Download Evaluation of Expected Annual Loss Probabilities of RC

World Academy of Science, Engineering and Technology
International Journal of Civil, Environmental, Structural, Construction and Architectural Engineering Vol:9, No:2, 2015
Evaluation of Expected Annual Loss Probabilities of
RC Moment Resisting Frames
Saemee Jun, Dong-Hyeon Shin, Tae-Sang Ahn, Hyung-Joon Kim

II. DESCRIPTION OF PROTOTYPE BUILDING
International Science Index, Civil and Environmental Engineering Vol:9, No:2, 2015 waset.org/Publication/10000491
Abstract—Building loss estimation methodologies which have
been advanced considerably in recent decades are usually used to
estimate socio and economic impacts resulting from seismic structural
damage. In accordance with these methods, this paper presents the
evaluation of an annual loss probability of a reinforced concrete
moment resisting frame designed according to Korean Building Code.
The annual loss probability is defined by (1) a fragility curve obtained
from a capacity spectrum method which is similar to a method adopted
from HAZUS, and (2) a seismic hazard curve derived from annual
frequencies of exceedance per peak ground acceleration. Seismic
fragilities are computed to calculate the annual loss probability of a
certain structure using functions depending on structural capacity,
seismic demand, structural response and the probability of exceeding
damage state thresholds. This study carried out a nonlinear static
analysis to obtain the capacity of a RC moment resisting frame
selected as a prototype building. The analysis results show that the
probability of being extensive structural damage in the prototype
building is expected to 0.01% in a year.
Keywords—Expected annual loss, Loss estimation, RC structure,
Fragility analysis.
S
I. INTRODUCTION
EISMIC fragility studies of building structures have been
increasingly carried out to estimate the earthquake losses
resulting from their structural damage. The seismic loss
estimation requires to identify the seismic vulnerability of a
building structure and to describe resulting structural
performance quantitatively.
There are numerous low-rise reinforced concrete (RC)
buildings in Korea. Such low-rise RC buildings could be
vulnerable to horizontal ground accelerations and suffered
serious structural damages, which causes significant
national-wide seismic losses. This paper has evaluated a
probability of expected annual loss for low-rise RC moment
resisting framed building. The annual seismic loss probability
is calculated by the fragility curve of a building and seismic
hazard in a certain area.
A. Design of Example Building and Analytical Model
A prototype structure, a 5-story reinforced concrete framed
building shown in Fig. 1 is chosen to expect the annual loss
probability of typical RC intermediate moment-resisting frames
(IMRF). The plan of prototype building consists of three 10 m
bays and the height of each story is 3.6 m. The building is
seismically designed according to a current Korean building
code, KBC 2009 [1]. For gravity loads, uniform dead loads of 5
kPa and live loads of 4 kPa are applied to each floor. It is
assumed that the building is located in Seoul, Korea of which
the site class is assigned to SD. The design spectral response
acceleration parameters at short period, SDS and at 1s period, SD1
are, respectively, 0.50, and 0.29. The response amplification
factor, R of the prototype RC IMRF is 5.0. It is found from a
preliminary eigenvalue analysis that the first mode period of the
building, T1 is 1.29 second. Using these values, the design base
shear, Vd is calculated as 500.6 kN that is vertically distributed
according to a rule prescribed in KBC 2009 [1] which is similar
to the American seismic design code, ASCE 7 [2]. Table I
summarises structural dimensions and reinforcement
arrangement of column and beam members of which the
locations are shown in Fig. 1. The compressive strength of
concrete is 28 MPa and the yield strength of a steel rebar is 400
MPa.
The prototype two-dimension (2D) RC IMRF is modeled
using a non-linear analysis simulation software, Ruaumoko 2D
[3]. The strength and stiffness degradation according to the
corresponding ductility are adopted using a modified Takeda
hysteresis rule. Reinforced concrete beam-column joints are
modeled according to a hysteretic rule suggested by [4] which
has been long known to properly capture the shear behavior of
RC beam-column joints.
Saemee Jun and Dong-Hyeon Shin are Graduate students with the
Department of Architectural Engineering, University of Seoul, Seoul, Korea.
Tae-Sang Ahn, Director, is with the Research Lab, DRB Dongil, Seoul,
Korea.
Hyung-Joon Kim, Associate Professor, is with the Department of
Architectural Engineering, University of Seoul, Seoul, Korea (corresponding
author to provide phone: +82-2-6490-2763; fax: +82-2-6490-2749; e-mail:
[email protected]).
International Scholarly and Scientific Research & Innovation 9(2) 2015
Fig. 1 Elevation of the prototype building
132
scholar.waset.org/1999.3/10000491
World Academy of Science, Engineering and Technology
International Journal of Civil, Environmental, Structural, Construction and Architectural Engineering Vol:9, No:2, 2015
T
TABLE
I
STRUCTURAL MEMBER SIZING A
AND REINFORCEM
MENT ARRANGEM
MENTS
Member
C
C1
(inteerior)
C
Columns
C
C3
(exteerior)
International Science Index, Civil and Environmental Engineering Vol:9, No:2, 2015 waset.org/Publication/10000491
Beams
G
G1
(inteerior)
G
G6
(exteerior)
Story
4-5
2-3
1
4-5
2-3
1
4-R
2-3
4-R
2-3
Section
5550x550
6
600x600
7
700x700
5
500x500
5
550x550
5
550x550
4
400x700
4
400x800
4
400x700
4
400x800
R
Rebar
6-2
2-D25
8-3
3-D25
10--4-D25
6-2
2-D25
6-3
3-D25
6-3
3-D25
6-D222, 3-D22
7-D222, 3-D22
6-D222, 3-D22
7-D222, 3-D22
Stiirrup
2-D10@400
2-D10@400
2-D10@400
2-D10@210
2-D10@240
2-D10@400
2-D10@300
2-D10@350
2-D10@300
2-D10@350
B. Seismic Hazard
Ha
in Seouul, Korea
The prototyppe building sitee, Seoul is a seeismologicallyy low or
m
moderate
seism
micity zone. The probabilistic seismic hazard
annalysis uses thhe uniform hazzard spectra deeveloped by Ministry
M
off Constructionn and Transportation in Korrea [5]. The sccenarios
haave 50, 100, 200, 500, 10000, 2400, annd 4800 yearss return
peeriods. The seiismic hazard iin Seoul is shoown in Fig. 2, derived
froom mean annuual frequencyy of exceedancce which is evvaluated
byy ground motiion intensity.
F 2 Hazard cuurve in Seoul, Korea
Fig.
K
III. EVA
ALUATION OF ANNUAL LOSS
S PROBABILITY
Y
A. Results off Fragility Anaalysis with CSM
M
ZUS [6]
The fragility analysis methhodology sugggested by HAZ
haas been widelly accepted tto investigate the vulnerabbility of
exxisting buildinngs. In this sttudy, a fragiliity curve is obtained
o
froom the capaciity spectrum method
m
(CSM)) based on thee results
off nonlinear staatic analysis, which
w
followss the methodoology of
H
HAZUS.
The capacity
c
specttrum for the prototype
p
buillding is
prresented in Fig.
F
3. Using the yield caapacity (Dy, Ay) and
ulltimate capacity (Du, Au) obtained from
m a nonlineaar static
annalysis of the prototype buiilding, the cap
pacity spectrum
m is, as
shhown in Fig. 3, idealized and
a is presented in the figuure as a
daashed line paassing throughh the yield an
nd ultimate capacity
c
pooints. The yielld capacity is defined
d
as thee onset where the
t first
nooticeable stifffness reductioon is observedd. After the ultimate
u
caapacity repressenting the maaximum strenngth of the prrototype
buuilding, it is assumed thatt the global structural systtem has
reeached a fully plastic state without
w
strenggth degradatio
on. This
asssumption siggnificantly deecreases the computation
c
t
time
in
finnding a perforrmance point for a given seeismic hazard level.
The fragilityy curve desccribes probabbilities of excceeding
peerformance crriteria, so-callled damage state,
s
ds, at different
d
levels of seism
mic input intennsity, and exprresses in a forrm of a
loog-normal cum
mulative distribbution functioon.
The conditionnal probabilityy of being in or
o exceeding ds
d given
sppectral displaccement, , is defined from::
P ds|
Ф
,
,
International Scholarly and Scientific Research & Innovation 9(2) 2015
(1)
(2)
Fig. 3 Capacity
C
spectruum of the protottype building
mulative distriibution
whhere Ф is thee standard loognormal cum
funnction, , is the median vvalue of att the thresholdd of ds,
is the log-sttandard deviattion of for ds. Specificallly, the
vaalue of
is evaluated
e
usinng a SRSS metthod of uncerttainties
consisting of thee variability off
in the dam
mage state thrreshold,
thee uncertaintyy of
in tthe structurall capacity annd the
unncertainty of
in seismic ddemand. The term
,
in (2) represents the combinned uncertainnty of capaciity and
s
Thiss uncertainty is obtained thrrough a
demand of the structure.
y intersection points,
convolution proocess, which iss produced by
mance points,, of the capaacity spectrum
m and
naamely perform
demand spectrum [7]. In this paper, the perrformance poiints are
obbtained by the intersection ppoints of the saampled capacity and
demand spectraa in tandem with a Montte Carlo simuulation
(M
MCS) based onn a Latin hypeercube samplin
ng (LHS).
The threshoolds of dam
mage states (Slight, Mooderate,
Exxtensive, and Complete)
C
as indicated in NEMA
N
report [8] are
callibrated by damage
d
state criteria (Opeerational, Imm
mediate
Occcupancy, Liffe Safety, andd Collapse Prevention) in FEMA
F
356 [9]. The dam
mage state thrresholds of a RC
R moment reesisting
marized in T
Table II. Thee probability of the
fraame are summ
133
scholar.waset.org/1999.3/10000491
World Academy of Science, Engineering and Technology
International Journal of Civil, Environmental, Structural, Construction and Architectural Engineering Vol:9, No:2, 2015
strructural respo
onses exceedin
ng damage state threshold is used
to
o estimate the term of
,
nd the result of
in
, an
Taable II is calcculated by SR
RSS of the teerm and the value
v
of
(=0.4). The results
r
of the fragility analy
ysis for the prrototype
RC moment fraame are shownn in Fig. 4.
International Science Index, Civil and Environmental Engineering Vol:9, No:2, 2015 waset.org/Publication/10000491
B. Expected Annual
A
Loss Probability
P
The ground motion inteensity in a certain
c
area can be
uantitatively expressed aas mean an
nnual frequen
ncy of
qu
ex
xceedance wh
hich is descrribed in the hazard curv
ve. The
prrobability of expected ann
nual loss is estimated usiing the
haazard curve, λ
and thhe fragility cu
urve of the building
b
m
modeled
by a lo
ognormal prob
bability density function, f |
w
which
is defineed on [10]:
(3)
|
P loss
Fig. 4 Resultts of fragility annalysis for the prototype
p
buildiing
The standard
d elastic accelleration response spectrum can be
co
onverted to an Accelleration-Displacement Reesponse
Sp
pectrum (AD
DRS) format [11]. The ex
xpected annu
ual loss
prrobability for the
t RC momeent framed buiilding is given
n in Fig.
5 and Table III.. As shown in the table, the expected annu
ual loss
e
eacch damage staate is less than
n 0.1%.
prrobability of exceeding
Th
he expected annual
a
probab
bility of exceeeding the ex
xtensive
daamage state iss 0.01%. Tablle III also lists the probabillities of
lo
oss in 40 yearss that is assum
med as the liffe duration off typical
RC buildings. The expecteed probability
y of exceediing the
Ex
xtensive damaage state is 0.3
33% in 40 yeaars.
IV. CONCLUSION
This paper describes the seeismic hazard
d in Seoul, Ko
orea and
ev
valuates the probability
p
of expected ann
nual loss for low-rise
reeinforced conccrete momentt framed builldings. The fragility
f
cu
urve is obtaineed from the C
Capacity Spectrum Method (CSM)
th
hrough the resu
ults of nonlineear static anallysis, and therreby the
an
nnual loss prob
bability is deriived from the fragility analy
ysis and
th
he hazard curv
ve.
From the ev
valuation, thee probability of being Ex
xtensive
strructural damaage (i.e. Lifee Safety levell in FEMA 356)
3
of
prrototype build
ding is expecteed to 0.01% in
n a year and 0..33% in
40
0 years. This study consid
ders only seissmic losses reesulting
fro
om damage in
n structural m
members. It iss noted that th
he most
ex
xtent of seism
mic risk on the building
g is caused by the
peerformance of nonstructurral componen
nts (e.g. mech
hanical,
ellectrical, plum
mbing, and arcchitectural com
mponents) [12
2]. Due
to
o lack of know
wledge and praactice on the seismic perfo
ormance
off nonstructuraal componentts, this study
y does not properly
p
ev
valuate seismiic losses caused from nonsstructural and facility
daamage. Thereefore, in-depth
h researches and experimeents on
no
onstructural an
nd facility seiismic damagee will be requiired for
acccurate assessm
ment of the seeismic risk.
TABLE II
MEDIAN AND LOG-STANDARD DEVIATION OF PROTOTYPE
R
BUILD
DING
FRAGIILITY CURVE
,
, mm
S
Slight
Mooderate
Exttensive
Com
mplete
57.3
0.48
991.6
0
0.53
183.3
0
0.64
3666.5
0
0.69
International Scholarly and Scientific Research & Innovation 9(2) 2015
Fig. 5 Estimation of annual loss prrobability
TA
ABLE III
EXPECTED
D ANNUAL LOSS PROBABILITIES OF
O EXCEEDANCE
FOR PROTO
OTYPE BUILDING
L
Loss
probability, %
Slight
Moderate
Extensive
Com
mplete
In a year
In 40 years
0.08
3.13
0.03
1.18
0.01
0.33
0.002
0
0.08
ACKNOW
WLEDGMENT
This research
h was supporrted by a gran
nt ‘Developm
ment of
So
ocio-economicc
Seismic
Loss
Prrediction
Models’
M
[N
NEMA-NH-20
012-67] from the Natural Hazard Mitigation
Reesearch Group
p, National Em
mergency Man
nagement Ageency of
Koorea.
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[1]
[2]
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134
AIK, Korean Building
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oul: Architectural Institute
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A
Societyy of Civil
Engineers, 201
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A. J. Carr, Ruaumoko
R
Manuaal. User Manual for the 2-Dim
mensional
Version: Ruauumoko2D Vol. 2.. Christchurch: University
U
of Cannterbury,
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scholar.waset.org/1999.3/10000491
World Academy of Science, Engineering and Technology
International Journal of Civil, Environmental, Structural, Construction and Architectural Engineering Vol:9, No:2, 2015
International Science Index, Civil and Environmental Engineering Vol:9, No:2, 2015 waset.org/Publication/10000491
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International Scholarly and Scientific Research & Innovation 9(2) 2015
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