Characterizing Ground Motions That
Collapse Steel Special Moment-Resisting
Frames or Make Them Unrepairable
Anna H. Olsen,
a)
M.EERI
, Thomas H. Heaton,
b)
M.EERI
, and John F. Hall
b)
This work applies 64,765 simulated seismic ground motions to four models
each of 6- or 20-story, steel special moment-resisting frame buildings. We con-
sider two vector intensity measures and categorize the building response as
“
collapsed,
”“
unrepairable,
”
or
“
repairable.
”
We then propose regression models
to predict the building responses from the intensity measures. The best models for
“
collapse
”
or
“
unrepairable
”
use peak ground displacement and velocity as inten-
sity measures, and the best models predicting peak interstory drift ratio, given that
the frame model is
“
repairable,
”
use spectral acceleration and epsilon (
ε
) as inten-
sity measures. The more flexible frame is always more likely than the stiffer
frame to
“
collapse
”
or be
“
unrepairable.
”
A frame with fracture-prone welds
is substantially more susceptible to
“
collapse
”
or
“
unrepairable
”
damage than
the equivalent frame with sound welds. The 20-story frames with fracture-
prone welds are more vulnerable to P-delta instability and have a much higher
probability of collapse than do any of the 6-story frames. [DOI: 10.1193/
102612EQS318M]
INTRODUCTION
Welded steel moment-resisting frame buildings have been built in metropolitan areas
with high seismicity since the early 1970s. Structural engineers have designed each building
to withstand loading conditions prescribed by the relevant building code in force at the time
of design and construction. Given adequate systems of construction and inspection, we can
assume that an existing building will not fail catastrophically under the loads it was designed
to withstand nor fail catastrophically under numerous other loads, which may be smaller or
larger than the design loads. Because we are exclusively interested in seismic loads, this work
addresses the question: What seismic excitations can a steel special moment frame (SMF)
withstand or, pessimistically, what seismic excitations may induce failure in this class of
building?
Academic and practicing engineers have studied this type of lateral force
–
resisting sys-
tem. When SMFs failed to perform as expected in the 1994 Northridge earthquake, the engi-
neering community established the causes of this failure. Their work
—
organized as the SAC
Joint Venture
—
documented the state of SMF design and construction and made recommen-
dations for improvements in both areas (see, e.g.,
Reis and Bonowitz 2000
for a list of rele-
vant FEMA and SAC reports).
Earthquake Spectra
, Volume 31, No. 2, pages 813
–
840, May 2015; © 2015, Earthquake Engineering Research Institute
a)
U.S. Geological Survey, Denver, CO
b)
California Institute of Technology, Pasadena, CA
813
Several research groups have simulated mid-rise (roughly 5- to 20-story) building
responses to seismic ground motions. For example,
Baker and Cornell (2005)
proposed
the use of spectral acceleration (
S
a
) and epsilon (
ε
) as a vector intensity measure. Epsilon
measures the difference between observed
S
a
and expected
S
a
from a ground motion pre-
diction equation (GMPE). The researchers applied 40 recorded ground motions, scaled to 13
intensity levels, to a reinforced concrete, moment-resisting frame model of an often studied
building in Van Nuys, California, and to 15 generic frame models representing many struc-
tural systems. They found that the vector intensity measure
ð
S
a
;
ε
Þ
predicted the frame mod-
els
’
responses better than
S
a
alone, and thus they recommended that
ε
be included as a
predictor of structural response or in the selection of ground motion records.
Jones and Zareian (2010)
considered the performance of eight 6- or 20-story SMF
models. Their study used: 18 large simulated ground motions from a M 7.15 earthquake
on the Puente Hills Fault, 40 recorded ground motions scaled to represent the maximum
considered earthquake ground motions for an area of downtown Los Angeles, and a further
40 records scaled to the conditional mean spectra of the considered buildings. The investi-
gators compared the numbers of 6- or 20-story frame models that exceeded a peak interstory
drift ratio of 0.06, concluding that the 20-story models were safer than the 6-story models
and, in particular, that the 20-story models were
“
less vulnerable
”
than the 6-story models to
the problem of fracture-prone welds.
The purpose of this study is to characterize seismic ground motions that cause significant
damage to existing mid-rise SMFs. Such a study could not be performed with recorded ground
motions alone because there are so few records with sufficient energy content at long periods to
induce SMF collapse. Ground motions with significant energy content at long periods are
expected to result primarily from large-magnitude earthquakes. In the past decade, earth scien-
tists have generated numerous seismic ground motions from simulations of fault rupture and
wave propagation. We collect almost 65,000 simulated time histories from scenario crustal
earthquakes in California, and we apply them to models of SMF buildings. The intensities
of these ground motions range from quite small to extreme. By covering this complete
range, we cancharacterize SMF buildingresponse from linear through nonlinearto highly non-
linear. We do not characterize the likelihood of these records; instead, we simply use them to
characterize the intensities of ground motions that cause collapse or unrepairable damage.
By identifying and describing ground motions that significantly damage existing mid-rise
SMFs, we also characterize the SMFs
’
seismic load
–
resisting capacity. There are many dis-
tinct building designs in the class of
“
existing mid-rise SMF,
”
but in this study we do not
attempt to fully represent this variety. Instead, we use building designs and models that allow
one-to-one comparisons of a shorter mid-rise frame versus a taller mid-rise frame, or a stiffer
and higher-strength frame versus a more flexible and lower-strength frame, or a frame with
sound versus fracture-prone welds. The building models that we use capture higher and lower
values of these important characteristics of existing mid-rise SMFs, but they are not repre-
sentative of all buildings in this class.
After describing the ground motions and frame models used in this study, we compare
four intensity measures
—
specifically, peak ground displacement (PGD), peak ground velo-
city (PGV), spectral acceleration, and epsilon
—
to determine which scalar or vector measure
best predicts building response. We propose several alternative functional relationships
814
A. H. OLSEN, T. H. HEATON, AND J. F. HALL
between intensity measure and building response measure and determine which best char-
acterizes this relationship. Thus, we also characterize the intensity of ground motions that
cause failure of steel special moment-resisting frames or the intensities that cause a certain
interstory drift ratio.
GROUND MOTIONS AND BUILDING MODELS
To establish a probabilistic relationship between ground motion intensity measures and
the seismic response of existing SMFs, we collect a set of 64,765 simulated ground motions
and use them in nonlinear time history analyses of eight SMF computational models. We
characterize the frame model response as
“
collapse
”
or
“
standing
”
and as
“
repairable
”
or
“
unrepairable
”
;if
“
repairable,
”
we calculate the peak interstory drift ratio (IDR). We char-
acterize the seismic ground motions using PGD, PGV,
S
a
, and
ε
either as scalar or vector
intensity measures. The following sections detail this methodology.
GROUND MOTIONS AND INTENSITY MEASURES
We collect simulated ground motions from several scenarios of crustal earthquakes in
California. Table
1
lists these scenarios with their important characteristics. The scenario
magnitudes range from 6.3 to 7.8, and the faults are under the greater Los Angeles and
San Francisco metropolitan areas. Note that the energy content of the simulated ground
motions is either long period (greater than 2 s) or broadband (greater than 0.1 s). The listed
references provide details on how the scenario earthquakes and resulting ground motions
were generated.
We use four metrics to characterize each ground motion: PGD, PGV,
S
a
at four periods,
and
ε
. To calculate the PGD (or PGV) of a ground displacement (velocity) time history, we
first find the vector amplitude (also known as the
L
2
norm) of the two orthogonal horizontal
components at each time step. A few simulated ground motions have a monotonically
increasing or decreasing baseline. This feature is not physical, and in some cases the largest
dynamic displacement is at the end of the record. To determine the maximum dynamic dis-
placement that occurs earlier in the record, we find the largest vector amplitude over the time
interval between the first seismic wave arrival and one-half of the remaining record length.
Based on a visual check of many dozens of records, we believe that this algorithm eliminates
Table 1.
Summary of scenario earthquakes from which the simulated ground motions were
generated
Fault
Reference
Magnitude
Energy
content Sites
1
Number
2
Loma Prieta
Aagaard et al. (2008b)
6.9
Long period 4,945
2
Northern San Andreas
Aagaard et al. (2008a)
7.8
Long period 4,945
3
Puente Hills
Graves and Somerville (2006)
7.15
Broadband 648
5
Various faults
in the Los Angeles basin
Day et al. (2005)
6.3
–
7.1 Long period 1,600
23
1
Number of ground motion sites for each scenario earthquake.
2
Number of scenario earthquakes for each study.
CHARACTERIZING GROUND MOTIONS THAT COLLAPSE STEEL SMFs OR MAKE THEM UNREPAIRABLE
815
the effects of baseline drift and finds the PGD during strong shaking. The large number of
simulated ground motions precludes checking all time histories. Note that the long-period
PGD and PGV are likely found at the same time step in the ground motion, but the broadband
PGD and PGV are not likely coincident at a time step. We denote PGDs and PGVs calculated
from a long-period ground motion with the subscript
lp
and those from a broadband ground
motion with the subscript
bb
.
We calculate
S
a
at the fundamental elastic period of each frame model (abbreviations are
described in the next section): 1.16 s (J6), 1.54 s (U6), 3.04 s (J20), and 3.47 s (U20). The
final intensity measure,
ε
, developed by
Baker and Cornell (2005)
, measures the difference
between an observed
log
e
ð
S
a
Þ
and the expected
log
e
ð
S
a
Þ
from a GMPE in units of standard
deviation. We use the GMPE in
Boore and Atkinson (2007
, Equation 3.1) to define the
expected
log
e
ð
S
a
Þ
for each simulated time history. Note that Boore and Atkinson estimated
the parameter values of their GMPE using recorded ground motions from past earthquakes.
By calculating
ε
in the way just described, we are comparing the
S
a
of a
simulated
ground
motion to the expected
S
a
based on
past observations
of seismic ground motions.
In the Introduction, we allude to our choice to use simulated, rather than recorded, seismic
ground motions in this study. The wealth of simulated ground motions allows us to calculate
SMF model responses over a wide range of intensity measure values. These frame model
responses, however, would not provide insight into SMF behavior if the simulated ground
motions were inconsistent with records or if a long-period ground motion induced a frame
model response inconsistent with that caused by the equivalent ground motion with short-
and long-period energy content. The studies listed in Table
1
, which generated the ground
motions used in this study, validated their models in part by comparing their simulation results
against corresponding records. Using records from the 1999 Chi-Chi and 2003 Tokachi-Oki
earthquakes,
Krishnan et al. (2006)
demonstrated that 13 records filtered to remove short per-
iods induced interstory drifts in their two 18-story moment-resisting frames consistent with
those caused by the unfiltered records. Thus, we believe that this study
’
s findings would not
change if tens of thousands of records were used in place of the simulated ground motions on
the same range of intensity measure values. Also, the findings on moment-resisting frame
behavior are consistent whether long-period or broadband ground motions are used.
Since recorded ground motions are broadband, we find a multiplicative factor for the
interested reader to convert from a long-period PGV to a broadband PGV. This conversion
is not implemented for any PGVs in this paper. We apply a fourth-order, low-pass Butter-
worth filter to all broadband ground motions and recalculate the PGV for these filtered time
histories. The PGVs from the broadband ground motions,
PGV
bb
, can be regressed on the
PGVs from the filtered ground motions,
PGV
f
, using a linear or quadratic relationship:
EQ-TARGET;temp:intralink-;e1;41;184
PGV
bb
¼
0.006715
þ
1.473
PGV
f
þ
ε
linear
(1)
or
EQ-TARGET;temp:intralink-;e2;41;139
PGV
bb
¼
0.1163
þ
1.167
PGV
f
þ
0.1224
PGV
2
f
þ
ε
quadratic
(2)
where the error is assumed to be normally distributed with mean zero and standard deviation
0.2364 m
∕
s
(linear) or
0.2211 m
∕
s
(quadratic). (Inspection of the logarithm of the data
816
A. H. OLSEN, T. H. HEATON, AND J. F. HALL
indicates that long-period and broadband PGVs are not related through a power law.) Figure
1
shows the data and the linear and quadratic fits. At large PGV values the data clearly deviate
from the line. Although we have no physical reason to expect a quadratic relationship
between
PGV
lp
and
PGV
bb
, we do expect to observe the largest PGVs in the near-source
area of a fault, which is also where we expect to see ground motions with the largest high-
frequency content. Based on our available data and interest in PGVs of
1
3m
∕
s
, the linear
equation provides an adequate conversion from long-period to broadband PGV: a broadband
PGV is approximately 1.5 times a long-period PGV with a standard deviation of
0.24 m
∕
s
.
The residuals of the linear fit are heteroscedastic in this range, so this relationship should be
used only as a rough approximation.
BUILDING MODELS AND RESPONSE METRICS
We use eight models of SMFs developed by
Hall (1997)
. The building height is either
6 or 20 stories, representing a shorter or taller mid-rise frame. For a given number of
stories, the frame is either stiffer and higher strength or more flexible and lower strength.
The lateral force
–
resisting system of the former satisfies the Japanese seismic building
provisions of 1992 [with design base shear normalized by weight,
Q/W
, equal to 0.20
(6 stories) or 0.08 (20 stories)], and the lateral force
–
resisting system of the latter satisfies
the 1994 Uniform Building Code seismic provisions [
V/W
equal to 0.04 (6 stories) or
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0
1
2
3
4
5
6
7
8
PGV
lp
(m/s)
PGV
bb
(m/s)
Broadband vs. long−period PGV for simulated ground motions
Figure 1.
Linear (gray line) and quadratic (light gray curve) relationships between long-period
and broadband PGV. We calculate the
PGV
lp
values from low-pass-filtered (2-s corner period)
versions of the broadband simulated ground motions from
Graves and Somerville (2006)
.
CHARACTERIZING GROUND MOTIONS THAT COLLAPSE STEEL SMFs OR MAKE THEM UNREPAIRABLE
817
0.03 (20 stories)]. Each design meets the proportioning and detailing requirements for beams,
columns, and beam-to-column connections in a special moment-resisting frame. Tables
2
and
3
list the values of important design parameters. The welds of each frame are either sound or
prone to fracture. Following
Hall (1997)
, we denote a particular building with a three-part
code: (1) J for the
“
Japanese seismic provisions of 1992
”
or U for the
“
1994 Uniform Build-
ing Code
”
; (2) the number of stories; and (3) P for
“
perfect
”
welds or B for
“
brittle
”
welds.
Thus, for example, a 20-story building satisfying the 1994 Uniform Building Code seismic
provisions with sound welds is coded as U20P.
We now describe the buildings
’
frames. The six-story buildings have a total height of
98.5 ft (30.0 m), including one basement. The first story and basement are each 18 ft (5.49 m)
tall, and all other stories are 12.5 ft (3.81 m) tall. The overall width of the six-story buildings
is 120 ft (36.6 m) and is divided into four bays of equal width. The overall depth of the six-
story buildings is 72.0 ft (21.9 m) and is divided into three bays of equal width. The 20-story
buildings have a total height of 274 ft (83.4 m), including one basement. The story and base-
ment heights are the same as those of the six-story building. The overall width of the 20-story
buildings is 100 ft (30.5 m), and the overall depth is 60.0 ft (18.3 m). As with the six-story
buildings, the width is divided into four bays, and the depth is divided into three bays.
Hall
(1997)
provided schedules for the columns, beams, slabs, and foundations. The exterior
frames (and the center three-bay frame of each J building) have moment-resisting connec-
tions; interior frames have simple connections and carry their tributary gravity loads.
We use finite-element models of each building design as detailed in Hall (1997), which
also describes the computer program
Frame-2d
used for the analyses.
Frame-2d
was spe-
cifically written to calculate the response of steel moment-frame and braced-frame buildings
to large ground motions.
Challa and Hall (1994)
,
Hall and Challa (1995)
, and
Hall (1998)
validated the special features of
Frame-2d
, such as joint modeling, nodal updating, and weld
fracture, by extensive numerical testing and comparison with experimental data. Also,
Table 2.
Values of 1992 Japanese seismic design parameters for the 6- and 20-story
building designs
Model
Z
Soil
R
t
T
(s)
C
o
Q
∕
W
Drift limit (
%
)
J6
1
Type 2
0.990
0.73
0.2
0.1980
—
J20
1
Type 2
0.410
2.24
0.2
0.0820
0.50
Source: Reproduced from
Hall (1997)
.
Table 3.
Values of 1994 Uniform Building Code seismic design parameters for the 6- and
20-story building designs
Model
ZIR
W
ST
(s)
CV
∕
W
Drift limit (
%
)
U6
0.4
1
12
1.2
1.22
1.312
0.0437
0.25
U20
0.4
1
12
1.2
2.91
0.736
0.0300
0.25
Source: Reproduced from
Hall (1997)
.
818
A. H. OLSEN, T. H. HEATON, AND J. F. HALL
Krishnan (2003)
extended
Frame-2d
into three dimensions and showed that both versions
give the same results for a specialized two-dimensional problem.
Although Hall takes advantage of building symmetry by modeling only half of each
building, all three-bay moment-resisting or gravity frames are explicitly modeled to the
same level of detail. Interior gravity frames contribute realistically to each building
’
s stiffness
and strength. The bending strength at a simple beam-to-column connection is modeled by
connecting only the web fibers to the joint. The models also fully account for geometric
nonlinearities (that is, moment amplification and P-delta): each member has geometric stiff-
ness, and the
Frame-2d
program updates the positions of end-member nodes. Structure-
foundation interaction is modeled with horizontal and vertical springs at the base of each
column. The stress-strain relationship of the springs is bilinear and hysteretic; see
Hall
(1997)
for specifications of the springs. We do not, however, believe that this interaction
contributes significantly to the behavior of the frame models (
Tall Buildings Initiative Guide-
lines Working Group 2010
, sec.
5.3
).
Figure
2
shows pushover curves for modified finite-element models of the eight buildings
following the procedure described in
Hall (1997)
. We modify the masses assigned to the
horizontal degrees of freedom such that the total mass is the seismic design mass and is
distributed in proportion to the seismic design loads. Then we apply a horizontal ground
0
0.02
0.04
0.06
(a)
(b)
0.08
0.1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Lateral roof displacement (fraction of building height)
Base shear (fraction of seismic design weight)
Pushover curves for 20-story models
J20B
J20P
U20B
U20P
0
0.02
0.04
0.06
0.08
0.1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Lateral roof displacement (fraction of building height)
Base shear (fraction of seismic design weight)
Pushover curves for 6-story models
J6B
J6P
U6B
U6P
Figure 2.
Pushover curves: (a) the 20-story frame models; (b) the 6-story frame models. The
circles, squares, and diamonds indicate the yield, peak, and ultimate points, respectively, for mod-
els with sound welds. The ductilities of these models are 3.9 (J20P), 4.2 (U20P), 8.8 (J6P), and
9.3 (U6P).
CHARACTERIZING GROUND MOTIONS THAT COLLAPSE STEEL SMFs OR MAKE THEM UNREPAIRABLE
819
acceleration that increases linearly at a rate of 0.3 g per minute and calculate the frame mod-
el
’
s response dynamically. Because the ground acceleration increases slowly, we can use a
dynamic analysis procedure to replicate a series of static calculations with the applied lateral
forces at each time step proportional to the seismic design forces. As seen in Figure
2
this
approach introduces dynamic vibrations in the frame models when the stiffness changes at
yielding and especially at weld fracture. This method of pushover analysis allows us to model
the strength-degrading part of the curve.
The finite-element models use the fiber method to capture the behavior of beams and
columns. The length of each beam or column is subdivided into eight segments, and the
cross section of each segment is divided into eight fibers representing the steel wide-flange
beam or column; for each beam, two additional fibers represent the concrete slab and the
metal deck. Each fiber has a hysteretic, axial stress-strain relationship, including a yield pla-
teau and strain hardening, and each segment has a linear shear stress-strain relation. The end
segments of the beams and columns are short to capture the spread of yielding at the plastic
hinge zones. The yield strength of steel is greater than the nominal value.
Hall and Challa
(1995)
compared models of steel members using the plastic hinge method or the fiber method
to experimental test data. The model using the fiber method (also employed in this study)
showed excellent agreement with the experimental results.
The weld fracture model is based on the failures observed after the 1994 Northridge
earthquake. In general, these welds proved to be brittle, fracturing prior to local flange buck-
ling. Beam-to-column, column splice, and column baseplate welds are represented by sets of
fibers at each weld location. The model randomly assigns an axial fracture strain to each weld
according to a user-defined distribution. If the developed tensile strain of a weld fiber exceeds
the fracture strain, then the fiber no longer resists tension. For frame models with fracture-
prone welds, the distribution of axial fracture strain,
ε
f
, normalized by the yield strain,
ε
y
,
throughout all welds in the building is as follows: for beam top-flange welds, column splices,
and welds at column baseplates, 40
%
have
ε
f
∕
ε
y
¼
1
,30
%
have
ε
f
∕
ε
y
¼
10
, and 30
%
have
ε
f
∕
ε
y
¼
100
; for beam bottom-flange welds, 20
%
have
ε
f
∕
ε
y
¼
0.7
,40
%
have
ε
f
∕
ε
y
¼
1
,
20
%
have
ε
f
∕
ε
y
¼
10
,10
%
have
ε
f
∕
ε
y
¼
50
, and 10
%
have
ε
f
∕
ε
y
¼
100
(again, these dis-
tributions are denoted B).
Hall (1998
, sec. 2.4
–
2.5) defined a different set of fracture strains
(denoted F) and found agreement between the model simulations and observations of weld
fractures in the Northridge earthquake.
Olsen (2008
, sec. 2.7.3) compared frame model
responses assuming the B and F distributions. For the same ground motion, the B distribution
resulted in frame models less likely to
“
collapse
”
than did the F distribution, and when the
frames did not
“
collapse,
”
frames with the B distribution tended to have smaller IDRs than
those with the F distribution. Thus, the fracture strain distributions used in this paper are less
“
bad
”
than those
Hall (1998)
used to compare with observations of weld fracture in the
Northridge earthquake.
Although weld fibers are allowed to fail in tension, welded connections maintain residual
bending strength through several mechanisms. First, our distribution of axial fracture strains
assumes that beam bottom-flange welds are more susceptible to fracture, consistent with
observations after the Northridge earthquake. Thus, in many simulations with weld fractures,
only the fibers representing the bottom-flange weld fail, leaving the other fibers intact.
Second, a fractured fiber is allowed to resist compression if the fracture gap closes.
820
A. H. OLSEN, T. H. HEATON, AND J. F. HALL
Third, the nodal positions of the beam segments are updated during the simulation, which
accounts for axial compression in the beam resulting from flange fracture. This prevents
some drop in the bending moment because of the higher force in the flange that is carrying
compression. Finally, fibers representing the shear tab cannot fracture.
Special elements model the behaviors of panel zones and basement concrete walls.
A panel zone is represented by an element with a nonlinear and hysteretic relationship
between moment and shear strain, calibrated with test data (
Challa 1992
). Also, the
panel-zone element has the capability to model doubler plates by increasing the thickness
of the panel zone. It occupies a properly dimensioned finite space within the column and
connects to beam elements on their edges. Thus the beams have clear-span dimensions.
For basement stories, a plane stress element represents the stiffness of concrete walls.
The simulated ground motions have three spatial dimensions, but the finite-element mod-
els are two-dimensional frames. To reduce the two horizontal components of a ground
motion into one, we define a series of resultants,
r
ð
t
;
θ
Þ
, which combine the east-west,
e
ð
t
Þ
, and north-south,
n
ð
t
), components:
EQ-TARGET;temp:intralink-;sec2.2;62;446
r
ð
t
;
θ
Þ¼
e
ð
t
Þ
cos
ð
θ
Þþ
n
ð
t
Þ
sin
ð
θ
Þ
(3)
where
θ
ranges from 0 to 179 degrees in 1-degree increments. We then find the angle,
θ
v
, that
produces the largest peak-to-peak velocity among all resultant ground motions. The resultant
r
ð
t
;
θ
¼
θ
v
Þ
is the horizontal component of ground motion applied in the direction of the
building
’
s weak lateral axis. Because damage in this class of buildings can be related to
peak-to-peak velocity, we believe that this is the most damaging orientation of the frame
model with respect to the ground motion.
We characterize the finite-element model behaviorwith: a variablerepresenting
“
standing
”
or
“
collapse
”
as a 0 or 1, respectively; a variable representing
“
repairable
”
or
“
unrepairable
”
as
a 0 or 1; and, if the model is
“
repairable,
”
a continuous variable representing the interstory drift
ratio. We label a frame model response as
“
collapse
”
when, as a result of excessive lateral story
displacements, the model no longer has the capability to support vertical loads because of
P-delta instability. As the model loses its lateral force resistance, its behavior becomes
more highly nonlinear, which is expensive to simulate computationally. We seek to identify
earlythatthemodelhasnoresistancetolateralforcesinordertoreducethecomputationaleffort
of our simulations. During the calculation of a frame model
’
s response to a ground motion,
we terminate the simulation if the peak interstory drift ratio exceeds 20.0
%
and deem it a
“
collapse.
”
If the simulation were allowed to continue to the end of the ground motion, a
model with a peak interstory drift ratio above 20.0
%
would eventually show a clear dynamic
instability as a result of its loss of lateral force resistance. As a check, the largest peak interstory
drift ratio of the strongest building
—
J6P
—
was 16
%
among 3,240 simulations. Thus, we
believe that terminating the simulations when the peak interstory drift ratio exceeds 20.0
%
does not miscategorize a
“
standing
”
model as
“
collapse.
”
After finding that a frame remains standing in a simulation, the second concern is whether
the lateral force
–
resisting system of an equivalent existing building would be deemed repair-
able or be demolished.
Iwata et al. (2006)
analyzed 12 steel buildings damaged in the 1995
Kobe earthquake and established
“
repairability limits
”
for this building class. This study
CHARACTERIZING GROUND MOTIONS THAT COLLAPSE STEEL SMFs OR MAKE THEM UNREPAIRABLE
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