NONLINEAR RESPONSE ANALYSIS AND DAMAGEEVALUATION OF A CITY OFFICE IN KORIYAMACITY
Pinar INCI KOCAK*MEE12616

Supervisor: Toshikazu KABEYASAWA**ABSTRACT
The focus of this research is a nonlinear response analysis of how a city office in Koriyama city wasaffected by The Great East Japan Earthquake, 2011. Nonlinear pushover and dynamic analysis areperformed in two different analytical models, designated first and second. The first structural model
only takes into consideration column flexural capacity without regards to deterioration in post-peak
behavior, and the second structural model takes account of shear capacity with regards to post-peak
behavior. Using these analyses, a damage evaluation is conducted and compared to the postearthquake damage report prepared by a research team from the Building Research Institute (BRI) andNational Institute for Land and Infrastructure Management (NILIM). Through the use of thesecomparison results, analytical models commonly used in literature are judged in terms of theiradequacy in representing the dynamic response of structures. In addition, there is a critical assessmentof the seismic evaluation process used in the Standard for Seismic Evaluation of Existing Reinforced
Concrete Buildings, 2001.
Keywords: Flexural, Shear, Post-peak, Seismic, Nonlinear response
1. INTRODUCTIONOn March 11, 2011, the Great East Japan Earthquake (Mw 9.0) hit the north-east of Japan at 14:46
JST (5:46GMT). The earthquake was a massive tsunami caused by the seismic shock, which resulted
in the death of more than ten thousand people and a huge number of buildings being completely or
partially destroyed or washed-away.
In order to learn from this terrible disaster and contribute to the improvement of disastermitigation measures against earthquakes and tsunami, both the National Institute for Land andInfrastructure Management (NILIM) and the Building Research Institute (BRI) sent research teams tothe affected areas and carried out a comprehensive survey on a variety of building types (BRI researchpaper, 2011). One of these buildings, a city office in Koriyama city damaged by ground motion wasexamined and a detailed damage report prepared. In this study, a nonlinear response analysis anddamage evaluation of a city office in Koriyama city has been performed, taking into consideration thedamage report on the structure.

2. DESCRIPTION OF A CITY OFFICE IN KORIYAMA CITY
A city office in Koriyama city, Fukushima, Japan, a three-storey building, was constructed in 1970
with an RC frame-wall system (Figure 1).
* Istanbul Technical University, Structural and Earthquake Engineering Laboratory, Istanbul, Turkey**National Institute for Land and Infrastructure Management, Tsukuba, Japan1

The column application can be seen in Figure 2. As seen inFigure 1, the building extends two spans transversally (ydirection) and nine spans longitudinally (x direction). RCwalls are located transversally. All columns have a 50x50cm
cross-section with different number of longitudinal rebar.
Concrete compressive strength was determined as 18.73,
12.60 and 11.19 for the first, second and third storey,
respectively and yield strength of plain reinforcing bar is294 MPa.

Figure 1. General view of a city
office in Koriyama city
5000

5500

5500

5500

5500

5500

5500

5000

C3

C3

C3

C1a

C1a

C1a

C1a

C3

C3

C2

C2

C2

C2

C2a

C2a

C2aC2C2C1C1C1C1aC1aC1aC1aC1C15000

C

7000

BA
98765432Figure 2. Column application plan of the structure (units in mm)

1The strong motion data
accumulated by FKS018
station located in Koriyama,
Fukushima Prefecture, is used
for nonlinear analysis of a city
office in Koriyama locatedabout 1.2km from the K-Net
Station recorded maximum
acceleration as 746.1cm/s/s,1069.3cm/s/s and 457.4cm/s/s
in N-S, E-W and U-D
directions, respectively.
The Joint Survey
Team investigated the city
office in accordance with thedamage criteria determined.
Medium and heavy damage
was found to the first storey
columns as results of theexistence of spandrel wall top
and bottom of the beams(Figure 3).

Figure 3. Shear failure of the first storey columns

3. ANALYTICAL STUDY
Actual structure is modeled for the members with or without consideration of strength deterioration(the first and second structural model, respectively) and nonlinear pushover and dynamic analysis areperformed using the CANNY structural analysis software. Performance levels of the structuralmembers are judged according to the Japanese Seismic Evaluation Standard for Existing RC Buildings.
In order to determine the member models, such well-known methods are performed in nonlinear
analysis and their applicability are tested, taking into account the comparison of the performance levelof members determined in analytical study and actual damage report.
3.1. Modeling of Structural Members
Rigid Zone

Linear-Elastic Rotational
SpringA modified version of a one-component element (Giberson,1967) is used to represent the beams whose force-deformation
relationship is linear elastic (Figure 4). One-component
Perfectly Elastic Massless Element
model is also proposed for the column members to represent Figure 4. Member model for beams

2force-deformation relationship of columns with or without consideration of strength deterioration inthe first and second structural model, respectively. Axial deformation is considered in two models. An
important point is that nonlinear rotational spring governed by shear deterioration is introduced insteadof a rotational spring or shear spring assigned serially in the second structural model (Figure 5).

Nonlinear
Axial Spring

Rigid Zone

Nonlinear
Rotational Spring

ForceMoment

FyMyorMu

f-modeCompression

Mcs-mode

Disp

Perfectly Elastic
Massless ElementRu

RotTension

Figure 5. Member model for columns and force-deformation relationships
In the first structural model, cracking
moment Mc and yield moment My is calculated
by using Eqs. (1) and (2). In the second
structural model, the ultimate shear strength ofthe columns are determined as the smaller valueof the ultimate shear force (Vu) andcorresponding shear force (Vy) of the yielding
moment (My). Then, the post-peak behavior of
the columns is determined as s-mode (shearfailure) columns or f-mode (flexural failure)columns according to the ultimate shear strength
capacity. For s-mode columns, ultimate shear Figure 6. Hysteresis curves of s-mode columns
force (Vy) is assigned (Eqs (3) and (4)). Skeleton
curves of the nonlinear springs can be seen in Figure 5. After determination of column failure mode as
s-mode or f-mode, to detect the stiffness properties of the rotational spring, the formulas introduced byYoshimura (2005) are used for s-mode columns Eq. (5) and f-mode columns Eq. (6). Hysteresis
curves of the s-mode columns can be seen in Figure 6. The axial nonlinear deformation relationship isdefined by using Eqs. (7) and (8) for both structural models.
Three vertical line element model (TVLEM) determined in Kabeyasawa et al., is assigned
for the transverse walls of the structure which has linear-elastic stiffness characteristics.
(1)
(2)
(3)
(4)
(5)
(6.a)
(6.b)
(7)
(8)

3

where σB is concrete compressive strength, Ze is section modulus, N is the axial force of the column,
D is the cross-sectional height of the column and Fc is the concrete compressive strength (like σB). pws
is the transverse bar ratio, σ0 is average axial stress over the entire wall cross-sectional area and j is ageometrical parameter. Ru is the collapse drift, ds is the displacement at the collapse for s-modecolumns, l is the column height, pw is the transverse reinforcement ratio (%), qs is the longitudinal
reinforcement ratio (%) and du is the displacement value for collapse for f-mode columns. Fy, Fy’ isthe axial force in compression and in tension, respectively, and As the total cross-sectional area of
longitudinal reinforcement.
3.2. Structural analysis
0.6

Story shear coefficient

The storey shear coefficient - storey drift ratio
relationships obtained by the nonlinear pushover anddynamic analyses for both the first and second
0.4
structural models are shown in Figure 7 and 8. As
distinct from actual structural damage in Figure 8, theresponse of the second storey seems greater than that
1st story of the 1st st.
0.2of the first in the second structural model. The
2nd story of the 1st st.
seismic performances of the structural models follow
3rd story of the 1st st.
1st story of the 2nd st.
the performance criteria laid out by the Standard for2nd story of the 2nd st.
Seismic Evaluation of Existing RC Buildings. The000.005
0.01
demand spectrum of the Great East Japan Earthquake
Story drift (rad)(Sa-Sd) is obtained through ViewWave software. The Figure 7. Storey shear coefficient - storey
displacement demand (D1) is determined and the drift ratio relationships of nonlinear pushovercorresponding displacement demand (D2) of the analysis
equivalent damping (he) of the building is obtained
where the capacity diagram and demand spectrum intersect (Figure 9). Corresponding demand points

1st story
2nd story
3rd story

0.40.20-0.03

-0.02

-0.01

0-0.2

0.01

Story shear coefficient

Flexural Shearmember member
0.95
0.95
0.75
0.6
0.5
0.3
0.1
000

Story shear coefficient

DamagelevelIIIIIIIVV

0.6

0.6

Table 1. Deterioration
factor-0.03

1st story
2nd story
3rd story

0.4
0.2
0-0.02

-0.01

00.01

-0.2

-0.4

-0.4

-0.6
Story drift (rad)-0.6
Story drift (rad)b)of the 1st storey columns a)
shear coefficient - storey drift ratio relationship a) 1staredetermined.
The Figure 8. Storeynd
deterioration factor (η) is st. model, b) 2 st. model
the ratio of residual
dissipation capacity (Er) to total dissipated energy capacity (Ed+Er) is calculated (Figure 10). The
deterioration factor (η= Er/( Ed+Er)) of columns is given in Table 1, which shows the damage levelfrom I to V as determined by analytical calculation. The damage rank of the first storey columns isgiven in the storey plan (Figure 11). In Figure 11, the first, second, third and the fourth damage rank ofa column represent the damage level determined by static and dynamic analysis of the first structuralmodel and static analysis of the second structural model and onsite survey (actual damage),respectively. The damage rank of the columns calculated through static and dynamic analysis
conforms to each other in the first structural model. This indicates the reliability of the nonlinear
dynamic analysis. However damage ranks determined from the second structural model and actual
damage ranks are not exactly the same, especially for inner side columns (axis B); results have4

acceptably minor differences in outer side columns (axes A and B). The difference in damage rank
results on the B axis is reasonable, considering the possible effects of nonstructural members on theinner axis columns.
30

30

EQ demand spectrum (Sa-Sd)
Sa, a (m/s2)

EQ demand spectra (he1)20

Sa, a (m/s2)

EQ demand spectra (Sa-Sd)

Capacity diagram (a-d)
10D200.000.050.10a)

EQ demand spectra (he=0.110)

20

Capacity diagram (a-d)

D2 D1
10D10.15

00.00

0.200.050.10b)

Sd,d (m)0.150.20

Sd,d (m)Figure 9. Capacity diagram and demand spectrum relationships a)1st structural model, b) 2nd structuralmodel
Moment

Mm=My
Mc

u

I-I-V-IV

II-I-V-IV II-I-V-III

I-I-IV-II II-II-V-III I-I-V-II

I-I-V-III

I-I-V-II

I-I-V-II

I-I-V-III I-I-V-II

II-I-V-III II-I-V-IV I-I-V-III

I-I-V-III

I-I-V-III

I-I-V-IV

I-I-V-IV

I-I-V-II

Ed
Er

Kuy

I-I-V-IV

B

Erm

I-I-V-IV

Ku'

Rot.

cRot.

y mu

Figure 10. Energydeterioration concept ofstructural members

A9875643II-I-V-III II-I-V2

1Figure 11. Damage ranks of the first storey columns

The strength index C and the ductility
index F are calculated in accordance with thesecond level screening procedure determined by theStandard for Seismic Evaluation of Existing
Reinforced Concrete Buildings, 2001 (Figure 12).
Good correlation was found between the storey
strengths obtained from the second level screening
procedure and nonlinear pushover analysis of thesecond structural model, it should be emphasizedthat the decreasing storey strength without regard to
any post-peak behavior in second level screening
procedure is a conservative approximation whencompared to the energy consuming capacities.

0.6

1st structural model
2nd structural model
2nd level screening procedure

0.4

C (m/s2)

Ku

II-II-V-II II-II-V-IV II-I-V-IV I-I-V-IV
C

Demandpoint

0.2(R=1/82)(R=1/250)

00

0.004

0.008

0.012

Ru (rad)Figure 12. Storey shear-inter-storey
displacement relationship for first storey

4. CONCLUSION
A city office in Koriyama city was modeled using CANNY structural analysis software to produce
two different models; the first and second structural models. These two structural models weresubjected to nonlinear pushover and dynamic analyses, and the seismic structure responses were5compared, both to each other and to the actual damage reports. At the same time, the strength index Cductility index F relationship, a common method to evaluate the seismic capacity of existing RCstructures proposed by the Japan Building Disaster Prevention Association, is compared to theanalysis results .
 The strength capacity of the second structural model can be increased to match that of the firststructural model by decreasing column hoop distance, but it should be kept in mind that only
increasing strength is not enough; ductility loss, as a result of strength deterioration in the crosssection of the columns, should also be considered.
 However in this study, the responses of the second structural model have been on the conservativeside when compared to the actual damage, it is obvious that a more detailed analysis is needed.
Especially, the existence of nonstructural walls, soil-structure interaction and slight cracks in thebeams can be modeled to reduce the difference in the damage levels of the second structural modeland the actual damage.
 The city office in Koriyama city represents a type of commercial office building often found inTurkey. So, in particular, further study is needed to compare methods of seismic evaluation ofexisting RC structures in Turkey and Japan to contribute to the reconstruction process led by theMinistry of Environment and Urbanization in Turkey.
 Comparison of the energy absorbing capacities from the under the area of the strength index curves
determined from the second structural model and by using the second level screening procedureshows us with clues that the second level screening procedure is more conservative damage
estimate method. The energy consuming capacity is still going on in second structural model,
when the strength is directly reduced in the second level screening procedure.

ACKNOWLEDGEMENTS
A special acknowledgment is extended to Mr. Mizuo Inukai and Dr. Kashima who helped atvarious stages of the thesis. City officer in Koriyama city is acknowledged for giving the information
about the city office in Koriyama.

REFERENCES
BRI Research Paper (Technical note of National Institute for Land and Infrastructure Management),(2011). Summary of the field survey and research on the ‘2011 off-the-Pacific coast of Tohoku
Earthquake’. ISSN 1346-7328, Technical note of NILIM No.647, ISSN 0453-4972, BRI
Research Paper No.150.
CANNY for three dimensional nonlinear static and dynamic structural analysis, version C06.
Giberson, M. F., (1967). The Response of Nonlinear Multi-Storey Structures Subjected to Earthquake
Excitation, Earthquake Engineering Research Laboratory, California Institute of Technology,
Pasadena, California, EERL Report.
Strong-motion seismograph networks (K-NET, KiK-net), http://www.kenchiku-bosai.or.jp
Japan Association for Building Disaster Prevention (2001). Standard for Seismic Evaluation ofExisting RC Buildings (in Japanese).
Kabeyasawa, T., Shiohara H., Otani S. and Aoyama, H., (1983). Analysis of the Full-scale Sevenstorey Reinforced Concrete Test Structure. The Faculty of Engineering, University of Tokyo, Vol.
XXXVII, No. 2, pp. 432 - 478.
ViewWave (2007), a viewer for strong motion records, Building Research Institute, Tsukuba, Japan.
Yoshimura, M. and Takaine, Y., (2005). Formulation of post-peak behavior of reinforced concretecolumns including collapse drift, Journal of Construction Engineering, Architectural Institute ofJapan, No.587, 163-171. (in Japanese).

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