Computers and Structures 89 (2011) 959–967

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Computers and Structures
journal homepage: www.elsevier.com/locate/compstruc

Numerical and experimental evaluation of seismic capacity of high-rise steelbuildings subjected to long duration earthquakes
D.G. Lignos a,⇑, Y. Chung b, T. Nagae c, M. Nakashima daDepartment of Civil Engineering and Applied Mechanics, McGill University, 817 Sherbrooke St. West, Room 278C, Montreal QC, Canada H3A 2K6
Division of Seismic Resistant Structures, Disaster Prevention Research Institute (DPRI), Kyoto University, #S301D Gokasho, Uji, Kyoto 611-0011, Japanc
National Research Institute for Earth Science and Disaster Prevention, Miki, Hyogo 673-0515, Japand
Division of Seismic Resistant Structures, Disaster Prevention Research Institute (DPRI), Kyoto University, #S307D Gokasho, Uji, Kyoto 611-0011, Japanba r t i c l e

i n f oArticle history:
Received 2 July 2010
Accepted 25 January 2011
Available online 18 February 2011
Keywords:
High-rise
Fracture
Cumulative damage
Long duration
Low cycle fatigue
Post-fracture seismic capacitya b s t r a c t
Occurrences of large earthquakes having a magnitude larger than eight along subduction zones have beenreported worldwide. Due to large number of load reversals the effect of cumulative damage on structuralcomponents due to deterioration becomes critical for steel buildings of old construction but may also
become critical for buildings designed based on current seismic provisions. A state-of-the-art analyticalmodel that simulates component deterioration and fracture due to low cycle fatigue has been developedand implemented in the OpenSees computational framework. The model serves for seismic evaluation ofsteel moment frame structures subjected to long duration records. The effectiveness of the numericalmodel in quantiﬁcation of the seismic capacity of high rise steel structures is demonstrated through validation with a full scale shaking table test of a high-rise steel building subjected to a long duration record
at the world’s largest shaking table facility (E-Defense). Limitations of the proposed numerical model arealso discussed.
Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction
Recent earthquakes around the world (Northridge, 1994; Kobe,
1995) raised many concerns regarding the seismic performance ofsteel moment resisting frames (MRF) due to the occurrence of brittle fractures of welded beam-to-column connections [1,2]. Various
analytical studies [3–6] summarized the effect of brittle fractures
on seismic capacity of existing steel moment frames. This forced
the earthquake engineering community to design improved steel
connections so that brittle fracture is avoided [7,8].
However, improved steel moment connections may not be
invincible when subjected to a large number of inelastic cycles
due to low cycle fatigue [9–14]. This is more evident in high-risesteel buildings that are subjected to long period long duration
ground motions that occur near subduction zones. The reason isthat the predominant period of these ground motions range fromseveral to 10 s, and their primary durations extend over several
minutes [15–17]. These ground motions tend to resonate high-risebuildings whose fundamental natural periods are above 2 s. Thisobservation was conﬁrmed by recent full-scale shake table tests⇑ Corresponding author. Tel.: +1 514 398 2198; fax: +1 514 398 7361.
E-mail addresses: dimitrios.lignos@mcgill.ca (D.G. Lignos), yulin.chung@ks7.ecs.kyoto-u.ac.jp (Y. Chung), nagae@bosai.go.jp (T. Nagae), nakashima@archi.
kyoto-u.ac.jp (M. Nakashima).
0045-7949/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.compstruc.2011.01.017

that represented typical high-rise construction in Japan [18]. These
tests took place at the world’s largest shake table facility at EDefense. Prior numerical studies [19] on high-rise steel buildings
subjected to long period long duration ground motions also
conﬁrmed the same observation.
During the past years a large number of numerical and experimental studies emphasized on the importance of fracture on theseismic capacity of steel MRF due to seismic loading. Nakashima
et al. [20] investigated the effect of moment redistribution causedby beam fracture in steel MRF based on static loading. The main
conclusion of this study was that sequential fractures are less likely
to occur during static moment redistribution when rotations corresponding to fracture are large. Utilizing a large number of steel
MRFs as part of the SAC phase II project in United States, Lucoand Cornell [21] investigated the effect of connection brittle fractures on seismic drift demands of steel MRFs using an empiricalanalysis model to assess brittle fracture. They concluded that theeffects of connection fractures are more pronounced at higher drift
demand levels.
Rodgers and Mahin [22] demonstrated both experimentally andnumerically that severe strength loss due to the combination ofnumerous fractures in steel MRFs and large excitation can haveadverse consequences, including collapse. Nakashima et al. [23]investigated experimentally the effect of residual strength of asteel MRF on connection fractures. The composite effect due to slab

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on connection fractures was also assessed in this study. They concluded that after fracture of the bottom ﬂange of a steel beam due
to slab effect occurs, the residual capacity of composite steel MRFs
is about 35% of the respective maximum strength at relatively large
drifts. Recent full scale shaking tables on high-rise steel buildings
conducted on the world’s largest shaking table at E-Defense[10,18,24] demonstrated the vulnerability of steel beam-to-column connections to long period long duration ground motions.
In these connections, fracture occurs due to the large number of
inelastic deformations resulting to severe strength deterioration.
Consequently, there is a need to investigate the effect of component deterioration and ductile fracture on the seismic capacity ofhigh-rise steel buildings. This will contribute to effective decisions
on retroﬁt techniques for steel beam-to-column connections. For
this purpose, a numerical model that is able to simulate complex
deterioration phenomena and ultimately connection fracture due
to low cycle fatigue has been developed and implemented in theOpen System for Earthquake Engineering Simulation (openSees)
platform [25], which is available from the Paciﬁc Earthquake Engineering Research Center (PEER). The component model has beencalibrated against a large number of steel component tests thathave been conducted over the past years around the world. The
validity of the numerical model is demonstrated with recently conducted full scale shaking table test of a high-rise steel building[18,24]. This test took place at the E-Defense facility in Japan.
The seismic capacity of the high-rise steel structure after the occurrence of connection fractures is evaluated numerically after utilizing the same numerical model. Limitations of the proposed
numerical model are also summarized at the end of this paper.

2. Numerical model for prediction of fracture due to low cycle
fatigue
Various models have been proposed to investigate the effect oflow cycle fatigue on steel beam-to-column connections. Berteroand Popov [26] derived a relationship between plastic strain amplitude and the number of cycles to fracture based on straincontrolled tests that lead to fracture of steel beam ﬂanges after
severe local buckling. Park et al. [27] incorporated the maximum
deformation and energy dissipation due to hysteresis in a damage
index. More recently, Krawinkler et al. [28] developed a numericalmodel that can simulate the effect of cumulative damage due toearthquake excitations based on Cofﬁn–Manson [29] relationshipconsidering the full loading history of a steel component subjected
to cyclic loading.
For prediction of inelastic buckling and fracture of steel braces
due to low cycle fatigue, a distributed plasticity model [30] thatincorporates rainﬂow counting was developed and validated withexperimental data of steel braces. Krishnan [31] developed an elastoﬁber element that can simulate inelastic post-buckling response
including fracture of steel braces and slender columns. Kanvinde
et al. [32–34] proposed and demonstrated the effectiveness of acyclic void growth model (VGI) to assess ductile fracture initiation
due to low cycle fatigue for steel connections and steel braces. Lin
et al. [35] utilized the VGI model in detailed ﬁnite element studies
for prediction of fracture initiation of ﬁeld welded steel connections. Lee and Stojadinovic [36] developed a new cyclic yield-line
plastic hinge model for estimating connection rotation capacity.
This model is applicable by designers to evaluate new steel connections before required proof of performance tests. Campbell et al.
[37] presented a summary of damage predictions in steel MRFs under earthquakes in which low cycle fatigue is incorporated basedon a compilation of salient analytical and experimental results.
This paper focuses on the capability of simulating component
deterioration and fracture due low cycle fatigue with an inelastic

concentrated plasticity element that was recently implemented
in the OpenSees computational framework [25] (http://opensees.berkeley.edu). In particular, a fracture rule was incorporated
in the modiﬁed Ibarra–Krawinkler deterioration model [38,39] thatallows modeling of (1) strength and stiffness deterioration and (2)rupture leading to complete severing of a steel beam-to-column
connection due to cyclic loading. This analytical model serves forseismic evaluation of steel MRFs at extreme seismic loading,including the quantiﬁcation of post-fracture response. The emphasis is on high-rise steel buildings subjected to long period long
duration ground motions. Because of the large number loading
reversals in these ground motions, steel connections deteriorate
cyclically in strength and stiffness and ultimately fracture due tolow cycle fatigue.
2.1. Component deterioration modeling
The modiﬁed Ibarra–Krawinkler phenomenological analyticalmodel is able to simulate stiffness and strength component deterioration by using a reference backbone curve shown in Fig. 1a. To
control cyclic deterioration, an energy-based rule proposed by
Rahnama and Krawinkler [40] is used. The hysteretic response of
the modiﬁed Ibarra–Krawinkler model has been calibrated extensively during the last few years by utilizing a steel component
database for deterioration modeling. This database includes tests
for more than 300 steel beams [39,41]. Fig. 1a shows an exampleof calibration of the elastic stiffness Ke, pre- and post-capping (after
local buckling occurs) rotation hp, hpc of a steel beam subjected tomonotonic loading. The modiﬁed Ibarra–Krawinkler model deteriorates cyclically using a deterioration parameter K. This parameteris a reference energy dissipation capacity of a steel component that
controls strength, stiffness and post-capping strength deterioration
modes (see Fig. 1b). A detailed description about the original andmodiﬁed Ibarra–Krawinkler deterioration model can be found in[38,39].
2.2. Modeling of fracture due to low cycle fatigue
In order to incorporate low cycle fatigue in the numerical model
discussed in Section 2.1, a fracture law was implemented. For asteel component, the number of cycles to fracture Nf is expressed
as a function of cumulative energy dissipation Ed of the steel component when subjected to cyclic loading. This expression can be
written according to Eq. (1),Nf ¼ a1 Ekdð1ÞThis relationship is analogous to the Cofﬁn–Manson [29] equation
for low-cycle fatigue simulation,

Nf ¼ bDeapð2Þwhere Dep is the amplitude of plastic strain of a steel component.
The difference between Eqs. (1) and (2) is that instead of the amplitude of plastic strain of the steel component, the dissipated hysteretic energy is expressed with respect to the number of cycles tofracture Nf. The logarithmic expression of Eq. (1) is given by,log Nf ¼ logða1 Þ  k logðEd Þ

ð3Þ

Eq. (3) is further simpliﬁed by,log Nf ¼ A  k logðEd Þ

ð4Þ

The parameters A and k in Eq. (4) depend on the loading history thata steel component experiences as part of a structure subjected to an
earthquake. Fig. 2 shows the effect of two different loading histories
on the parameters A and k. The two protocols that are used are astandard symmetric loading protocol and a near-fault loading

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InitialBackBone CurveMrθp

MomentMcyMomentMθpc

Unload.
Stiffness Det.
Post Cap.
Strength Det.

Ke

Strength Det.
Chord Rotation θθu(a) backbone curve

Chord Rotation θ(b) basic modes of cyclic deterioration

Fig. 1. Modiﬁed Ibarra–Krawinkler deterioration model (Lignos and Krawinkler [39]).

Fig. 2. Effect of loading history on fracture due to low cycle fatigue (a) symmetric loading protocol; (b) near-fault loading protocol; (c) hysteretic response due to symmetricloading protocol; (d) hysteretic response due to near-fault loading protocol; (e) cycles to fracture versus normalized cumulative dissipated energy due to symmetric loading
protocol; (f) cycles to fracture versus normalized cumulative dissipated energy due to near-fault loading protocol.

protocol [42] (see Fig. 2a and b). The same steel-beam-to-column
connection is used in both examples (i.e. the set of A and k parameters is identical for both cases). When a symmetric loading protocol with increased inelastic cycles is utilized, the steel component
fractures at a chord rotation of about 4.4% (see Fig. 2c). In the caseof the near-fault loading protocol, the same component fractures atabout 8% chord rotation (see Fig. 2d). Due to the small amplitude of
inelastic cycles prior to the main pulse of the near-fault protocol(see Fig. 2b) the steel component does not dissipate much energy;
thus it does not fracture. The same observation can be seen from

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Fig. 2e and f. These ﬁgures show the number of inelastic cycles tofracture versus the dissipated energy of the same steel component
subjected to the symmetric and near-fault loading protocol, respectively. In these ﬁgures the dissipated energy of the steel component
is normalized with respect to its plastic moment capacity.
The parameters A and k are calibrated with available experimental data from a steel component database for deterioration
modeling [36]. Forty-three test specimens with different beam
sizes were utilized in order to calibrate the two parameters (A, k)
for fracture simulation of Welded Unreinforced Flange (WUF) connections. An example of this connection type is shown in Fig. 3a[43]. The calibration of the parameters A and k is based on nonlinear least-square optimization [44] using the Levenberg–Marquardt
algorithm [45]. The objective function that was used was the difference between the simulated and measured bending strength
at a given beam rotation. Based on the steel component tests thatwere used to calibrate the parameters A and k, it is concluded thata constant k may be used to represent steel components that fail ina ductile manner. A larger A value implies that a steel component ismore ductile compared to another one with smaller A, i.e., the component is able to dissipate more energy prior to fracture. Kuwamura and Takagi [46] reached to the same conclusion. In theirassessment, they related the number of cycles to fracture of a steel
component with its cumulative plastic strain normalized with respect to the yield strain. The steel specimens that are considered
for calibration of the numerical model discussed in this paper all
fail in a ductile manner (fracture due to low cycle fatigue). Cases
that steel beam-to-column connections fail in a brittle manner(e.g. pre-Northridge connections) is not part of this data set since
the focus of this paper is to evaluate the seismic capacity ofhigh-rise steel buildings due to large number of inelastic cycles
prior to fracture. However, based on [46] a similar expression with
Eq. (2) is applicable for brittle fracture simulation. An example ofcalibration of the simulated response of a WUF steel connection
is shown in Fig. 3b. This ﬁgure indicates a relatively good match
between simulated and experimental hysteretic response of a

WUF connection including fracture. Fig. 4a and b shows the bending strength and unloading stiffness deterioration per cycle of thesame steel component for both loading directions, respectively.
From these ﬁgures it can be seen that there are four ranges of deterioration with respect to number of cycles. During the ﬁrst range,
there is no indication of local buckling; during the second range,
deterioration occurs at a high rate associated with the continuous
growth of local buckles; during the third range deterioration occurs at constant rate due to the stabilization in buckle size and during the last range, deterioration occurs due to crack propagation at
the welds or buckles. Earlier experimental studies [28] havereached to the same conclusions regarding the effect of cyclic loading on component deterioration and fracture due to low cycle
fatigue.
Fig. 4c shows the cumulative dissipated hysteretic energy versus the number of inelastic cycles of the same steel component
that is shown in Fig. 3b. In this ﬁgure, the cumulative dissipatedenergy is normalized with respect to the plastic bending strengthof the steel component. Fig. 4d shows the relationship of dissipatedhysteretic energy versus number of cycles to fracture in logarithmic scale for the set of specimens used from [39,41]. This relationship is close to linear (linear regression coefﬁcient R2 = 0.86), whichis in accordance with Eq. (5).
3. Benchmark high-rise building for validation of the numericalmodel
In order to validate the ability of the modiﬁed Ibarra–Krawinkler
deterioration model with low cycle fatigue to predict steel connection fractures, we utilized the experimental data from a recently
conducted full scale shaking table test of a steel building (seeFig. 5a). This specimen represents a prototype 21-story steel building built in Japan in 1970s. The structure was tested at the world’s
largest earthquake simulator facility at E-Defense in Japan [18,24].
This earthquake simulator can accommodate a specimen up to aweight of 1200 metric tons and a height of 22 m (see [24]). Hencethe concept adopted for the test was to establish a partial frame
structure with full-scale steel members that would be able to reproduce the possible seismic responses of the prototype. The ﬁrst 4-stories of the equivalent test specimen represented the bottom storiesof the prototype 21-story structure. Three concrete substitute layers
represented the mass and stiffness of the remaining stories. Theselayers were connected with rubber bearings placed on top of thestructure. The layers and rubber bearings were tuned in such a
way to represent the total mass and lateral stiffness of every 5stories of the upper portion of the 21-story prototype steel structure.
A steel damper was placed at the centroid of each concrete layer toreproduce possible nonlinearity and energy dissipation of the upper
stories of the prototype structure. The geometry and structural
sections of the test specimen is shown in Fig. 5b. It was proven bothanalytically and experimentally (see [18,24]) that the test specimen
represented well the response of the prototype structure. A total of
678 channels of data acquisition were used during the earthquake
simulator test. Based on white noise tests prior to the testing
program, the ﬁrst three periods of vibration of the test frame inthe longitudinal direction (see Fig. 5b) were 2.13 s, 0.80 s and0.53 s. The ﬁrst three damping ratios in the same loading direction
were 2.6%, 3.4% and 4.7%. Detailed information regarding the test
setup and specimen can be found in [18].
3.1. Testing program

Fig. 3. Welded Unreinforced Flange (WUF) connection. Simulated versus experimental hysteretic response of a WUF connection (experimental data from Ricles
et al. [13]).

The test specimen shown in Fig. 5 was subjected to a sequenceof ordinary and long period long duration ground motions that represented design Levels 2–3 in Japanese seismic design including

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Fig. 4. Effect of cumulative damage on component hysteretic behavior of steel beams.

HSS400x400x25

1500mm
1500mm
1500mm(a) benchmark high-rise steel buildingon the E-Defense shaking table

H500x200x9x16

H400x200x8x13

3800mm

H600x200x9x19

H400x200x8x13

3800mm

H600x200x9x19

H400x200x8x13

3800mm

H600x200x9x19

H400x200x8x13

6000mm

6000mm

4500mm(b) numerical model in thelongitudinal direction

Fig. 5. Benchmark high-rise steel building and analytical model in the longitudinal direction.

ElCentro, Hog and three times the San wave. These motions wereapplied to the structure sequentially. The Hog and San seismic
waves are synthesized long period long duration ground motions
that are often used in recent research in Japan on the effects of suchground motions on steel structures [10,18,24]. These two waves
have a predominant period of about three seconds and durationsof 200 and 320 s, respectively. The Hog wave was predicted at
the Kawasaki site near Tokyo (PGA = 145 cm/s2, PGV = 40 cm/s).
The San wave was predicted at a Nagoya site (PGA = 186 cm/s2,

PGV = 51 cm/s). Fig. 6 shows the acceleration and velocity spectrum of both ground motions in comparison with an ordinary
ground motion such as ElCentro. More information about the two
motions can be found in [18,24].
4. Numerical modeling of the test specimen and veriﬁcation
A two dimensional numerical model of the steel MRF in the longitudinal loading direction was built in the OpenSees simulation

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2

1500

Hog
San

Moment [kN-m]

1.5

Sa/g

1000

ElCentro

1

500
0
-500
-1000

0.5

-1500
-0.04
0
0

1

2

3

-0.02

4

(a) Acceleration spectrum

0.04

1500

4

1000

Hog

Moment [kN-m]

San

SV [m/s]

0.02(a) numerical simulation

Period T [sec]ElCentro

30Chord Rotation [rad]

2

500
0
-500
-1000

1

-1500

-0.04

0

0

1

2

3

-0.02

Period T [sec]0.04(b) experimental data

4(b) velocity spectrum

0
0.02
Chord Rotation [rad]Fig. 7. Simulated versus experimental data for steel beam-to-column subassembly(experimental data from [18]).

Fig. 6. Acceleration and velocity spectrum of ElCentro, Hog and San seismic waves.

platform [25]. Beams and columns of the steel MRF are represented
with an elastic element. The nonlinear response of the same components is simulated with two concentrated plasticity springs at
the ends of the elastic elements. These springs follow the hysteretic response of the modiﬁed Ibarra–Krawinkler deterioration
model including fracture due to low cycle fatigue. Available experimental data [10] for steel beam-to-column subassemblies of thespecimen were used to simulate component deterioration andfracture. A comparison between the simulated and experimental
hysteretic response of one of those connections is shown in
Fig. 7a and b, respectively. As seen from Fig. 7, the component
model is able to represent fairly well the hysteretic response of
the steel beam-to-column connection of the test specimen till fracture occurs. The implication of fracture in the numerical model isthat the bending strength of the steel beam drops to zero in theloading direction that fracture occurs.
The ﬂexibility of the panel zone including panel zone shear distortion is simulated with the Krawinkler model as proposed in[47]. However, based on the shaking table test results, no inelastic
behavior was observed in the panel zones. The concrete layers at
the top of the steel structure were represented with ‘‘rigid’’ elements in the analytical model of the test frame. The rubber bearings at each concrete layer were modeled with a parallelogram
model that deforms in shear. Steel dampers between the concrete
layers were modeled with a bilinear model. This model was calibrated with experimental data released from the steel damper

manufacturer. Second order effects (P-Delta) were considered in
the numerical simulation with OpenSees. Rayleigh damping ratios
were assumed to be 2.6% and 4.7% for the ﬁrst and third mode,
respectively. The numerical model of the steel MRF in the longitudinal loading direction was subjected to the same earthquake sequence discussed in Section 3.1. Cumulative damage effects fromphase to phase were also considered.
4.1. Results and discussion
This section discusses the main observations obtained from theseismic response of the test specimen during the sequential groundmotion shaking. These observations are based on a comparison between numerical simulations versus measured experimental dataof the test specimen. The emphasis is on the last phase of the testing sequence (San3) discussed in Section 3.1. During this phase,
fractures due to low cycle fatigue occurred at the ﬂoor beams of
the bottom stories of the steel MRF in the longitudinal direction.
The simulated and measured peak story drift ratio (SDR) proﬁlealong the height of the test frame for the ElCentro wave is shown in
Fig. 8a. From this ﬁgure it is notable that both analytical and measured data are well correlated. During this earthquake record (Level 2 earthquake in Japan) the maximum SDRs did not exceed 1%
radians. This indicates that the structure complies with the Japanese seismic code for Level 2 earthquakes. Fig. 8b illustrates the
SDR proﬁle along the height of the steel MRF during San3 wave
as predicted by analysis with/without fracture. Superimposed isthe measured SDR response during the earthquake simulator test

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20

0.015

16

Floor

14
12

Simulation
Experiment

SDR1 [rad]Simulation
Experiment

18

0

10

0.015
80

8

100

120

2

180

0

0.005

0.01

0.015

0.02

0.025

(a) ElCentro
20

Simul.(With Fracture)
Experiment
Simul.(W/out Fracture)

18
16

SDR2 [rad]0.030

Maximum SDR (rad)Simulation
Experiment

0.015
0-0.015-0.030
80

100

120

140

160

180

Time [sec]

(b)

14
12

Floor

160

(a)

4

0

140

Time [sec]6

Fig. 9. Comparison of simulated versus experimental response of story drift ratios
at ﬁrst and second story of the test frame during San3 (experimental data from[18]).

108
6
4

4.2. Effect of fracture on the remaining seismic capacity of the highrise steel building

2
0

0

0.005

0.01

0.015

0.02

0.025

Maximum SDR (rad)(b) San3
Fig. 8. Maximum story drift ratios along the height of the steel frame inlongitudinal direction for ElCentro and San3 seismic waves.

in the longitudinal direction. From this ﬁgure, the SDR distribution
proﬁle of the San3 long period long duration ground motion
exceeds 2% radians at the bottom stories and migrates to the top
stories. This drift proﬁle along the height of the test frame agrees
with an extensive number of analytical studies on high-rise steel
MRFS as discussed in [8,47,48]. From the same ﬁgure, it is also evident that fracture modeling is critical for accurate representationof dynamic response of the high-rise steel structure at the bottom
stories. During the earthquake simulator test, SDRs are ampliﬁed
due to two beam fractures at the 2nd and 3rd ﬂoor beams. The
fractures occurred on the right side of both beams. The numericalmodel seems to underestimate the peak SDRs in the ﬁrst story of
the test frame. However, after looking carefully at a 100 s time
window of the overall ﬁrst story drift history during San3 wave
(see Fig. 9a), it is indicated that there is satisfactory correlation between simulated and measured story drift history response. The
same observation can be made for the 2nd story drift ratio history,
which is shown in Fig. 9b. From the same ﬁgure, it is also observedthat the overall post-fracture response of the test frame is predicted fairly well with the component model, which proposed inthis paper. The difference of the simulated response of the 2-D
model compared to the experimental data after fractures occur is
attributed to torsional effects that were observed during the shaking table test series after the occurrence of fractures [18]. The torsional effects were not considered in the 2-D modeling of the steel
MRF. Another reason for the observed differences is that thenumerical model discussed in Section 2.1 is not able to simulate
the remaining bending capacity of a steel beam after the occurrence of the ﬁrst fracture.

After completion of the San3 wave two steel beam-to-column
connections of the test specimen in the longitudinal direction are
fractured. Due to safety reasons the shaking table test series
stopped. However, the numerical model discussed in this paper allows for further investigation of the effect of fractured connections
on the seismic capacity of the steel MRF, since the experimental results from the earthquake simulator tests were replicated fairly
well up to San3 wave. The numerical model of the steel MRF in
the longitudinal direction is subjected to a fourth San wave (noted
as San4). Cumulative damage effects from the ElCentro, Hog andSan1 to San3 waves are simulated. Fig. 10 shows the peak story
drift ratios along the height of the high-rise building after zoomingat the ﬁrst 3-stories of interest. For reference, we have superimposed the measured peak SDR proﬁle from San3 wave. From thesame ﬁgure it can be seen that the peak SDR in the 2nd story of
the steel MRF exhibits 3% rad. The ampliﬁcation of the 2nd story
drift ratios during San4 is attributed to sequential fracture of thesteel beam connections in the same story due to moment redistribution. In the same ﬁgure we have superimposed the peak SDR
proﬁle of the same steel MRF when fracture is not simulated in
the numerical model. The seismic response of the steel MRF isclearly underestimated by more than 50% in terms of SDRs. This
indicates that modeling of fracture due to low cycle fatigue is critical in order to estimate the post-fracture seismic capacity of ahigh-rise steel building subjected to long period long duration
ground motions. P-Delta effects at the bottom stories of the steel
MRF are ampliﬁed due to large story drift ratios. P-Delta effects
dominate the seismic response of a high-rise steel building in thehighly inelastic range and typically lead to a collapse mechanismthat involves only the bottom stories of a steel building. This has
also been pointed out by other analytical studies [21,47,48].
5. Numerical model limitations
This section discusses limitations of the proposed phenomenological model that simulates fracture due to low cycle fatigue. After

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10Simul. San4 (With Fracture)
Experiment, San3

8

Simul. San 4 (W/Out Fracture)
Floor

6

3. After connection fractures occur during dynamic loading, story
drift ratios at the bottom stories of a high-rise building amplify
due to sequential fracture that occurs due to moment redistribution of the steel components.
The main limitation of the proposed numerical model that simulates fracture due to low cycle fatigue is that it is not able to simulate the post-fracture remaining bending capacity of a steel
connection after the occurrence of the ﬁrst fracture.

4

2

Acknowledgements
0

0

0.01

0.02

0.03

Maximum SDR (rad)Fig. 10. Maximum story drift ratios along the height of the steel frame during
simulated San4 (Level 3) intensity (experimental data from [18]).

beam-to-column connection fractures occur, the bending strengthof the steel component that fractures drops to zero based on the
numerical model discussed in this paper. However, based on the
post-fracture hysteretic response of a steel component there is aremaining bending capacity due to web and ﬂange resistance thathas not fractured yet (see Fig. 7b). Because of limited experimental
data related to post-fracture performance of WUF connections it is
not possible to quantify the remaining bending capacity of a steel
beam after the occurrence of the ﬁrst fracture. Most of the beamto-columns tests conducted in the past stop due to safety issues
after the occurrence of the ﬁrst fracture during the monotonic or
cyclic response. Another limitation of the proposed model is that
it is not able to accurately simulate the hysteretic response ofbolted steel connections. The primary problem in this case is thatthe hysteretic response of a bolted connection becomes pinched
if a bolt or a number of bolts slip.
6. Conclusions
This paper proposes a numerical model that simulates component deterioration and fracture due to low cycle fatigue of steel
beam-to-column connections. Fracture due to low cycle fatigue isexpressed with respect to the dissipated energy of a steel component when subjected to cyclic loading. The proposed numericalmodel has been implemented in a widely used open source numerical simulation platform. This model is particularly useful for quantiﬁcation of the seismic capacity of high-rise steel buildings
subjected to long period long duration ground motions. Component deterioration and fracture in this case is profound due to large
number of inelastic deformations. The main ﬁndings in this paper
are summarized as follows:
1. The number of cycles to fracture for a steel component withrespect to its dissipated energy during cyclic loading follows
a power law. It was shown that the exponent of this relationship could be kept as a constant. A set of beam-to-column
connections that fail in a ductile manner was utilized for thispurpose.
2. After validation of the proposed numerical model with landmark experimental data from a recently conducted full scale
shaking table test of a high-rise steel building at the world’s
largest earthquake simulator at E-Defense, it was shown thatconnection fractures due to cumulative damage amplify maximum story drift ratios at lower stories of high rise buildings.
Post-fracture response is signiﬁcantly underestimated if deterioration and connection fractures are not simulated in the nonlinear dynamic analysis.

This study was based on work supported by a post-doctoral research fellowship from the Japan Society for the Promotion of Science (award number P09291) awarded to the ﬁrst author. The
ﬁnancial support is gratefully acknowledged. Any opinions, ﬁndings, and conclusions or recommendations expressed in this paper
are those of the authors and do not necessarily reﬂect the views of
the sponsors.

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