Appendix G
Preliminary Multiple-Degree-of-
Freedom System Studies
In focused analytical studies on single-degree-of-freedom (SDOF) systems, it
was observed that nonlinear response of a system depends on the
characteristics of the force-displacement capacity boundary. It was
demonstrated that lateral dynamic instability of SDOF systems could be
evaluated through the use of approximate equations or simplified nonlinear
dynamic analyses based on the characteristics of the system forcedisplacement
capacity boundary.
Multiple-degree-of-freedom (MDOF) systems are more complex, and their
dynamic response is more difficult to estimate than that of SDOF systems.
Recent studies have suggested that it may be possible to estimate the collapse
capacity of MDOF systems by using static pushover analyses and performing
dynamic analysis on equivalent SDOF systems (Bernal, 1998; Vamvatsikos,
2002; Vamvatsikos and Cornell, 2005a, 2005b). In particular, Vamvatsikos
and Cornell (2005b) suggested that the seismic response of MDOF systems
could be estimated through the use of incremental dynamic analyses on a
reference SDOF system whose properties are determined through a nonlinear
static (pushover) analysis.
This appendix presents the results of preliminary studies of multiple-degreeof-
freedom (MDOF) systems. It explores the application of nonlinear static
analyses combined with dynamic analyses of SDOF systems to evaluate the
lateral dynamic instability of MDOF systems. On a preliminary basis, it tests
how approximate measures of lateral dynamic instability developed for
SDOF systems might work on more complex MDOF systems. These
approximate measures include the proposed equation for Rdi (Equation 5-8)
and the open source software tool Static Pushover 2 Incremental Dynamic
Analysis, SPO2IDA (Vamvatsikos and Cornell, 2006).
A total of six buildings ranging in height from 4 to 20 stories are used in this
investigation. This set includes two steel moment-resisting frame structures
and four reinforced concrete moment-resisting frame structures. Four were
previously studied by Haselton (2006), and two were previously studied by
G-2 G: Preliminary Multiple-Degree-of-Freedom System Studies FEMA P440A
Vamvatsikos and Cornell (2005b). Results are described in the sections that
follow.
G.1 Four-Story Code-Compliant Reinforced Concrete
Building
The subject building is a four-story reinforced concrete special perimeter
moment frame designed in accordance with modern building code provisions
(ICC 2003, ASCE 2002, ACI 2002). The building has a story height of 15 ft
in the first story, and 13 ft in the remaining stories. The design base shear
coefficient was 0.092. The building was modeled in OpenSEES and analyzed
using incremental dynamic analysis using 80 recorded time histories which
were scaled at twenty-two different ground motion intensities. The pushover
analysis was conducted using a lateral force distribution in accordance with
ASCE/SEI 7-05 Minimum Design Loads for Buildings and Other Structures
(ASCE, 2006). Ground motions were scaled to increasing values of the
pseudo-acceleration spectral ordinate at the fundamental period of vibration
of the building (T1=1.12s). For a more detailed description of the building
and its modeling, the reader is referred to Haselton (2006).
Figure G-1 shows the results from the nonlinear static (pushover) analysis.
The figure on the left shows the force-deformation curve while the figure on
the right shows the distribution of story drift ratios at a roof drift ratio of 6%.
It can be seen that story drifts primarily concentrate in the lower two stories.
The force-deformation pushover curve is characterized by a gradual loss in
lateral strength for roof drift ratios between 1% and 3.5%, followed by a
more pronounced loss in lateral strength for roof drift ratios greater than
3.5%.
Figure G-1 (a) Monotonic pushover force-deformation curve and (b) story drifts at a roof drift
ratio of the 0.06 in a four-story concrete frame building (Haselton 2006).
FEMA P440A G: Preliminary Multiple-Degree-of-Freedom System Studies G-3
Figure G-2 shows one of three simplified tri-linear force-displacement
capacity boundaries selected to estimate the seismic response of the structure.
Alternates are shown in Figure G-4 and Figure G-5. Although a sloping
intermediate segment might have been somewhat more appropriate for this
structure, a horizontal intermediate segment was selected in order to evaluate
the proposed equation for Rdi and results using SPO2IDA.
Figure G-2 Tri-linear capacity boundary selected for approximate analysis.
Figure G-3 shows the median seismic behavior computed from incremental
dynamic analyses conducted by Haselton (2006). These results are indicated
as MDOF IDA in the figure. Also shown are results computed using the
proposed equation for Rdi and approximate results from SPO2IDA. In the
figure, Rdi and SPO2IDA both provide a good approximation of the collapse
capacity of the building.
Figure G-3 Comparison of median collapse capacity for a four-story codecompliant
concrete frame building computed using incremental
dynamic analysis and approximate procedures.
0.0
0.5
1.0
1.5
2.0
2.5
0.00 0.02 0.04 0.06 0.08 0.10 0.12
Maximum Story Drift Ratio
Sa (T=1.12)/g
MDOF IDA
SPO2IDA
Rdi
G-4 G: Preliminary Multiple-Degree-of-Freedom System Studies FEMA P440A
To explore sensitivity to the idealization of the force-displacement capacity
boundary, two alternate idealizations, along with corresponding results, are
shown in Figure G-4 and Figure G-5. Although median collapse capacities
change with the selection of the force-displacement capacity boundary, the
observed changes are relatively small.
Figure G-4 Effect of selecting an alternate force-displacement capacity boundary on
estimates of median collapse capacity for a four-story code-compliant concrete
frame building.
Figure G-5 Effect of selecting an alternate force-displacement capacity boundary on
estimates of median collapse capacity for a four-story code-compliant concrete
frame building.
The median results shown above represent a measure of the central tendency
of the response of the system; however, considerable dispersion exists around
the median. To illustrate record-to-record variability, Figure G-6 shows
0.0
0.5
1.0
1.5
2.0
2.5
0 0.02 0.04 0.06 0.08 0.1 0.12
Maximum Story Drift Ratio
Sa (T=1.12)/g
MDOF IDA
SPO2IDA
Rdi
0.0
0.5
1.0
1.5
2.0
2.5
0 0.02 0.04 0.06 0.08 0.1 0.12
Maximum Story Drift Ratio
Sa (T=1.12)/g
MDOF IDA
SPO2IDA
Rdi
FEMA P440A G: Preliminary Multiple-Degree-of-Freedom System Studies G-5
incremental dynamic analysis results for all 80 ground motions. It can be
seen that there are ground motions that produce the collapse of the structure
at intensities equal to one third of the median intensity. Similarly, there are
ground motions that require an intensity that is twice as large as the median
intensity in order to produce the collapse of the structure.
Also shown in Figure G-6 are the 16th and 84th percentiles of the results.
Approximately 70% of the ground motions fall between these two dashed
lines. When estimating the collapse probability of a structure, it is important
to consider this variability. For more information, the reader is referred to
Haselton (2006).
0.0
0.5
1.0
1.5
2.0
2.5
0.00 0.02 0.04 0.06 0.08 0.10 0.12
Max IDR
Sa (T=1.12s) / g
84%
16%
50%
Figure G-6 Incremental dynamic analysis results for a four-story code-compliant
concrete frame building subjected to 80 ground motions (adapted from
Haselton, 2006).
G.2 Eight-Story Code-Compliant Reinforced Concrete
Building
The subject building is an eight-story reinforced concrete special perimeter
moment frame designed in accordance with modern building code provisions
(ICC 2003, ASCE 2002, ACI 2002). The building has a story height of 15 ft
in the first story, and 13 ft in the remaining stories. The design base shear
coefficient was 0.05. The building was modeled in OpenSEES and analyzed
using incremental dynamic analysis with the same 80 recorded ground
motions that were used to analyze the four-story building. The pushover
analysis was performed using a lateral force distribution in accordance with
Maximum Story Drift Ratio
G-6 G: Preliminary Multiple-Degree-of-Freedom System Studies FEMA P440A
ASCE/SEI 7-05. The fundamental period of vibration of the building is
T1=1.71s. For a more detailed description of the building and its modeling,
the reader is referred to Haselton (2006).
Figure G-7 shows the results from the nonlinear static (pushover) analysis of
the building. The figure on the left shows the force-deformation curve while
the figure on the right shows the distribution of story drift ratios at a roof
drift ratio of 2.6%. It can be seen that story drifts primarily concentrate in the
lower four stories. The force-deformation pushover curve is characterized by
a hardening segment for roof drift ratios between 0.3% and 0.8%, followed
by softening segment for roof drift ratios greater than 0.8%.
Figure G-7 (a) Monotonic pushover force-deformation curve and (b) distribution of story drift
demands at a roof drift ratio of 2.6% in an eight-story concrete frame building
(Haselton 2006).
Figure G-8 shows the simplified tri-linear force-displacement capacity
boundary selected to evaluate the proposed equation for Rdi and results using
SPO2IDA.
Figure G-8 Tri-linear capacity boundary selected for approximate analyses using SPO2IDA.
FEMA P440A G: Preliminary Multiple-Degree-of-Freedom System Studies G-7
Figure G-9 shows the median seismic behavior computed from incremental
dynamic analyses conducted by Haselton (2006). These results are indicated
as MDOF IDA in the figure. Also shown are results computed using the
proposed equation for Rdi and approximate results from SPO2IDA. In the
figure, Rdi provides a good estimate of the median collapse capacity, while
SPO2IDA overestimates the collapse capacity somewhat. Figure G-10
shows incremental dynamic analysis results for all ground motion records.
Figure G-9 Comparison of median collapse capacity for an eight-story
code-compliant concrete frame building computed using
incremental dynamic analysis and approximate procedures.
0.0
0.5
1.0
1.5
2.0
0.00 0.02 0.04 0.06 0.08 0.10 0.12
Max IDR
Sa (T=1.71s) / g
84%
16%
50%
Figure G-10 Incremental dynamic analysis results for an eight-story code-compliant
concrete frame building subjected to 80 ground motions (adapted from
Haselton, 2006).
0.0
0.4
0.8
1.2
1.6
0.00 0.02 0.04 0.06 0.08 0.10 0.12
Maximum Story Drift Ratio
Sa(T=1.71)/g
MDOF IDA
SPO2IDA
Rdi
Maximum Story Drift Ratio
G-8 G: Preliminary Multiple-Degree-of-Freedom System Studies FEMA P440A
G.3 Twelve-Story Code-Compliant Reinforced
Concrete Building
The subject building is a twelve-story reinforced concrete special perimeter
moment frame designed in accordance with modern building code provisions
(ICC 2003, ASCE 2002, ACI 2002). Similarly to the two previous buildings,
the story height is 15 ft in the first story and 13 ft in the remaining stories.
The design base shear coefficient was 0.044. The building was modeled in
OpenSEES and analyzed using an incremental dynamic analysis using the
same 80 recorded ground motions that were used to analyze the four-story
building. The pushover analysis was again done using a lateral force
distribution in accordance with ASCE/SEI 7-05. The fundamental period of
vibration of the building is T1=2.01s. For a more detailed description of the
building and its modeling, the reader is referred to Haselton (2006).
Figure G-11 shows the results from the nonlinear static (pushover) analysis
of the building. The figure on the left shows the force-deformation curve
while the figure on the right shows the distribution of story drift ratios at a
roof drift ratio of 2.7%. It can be seen that story drifts decrease
approximately linearly with increasing height with the largest story drifts
occurring in the two lower stories. The force-deformation pushover curve is
characterized by a hardening segment for roof drift ratios between 0.3% and
0.8%, followed by softening segment for roof drift ratios greater than 0.8%.
Figure G-11 (a) Monotonic pushover force-deformation curve and (b) distribution of story drift
demands at a roof drift ratio of 2.7% in a twelve-story concrete frame building
(Haselton 2006).
Figure G-12 shows the simplified tri-linear force-displacement capacity
boundary selected to evaluate the proposed equation for Rdi and results using
SPO2IDA. It is assumed that at a roof drift ratio of 2.6% the structure
reaches its maximum deformation capacity and a total loss in strength occurs.
FEMA P440A G: Preliminary Multiple-Degree-of-Freedom System Studies G-9
Figure G-13 compares the median seismic behavior computed from
incremental dynamic analyses conducted by Haselton (2006), indicated in the
figure as MDOF IDA, with results computed using the proposed equation for
Rdi and approximate results from SPO2IDA. In the figure, both approximate
methods somewhat overestimate the collapse capacity of the structure.
Figure G-14 shows incremental dynamic analysis results for all ground
motion records.
Figure G-12 Tri-linear capacity boundary selected for approximate analyses
using SPO2IDA.
Figure G-13 Comparison of median collapse capacity for a twelve-story
code-compliant concrete frame building computed using
incremental dynamic analysis and approximate procedures.
0.0
0.4
0.8
1.2
1.6
0.00 0.02 0.04 0.06 0.08 0.10 0.12
Maximum Story Drift Ratio
Sa(T=2.01)/g
MDOF IDA
SPO2IDA
Rdi
G-10 G: Preliminary Multiple-Degree-of-Freedom System Studies FEMA P440A
0.0
0.5
1.0
1.5
2.0
0.00 0.02 0.04 0.06 0.08 0.10 0.12
Max IDR
Sa (T=2.01s) / g
84%
16%
50%
Figure G-14 Incremental dynamic analysis results for a twelve-story codecompliant
concrete frame building subjected to 80 ground
motions (adapted from Haselton, 2006).
G.4 Twenty-Story Code-Compliant Reinforced
Concrete Building
The subject building is a twenty-story reinforced concrete special perimeter
moment frame designed in accordance with modern building code provisions
(ICC 2003, ASCE 2002, ACI 2002). The story height is 15 ft in the first story
and 13 ft in the remaining stories. The design base shear coefficient was
0.044. The building was modeled in OpenSEES and analyzed using an
incremental dynamic analysis using the same 80 recorded ground motions
that were used to analyze the four-story building. The pushover analysis was
again done using a lateral force distribution in accordance with ASCE/SEI 7-
05. The fundamental period of vibration of the building is T1=2.63s. For a
more detailed description of the building and its modeling, the reader is
referred to Haselton (2006).
Figure G-15 shows the results from the nonlinear static (pushover) analysis
of the building. The figure on the left shows the force-deformation curve
while the figure on the right shows the distribution of story drift ratios at a
roof drift ratio of 1.8%. It can be seen that story drifts decrease
approximately linearly with increasing height, with the largest story drifts
occurring in the lower two stories. The force-deformation pushover curve is
characterized by a slight softening segment for roof drift ratios between 0.3%
Maximum Story Drift Ratio
FEMA P440A G: Preliminary Multiple-Degree-of-Freedom System Studies G-11
and 0.9%, followed by steeper softening segment for roof drift ratios greater
than 0.9%.
Figure G-15 (a) Monotonic pushover force-deformation curve and (b) distribution of story drift
demands at a roof drift ratio of 1.8% in a twenty-story concrete frame building
(Haselton 2006).
Figure G-16 shows the simplified tri-linear force-displacement capacity
boundary selected to evaluate the proposed equation for Rdi and results using
SPO2IDA. It is assumed that at a roof drift ratio of 1.85% the structure
reaches its maximum deformation capacity and a total loss in strength occurs.
Figure G-16 Tri-linear capacity boundary selected for approximate analyses
using SPO2IDA.
Figure G-17 compares the median seismic behavior computed from
incremental dynamic analyses conducted by Haselton (2006), indicated in the
figure as MDOF IDA, with results computed using the proposed equation for
Rdi and approximate results from SPO2IDA. In the figure, proposed equation
for Rdi provides a good estimate of the median collapse capacity, while
SPO2IDA somewhat overestimates the collapse capacity. Figure G-18
shows incremental dynamic analysis results for all ground motion records.
G-12 G: Preliminary Multiple-Degree-of-Freedom System Studies FEMA P440A
Figure G-17 Comparison of median collapse capacity for a twenty-story
code-compliant concrete frame building computed using
incremental dynamic analysis and approximate procedures.
0.0
0.5
1.0
1.5
0.00 0.02 0.04 0.06 0.08 0.10 0.12
Max IDR
Sa (T=2.63s) / g
84%
16%
50%
Figure G-18 Incremental dynamic analysis results for a twenty-story codecompliant
concrete frame building subjected to 80 ground
motions (adapted from Haselton, 2006).
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.02 0.04 0.06 0.08 0.10 0.12
Maximum Story Drift Ratio
Sa(T=2.63)/g
MDOF IDA
SPO2IDA
Rdi
Maximum Story Drift Ratio
FEMA P440A G: Preliminary Multiple-Degree-of-Freedom System Studies G-13
G.5 Nine-Story Pre-Northridge Steel Moment-Resisting
Frame Building
The subject building is a nine-story steel moment-resisting frame designed
for the FEMA-funded SAC project in accordance with pre-Northridge code
requirements for Los Angeles (ICBO, 1994). The building has a single-story
basement that is 12 ft in height. The first story height is 18 ft and the
remaining stories are 13 ft uniformly. The building is symmetric in plan with
six bays of 30 ft in each direction. There is a perimeter moment-resisting
frame designed for lateral-force-resistance, while internal gravity columns
carry most of the vertical load. The building was modeled in OpenSEES and
analyzed using incremental dynamic analysis with 30 “ordinary” ground
motions. The pushover analysis was done using a triangular lateral force
distribution. The fundamental period of vibration of the building is T1=2.3s.
For a more detailed description of the building and its modeling, the reader is
referred to Gupta and Krawinkler (1999).
The results from a nonlinear static (pushover) analysis of the building are
shown in Figure G-19. The force-deformation pushover curve is
characterized by a hardening segment for roof drift ratios between 1% and
2.5%, followed by a softening segment that terminates when the building
reaches zero strength at 5% roof drift. The simplified tri-linear forcedisplacement
capacity boundary, also shown in Figure G-19, was selected to
evaluate the proposed equation for Rdi and results using SPO2IDA. In both
cases the hardening segment has 13% of the elastic stiffness while the
negative stiffness is -74% of elastic.
Figure G-20 shows the median seismic behavior computed from incremental
dynamic analyses conducted by Vamvatsikos and Fragiadakis (2006). These
results are indicated as MDOF IDA in the figure. Also shown are results
computed using the proposed equation for Rdi and approximate results from
SPO2IDA. In the figure, both Rdi and SPO2IDA provide a good
approximation of the collapse capacity of the building.
G-14 G: Preliminary Multiple-Degree-of-Freedom System Studies FEMA P440A
0
2000
4000
6000
8000
10000
12000
0.00 0.01 0.02 0.03 0.04 0.05 0.06
Roof Drift Ratio
Base Shear (kN)
pushover
approx
Figure G-19 Monotonic pushover force-deformation curve, and tri-linear
approximation, for a nine-story pre-Northridge steel moment
frame building (adapted from Gupta and Krawinkler, 1999).
Figure G-20 Comparison of median collapse capacity for a nine-story pre-
Northridge steel moment frame building computed using
incremental dynamic analysis and approximate procedures.
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.02 0.04 0.06 0.08 0.10 0.12
Maximum Story Drift Ratio
Sa(T=2.28s)/g
MDOF IDA
SDO2IDA
Rdi
FEMA P440A G: Preliminary Multiple-Degree-of-Freedom System Studies G-15
G.6 Twenty-Story Pre-Northridge Steel Moment-
Resisting Frame Building
The subject building is a twenty-story steel moment resisting frame designed
for the FEMA-funded SAC project in accordance with pre-Northridge code
requirements for Los Angeles (ICBO, 1994). The building has a basement
consisting of two stories that are 12 ft in height. The first story height is 18 ft
and the remaining stories are 13 ft uniformly. The building is slightly
asymmetric in plan, with five bays of 20 ft in one direction and six bays of 20
ft in the other direction. There is a perimeter moment-resisting frame
designed for lateral-force-resistance. Four internal gravity columns carry the
vertical loads. The building was modeled in Drain-2DX and analyzed using
incremental dynamic analysis with 30 “ordinary” ground motions. The
pushover analysis was done using a parabolic (k = 2) lateral force
distribution. The fundamental period of vibration of the building is T1=4.0s.
For a more detailed description of the building and its modeling, the reader is
referred to Gupta and Krawinkler (1999).
The results from the nonlinear static (pushover) analysis of the building are
shown in Figure G-21. The force-deformation pushover curve is
characterized by a short hardening segment (5% stiffness ratio) from 0.7% to
1.2% roof drift ratio that then turns negative (-24% stiffness ratio) and
terminates when the building reaches zero strength at 4% roof drift. The
simplified tri-linear force-displacement capacity boundary, also shown in
Figure G-21, was selected to evaluate the proposed equation for Rdi and
results using SPO2IDA.
Figure G-22 shows the median seismic behavior computed from incremental
dynamic analyses conducted by Vamvatsikos and Cornell (2006). These
results are indicated as MDOF IDA in the figure. Also shown are results
computed using the proposed equation for Rdi and approximate results from
SPO2IDA. In the figure, Rdi overestimates the collapse capacity of the
building by about 25%, while SPO2IDA provides a good approximation.
G-16 G: Preliminary Multiple-Degree-of-Freedom System Studies FEMA P440A
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0.00 0.01 0.02 0.03 0.04 0.05
Roof Drift Ratio
Base Shear (kN)
pushover
approx
Figure G-21 Monotonic pushover force-deformation curve, and tri-linear
approximation, for a twenty-story pre-Northridge steel moment
frame building (adapted from Gupta and Krawinkler, 1999).
Figure G-22 Comparison of median collapse capacity for a twenty-story pre-
Northridge steel moment frame building computed using
incremental dynamic analysis and approximate procedures.
0.0
0.2
0.4
0.6
0.8
1.0
0.00 0.05 0.10 0.15 0.20
Maximum Story Drift Ratio
Sa(T=4.0s)/g
MDOF IDA
SDO2IDA
Rdi
FEMA P440A G: Preliminary Multiple-Degree-of-Freedom System Studies G-17
G.7 Summary and Recommendations
The studies documented above indicate that the application of procedures
developed for SDOF systems to several representative MDOF moment frame
systems produces reasonable approximations of the median intensity causing
lateral dynamic instability. This was true in the case of both the proposed
equation for Rdi and simplified nonlinear dynamic analysis using SPO2IDA.
These results lead to a recommendation for more thorough investigation of
MDOF systems to modify, or further refine, the procedures presented here.
FEMA P440A H: References and Bibliography H-1
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FEMA P440A I: Project Participants I-1
Project Participants
ATC Management and Oversight
Christopher Rojahn
Project Executive Director
Applied Technology Council
201 Redwood Shores Parkway, Suite 240
Redwood City, California 94065
Jon A. Heintz
Project Quality Control Monitor
Applied Technology Council
201 Redwood Shores Parkway, Suite 240
Redwood City, California 94065
William T. Holmes
Project Technical Monitor
Rutherford & Chekene
55 Second Street, Suite 600
San Francisco, California 94105
Federal Emergency Management Agency
Michael Mahoney
Project Officer
Federal Emergency Management Agency
500 C Street, SW
Washington, DC 20472
Mai (Mike) Tong
Project Monitor
Federal Emergency Management Agency
500 C Street, SW
Washington, DC 20472
Robert D. Hanson
FEMA Technical Monitor
Federal Emergency Management Agency
2926 Saklan Indian Drive
Walnut Creek, California 94595
Project Management Committee
Craig D. Comartin
Project Technical Director
Comartin Engineers
7683 Andrea Avenue
Stockton, California 95207
Eduardo Miranda
Senior Advisor on Strength Degradation
Stanford University
Civil & Environmental Engineering
Terman Room 293
Stanford, California 94305
Michael Valley
Senior Advisor for Structural Engineering
Magnusson Klemencic Associates
1301 Fifth Avenue, Suite 3200
Seattle, Washington 98101
I-2 I: Project Participants FEMA P440A
Working Group
Dimitrios Vamvatsikos
University of Cyprus
75 Kallipoleos Street
P.O. Box 20537
Nicosia, 1678, Cyprus
Project Review Panel
Kenneth Elwood
University of British Columbia
Dept. of Civil Engineering
6250 Applied Science Lane, Room 2010
Vancouver, British Columbia V6T 1Z4 Canada
Subhash C. Goel
University of Michigan
Dept. of Civil and Envir. Engineering
2350 Hayward, 2340 G.G. Brown Building
Ann Arbor, Michigan 48109-2125
Farzad Naeim
John A. Martin & Associates, Inc.
1212 S. Flower Street, 4th Floor
Los Angeles, California 90015
Workshop Participants
Mark Aschheim
Santa Clara University
500 El Camino Real
Dept. of Civil Engineering
Santa Clara, California 95053
Michael Cochran
Weidlinger Associates
4551 Glencoe Avenue, Suite 350
Marina del Rey, California 90292-7927
Craig D. Comartin
Comartin Engineers
7683 Andrea Avenue
Stockton, California 95207
Anthony Court
A. B. Court & Associates
4340 Hawk Street
San Diego, California 92103
Kenneth Elwood
University of British Columbia
Department of Civil Engineering
6250 Applied Science Lane, Room 2010
Vancouver, British Columbia V6T 1Z4 Canada
Subhash C. Goel
University of Michigan
Department of Civil and Envir. Engineering
2350 Hayward, 2340 G.G. Brown Building
Ann Arbor, Michigan 48109
Robert D. Hanson
Federal Emergency Management Agency
2926 Saklan Indian Drive
Walnut Creek, California 94595
Curt Haselton
California State University, Chico
Department of Civil Engineering
Langdon 209F
Chico, California 95929
Jon A. Heintz
Applied Technology Council
201 Redwood Shores Pkwy., Suite 240
Redwood City, California 94065
FEMA P440A I: Project Participants I-3
YeongAe Heo
University of California at Davis
Dept. of Civil Engineering
Davis, California 95616
William T. Holmes
Rutherford & Chekene
55 Second Street, Suite 600
San Francisco, California 94105
Sashi Kunnath
University of California, Davis
Dept. of Civil & Env. Engineering
One Shields Ave., 2001 Engr III
Davis, California 95616
Joseph Maffei
Rutherford & Chekene
55 Second Street, Suite 600
San Francisco, California 94105
Stephen Mahin
University of California, Berkeley
777 Davis Hall, Dept. of Civil Engineering
Berkeley, California 94720
Michael Mahoney
Federal Emergency Management Agency
500 C Street, SW
Washington, DC 20472
Michael Mehrain
URS Corporation
915 Wilshire Blvd., Suite 700
Los Angeles, California 90017
Eduardo Miranda
Stanford University
Civil & Environmental Engineering
Terman Room 293
Stanford, California 94305
Mark Moore
ZFA Consulting
55 Second Street, Suite 600
San Francisco, California 94105
Charles Roeder
University of Washington
Department of Civil Engineering
233-B More Hall Box 2700
Seattle, Washington 98195
Mark Sinclair
Degenkolb Engineers
225 Bush Street, Suite 1000
San Francisco, California 94104
Peter Somers
Magnusson Klemencic Associates
1301 Fifth Avenue, Suite 3200
Seattle, Washington 98101
Mai (Mike) Tong
Federal Emergency Management Agency
500 C Street, SW
Washington, DC 20472
Luis Toranzo
KPFF Consulting Engineers
6080 Center Drive, Suite 300
Los Angeles, California 90045
Michael Willford
ARUP
901 Market Street, Suite 260
San Francisco, California 94103