Numerical Evaluation of Fracture in High-Rise Buildings Subjected toLong Duration Earthquakes
Hashini HERATH
Candidate for the Degree of Master of Engineering
Supervisor: Professor Dr. Taichiro Okazaki
Division of Architectural and Structural DesignIntroduction
Subduction zone earthquakes can generate long period, long
duration ground motions that can resonate high-rise buildings.
There is a serious concern that such load effect can cause alarge number of load reversals that lead to fatigue fracture ofsteel moment connections [1]. This paper presents a numerical
study to simulate the response of a typical steel high-risebuilding including fracture at the connections. Focus is placedon the sensitivity of the analysis results on key materialvariables.

The test frame was subjected to increasing magnitudes ofground motions from Level 2 to 3 in Japanese seismic design.
The ground motions included El Centro (1940, amplified toPGV of 0.5m/s), Higashi Ogijima (or HOG, a synthesized
Tokai earthquake) and Sannomaru (or SAN, a synthesized
Tokai-Tonankai earthquake) repeated three times. During thefirst SAN, three connections in the east frame and one
connection in the west frame fractured. After two more SAN
repetitions only in the longitudinal direction, two connectionsin the north frame fractured.

Fracture model
E-Defense test
Two of the most typical moment connections in early highrise buildings in the 1970s, the field welded, welded flangebolted web connection and the shop welded, welded flangewelded web connection were featured in an E-Defense shake
table test conducted in 2008 [1]. The specimen, which
represented a prototype high-rise building of 21 stories,
consisted of a four-story, two span-by-one bay steel moment
frame underneath three substitute layers, each comprising acondensated mass, rubber bearings, and a damper as depicted
in Fig. 1.
Substitute layers

The numerical study used OpenSees, a general-purpose
structural analysis framework [2]. OpenSees provides afatigue material model that assumes a linear damage
accumulation in terms of plastic strain and reduces thestrength of a fiber to zero when the limit based on CoffinManson relationship and Miner’s rule is exceeded [3]. Fatigue
parameters were calibrated based on constant amplitude, lowcycle fatigue tests on beam-to-column connections [4] that
adopted details similar to that used in the E-Defense testframe. Fig. 2 shows the 2D model of the specimen and how
closely it reproduced the strength degradation observed in thetest. The columns were represented by elastic beam-columnelements. The beam was represented by a beam-with-hinges
element with a designated plastic hinge segment taken as 1/6of the element length and 3 integration points along the length.
500

Numerical
Experimental 400

3800

Rotation (rad)1/200 1/100

Qp

300

3800

Q (kN)

2003800

100-804500-60-400-20-100 020

6000

②6000

③ⒶⒷN

406080-200-300

①

1/50

8000

Ⓑ(Unit: mm)

Qp-400Integration points-500

Q,δbδb (mm)Plastic hinge
lengthⒶ
Figure 1. Test frame configuration

Figure 2. Model for beam-column sub-assemblage

The cross-section was discretized into finer fibers (128) in thehinge region than in the rest of the element (40). Cyclicmaterial property was represented by a Menegotto-Pinto
model with combined kinematic and isotropic strainhardening. The parameters were calibrated to result in the best
fit to four test results from identical specimens subjected todifferent loading amplitudes.

Frame model

the phase to phase damage accumulation. The computed
vibration modes of the first through third vibration periods ineach direction (2.21, 0.84, and 0.56 s in transverse and 2.19,0.84, and 0.56 s in longitudinal frame) were within 4% of thereported values.
Fig. 4 shows the computed and observed storey drifts of thethird and fourth story of the transverse frame along withoccurrences of connection fractures during the first SANexcitation. The agreement between the simulated andmeasured story drift responses was satisfactory. Until
multiple connections fractured at about 100s, the vibration

Beam End Moment (kNm)

Drift (rad)Drift (rad)The longitudinal and transverse frames of the ERigid Element
Defense test were represented by 2D OpenSees
1500
1500
Two-node
models individually. Fig. 3 shows the numerical
1500
1500
link element
model of the longitudinal and transverse frames.
1500
1500
Each column was represented by a3800
3800
displacement-based beam-column element withfiber sections at five integration points.
4141
42
42
Contribution of the concrete floor slabs was
Rigid link
3800
3800
included by forming the beam cross-section as afully composite concrete section above the steel
31313232
3800
beam section. The castellated beam sections of3800
the transverse frame were expressed by sections
2121
2222
with a reduced web thickness. Each beam was
4500
4500
represented by a beam with hinges element withfiber sections at six integration points and
8000
8000
4000
6000
6000
designated plastic hinge segments at the ends.
(b)(a)
Properties of steel was modelled by a
Figure 3. Frame models: (a) Transverse; and (b) Longitudinal (units in mm)
Menegotto-Pinto model with combined
kinematic and isotropic strain
0.03
31 32 31
hardening, while concrete wasExperimental
0.02
Numerical
modelled
byConcrete01
0.01
material with zero tensile
0strength. The fatigue model
50
100
150-0.01
described
above
was-0.02
implemented in the steel section
41414242(a)-0.03
of the beams. Panel zones wereTime (s)31assumed to remain elastic as32
32
310.014141 42reported from the tests.
Condensed concrete mass
21222221layers were modelled with rigid
050
100
150
elements.
The column bases wereModel
Test(b)modelled as fixed. Floor mass
-0.01
Time (s)was lumped at the joints inproportion to the tributary floor
Figure 4. Response of transverse frame: (a) 3rd-story response; (b) 4th-story responsearea. The combined action ofsteel dampers and rubber
1500
1500
Mp - SteelMp - Steelbearings were simulated with
1000
1000
two node-link elements with
500
500
equivalent shear springs andrigid axial springs. Rayleigh00
damping was assumed with a-0.02
-0.01
00.01
0.02 -0.02
-0.01
00.01
0.02
-500
-500
critical damping ratio of 3.5%
for the computed first and third
-1000
-1000
vibration periods.
-1500
Mp - Steel -1500
Mp - SteelThe numerical models were
(a)
(b)
-2000
-2000
subjected
tothesame
Beam Rotation (rad)earthquake sequences as theFigure 5. Moment-rotation behavior of connection 31: (a) Numerical response; (b) Experimental
shake table test to account forresponselog(Nf)
0.5

11.5

2

2.5

-1.4

Fatigue - I
Fatigue - II

-1.6
-1.8

log(Δεi)

period matched very well. The timing of fracture was close
but not same. (Although not discussed here, connection
fractures started much earlier than in the test in thelongitudinal frame). In the model, fracture progressed more
rapidly and spread more widely, leading to greater elongationof vibration period than the observed. Fig. 5 comparescomputed versus experimental hysteresis of beam 31, whichfractured during the first SAN excitation. The computation
reproduced the gradual strength degradation caused by crack
initiation and propagation, but the degradation was more rapid
than the observed, and the strength in negative bending wassmaller. Both test and model responses suggest the beams
were unable to develop their plastic strength.

ε0-2-2.2-2.4-2.6

Figure 6. Distribution of fatigue parameters

Response sensitivity analysis
Monte Carlo simulations were conducted to examine how thesimulation is affected by variability in key properties. In thisresearch, two sources of uncertainty were selected: (1) thefatigue parameters and (2) column-to-beam yield stress ratio.
MATLAB, together with OpenSees, was used to conduct
these simulations.
Fatigue parameters
Strain amplitude parameter ε0 of the Coffin-Mansonrelationship is taken as a random variable with a Gaussian
distribution. Fatigue-I stands for a distribution with smaller
coefficient of variation that represents the variability observedin the four experimental data points. Fatigue-II tripled thecoefficient of variation of Fatigue-I. Fig. 6 shows the twodifferent distributions, controlled by the coefficient ofvariation for the strain amplitude parameter ε0. A hundredtrials were generated where in each trial, the six connectionsof interest are provided with a different ε0 value.
Column to beam yield stress ratio (CBYR)

Figure 7. Distribution of CBYR

The simulated response was hardly affected by the fatigue
parameter. Interestingly, nearly all connections at the 3rd and4th floors of both frames fractures for each set of simulation.
For Fatigue-I & CBYR, the occurrence of fracture in thelongitudinal frame was similar to that obtained from thedeterministic approach.

Fracture probability

Fracture probability

The variability in yield strength of the columns and beams
was addressed by a single parameter, the ratio of yield
21 Storey model
strength of the columns over that of the beams. The E-Defense
specimen used SM490A steel for all beams and columns. Fig.
The same analysis technique was extended to the prototype
7 shows the distribution of column-to-beam yield stress ratio
21-storey building. The two parallel frames were included incomputed based on statistical data of SM490A steel.
Five hundred trials were
Fatigue - I
Fatigue - II
CBYR
generated with two independent
11
sources of variability, parameter ε0of the Coffin-Manson relationship0.80.8according to Fatigue-I and column
to beam yield strength ratio
0.60.6(CBSR). All columns were0.40.4
provided with a fixed yield strength
value. The yield strength of the0.20.2
beams was given as the product of
the yield strength of the columns
0012345123
45
6426
41
2232
2142
31
21223132
41
and the CBSR for that trial.
Connections
The trial results are presented inConnections(a)(b)
Fig. 8 in terms of fractureprobability of the six connections inFigure 8. Fracture probability of connections: (a) Transverse frame; (b) Longitudinal frametransverse and longitudinal frames.

HOG

during SAN. Fig. 10 compares the maximum storey drifts
obtained from the prototype model and E-Defense model. EDefense frame model modeled storey shear adequately but
was unable to produce the overturning moment. Naturally, thesubstitute layers could not capture connection fractures at theupper floors, and consequently predicted smaller drift at theupper floors.

SANConclusions
A numerical model using OpenSees was developed tosimulate the fracture and strength deterioration of steel
components due to low cycle fatigue. The model reproduced
the experimental behaviour of an E-Defense test specimen
adequately. Response sensitivity of the model to the variationof fatigue parameters and column- to- beam yield stress ratio
was tested and was found to be minimal. Extending thesimulation to the prototype 21 storey building brought out thediscrepancies resulted from the contraction process. The twodimensional modelling approach, which represents fracture
progression only along the flange thickness but not along theflange width of steel beams, resulted in a drastic strength
deterioration in the steel beam once the fracture initiated.
Once a connection fractured at one end of a beam, the otherend tended to fracture immediately, thus leading to rapid
progression of fractures over the frame.

Figure 9. Damage distribution of 21 storey model

the analysis. The beams were modelled using the sameelement and same discretization as in the E-Defense model.
The columns were modelled as displacement-based beamcolumn elements with five integration points for the first fivestoreys and by single elastic beam-column elements for therest of the stories. The same fatigue material model used inthe longitudinal frame of the E-Defense frame wasimplemented in the steel beams. Panel zones were assumed toremain elastic. The model was subjected to the same El
Centro, HOG and SAN motions.
The computed vibration modes of the first and second
vibration periods 2.32 and 0.83 s were within 6% and 1%,
respectively, of the values for the E-Defense frame model.
None of the connections fractured during El Centro. Fig.9illustrates the damage distribution from HOG and SAN.
Contrary to the E-Defense model, several connections in theprototype model fractured during HOG. Connection fracture
spread widely during SAN. Much of the damage wasconcentrated in the first 10 floors. Much of the damage to theupper floors were from HOG and very few of them fractured
2020

Prototype

Prototypemodel

model

E-Defense

E-Defense

1510model

Storeymodel

StoreyStorey15

References

1055(a)(b)00
00.0250.05

00.0250.05

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performance of beam-to-column moment frame
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Eng., AIJ, No. 685, 569-578, Mar., 2013.
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[3.] Uriz, P., Towards Earthquake Resistant Design ofConcentrically Braced Steel
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Engineering,
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10[4.]
Hasegawa, T. etal.: Study on seismic
performancefor superhigh-rise steel buildings
5against
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earthquake ground motions,
BRI Research Data No.161,(c)
Building Research Institute,
0Jul., 2014.
00.025Figure 10. Damage distribution of 21 storey model during: (a) ElCentro; (b) HOG; (c) SAN

0.05