects of partition walls are considered.
6.2 Recommendations
The following might be suggested as topics for future study:
1.
While construction quality issues (i.e., missing fasteners and level of
construction quality) were investigated in this study, there are a number of
other construction quality issues which could significantly influence overall
shearwall behavior. Among these are misplaced fasteners and anchors,
deterioration of structural and nonstructural finish materials, improper
selection of fasteners, under-driven or over-driven fasteners, missing blocking,
the use of smaller panel segments, cutouts in framing members (e.g., for
installation of conduit), and so forth.
2. The numerical model (CASHEW) used to develop global hysteretic parameters
for shearwall given nail hysteretic parameters assumes rigid hold-downs and
assumes that all fasteners have the same hysteretic parameters. Both of these
restrictions should be removed to permit more comprehensive investigations of
219
walls having different (and more realistic) anchorage and connection
properties.
3.
Durability is an important consideration in woodframe structures. The primary
durability issues for wood structures are decay, corrosion of connectors, and
insect attack. Recently completed tests of connections with various levels of
decay are available. These results can be used, for example, to develop new
fastener hysteretic parameters for use with the CASHEW model, and thereby
investigate the effects of decay on shearwall performance.
4.
Unidirectional earthquake records were used in this study. A suite of bidirectional earthquake records, which can be obtained from the SAC project
(e.g.,), can be used to more accurately reflect ground motion characteristics
and their effects on the three-dimensional structure. The SAWS program can
be used with bi-directional earthquake records. Also, near-fault ground motion
records were not considered in most of this study. Therefore, a more
comprehensive study considering bi-directional and near-fault records might
be conducted.
5. Performance curves and design charts were developed considering only limited
sheathing types/thickness and nail types (sizes). In order to extend these design
tools to include a wider range of products, additional sheathing and fastener
types will need to be considered.
6.
While it is recognized that the presence of NSF materials can significantly
improve shearwall performance, and evidence of this has been documented in
220
a number of recent studies, the degree to which this benefit (1) can be counted
upon for the design life of the structure, and (2) can be quantified for design
purposes, remains to be studied.
7. While the drift limits used in this study were adopted directly from FEMA 356,
their definition is qualitative. More quantitative definitions may be needed
which correlate more realistically with observed damage following actual
earthquake. Suitable drift limits and other performance measure are being
investigated by other researchers.
8.
Woodframe construction elsewhere in the U.S. is conventional rather than
engineered and does not rely on large shearwalls, seismic hold-downs, or dense
nailing schedules. It may be useful, particularly for assessment and evaluation
purposes, to develop fragility curves using the approach developed in this
study for these types of structures.
221
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230
APPENDICES
231
APPENDIX A: Example showing convolution of hazard curve and fragility curve
232
Fragility curves such as those developed in Section 4.4.2.1 can be convolved
with a hazard curve to evaluate failure probability. The probability of failure can be
obtained using the following equation;
Pf
(A-i)
=fPx(x)FR(x)dx
where, Pf = failure probability, Px(x) = probability density function of hazard (in this
case 50-year seismic hazard), and FR(x) = fragility. One example using a hazard curve
for southern California (specifically, Landers region) and a fragility curve for an
isolated shearwall considering a 3"/12" nailing schedule, various R factors, and the
LS (10/50) hazard level is shown in Figure A.1.
0.9
Hazarçi Curve (Landers)
0.8
/,/
0.7
-
/
80.
a)
L.
I\
\
,'\ /
1
Q
U)
//
0.2
\/
,'
//
0.1
/
I
Fragility Curve
R = 5.5 (3/12") -3 Pf= 0.16880
P = 0.12600
R = 4.5 (3/12")
Pf =0.08417
R = 3.5 (3/12")
R = 2.5 (3/12") -* Pf = 0.03697
-I-,
0
0.5
1
1.5
2
Sa(g)
Figure A.! Convolution of hazard curve and fragility curve
2.5
3
233
APPENDIX B: Deterministic modification factors for construction quality
234
Index
Building
Type
F0
Quality
Story
Sheathing
.
kip
K0
kips
OSB only
OSB +
GWB
OSB only
Typical
Small
House
Poor
OSB only
OSB
+
Stucco
I
OSB +
Stucco +
GWB
OSB only
OSB
+
Stucco
Typical
2
OSB +
Stucco +
GWB
OSB only
OSB
+
Stucco
Large
House
OSB +
Stucco +
GWB
OSB only
OSB
+
Stucco
oor
2
OSB+
Stucco+
F0
F1
r2
r3
a
3
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
1.01
1.01
1.01
r1
kip
kip
0.87
0.87
0.97
0.87
0.86
1.02
0.89
0.88
0.98
0.89
0.88
1.01
1.00
1.00
1.00
0.86
0.86
0.98
0.86
0.85
1.01
1.00
1.00
1.00
0.87
0.87
0.99
0.87
0.87
1.01
1.00
1.00
1.00
tL84
0.85
1197
0.84
0.84
1.04
1.00
1.01
1.00
0.87
0.88
0.99
0.87
0.87
1.02
1.00
1.00
1.00
0.84
0.85
0.99
0.85
0.85
1.02
1.00
1.00
1.00
0.86
0.87
0.99
0.86
0.87
1.01
1.00
1.00
1.00
0.62
0.60
1.00
0.61
0.61
0.96
1.02
1.01
1.01
0.66
0.65
1.00
0.65
0.66
0.98
1.01
1.00
1.00
0.68
0.67
1.00
0.68
0.68
0.98
1.01
1.00
1.00
0.69
0.68
1.00
0.69
0.69
0.99
1.01
1.00
1.00
0.66
0.59
1.01
0.65
0.58
0.97
1.01
1.00
1.00
0.68
0.64
1.00
0.68
0.64
0.99
1.00
1.00
1.00
0.71
0.67
1.00
0.70
0.67
0.99
1.00
1.00
1.00
0.70
0.68
1.00
0.70
0.68
0.99
1.00
1.00
1.00
0.85
0.87
0.99
0.84
0.85
0.93
1.00
1.00
1.00
0.87
0.88
1.00
0.87
0.87
0.96
1.00
1.00
1.00
0.85
0.86
1.00
0.85
0.85
0.96
1.00
1.00
1.00
0.87
0.87
1.00
0.86
0.86
0.98
1.00
1.00
1.00
0.85
0.87
0.99
0.85
0.85
0.97
1.00
1.00
1.00
0.88
0.88
0.99
0.88
0.87
0.98
1.00
1.00
1.00
0.85
0.86
0.99
0.85
0.85
0.98
1.00
1.00
1.00
0.87
0.87
1.00
0.87
0.87
0.99
1.00
1.00
1.00
0.63
0.63
0.99
0.62
0.62
0.93
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
GWB
OSBonly
Town
House
05B
+
Stucco
1
OSB +
Stucco +
GWB
OSB only
OSB
+
Stucco
Typical
2
Poor
I
OSB +
Stucco +
GWB
OSB only
OSB+
Stucco
0.66
0.67
0.99
0.66
0.66
0.97
0.69
0.69
0.99
0.69
0.68
0.97
235
OSB +
0.69
0.69
1.00
0.69
0.69
0.98
1.00
1.00
1.00
1162
1161
1198
0.62
(161
1197
1.00
L00
1.00
0.66
0.65
0.99
0.66
0.66
0.98
1.00
1.00
1.00
0.69
0.68
0.99
0.68
0.68
0.98
1.00
1.00
1.00
Stucco+
0.69
0.69
0.99
0.69
0.69
0.99
1.00
1.00
1.00
GWB
OSB only
0.86
0.82
1.00
0.86
0.86
0.97
1.00
1.00
1.00
0.88
0.86
1.00
0.88
0.88
0.99
1.00
1.00
1.00
0.85
0.83
1.00
0.85
0.88
0.99
1.00
1.00
1.00
0.87
0.86
1.00
0.87
0.88
0.99
1.00
1.00
1.00
(184
(186
(199
(184
(184
(197
L00
1.00
L00
0.87
0.88
0.99
0.87
0.87
0.99
1.00
1.00
1.00
0.85
0.86
0.99
0.85
0.85
0.99
1.00
1.00
1.00
0.86
0.87
1.00
0.86
0.86
0.99
1.00
1.00
1.00
0.65
0.68
0.97
0.65
0.65
0.67
0.69
0.99
0.67
0.68
0.70
0.72
0.99
0.70
0.72
0.70
0.71
0.99
0.70
0.71
0.61
0.58
1.00
0.61
0.60
0.65
0.64
1.00
0.65
0.65
Stucco+
GWB
OSB onjy
OSB
+
Stucco
2
OSB +
OSB+
Stucco
1
OSB +
Stucco +
GWB
OSB only
OSB
+
Stucco
Typical
2,3
OSB +
Stucco +
GWB
OSB only
OSB
+
Stucco
Apartment
Building
1
OSB +
Stucco +
GWB
OSB only
OSB
+
Stucco
oor
2,3
0.68
0.67
1.00
0.68
0.68
OSB +
Stucco +
GWB
0.69
0.68
1.00
0.69
0.69
OSB only
0.85
0.86
0.99
0.85
0.85
0.99
1.00
1.00
1.00
0.99
1.00
1.00
1.00
Typical
Modification
Factor
Poor
NSF
OSB onjy
OSB
+
Stucco
OSB +
NSF
(GWB)
0.86
0.87
0.99
0.86
0.87
1163
1161
(199
1163
(161
(197
LOl
11)0
L00
0.67
0.66
1.00
0.66
0.66
0.98
1.00
1.00
1.00
0.69
0.69
1.00
0.69
0.69
0.98
1.00
1.00
1,00
Table B. 1 Deterministic modification factors for construction quality
236
APPENDIX C: Scaling earthquake records to response spectra considering different
scaling methods
237
2.5
2.0
1.5
(I)
1.0
0.5
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Peirod (sec)
Figure C. 1 20 0GM records (CUREE) scaled over the plateau re ion of the response
spectrum (LS, 10/50)
3.0
2.5
2.0
0)
1.5
U)
1.0
0.5
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Period (sec)
Figure C.2 20 0GM records (CUREE) scaled at a period of 0.2 sec to the response
spectrum (LS, 10/50)
238
3.0
2.5
2.0
C)
1.5
C,)
1.0
0.5
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Period (sec)
Figure C.3 20 0GM records (CUREE) scaled at a period of 0.5 sec to the response
spectrum (LS, 10/50)
239
APPENDIX D: Earthquake records used in this study
240
EQ Event
& Year
File
SUPI
Superstition
Hills
(1987)
SUP2
SUP3
NOR2
NOR3
NOR4
Northridge
(1994)
NOR5
NOR6
NOR9
NORIO
LP1
LP2
Loma
Prieta
(1989)
LP3
LP4
LP5
LP6
Cape
Mendocino
(1992)
Landers
(1992)
CM1
CM2
LAN1
LAN2
Station
Brawley
El Centro
imperial
Plaster
City
Beverly
Hills
Canoga
Park
GlendaleLas Palmas
LAHollywood
LA N.
Faring
North
Hollywood
Sunland
Mt
Capitola
Gilroy
Array #3
Gilroy
Array #4
Gilroy
Array #7
Hollister
Diff. Array
SaratogaWest Val.
Fortuna
Boulevard
Rio Dell
Overpass
Desert Hot
Springs
Yermo Fire
Station
MW1
D
j
(2)
km
6.7
18.2
6.7
13.9
6.7
21.0
6.7
19.6
6.7
15.8
6.7
25.4
6.7
25.5
6.7
23.9
6.7
14.6
6.7
17.7
6.9
14.5
6.9
14.4
6.9
16.1
6.9
24.2
6.9
25.8
6.9
13.7
7.1
23.6
7.1
18.5
7.3
23.3
7.3
24.9
FM
(3)
strikeslip
strikeslip
strikeslip
reverseslip
reverseslip
reverseslip
reverseslip
reverseslip
reverseslip
reverseslip
reverseoblique
reverseoblique
reverseoblique
reverseoblique
reverseoblique
reverseoblique
reverseslip
reverseslip
strikeslip
strikeslip
f
DT (4)
sec
0.010
0005
0.010
0010
0.010
0.010
0.020
0.010
0.010
0.010
0.005
0.005
0.005
0.005
0.005
0.005
0.020
0.020
0.020
0.020
D5
sec
21.96
0
5
22.22
0
29.98
0
24.98
0
29.98
0
39.98
0
29.98
0
21.91
0
29.98
0
39.95
0
39.94
0
39.94
5
39.94
5
39.63
5
39.94
5
43.98
0
35.98
0
49.98
0
43.98
0
ST
I PGA 1
(2)
(3)
(4)
(5)
Moment magnitude
Closest source-to-site distance
Faulting mechanism
Recording time interval
Duration
r
[
PGD
cm
D
0.116
17.2
8.6
D
0.258
40.9
20.2
D
0.186
20.6
5.4
C
0.416
59.0
13.1
D
0.356
32.1
9.1
D
0.357
12.3
1.9
D
0.231
18.3
4.8
D
0.273
15.8
3.3
C
0.271
22.2
11.7
C
0.157
14.5
4.3
D
0.529
36.5
9.1
D
0.555
35.7
8.2
D
0.417
38.8
7.1
D
0.226
16.4
2.5
D
0.279
35.6
13.1
C
0.332
61.5
36.4
C
0.116
30.0
27.6
C
0.385
43.9
22.0
C
0.154
20.9
7.8
D
0.152
29.7
24,7
Table D.1 Set of LA ordinary ground motion records (CUREE project)
(1)
PGV
j
1
241
EQ Event
& Year
I
I
Imperial
Valley
(1979)
(1994)
L Jso
10.0
LAO2
El Centro
6.9
10.0
LAO3
Array#5
6.5
4.1
LAO4
Array #5
6.5
4.1
LAOS
Array #6
6.5
1.2
LAO6
Array #6
6.5
1.2
7.3
36.0
7.3
36.0
7.3
25.0
7.3
25.0
LAO8
LAO9
LAII
LAI2
LA13
LA14
LA 17
Landers,
Barstow
Landers,
Barstow
Landers,
Yermo
Landers,
Yermo
Gilroy
Gilroy
Newhall
Newhall
Rinaldi RS
Rinaldi RS
Northridge
Sylmar
Norlhridge
2.0
FM (31
F
of
Points
strikeslip
strike
slip
strikeslip
strikestrikeslip
strikeslip
strikeslip
strikeslip
strikeslip
strikeslip
oblique
oblique
PGA
D5
J
I
ST
I
I
I
I
I
I
I
I
I
I
[
I
______
DT (4)
,
sec
i
I
lO%/
SOyrs
(2)
(3)
(4)
(5)
0GM
.
0.020
53.460
D
452.03
2.01
0.229
2674
0.020
53.460
D
662.88
2.01
0.336
3939
0.010
39.380
0
386.04
1.0!
0.390
3939
0.010
39.380
D
478.65
1.01
0.483
3909
0.010
39.080
D
295.69
0.84
0.359
3909
0.010
39.080
D
230.08
0.84
0.279
4000
0.020
79.980
0
412.98
3.20
0.132
4000
0.020
79.980
D
417.49
3.20
0.133
4000
0.020
79.980
0
509.70
2.17
0.240
4000
0.020
79.980
D
353.35
2.17
0.166
2000
2000
3000
3000
2990
2990
0.020
0.020
0.020
0.020
0.005
0.005
39.980
39.980
59.980
59.980
D
D
1.79
1.79
1.03
1.03
14.945
14,945
0
0
0
0
652.49
950.93
664.93
644.49
523.30
568.58
0.79
0.79
0.372
0.542
0.658
0.638
0.675
0.734
7.0
7.0
6.7
6.7
6.7
6.7
12.0
6.7
6.7
7.5
7.5
6.7
6.4
3000
0.020
59.980
D
558.43
0.99
0.575
LAI9
LA2O
,Sylmar
6.7
6.4
3000
0.020
59.980
D
801.44
0.99
0.825
North
Palm
Springs
North
Palm
Springs
6.0
6.7
oblique
3000
0.020
59.980
D
999.43
2.97
0.343
6.0
6.7
oblique
3000
0.020
59.980
0
967.61
2.97
0.332
Moment magnitude
Closest source-to-site distance
Faulting mechanism
Recording time interval
Duration
SF
2674
Table D.2 Set of LA earthquake ground motions with 10% probability
in 50 years (SAC project)
(1)
I
I
,
LAI8
N. Palm
Springs
(1986)
I
6.9
LAI5
LAI6
Northridge
I
El Centro
LAIO
Loma
Prieta
(1989)
I
-
Number
f
I
LAO!
LAO7
Landers
(1992)
MW1
___________ _______
___________ [
Imperial
Valley
(1940)
Station
File
D (2)
of exceedence
242
EQ
Event &
Year
1
Station
File
MW'
I
Morgan
Hill
(1984)
SF02
SE03
SEO4
SEO5
SF06
Olympia
(1949)
SF07
SE08
N. Palm
Springs
(1986)
SEO9
SEIO
SEt I
SF12
SF13
Seattle
(1949)
SF14
SEIS
SEI6
SEI7
SF18
Valparaiso
(1985)
FM
3)
SF19
SF20
of
Points
I
j
Imperial
Valley
(1979)
Number
D12
I
Long
Beach,
Long
Beach,
Morgan
Hill,
Gilroy
Morgan
Hill,
Gilroy
West
WA,
West
WA,
Olympia
West
WA,
Tacoma
County
Tacoma
County
Llolleo,
Chile
Llolleo,
Chile
Vinadel
Mar,
Vinadel
Mar,
Chile
I
I
s_ I
ST
sec
l0%/
I
5oyrs
SF
Strike-slip
3909
0.010
39.080
D
170.55
0.49
0.355
6.5
1.2
strike-slip
3909
0.010
39.080
D
132.70
0.49
0.276
6.2
15.0
strike-slip
3000
0.020
59.980
D
378.82
2.84
0.136
6.2
15.0
strike-slip
3000
0.020
59.980
D
649.80
2.84
0.233
6.5
56.0
subduction
intraplale
4000
0.020
79.980
0
376.18
1.86
0.206
6.5
56.0
subduclion
iniraplate
4000
0.020
79.980
0
345.11
1.86
0.189
6.5
80.0
3335
0.020
66.680
D
289.19
5.34
0.055
6.5
80.0
subduction
intraplale
3335
0.020
66.680
D
381.26
5.34
0.073
6.0
6.7
oblique
3000
0.020
59.980
0
576.45
1.71
0.344
6.0
6.7
oblique
3000
0.020
59.980
D
558.10
1.71
0.333
7.1
80.0
subduction
intraptate
4092
0.020
81.820
0
737.82
4.30
0.175
7.1
80.0
subduction
intraplate
4092
0.020
81.820
D
584.52
4.30
0.139
7.1
61.0
subduction
intraplate
3705
0.020
74.080
0
362.31
5.28
0.070
7.1
61.0
subduction
intraplate
3705
0.020
74.080
D
297.30
5.28
0.057
7.1
60.0
subduction
inlraptate
3000
0.020
59.980
13
284.72
8.68
0.033
7.1
60.0
subduction
intraplale
3000
0.020
59.980
D
563.47
8.68
0.066
8.0
42.0
subduclion
inlerplate
4000
0.025
99.975
0
684.27
1.24
0.563
8.0
42.0
subduction
interplate
4000
0.025
99.975
13
657.89
1.24
0.541
8.0
42.0
subduclion
interplate
4000
0.025
99.975
13
531.05
1.69
0.320
8.0
42.0
subduction
interplate
4000
0.025
99.975
D
376.88
1.69
0.227
Moment magnitude
Closest source-to-site distance
(3)
Faulting mechanism
(4)
Recording time interval
(5)
Duration
(2)
0GM
1.2
subduction
Table D.3 Set of Seattle earthquake ground motions with 10% probability of
exceedence in 50 years (SAC project)
(1)
f
ISC
6.5
intraplate
Seattle___________
West
WA,
Seattle
North
Palm
Springs
North
Palm
Springs
WA,
Olympia,
WA,
Olympia,
WA,
Federal
OFC B
WA,
Federal
PGA
D5
DT14
243
EQ
Event &
Year
File
B002
New
Hampshi
re
(1982)
B003
B004
BOOS
B006
B007
BOO8
Nahanni
(1985)
B009
BOlO
B011
B0l2
BOI3
BOI4
BOI5
Ssguena
y (1988)
I
FM
3)
B0l6
B0l7
BO18
B0l9
B020
Simulation,
Hanging
Wall
Simulation,
Hanging
Wall
Simulation,
Foot Wall
Simulation,
Foot Wall
New
hampshire
New
hampshire
Nahanni
Nahanni
Nahanni
Nahanni
Nahanni
Nahanni
Saguenay
Saguenay
Ssguenay
Saguenay
Ssguenay
Ssguenay
Ssguenay
Saguenay
of
Points
I
Reverse
2
Station
Number
2
km
BOOl
Reverse
D
j
PGA
DT
D3
(4)
[
see
0.39
0.319
D1t61
72.93
0.39
0.191
29.990
D161
141.37
0.54
0.267
29.990
D16t
109.65
0.54
0.207
30.0
reverse
3000
0.010
29.990
6.5
30.0
reverse
3000
0.010
29.990
6.5
30.0
reverse
3000
0.010
6.5
30.0
reverse
3000
0.010
4.3
6.9
6.9
6.9
6.9
6.9
6.9
5.9
5.9
5.9
5.9
5.9
5.9
5.9
5.9
8.4
8.4
reverse
reverse
9.6
9.6
6.1
6.1
18.0
18.0
96.0
96.0
980
98.0
118.0
118.0
132.0
132.0
reverse
reverse
reverse
reverse
reverse
reverse
reverse
reverse
3847
0.005
cn5sc
j
121.97
6.5
4.3
°
ST
I
sec
i:
1
19.230
3847
0.005
19.230
4068
4068
3752
3752
3804
3804
3548
3548
2958
2958
3906
3906
3325
3325
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.010
0.010
0.010
0.010
0.010
0.010
20.335
20.335
18.755
18.755
19.015
19.015
17.735
17.735
29.570
29.570
39.050
39.050
33.240
33.240
B
0
i5
564.78
309.51
i5Y
86.29
81.18
59.48
72.23
130.69
D
133.21
196.50
D
D1
268.44
513.58
243.68
179.47
222.98
172.96
267.23
103
10.7
5
0.09
0.09
0.20
0.20
0.92
0.92
1.57
1.57
3.21
3.21
3.25
3.25
3.34
3.34
Table D.4 Set of Boston earthquake ground motions with 10% probability of
exceedence in 50 years (SAC project)
(I)
Moment magnitude
Closest source-to-site distance
(3)
Faulting mechanism
(4)
Recording time interval
(5)
Duration
(6)
Rock converts to soil
(2)
0.054
0.029
0.978
0.920
0.303
0.368
0.145
0.148
0.128
0.174
0.163
0.077
0.056
0.070
0.053
0.082
244
APPENDIX E: Peak displacement distributions considering different R factors
245
0.9
0.8
/
0.7
/
R2.5, W1940 lbs/ft
/
0.6
R=3.5, W=2720 lbs/ft
/
/
R4.5, W3500 lbs/ft
/
R=5.5 W=4270 lbs/ft
I
0.5
U-
0.4
0.3
8ft.
I//
0.2
8ft.
/
/
0.1
//
/
/
BW (8 x 8), 8d@2"/1 2, OSB (/8)
ED=3/8',G= 185ksi,=2%, 10(50/50)
J I
n
0
0.2
0.4
0.6
0.8
1.4
1.2
1
1.6
1.8
2
6max (in.)
Figure E.1 Peak displacement distributions considering different R factors (2"/12",
JO)
0.9
0.8
0.7
;
/
0.6
0.5
/
/
U-
5 W=3500 lbs/ft
R=5.5, W4270 lbs/ft
0.4
/
I
0.3
II,
//,,
/ ',
I
0.1
__
/
I
0.2
8ft.
0
BW (8' x 8'), 8d@2"/12", 0S (/"),
'i"
ED=3/8",G=185ksi,2°4,LS(10/50)
U
0
0.5
1
1.5
2
2.5
3
max
3.5
4
4.5
5
5.5
6
(in.)
Figure E.2 Peak displacement distributions considering different R factors (2"/12",
LS)
246
0.9
R=2.5, W=1940 lbs/ft
0.8
R3.5, W=2720 lbs/ft
0.7
R=4.5, W=3500 lbs/ft
0.6
R=5.5, W4270 lbs/ft
0.5
0.4
0.3
8ft.
0.2
8ft.
0.1
/
0
BW(8>< 8'), 8d@2/12', OSB (/')
ED=3/8',G= 185ksi,=2%,CP(2/5O)
0
0
0.5
1.5
1
2.5
2
3
max
3.5
4.5
4
5
5.5
6
(in.)
Figure E.3 Peak displacement distributions considering different R factors (2"/12",
CP)
0.9
0.8
R2.5, W1147 lbs/ft
0.7
:=::
0.6
c::::: :
R=5.5, W2521 lbs/ft
0.5
II
0.4
1
0.3
/
0.2
8L
0.1
-
n
0
0.2
0.4
/
x
H
8'), 8d@4"112", OSB
(/8"),
ED=3/6",G=l8Oksi,ç=2%, 10(50/50)
0.6
0.8
1.2
1
max
1.4
1.6
1.8
2
(in.)
Figure E.4 Peak displacement distributions considering different R factors (4"/12",
JO)
247
-
0.9
0.8
----
/
/
0.7
/
0.6
/ //
/
/
0.5
/
0.4
/
0.3
R=4.5, W=2065 lbs/ft
R=5.5, W2521 lbs/ft
LI
8ft.
0.2
/
1/"
0.1
8
BW(8 x8), 8d©4 /12, OSB (/
G = 180 ksi,
= 2%, LS (10/50)
ED =
),
-
n
0
0.5
1
1.5
2.5
2
3
3.5
4
4.5
5
5.5
6
max(fl.)
Figure E.5 Peak displacement distributions considering different R factors (4"/12",
LS)
0.9
R=2.5, W=1 147 lbs/ft
0.8
R=3.5, W=1605 lbs/ft
0.7
R=4.5, W=2065 lbs/ft
0.6
R=5.5, W=2521 lbs/ft
LL
0.4
/ /1
0.3
0.2
HH//
0.1
8ft.
°
BW(8 x 8'), 8d@4"/12", OSB (/"),
ED3/8",G180ksi,2%,CP(2/50)
n
0
0.5
1
1.5
2
2.5
3
6max
3.5
4
4.5
5
5.5
6
(in.)
Figure E.6 Peak displacement distributions considering different R factors (4"/12",
CP)
0.9
R=2.5, W=73OthsIft
0.8
0.7
7 :"L ::::
0.6
:
R=5.5, W1610 lbs/ft
0.5
LL
Il
0.4
0.3
/
8ft.
0.2
8ft.
/
0.1
BW (8 >< 8), 8d@6/12", OSB (/)
/
ED=3/G 185ksi,=2%, 10(50/50)
n
0
0.2
0.4
0.6
0.8
1.4
1.2
1
6max
1.6
1.8
2
(in.)
Figure E.7 Peak displacement distributions considering different R factors (6"/12",
JO)
0.9
0.8
/
0.7
/
0.5
U-
R4.5, W=1321 lbs/ft
/
I
0.4
R5.5
/
'r/
/
/
0.3
R3.5, W=1026 lbs/ft
/
/
0.6
R2.5, W730 lbs/ft
4
/
Bft.
0.2
/ /,'/!
0.1
-
'/
BW (8 x 8), 8d@6"/12, OSB (/8),
ED =/", G= 185 ksi,ç=2%, LS(10/50)
n
0
0.5
1
1.5
2
2.5
3
max
3.5
4
4.5
5
5.5
6
(in.)
Figure E.8 Peak displacement distributions considering different R factors (6"/12",
LS)
249
0.9
R=2.5, W=730 lbs/ft
0.8
R=3.5, W=1026 lbs/ft
0.7
R=4.5, W=1321 lbs/ft
,'
0.6
R=5.5, W=1610 lbs/ft
'1
0.5
LI
0.4
0.3
0.2
8ft.
0.1
v-"
-
n
0
0.5
1
1.5
2
/
°
BW(8 x 8), 8d©6/12, OSB (/'),
ED =I', G = 185 ksi,
2.5
3
max
3.5
4
4.5
= 2%, CP(2150)
5
5.5
6
(iii.)
Figure E.9 Peak displacement distributions considering different R factors (6"/12",
CP)
250
APPENDIX F: Fragility curves for baseline wall (BW1) considering different hazard
levels
251
0.9
0.8
0.7
0.6
o
0.5
0.4
0.3
0.2
0.1
(1
0
0.2
0.4
0.6
0.8
1.2
1
1.4
1.6
1.8
2
Sa(g)
Figure F.l Fragility curves (R = 2.5, 2"/12")
0.9
0.8
/
8ft.
BW (8 < 8'), 8d@3"/12", OSB (/8"),
0.7
/
/
ED=3/8",G=200ksi,/=2%, R=2.5/
W = 1400 lbs/ft (52.1 kN total)
/
0.6
o
/
/
0.5
/
0.4
0 (50/50)
0.3
0.2
/
LS(10/50)
0.1
n
0
0.5
1.5
1
Sa(g)
Figure F.2 Fragility curves (R = 2.5, 3"/12")
2
2.5
252
//7
0.9
0.8
0 (50/50)
0.7
LS
/
/
0.6
o
//
0.5
0.4
/
/
0.3
0.2
/
/
//
/
/
/
0.1
BW(8
x
8'), 8d@4'/12", OSB
(/8"),
ED=3/5",G=180ksi,=2%,R=2.5
W = 1147 lbs/ft (40.8 kN total)
0
0
0.5
2
1.5
1
2.5
Sa(g)
Figure F.3 Fragility curves (R = 2.5, 4"/12")
1
0.9
0.8
8W (8'
0.7
x
/
8), 8d@6"/12", OSB (/'),
3/, G
185 ksi, = 2%, R = 2.5
W = 731 lbs/ft (26.0 kN total)
ED
0.6
0.5
/
/
8ft.
/
/
//
0.4
/
0.3
IO (50/50)
/
0.2
/LS1O/5O
/
0.1
0
0
0.5
1.5
1
Sa(g)
Figure F.4 Fragility curves (R = 2.5, 6"/12")
2
2.5
253
1
0.9
0.8
88.
SW (8' x 8'), 8d@2"/12", OSB
0.7
ED
3/, G = 185 ksi, ç = 2%, R -3.5
W = 2720 lbs/ft (96.8 kN total)
0.6
/
0.5
10 (50/50)
/
//
0.4
/
0.3
0.2
/,,,'
/
0.1
It,,,
n
0
0.5
1.5
1
2
2.5
Sa(g)
Figure F.5 Fragility curves (R
3.5, 2"/12")
1
0.9
0.8
88.
BW (8' x 8'), 8d@3"/12", OSB (3/../
0.7
ED'3/g",G'200ksi,/'2%, Rfr3.5
W = 2051 lbs/ft (73.0 kN total)
/
0.6
0
'
/
/
o.s
'
CP (2/50)
'
/
0.4
0 (50/50)
/
//,,,,
0.3
//,"
0.2
0.1
n
0
0.5
1.5
1
Sa(g)
Figure F.6 Fragility curves (R
3.5, 3"/12")
2
2.5
254
0.9
0 (50/50)
/
0.8
LS (10/50)
0.7
CP (2/50)
0.6
0.4
0.3
86.
/
0.2
/
/
0.1
/,,
/
J6
BW (8' x 8'), Sd©4'112", OSB (I"),
/
ED = J8", G = 180 ksi, ç = 2%, R = 3.5
,/
W = 1605 lbs/ft (57.1 kN total)
-
0
0
0.5
1.5
1
2
2.5
2
2.5
Sa(g)
Figure F.7 Fragility curves (R = 3.5, 4"/12")
I
0.9
86.
0.8
//
8ft.
BW (8' x 8'), 8d©6"/12", OSB (/"),
/
ED=3/8',G= 185ksi,=2%, R=3.5/
0.7
W = 1026 lbs/ft (36.5 kN total)
0.6
o
0.5
0.4
0.3
CF (2/50)
/
0.2
/
0.1
(1
0
0.5
1.5
1
Sa(g)
Figure F.8 Fragility curves (R = 3.5, 6"/12")
255
0.9
0.8
/lO (50/50)
/
0.7
0.6
,.LS(10/50)
/
/
CP (2/50)
0.5
/
0.4
/
0.3
/,,,
/
0.2
88.
8ft.
/
0.1
BW (8
/
0
0.5
8), 8d@2"/12", OSB (/8"),
ED=3/8",G=l85ksi,ç=2%,R=4.5
W = 3501 lbs/fl (124.6 kN total)
-
C)
x
2
1.5
1
2.5
Sa(g)
Figure F.9 Fragility curves (R = 4.5, 2"/12")
I
0.9
0.8
/
0.7
0.6
o
0.5
::
/
0.4
0 (50/50)
/
/,,"
/ ///,,,'
/
0.3
0.2
88.
/
/
/
0.1
88.
BW (8
/,
x
8'), 8d@3"112", OSB
(I8"),
ED=3/8",G200ksi,l2%, R=4.5
W = 2637 lbs/ft (93.9 kN total)
n
0
0.5
1.5
1
Sa(g)
Figure F.1O Fragility curves (R = 4.5, 3"/12")
2
2.5
256
0.9
0.8
/
0.7
10 (50/50)
/
/
/
0.6
CP (2/50)
I
/
o
LS(10/50)
0.5
/
0.4
/,,,,
/
0.3
/,,,'
8ff.
/
0.2
0.1
88.
IBW (8
x
8), 8d@4"112", OSB (/8"),
ED=3f8G- 180ksi,=2%, R=4.5
W = 2065 lbsfft (73.5 kN total)
11
0
0.5
2
1.5
1
2.5
Sa(g)
Figure F. 11 Fragility curves (R = 4.5, 4"/12")
0.9
0.8
/
0.7
0.6
a
10 (50/50)
/
/
0.5
/
0.4
/
0.3
/,,,
/
0.2
/:'
/
/
/
,/
0.1
0
0
0.5
88.
/
8ft.
/'
BW (8'
x
8), 8d©6112", OSB (I8'),
ED=3/8",G=185ks1,ç=2%,R=4.5
= 1321 lbs/ft (47.0 kN total)
1.5
1
Sa(g)
Figure F. 12 Fragility curves (R = 4.5, 6"/12")
2
2.5
257
APPENDIX G: Fragility curves for baseline wall (BW1) considering different R
factors and nailing schedules
258
1
0.9
8d©3"/12", W1464 lbs/ft
0.8
8d@4"/12", W=1147 lbsIft/
0.7
0.6
ci:-
/
8d©2"/12", W=1940 lbs/ft
8d©6"/12", W730 lbs/ft
/
0.5
0.4
0.3
7',,"
8ff.
0.2
/,
0.1
/,
-
SW (8 x 8'), OSB(31,"), ED =
?=2%, R=2.5, 10 (50/50)
-
('I
0
0.2
0.4
0.6
0.8
1.2
1
1.4
1.6
1.8
2
Sa(g)
Figure G. 1 Fragility curves considering R = 2.5 (JO, 50/50 hazard level)
1
0.9
o
0.8
8d@3"/12", W2051 lbs/ft
8d@4"/12", W1605 lbs/ft
0.7
8d@2"/12", W2720 lbs/ft
0.6
8d@6"/12", W=1026
7/ ,'
/ I
//
Ibs/ft77'/
0.5
0.4
/,
0.3
/'//'
0.2
/
/
0.1
n
0.2
0.4
__8ff.
///
//
BW (8'
0.6
0.8
8'),OSB (3/,), ED =
=2%, R=3.5, 10(50/50)
/'
-'
0
/
1
1.2
1.4
1.6
1.8
Sa(g)
Figure G.2 Fragility curves considering R = 3.5 (JO, 50/50 hazard level)
2
I
259
0.9
/
0.8
/
0.7
8d3"/12", W2639 lbs/ft
8d(4"/12", W2065 lbs/ft
,/ /
/ //
0.6
/
///
0.5
,,'
0.4
8d@2"/12", W3500 lbs/ft
8d@6"/12", W1321 lbs/ft
/
/ ///
0.3
__8ft.
/ ///
0.2
/ //'
/
/
0.1
n
0
0.2
0.4
BW (8' x 8'), OSB (/8"), ED = /8,
ç
0.6
0.8
1
1.2
= 2%, R = 4.5, 10 (50/50)
1.4
1.6
1.8
2
Sa(g)
Figure G.3 Fragility curves considering R = 4.5 (10, 50/50 hazard level)
1
0.9
/
8d3"/12", W3220 lbs/ft
///
8d2"/12", W4270 lbs/ft
0.8
8d@4"/12", W2521 lbs/ft
//I
0.7
0.6
///
8d@6"/12", W1610 lbs/ft
0.5
////
0.4
1/
0.3
8 ft.
0.2
/i'
0.1
/
BW (8' x 8'), OSB (/8"), ED =
2%, R = 5.5, 10 (50/50)
n
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Sa(g)
Figure G.4 Fragility curves considering R = 5.5
(10, 50/50
hazard level)
2
260
1
0.9
0.8
;
0.7
8d©4"/12", W=1605 lbs/ft
0.6
8d@3"/12", W=2051 Ibs/ft
Q0.5
0.4
0.3
/
/
0.2
0.1
H
BW (8
0
0.5
8'), OSB e/8"), ED =,
ç = 2%, R = 3.5, CP (2/50)
n
2
1.5
1
2.5
Sa(g)
Figure G.5 Fragility curves considering R = 3.5 (CP, 2/50 hazard level)
1
0.9
1
88.
0.8
///
88.
BW (8' x 8'), OSB (3/e") ED = /8",
0.7
/
ç=2%, R=4.5,CP(2/50)
0.6
d
/
0.5
8d©3"Il 2", W=2639 lbs/ft
0.4
0.3
0.2
0.1
n
0
0.5
1.5
1
2
Sa(g)
Figure G.6 Fragility curves considering R = 4.5 (CP, 2/50 hazard level)
2.5
261
1
0.9
_8ff.
0.8
BW (8' x 8), OSB (/'), ED =
0.7
= 2%, R = 5.5, OP (2/50)
0.6
0.5
8d@6"/12", W=1610 lbs/ft
0.4
8d@3"/12", W=3220 lbs/ft
8d@4"/12", W=2521 lbs/ft
0.3
8d©2"/12", W=4270 lbs/ft
0.2
0.1
0
0
0.5
1.5
1
2
Sa(g)
Figure G.7 Fragility curves considering R = 5.5 (CP, 2/50 hazard level)
2.5
262
APPENDIX H: CDF for baseline wall (BW1) considering ultimate force with various
R factors
263
0.9
0.8
R=2.5
0.7
0.6
'1
/
I
0.5
I
U-
/
0.4
0.3
/
I
/
n
i,
/
/
/
/
2000
/
/
/
0.2
0.1
H
/
/
I/j
j,
4000
aft.
2
6000
BW (8' x 8'), 8d@2"/12", OSB (/8").
ED
I8", G = 185 ksi,
10000
8000
Fmax
12000
= 2%, 0 (50/50)
14000
16000
(lbs.)
Figure H.1 CDF for ultimate force with various R factors (2"/12", JO)
0.9
0.8
H
H
0.7
H
0.6
H
/
/
/
,''
/
0.5
/
/
0.4
,,/
/
/
0.2
/
/
0.1
6000
/
/
0.3
/
8000
/
_--2'
10000
8ft.
'1
88.
,'/
"
12000
Fmax
BW (8' >< 8'), 8d@2"/12", OSB (/8"),
ED=3/8",G
14000
l85ksi,ç=2%, LS(10/50)
16000
18000
(lbs.)
Figure H.2 CDF for ultimate force with various R factors (2"/12", LS)
20000
264
0.9
/1
0.8
/ /
R=2.5
0.7
R=3.5
/
i/hV/
0.6
R=4.5
II
0.5
R5.5
0.4
0.3
88.
'I
0.2
/'/
7,,
88.
0.1
BW (8 x 8'), 8d@2"112", OSB (/8"),
/ :'
G = 185 ksi,
ED =
= 2%, CP(2/50)
C)
10000
12000
16000
14000
Fmax
20000
18000
(lbs.)
Figure H.3 CDF for ultimate force with various R factors (2"/12", CP)
0.9
88.
0.8
:2.5
8L.
0.7
BW (8x8'), 8dq4"/12"
/
/
OSB(/8),ED= /8,
I
/
G
180 ksi,
= 2%,
I
10(50/50)
0.6
/
,'
R3.5
'W.J
/- R=4.5
,'
1
I
R=5.5
0.5
U-
0.4
/
0.3
I
0.2
I
'/
I
I/
,'
II
/
"
0.1
//
___/
n
0
2000
/,,'/
(1)1::
1
__/_____
-J
4000
Fmax
6000
8000
(lbs.)
Figure H.4 CDF for ultimate force with various R factors (4"/12", JO)
10000
265
.1
0.9
0.8
0.7
0.6
0.5
U-
0.4
0.3
0.2
0.1
n
4000
5000
6000
7000
8000
Fmax
9000
10000
11000
12000
(lbS.)
Figure H.5 CDF for ultimate force with various R factors (4"/12", LS)
0.9
0.8
0.7
0.6
0.5
U-
0.4
0.3
0.2
0.1
n
4000
5000
6000
7000
8000
Fmax
9000
10000
11000
(lbs.)
Figure H.6 CDF for ultimate force with various R factors (4"/12", CP)
12000
266
0.9
88.
0.8
0.7
/
8ft.
BW (8 x 8'), 8dc6'I12",
OSB (I8"), ED =
a"
G=l85ksi,ç=2%,
0.6
/
/
/
/
/
/
40.5
"
/
0(50/50)
/
R=2.5
R=3.5
/
I
/
R=4.5
R=5.5
,'
0.4
0.3
0.2
0.1
n
1000
2000
4000
3000
6000
5000
Fmax (lbs.)
Figure H.7 CDF for ultimate force with various R factors (6"/12", JO)
0.9
0.8
/
0.7
0.6
IT"
,;,
/
40.5
/
0.4
0.3
R=5.5
,,/
,,,/I
88.
/ "7
0.2
/ ," /
/ __/' /
0.1
/
88.
BW (8' x 8'), 8d6"/12",
m
OSB(3/8"),ED
/8",
G=185ksi,=2%,
LS(10150)
n
2000
3000
4000
5000
6000
7000
Fmax (lbs.)
Figure H.8 CDF for ultimate force with various R factors (6"/12", LS)
8000
267
1
0.9
0.8
0.7
O.5
R=4.5
/
0.4
R=5.5
0.3
8ft.
/
(0
(0
0.2
8ft.
I
ii
8W (8' x 8'), 8d©6"/12", OSB (/8"),
/ /
0.1
ED
/ /
/
-J
G = 185 ksi,
= 2%,
CF (2/50)
0
3000
4000
5000
Fmax
6000
7000
(lbs.)
Figure H.9 CDF for ultimate force with various R factors (6"/12", CP)
8000