us-japan collaborative study on seismic damage of

US-Japan Collaborative Study on Seismic Damage of Buildings and their Mechanism

Japanese PI: Hitoshi Shiohara, The University of Tokyo Counterpart PI: John W. Wallace, UCLA

Objective: To collect and recording of the the data on structural damage of engineered buildings as well as to investigate the factor which caused each structural damage, carried out as a joint effort of Japan (AIJ) and US (EERI).

Major Outcomes 1) Joint reconnaissance efforts of building damage by

Japanese and US researchers 2) Jointly participated and presented at International

Symposium of JAEE in March 2012, Tokyo 3) Presentation at special session of 11WCEE 4) Contribution to the publication of reconnaissance

report from AIJ in 2013

Preliminary Reconnaissance Report of the 2011 Tohoku-Chiho Taiheiyo-Oki Earthquake

Edited by the Architectural Institute of Japan

Geotechnical, Geological and Earthquake Engineering series

7 The only official reconnaissance report of the Architectural Institute of Japan

7 Full of concrete information on building damages in the Tohoku and Kanto regions

7 Mainly consists of field information in the damaged areas without detailed analysis

DUESEPTEMBER

2012

springer.comPREFACE Devastating damage in the Tohoku region of Japan occurred during and after the earthquake off the Pacific coast of Tohoku earthquake on March 11, 2011. The report summarizes damage associated with ground failures including landslide and liquefaction as well as non-structural damages such as to equipment and facilities, partitioning walls and ceilings, and functional failures in skyscrapers. Also brief description of the Japanese Seismic Design Code will be provided in the Appendix. A proposed scheme of anti-tsunami design for buildings is also included.

Publication: Reconnaissance Report (by AIJ)

Second Phase: 2010～

A

B

C

D

A

B

C

D

BA

CD

BA

CD

Beam-column joint:Full Scale Shaking Table Test at E-Defense in 2010

E-Defense test on RC Building in December 2010

93

22

15 m

20 m

X

Y

F igure 2.1 E-Defense shaking table

F igure 2.2 Overview of test setup on the shaking table

E-Defense 3D Shaking Table

Four Storied Wall-FrameRC Structure

76

Table A .1 L ist of steel reinforcement

H bar Hoop35d

400

250

400

List of Wall

10-D22 10-D22500 x 500 500 x 500

3,4-D10@100 3,4-D10@1002,2-D10@140 2,2-D10@140

B x DRebarHoopJoint

RFl.4Fl.

TopBottom

Stirrup

Section

B x D

Web

Location

3Fl.Top

Bottom

Stirrup

Section

B x D

Web

2Fl.Top

Bottom

Stirrup

Section

B x D

Web

BottomSection

8-D22500 x 500

2,3-D10@1002,2-D10@140

B x D

HoopRebar

Joint

TopSection

8-D22 10-D22500 x 500500 x 500

2,3-D10@100 2,4-D10@1002,2-D10@140 2,2-D10@140

2Fl.

Hoop

B x DRebar

Joint

Section

8-D22500 x 500

2,2-D10@100 2,2-D10@10010-D22

500 x 500

2,2-D10@140 2,2-D10@140

4Fl.3Fl.

Hoop

B x DRebar

Joint

Section

C2C1

AC

2,3-D10@802,3-D10@100

2 x 6-D19

2 x 6-D19

2,2-D10@100 AC

D13@300 (W)D10@125 (W)D10@200 (W)

AC

D13@300 (W)D10@125 (W)D10@200 (W)

Vertical2,500 x 250

Wall

2,500 x 250

2,2-D10@150

Vertical

2,2-D10@150

2Fl.3Fl.4Fl.

Section

Hoop

B x DRebar

Hoop

Section

B x DRebar

Joint

Joint

S1

CS1

CS2

CS3

Top

Top

Top

Top

Bottom

Bottom

Bottom

Bottom D10@200

D10@250D10@250D10@250D10@250

D10,D13@200

D10@250D10@250

Longer directionD10@200

D10@200

D10@200

D10@200D10@200

D10@200D10,D13@200

D10,D13@200

Shorter direction

G1

4-D22 3-D22 4-D223-D22 3-D22 3-D22

4-D10

300 x 600

2-D10@200

CenterEnd End

5-D22 3-D22 5-D223-D22 3-D22 3-D22

4-D10

300 x 600

2-D10@200

6-D22 3-D22 6-D223-D22 3-D22 3-D22

4-D10

300 x 600

2-D10@200

RFl.Top

Bottom

Stirrup

Section

B x D

Web

Location

4Fl.3Fl.2Fl. Top

Bottom

Stirrup

Section

B x D

Web

All

Location

Top

Section

B x D

Bottom

StirrupWeb

G2Center

3-D19 3-D192-D19 3-D19

300 x 300

End

-

3-D19 4-D193-D19 3-D19

300 x 300

-

B1

3-D194-D19 7-D19

3-D19

CenterEnd

2-D102-D10@200

300 x 400

4Fl.3Fl.2Fl.

Section

TopBottom

Stirrup

B x D

Web

Location

TopBottom

Stirrup

Section

B x D

Web

G3Center

3-D195-D193-D19 4-D19

2-D10

300 x 400

2-D10@200

End

4-D19 3-D193-D19 4-D19

2-D10

300 x 400

2-D10@200

List of Column

List of Girder List of GirderList of Girder

List of Slab

List of beam

Depth: 130mm

2-D10@100(KSS785)

2-D10@100(KSS785)

Horizontal

Horizontal

1Fl.

1Fl.

1Fl.

76

Table A .1 L ist of steel reinforcement

H bar Hoop35d

400

250

400

List of Wall

10-D22 10-D22500 x 500 500 x 500

3,4-D10@100 3,4-D10@1002,2-D10@140 2,2-D10@140

B x DRebarHoopJoint

RFl.4Fl.

TopBottom

Stirrup

Section

B x D

Web

Location

3Fl.Top

Bottom

Stirrup

Section

B x D

Web

2Fl.Top

Bottom

Stirrup

Section

B x D

Web

BottomSection

8-D22500 x 500

2,3-D10@1002,2-D10@140

B x D

HoopRebar

Joint

TopSection

8-D22 10-D22500 x 500500 x 500

2,3-D10@100 2,4-D10@1002,2-D10@140 2,2-D10@140

2Fl.

Hoop

B x DRebar

Joint

Section

8-D22500 x 500

2,2-D10@100 2,2-D10@10010-D22

500 x 500

2,2-D10@140 2,2-D10@140

4Fl.3Fl.

Hoop

B x DRebar

Joint

Section

C2C1

AC

2,3-D10@802,3-D10@100

2 x 6-D19

2 x 6-D19

2,2-D10@100 AC

D13@300 (W)D10@125 (W)D10@200 (W)

AC

D13@300 (W)D10@125 (W)D10@200 (W)

Vertical2,500 x 250

Wall

2,500 x 250

2,2-D10@150

Vertical

2,2-D10@150

2Fl.3Fl.4Fl.

Section

Hoop

B x DRebar

Hoop

Section

B x DRebar

Joint

Joint

S1

CS1

CS2

CS3

Top

Top

Top

Top

Bottom

Bottom

Bottom

Bottom D10@200

D10@250D10@250D10@250D10@250

D10,D13@200

D10@250D10@250

Longer directionD10@200

D10@200

D10@200

D10@200D10@200

D10@200D10,D13@200

D10,D13@200

Shorter direction

G1

4-D22 3-D22 4-D223-D22 3-D22 3-D22

4-D10

300 x 600

2-D10@200

CenterEnd End

5-D22 3-D22 5-D223-D22 3-D22 3-D22

4-D10

300 x 600

2-D10@200

6-D22 3-D22 6-D223-D22 3-D22 3-D22

4-D10

300 x 600

2-D10@200

RFl.Top

Bottom

Stirrup

Section

B x D

Web

Location

4Fl.3Fl.2Fl. Top

Bottom

Stirrup

Section

B x D

Web

All

Location

Top

Section

B x D

Bottom

StirrupWeb

G2Center

3-D19 3-D192-D19 3-D19

300 x 300

End

-

3-D19 4-D193-D19 3-D19

300 x 300

-

B1

3-D194-D19 7-D19

3-D19

CenterEnd

2-D102-D10@200

300 x 400

4Fl.3Fl.2Fl.

Section

TopBottom

Stirrup

B x D

Web

Location

TopBottom

Stirrup

Section

B x D

Web

G3Center

3-D195-D193-D19 4-D19

2-D10

300 x 400

2-D10@200

End

4-D19 3-D193-D19 4-D19

2-D10

300 x 400

2-D10@200

List of Column

List of Girder List of GirderList of Girder

List of Slab

List of beam

Depth: 130mm

2-D10@100(KSS785)

2-D10@100(KSS785)

Horizontal

Horizontal

1Fl.

1Fl.

1Fl.

Joint shear / Nominal joint shear capacity

Margin of joint shear capacity

Column-to-beam strength ratios

Column-to-beam strength ratio

JMA Kobe 50%

JMA Kobe 100%

3D Full Scale RC Frame Structure Shaking Table Test at E-Defense in 2010

• Four-story full scale RC frame structures were tested,- The building structure was designed and constructed such that it conforms to

current seismic provisions in Japan and the US.

• Shear failure of lightly reinforced beam-column joints were confirmed,- BC joints with column-to-beam strength ratio between 1.0 showed joint shear

failure.

- Vulnerabilities of frame structure with lightly BC joint has been demonstrated.

17

SEISMIC DAMAGE OF A NINE-STORY RC RESIDENTIAL BUILDING IN SENDAI DESIGNED BY OLD SEISMIC CODES

Nagamachi - Dwelling Complex

1968

1971

1978

1981

1995

2000 20

11

1968 Tokachi-oki EarthquakeAmendment of BSL Enforcement Order

1978 Miyagiken-oki Earthquake Amendment of BSL Enforcement Order

Brief History of RC buildings and Seismic Codes in Japan

1995 Hyogo-ken Nambu Earthquake

Act on Promotion of Seismic Retrofitting of Existing Buildings

Amendment of BSL Enforcement Order

2011 Tohoku-chiho Taiheiyo-oki Earthqukae

I ～ 1971

II～ 1981

III1981 ～

*BSL : Building Standard Law

( Prevention of column shear failure )

( The “shin-taishin”, new standard )

( Effectiveness of the 1981 revision was confirmed )

( Performance based criteria introduced )

( To urge building owners to retrofit existing vulnerable buildings )

Nagamachi - Dwelling Complex

• RC/SRC 9 floors.

• Completed in 1969

• No seismic retrofit

• Survived major earthquakes in 1978, 2003 and 2005.

• Fc 210 & 180

• Grade SD35 rebars

Taihaku ward, Sendai City

Izumi ward

Miyaginoward

Wakabayashiward

Taihaku ward

Aoba ward

JR Sendai Station

Port of Sendai

Pacific Ocean

Site of the building

City of Sendai

1st floor plan and damage rate

X1 X2 X3 X4 X5 X6 X7 X8X0

Y1

Y2

Y3

Y4

Y0

Y5

V

V VIV

IV

IVs

III

III

IVs

V

Vs

IIIs

III

IIIs IIIs

III

III IIIs IIIs IIIs

III

IIs

II

IIs

IIs IIs

IIs

II

II

II II

IIs

IIs

II

Is Is

IsIs

I I Is

IsIs

Is

II

O O O

O

OO

O

O

O

O O

OO

O

see Fig. 7

Entrance

west

east

south north

Municipal offices

Medical Service

2nd floor plan and damage rate

Y1

Y2

Y3

Y4

Y0

Y5

X1 X2 X3 X4 X5 X6 X7 X8X0

III

III IIIs III

II

II

IIIIs IIs

IIs

I

I IIs

Is

Vs

I

I

Is I

IIs

I

I

Is

II

I Is Is Is Is

IsIs

Is I I

II

IO O O O

O

O

O O O

OOO

OO

OO

O

OO

O

OO

west

east

south northMunicipal offices

3rd floor plan and damage rate

Y1

Y2

Y3

Y4

Y0

Y5

X1 X2 X3 X4 X5 X6 X7 X8X0

III

III IIIs III

II

II

IIIIs IIs

IIs

I

I IIs

Is

Vs

I

I

Is I

IIs

I

I

Is

II

I Is Is Is Is

IsIs

Is I I

II

IO O O O

O

O

O O O

OOO

OO

OO

O

OO

O

OO

Y1

X1 X2 X3 X4 X5 X6 X7 X8

Y2

Y3

Y4

Is Is

IIs IIs

IIIs

IVs

IVsIVs

IVs

Is Is Is Is Is

west

east

south north

Apartment units

Corridor

RC non-structural partition

Damage Grading Criteria of RC Members

Damage gradeDamage grade Criteria

0 No damage No damage

I Slight Structural concrete cracking of width less than 0.2mm

II Minor Structural concrete cracking of width larger than 0.2mm and less than 1.0mm.

III Moderate Structural concrete cracking of width larger than 1.0mm and less than 2.0mm.

IV MajorStructural concrete cracking of width larger than 2.0mm, with cover concrete spalling and visible reinforcement

V Severe Cover concrete spalling off, with some concrete crushes and longitudinal reinforcement buckling

Residual Lateral Capacity of RC Structural Member

L

oad

Car

ryin

g C

apac

ity

Loa

d C

arry

ing

Cap

acity

Remained

Remained

Deteriorated

Damage Class

Lateral Load

! " # $ % Vertical Load

Deflection

Remained Lost

Remained Lost

(a) Ductile member

Lateral Load

! " # $ % Vertical Load

Damage class

(b) Brittle member

Yielding of

tensile rebars

Cracking Buckling of rebars and

falling of covering concrete

Compression failure

of concrete starts

Cracking

Falling of covering concrete

Expansion of shear cracks

Buckling and/or

fracture of

Deflection

Deteriorated

Deteriorated

Lost

Lost

Figure 1: Idealized lateral force-displacement relationships and damage class

In the Seismic Evaluation Standard, most fundamental component for Is-index is E0-index, which is basic structural seismic capacity index calculated from the product of strength index (C), and ductility index (F). Accordingly, deterioration of seismic capacity was estimated by energy dissipation capacity in lateral force- displacement curve of each member, as shown in Figure 2. Seismic capacity reduction factor η is defined by Eq.(2).

t

r

E

E=η (2)

where, dE : dissipated energy, rE : residual absorbable energy,

tE : entire absorbable energy ( rdt EEE += ).

Loa

d

! " # $ Damage class

Dissipated energy Ed

Residual Deflection Ultimate Deflection

%

Absorbable Energy Er

Reduction factor

rd

r

EEE+

=η Max. Deflection

Figure 2: Seismic capacity reduction factor η

Elevation of Y4 frame in longitudinal direction

X8 X7 X6 X5 X4 X3 X0X2 X1

1FL

GL

2FL

3FL

4FL

5FL

6FL

7FL

8FL

9FL

RFL

PHRFL 36,150

4,100

7,400

10,150

12,850

15,550

18,150

20,750

23,350

26,150

500

5 400 8 = 43 200

IVs

IVs

IVs

IVs

IVsIVs

shear crack on beam-column joint

IsO

O O O O

O OIIs Is

Is

I

II

I IIs II IIIII

Is II

Unit in mm

see Fig. 10

Shear failure of columns

Latice steel

Failure of Beam-column Joints

Elevation of X1 frame in longitudinal direction

steel shape in concrete

O

IIIs

Y0 Y1 Y2 Y3 Y4 Y5

4 500 4 5006 0006 0006 000

O

III II

OI Is

Is

Is

IIs

III

III

III

OIII IVV V

unit in mm

see Fig. 7

shear cracks on coupling beams

Elevation of X1 frame in longitudinal direction

steel shape in concrete

O

IIIs

Y0 Y1 Y2 Y3 Y4 Y5

4 500 4 5006 0006 0006 000

O

III II

OI Is

Is

Is

IIs

III

III

III

OIII IVV V

unit in mm

see Fig. 7

flexural failure and buckling of rebars at the bottom of column

Values of Seismic Index Is

Story Longitudinaldirection

Transversedirection

9 0.37 1.498 0.27 1.047 0.23 0.826 0.20 0.705 0.21 0.624 0.19 0.513 0.20 0.712 0.44 0.441 0.62 0.39

Seismic Evaluation Standards by JBDPA

no good correlation

good correlation

Beam-column Joints in Y4 frame

(a) Beam-column joint at 7F (X5-Y4)

10-D19hoop φ9@250

750

450

450

220

220

1150

horizontal sectionof column

vertical sectionof beam

4-D19

3-D19

(b) Beam-column joint at 5F (X5-Y4)

4-D22+6-D19hoop φ9@250

750

600

600

220

220

1250

unit in mm

horizontal sectionof column

vertical section of beam

4-D22

4-D22

Shear failurein kN

Shear failurein kN

Shear failurein kN

Flexural hingein kN

Flexural hingein kN

Flexural hingein kN



Joint shear

strength margin*

column beam joint columncase 1*

columncase 2* beam case 1 case 2

Joint shear

strength margin*

9FL 544.4 858.7 863.4 522.5 396.7 231.7 2.25 1.71 3.73

8FL 555.0 929.1 984.0 650.8 454.0 320.2 2.03 1.42 3.07

7FL 589.2 1043.2 1112.3 751.5 496.7 335.0 2.24 1.48 3.32

6FL 799.7 1148.5 1150.1 906.6 574.8 432.2 2.10 1.33 2.66

5FL 907.8 1162.5 1624.0 1082.9 664.0 528.3 2.05 1.26 3.07

Tributary area of gravity load

Column

Wall

floor plan

Calculated story shear

Concluding Remarks

• Nagamachi Dwelling Complex Building

• Flexural failure of the first story SRC column

• deficiency of steel lattice not embedded into the foundation which just ends at the first floor level.

• abrupt change of section caused the damage.

• Shear failure of lightly reinforced beam-column joints.

• calculated margin of joint shear strength is 2.0 or more.

• column-to-beam strength ratio is in the range of 1.26 to 1.48.

• vulnerablity of column-to-beam strength ratio between 1.0 and 1.5 are to joint shear failure.

• problem in failure mode prediction

New beam-column joint macro element and nonlinear dynamic analysis on 4 story frame RC structure

37

• Members; beams or columns framing into the joints- Full flexural capacity of the members to be achieved

Life Safety Requirements to Beam-Column Joint

Not easy to meet in practice

Δ

P

V

Collapse mechanism by Joint hinging

Subsequent repetition due toCyclic loading

The 14th

World Conference on Earthquake Engineering

October 12-17, 2008, Beijing, China

Figure 14 Total collapse of school building. Figure 15 Severe diagonal shear cracks on the

gravity wall between window openings.

Figure 16 Severe damage of school building. Figure 17 Pancake type of failure due to weak

columns.

Figure 18 Collapse of school buildings. Figure 19 Building collapse due to joint failure.

Figure 20 Column failure due to insufficient

transverse reinforcement. Figure 21 Soft story collapse.

Collapsed Structure : Wencheuan Earthquake (2008)

PSkeleton

curveP-delta Effect

Slip

• Control Joint hinging in seismic Design- Performance to prevent collapse and instability of lateral resisting frame due to

subsequent repetitions of earthquake loading needs to be evaluated.

ᅗ 1 ᰕᱱ᥋ྜ㒊ࡢᦆയᯫᵓࡢኚᙧJoint hinging

38• No suitable model has been developed before.

New Macro Element for Interior BC Joint

39

rigid panel

rigid panel

steel elementbond link

bond link

steelelement

concrete springconcrete element

concrete element

steel element

steel element axial stiffness is factored consideringpull-out of bars from member end

diagonal concrete

horizontal reinforcing bars vertical reinforcing bars

vertical & horizontal concrete

A A' {bA'}={bA}

macro element ofbeam-column joint

force-based beam-column element

node

superimpose

Frame StructureP-Delta effect is incorporated

to stiffness matrix

Uniaxial Constitutive Models for Elements

-Kfc

-KfcZm

-0.2Kfc

ft

-ft

0.25ft ¡¡t2¡t1

-K¡c-¡u

m

concrete

Tension

Compression

Modified Kent & Park

¡

m

my

1.5my

¡y

-my

-¡y Es Es

Es/4

steel

Tension

Compression

Modified Bi-linear

ss1 s2s3 s4 s5

o

o1

o2o3

bond-slip

Modified Eligehausen

40

Validation of the Macro Element by the Tests

-100

-50

0

50

100

-4 -2 0 2 4 -4 -2 0 2 4

Db/Dc=1ʫMcu/ʫMbu=1.0V ju/Vu=1.03

B02

-100

-50

0

50

100

-4 -2 0 2 4 -4 -2 0 2 4


B05

Db/Dc=0.5ʫMcu/ʫMbu=1.03V ju/Vu=1.06

D05


H01

stor

y sh

ear i

n kN

story drift in kN

TestAnalysis

• The new model is suitable to simulates strength and hysteresis behavior of sub structure with BC joints

41

Input Ground Acceleration Record

0 1 2 3 4 50

500

1000

1500

2000

2500

3000

S a (cm

/sec

2 )

JMA Kobe 1995JR Takatori 1995SCT1 1985

T1 =0.46 secT2 =0.15 sec

Period in second

Spectra of Max. Response Acc. Damping = 5%

(Y[PÄJPHS��9LX\PYLK�I`�*VKL�

•Four input ground motions are selected for dynamic analysis42

Four Story Building Collapse Simulationwith non-linear BC Joint model with elastic BC Joint model

43

Unstable Limit ; beyond Ultimate Limit

Mcu/Mbu=1.0

Mcu/Mbu=1.5

Mcu/Mbu=1.5

Mcu/Mbu=1.0

0 0.05 0.10

0.1

0.2

0.3

0.4

0 0.05 0.10 0.05 0.10

0.5

1.0

1.5

2.0

2.5

3.0

Sa(T

1=0.

46s,5

%),

g

EQ 1.0

0 0.05 0.10

1.0

2.0

3.0

4.0

5.0

6.0

Sa(T

1=0.

46s,5

%),

g

0 0.05 0.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Sa(T

1=0.

46s,5

%),

g

0

0.5

1.0

1.5

2.0

2.5

Sa(T

1=0.

46s,5

%),

g

EQ 1.0EQ 1.0

EQ 1.0

JMA Kobe JR Takatori SCT1

story drift in rad

(Y[PÄJPHS

UVU�SPULHY�QVPU[

UVU�SPULHY�QVPU[LSHZ[PJ�QVPU[

LSHZ[PJ�QVPU[

\UZ[HISL�SPTP[

H[[HPULK�TH_PT\T�Z[VY`�KYPM[�PU�YHK

:[H[PJ�W\ZOV]LY�HUHS`ZPZ

+`UHTPJ�W\ZOV]LY�HUHS`ZPZ��0+(�

IHZL�ZO

LHY�J

VLMÄJPL

U[

44

= collapse limit

Column-to-beam Strength Ratio and Unstable Limit

0 0.05 0.1 0.150

0.5

1.0

1.5

2.0

2.5

3.0

Sa(T

1=0.

46s,5

%),

g

EQ 1.0

0 0.05 0.1 0.15

Mcu/Mbu=1.0Mcu/Mbu=1.1Mcu/Mbu=1.2Mcu/Mbu=1.3Mcu/Mbu=1.4Mcu/Mbu=1.5



0 0.05 0.1 0.150

1.0

2.0

3.0

4.0

5.0

6.0

Sa(T

1=0.

46s,5

%),

g

0 0.05 0.1 0.15

0 0.05 0.1 0.150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Sa(T

1=0.

46s,5

%),

g

0 0.05 0.1 0.15

0 0.05 0.1 0.150

0.5

1.0

1.5

2.0

2.5

Sa(T

1=0.

46s,5

%),

g

EQ 1.0

EQ 1.0 EQ 1.0


(Y[PÄJPHS (Y[PÄJPHSUVU�SPULHY�QVPU[

UVU�SPULHY�QVPU[ UVU�SPULHY�QVPU[

LSHZ[PJ�QVPU[

LSHZ[PJ�QVPU[

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• Frame with beam-column joint of C-to-B ratio of 1.0 become unstable at smaller ground motion amplification factor

• The difference is due to concentration of story drift at particular story 45

New beam-column joint macro model and nonlinear dynamic analysis on RC frames

• Instability of moment resisting frame occurs at extremely large excitation- Inappropriateness of non-linear frame model without consideration of non-linear

beam-column joint is demonstrated,

- Performance of beam-column joint is essential to attain stable seismic response at large displacement response level of ductility factor of 5 or more,

- Joint hinging causes local concentration of story drift at particular story,

- Then the frame becomes vulnerable to collapse due to P-Delta effect.

- Large column-to-beam strength ratio is necessary to to avoid collapse due to instability

- Safety margin for extremely large earthquake is smaller if small column-to-beam strength ratio is used for seismic design

46

us-japan collaborative study on seismic damage of

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