Non-linear numerical analyses to improve the seismic design method for soft first story RC building.pdf

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13th

World Conference on Earthquake EngineeringVancouver BC Canada

August 1-6 2004Paper No 2224

NON-LINEAR NUMERICAL ANALYSES TO IMPROVE THE SEISMIC

DESIGN METHOD FOR SOFT FIRST STORY RC BUILDING

Kheir-Eddine RAMDANE1 Koichi KUSUNOKI

1 Masaomi TESHIGAWARA

1 and Hiroto KATO

1

SUMMARY

Soft first story buildings are one of the most vulnerable structural types during severe earthquakes Suchstructures notably RC buildings are required in overpopulated areas

Kobe earthquake which is considered to be one of the most devastating and costly natural disaster in recent

history bearing in mind the number of buildings destroyed the number of people killed and injured and the

damage extended to a wide range of structural types It was found that many buildings that were constructed

with open retail space or parking on the first floor collapsed

The collapse of the soft first story structure was attributed to inadequate transverse reinforcement in terms of

its amount and detailing more flexible andor weaker story and to relatively smaller amount of shear walls to

allow for the access to the open space than the ones above Hence the Building Standard Law Enforcement

Order of Japan revised after the Kobe earthquake adopted stricter guidelines for the construction of soft first

story buildings That was a tentative approach but no reliable methodology for the design of this type of

structure exists so far

The aim of this study is to evaluate the seismic capacity and conduct non-linear numerical analyses of typical

RC buildings of 6- 10- and 14 stories with soft first story investigate the response characteristics and

improve the seismic design method of this type of structures An expression is derived based on the energy

constant law for the strength increasing factor and compared with results from the numerical analyses to

verify the adequacy of this expression

INTRODUCTION

Ground shaking produced by an earthquake will search for any structural vulnerability These vulnerabilities

are usually created by sharp changes in stiffness strength andor ductility lack of shear walls in the firststory and the effects of these vulnerabilities are accentuated by poor distribution of masses As a result one

of the most vulnerable structural types is the multistory commercial and residential buildings built of

reinforced concrete with little or no lateral resistance of the first story These buildings are called ldquoPilotirdquo or

ldquosoftrdquo first story buildings

1 Building Research Institute 1 Tachihara Tsukuba Ibaraki Japan 305-0802 Email eddine_ryahoofr



Generally soft stories have less stiffness than the upper stories Together with a lack of ductile capacity in the

reinforced concrete columns beams and joints these soft stories can cause many brittle failures during an

earthquake ground motion The 1978 Miyagi-ken Oki Earthquake caused brittle and severe damage of the

columns of the first floors to RC buildings which had shear walls except in the first floors This type of

damage was more noticed in the 1995 Kobe Earthquake Based on this fact a design procedure which does

not allow column side-sway mechanism (soft first story collapse) was recommended in the Japanese Seismic

Design Guidelines

On the other hand soft first story collapse might be permissible even in Piloti buildings if the maximum

response deformation angle of the first story can be kept to the level of the maximum response deformation

angle supposed in beam sideway mechanism (total collapse) buildings And since soft first story buildings

have fewer andor no shear walls to absorb the energy generated by an earthquake than those total collapse

buildings thus in order to hold the maximum response deformation angle of soft first story buildings to the

same level as that of total collapse buildings and according to the energy constant law the horizontal load-

carrying capacity required in the soft first story buildings must be increased in comparison with total collapse

buildings

In this paper a procedure to determine the failure modes of a building with a soft first story from the failure

modes of columns and walls at the soft story is demonstrated This will be used to develop a designprocedure to secure the safety of those buildings allowing the soft first story collapse mechanism Then a

strength increasing factor pα which represents the capacity demand for the soft story in order to get the

same total collapse of the system is determined based on the energy constant law so that the ductility factor

for buildings with a soft first story collapse micro is equal to the ductility factor for buildings with total

collapse mechanism micro

The buildings considered in this study are designed according to the specification prior to the 1995 Japanese

code The values of the base shear coefficient C b divided by the vibration factor Rt are 043 046 and 043

for the considered RC buildings of 6- 10- and 14 stories with soft first story respectively Then the base

shear is varied with respect to the original value and the stiffness of the first story is assumed as constant

OUTLINE OF THE SEISMIC DESIGN CODE IN JAPAN

Significant developments occurred in the Japanese Seismic Design Code since the restoration of Meiji period

in 1968 Following the 1923 Kanto Earthquake the Urban Building Law which concerned only six major

cities in Japan required the use of a seismic coefficient of 01 in conjunction with a materials safety factor of

3 on ultimate stress These requirements were revised from time to time following devastating earthquake

disasters

The first Building Standard Law applicable to all buildings in Japan was revealed in May 1950 The

purpose of the law is to safeguard the life health and property by providing minimum standards concerning

the site structure equipment and use of building The Law requires that a building owner must submit

before construction work an application to building officials to confirm that the building plan site structure

and equipment satisfy the provisions of the law This requirement made the code prescriptive because

building officials must be able to judge the conformity The structural design was based on the allowable

stress design

The 1978 Miyagi-ken Oki Earthquake which caused serious damage led to accelerated implementation of the

revised Building Standard Law in 1981 The Building Standard Law included a seismic coefficient that

varies with structural vibration period and introduced a two-level design procedure The first level design



follows the traditional allowable stress design approach with steel allowable stress equal to the yield stress

and concrete allowable stress equal to 23 of the specified compressive strength The second level design is a

direct and explicit evaluation of strength and ductility and maybe regarded as a check of whether these are

sufficient for severe ground motion

In the first level design the seismic (elastic response) coefficient C i at each floor level i is determined as

0C A R Z C it i sdotsdotsdot= Eq(1)

where Z seismic zone factor Rt vibration characteristic factor Ai factor representing vertical distribution of

the seismic story shear coefficient C o basic base shear coefficient (02 for allowable stress design and 10 for

the examination of story shear resisting capacity)

Further in the second level design the story shear resisting capacity must be greater than the required

horizontal load-carrying capacity unQ at the soft story which is given by

sumsdotsdotsdotsdot=

iiseS un

W C F F DQ Eq(2)

where Ds structural characteristic factor (030 ndash 055) representing the ductility of hinging members of the

story F e coefficient representing the eccentricity in a story F s representing the distribution of stiffness

along the height C i story shear coefficient sum iW total dead and live loads above story i However

buildings not more than 31 m and satisfying certain conditions are not required to examine the story shear

resisting capacity Other structures of heights between 31 m and 60 m must be checked by both design

procedures Structures over 60 m in height are subject to special approval

When the first story is ductile Ds become small and so is the required horizontal load-carrying capacity In

this case the whole building dissipates the energy uniformly However a soft story building needs to

dissipate almost all the earthquake energy at the first floor If Eq(2) is applied to the soft first story building

the latter shows a large deformation Hence it is proposed that the maximum ductility or maximum

deformation angle of the soft first story building must be kept to the same level as for the total collapse

building Therefore considering the fact that the damage concentrates in the soft first story for the required

horizontal load-carrying capacity of the first story the larger of pα and F s as shown in Eq(3) should be

used instead of F s in Eq(2)

max)( s p F α Eq(3)

where pα is the strength increasing factor to limit the deformation of the soft first story

FAILURE MECHANISM OF SOFT STORY BUILDING

Inspections of earthquake damage as well as the results of analytical studies have shown that structural

systems with a soft story can lead to serious problems during severe earthquake ground shaking

For instance Fig1 and 2 illustrate such damages Fig 1 shows the failure mechanism of soft story building

These are a) Bending (tensile yielding of reinforcing bar) b) collapse of first story (yield in column) and c)

collapse of first story (shear failure of column) As for a soft story with walls two types of failure mechanism

are observed in a frame with a wall a) bending (bending yield at wall bottom) and b) shear collapse of first



story (shear failure) The failure mechanism of the frame with wall is predominant and therefore controls the

failure mechanism of the whole system (building)

(a) (b) (c)

Fig 1 Failure types of soft story building

(a) (b) Fig 2 Failure types of soft story with walls

Based on the above observed types of failure the following section illustrates the Model which is

considered in this study

MODEL FOR THE STRUCTURE

The model considered in this study is shown in Fig 3 Continuous shear walls from the second to the top

story are modeled as equivalent one column as shown in Fig 3(a) and each mass represent the weight of

each floor Columns in the first story are modeled as two columns The total weight of the first story is

distributed into three masses and each mass of the first story is equivalent mass Beams in the first story

are modeled as a rigid element

983122983145983143983145983140 983138983141983137983149983122983145983143983145983140 983138983141983137983149

983127983137983148983148

983127983137983148983148

983127983137983148983148

983127983137983148983148

983127983137983148983148

983107983151983148983157983149983150983107983151983148983157983149983150

983122983145983143983145983140983085 983152983148983137983155983156983145983139 983155983152983154983145983150983143983142983151983154 983142983148983141983160983157983154983137983148 983138983141983144983137983158983145983151983154

983122983145983143983145983140983085983152983148983137983155983156983145983139 983155983152983154983145983150983143983142983151983154 983142983148983141983160983157983154983137983148 983138983141983144983137983158983145983151983154

983116983145983150983141983137983154 983155983152983154983145983150983143

983142983151983154 983155983144983141983137983154

983116983145983150983141983137983154 983155983152983154983145983150983143983142983151983154 983137983160983145983137983148 983138983141983144983137983158983145983151983154

983109983148983137983155983156 983145983139 983138983141983144983137983158983145983151983154 983109983148983137983155983156 983145983139 983138983141983144983137983158983145983151983154

(a) Model for structure (b) Model for member

Fig 3 Model for structure and member

For the first story the shear and the axial springs are assumed to be elastic as shown in Fig 3(b) As for the

flexural spring the Takeda Model is applied For the second story and above the shear the axial and the

flexural springs are assumed to be linear Moreover the applied damping is proportional to the instant

stiffness of 5



INPUT MOTIONS

The NS component of the record at the El Centro Hachinohe and Kobe were used as the input earthquake

motions in addition to four artificial waves (wg60 wg61 wg62 and wg63) Each record is normalized so

that the maximum velocity is 500 mmsec2 The Peak Ground Acceleration (PGA) of each record is shown

in Table 1 and the response acceleration spectra for each of the seven input motions is shown in Fig 4

Table 1 PGA of each record

Record PGA (cmsec2)

El Centro NS 44812

Hachinohe NS 27791

Kobe NS 44405

Wg60 48430

Wg61 46733

Wg62 52292

Wg63 51004

983088983086983088 983088983086983093 983089983086983088 983089983086983093 983090983086983088 983090983086983093 983091983086983088

983088983086983088

983090983086983088

983092983086983088

983094983086983088

983096983086983088

983089983088983086983088

983089983090983086983088

983089983092983086983088

983089983094983086983088

983122

983141 983155 983152 983151 983150 983155 983141

983105

983139 983139 983141 983148 983141 983154 983137 983156 983145 983151 983150

983080 983149

983087 983155 983141 983139

983090 983081

983120983141983154983145983151983140 983080983155983141983139983081

983109983148 983107 983141983150983156983154983151 983118 983123

983112983137983139983144983145983150983151983144983141 983118983123

983115983151983138983141 983118983123

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983089

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983090

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983091

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983092

Fig 4 Response acceleration spectrum for each input motion

METHOD FOR DERIVING THE FACTOR pα

The energy constant law as shown in fig 5 was considered when investigating the responses of soft first

story and total collapse mechanism buildings The assumed magnitude of external forces is based on anelastic response of 10G For strengths lower than 10G the building yields As a result and assuming

that the energy constant law is satisfied the shear strength coefficient Ds and ductility micro can be expressed

by Eq(4) given as

12

1

minus

=

micro s

D Eq(4)



Furthermore fig 5 shows the relationship between the strength and the deformation for a one-mass

system Assuming that the constant energy law is satisfied it can be shown for instance that the Work W(1)

= W(03) Also in cases where all stories yield in the same manner and the restoring force characteristics of

each story constitute a perfect elasto-plastic system the ductility of a one-mass system is identical to the

ductility of each story of multi-mass system

983088 983089 983090 983091 983092 983093 983094

983088983086983088

983088983086983093

983089983086983088

983119983150983141983085983149983137983155983155 983155983161983155983156983141983149

983127 983080983088983086983091983081

983127 983080983089983081

983080983088983086983091983081

983080983088983086983093983081

983080983089983081

∆983089983161

983123 983156 983154 983141 983150 983143 983156 983144

983080 983111 983081

983108983145983155983152983148983137983139983141983149983141983150983156 983154983137983156983145983151 983080 ∆983087 ∆983089983161

983081

Fig 5 Energy constant law

As for the factor pα it is determined so that the ductility factor micro for column sidesway building is equal

to the ductility factor micro for beam sidesway building It is assumed that the required internal work for both

types of buildings is the same and the distribution of external load and displacement is an inverted triangle

The weight and the height of each floor are the same for both types of building The structural

characteristic index is S

D for the soft first story building and S D for the total collapse building as shown

in Fig 6 Furthermore the hysteresis for the i-th floor is assumed as an elasto-plastic model and each

floor has the same stiffness for both buildings Hence the ratio of S

D to S D to obtain micro = micro can be

expressed by Eq (5)

S

S p

D

D

=α Eq(5)

By assuming n is the number of stories in the total collapse system m and h are the weight and height of

each story respectively and are equal for both types of collapses and yh θ sdot is the yield displacement

(story drift) and also by considering an inverted triangular distribution of the external force-deformation as

shown in Fig 7 the internal work for the total collapse system W in is expressed by Eq 6 given below

( )

( ) ( )1214

1

12

1

1

minussdotsdotsdotsdotsdot+sdot=

sdotsdotsdotsdotsdotminus+sdotsdotsdotsdot=sum=

μθ

θμθ

yS

n

i

y yS in

h Dmnn

h Dsmih DmiW Eq (6)

where Ds is the demand story shear coefficient defined in the 2001 Japanese Seismic Design Regulation

(C b for first story) and micro is the maximum ductility factor to assume a total collapse system The

displacement of each floor is described in Fig8



μ

983108983155

μ 991257

983108983155991257

(a) Total collapse system (b) Soft first story collapse

Fig 6 Total collapse system and soft first story collapse

As for the soft first story collapse system almost the whole deformation is concentrated at the first floor

hence the distribution shape shown in Fig 9 is considered It is assumed that the weight and height are

uniform in all stories and are the same as in the total collapse system Thus the internal work done by the

soft story is given by Eq (7)

( ) 1

2

1 yS yS h Dmnh Dmn θμθ sdotsdotsdotsdotsdotminus+sdotsdotsdotsdot Eq (7)

where

yh θ sdot is the story drift at yielding for soft first story collapse system Dsrsquo is calculated as Ds timesα p

and microrsquo is the maximum ductility factor assuming a soft first story collapse

Fig 7 External force-deformationdistribution for total collapse system

983145983149983108983155

983144θ983161

μ 983144θ983161

Fig 8 Restoring force characteristics ofrespective stories

The upper stories of the soft first story building are assumed elastic This elastic work with respect to the

total work changes depending on the capacity and stiffness of each floor Here the distribution shape is

assumed to be an inverted triangle as shown in Fig 10 As can be seen from the figure the upper stories

perform no work for α=00 and if α=10 upper stories can dissipate the same amount of energy as the first

story which is elastic Hence the elastic work of the i-th story is expressed by Eq 8 given as



)1(

2

1 yS h Dmin θα sdotsdotsdotsdotminus+sdotsdot Eq (8)

where α is the coefficient representing the rate of elastic work load contribution above the first story of the

soft first story building

Fig 9 External force-deformation distribution

of soft first story collapse system

弾性限界 α 983101983088 α 983101983089983088983100α 983100983089

Fig 10 Distribution shape

Accordingly the total internal work for a building with a soft story W inrsquo is expressed as

( )

( )

minus+sdotminussdotsdotsdotsdotsdot=

sdotsdotsdotsdotsdotminus+sdotsdotsdotsdotsdot+sdotsdotsdotsdotsdotsdot=summinus

2

11

4

1

12

1

2

1

1

μθ

θμθθα

α nh Dmn

h Dmnh Dmnh DmiW

yS

yS yS

n

i

yS in

Eq (9)

And as shown in Fig 11 below it assumed that the rigidity of each story in the total collapse system is thesame as for the soft first story collapse systems thus the following relationship given by Eq(10) can be

obtained

S

S

y

y

D

D

=

θ

θ Eq (10)

983145983149983108983155991257

983144θ983161

983145983149983108983155

983144θ983161

991257

α 983145983149983108983155991257

α 983144θ983161

991257 Fig 11 The relation between y and y

rsquo



Since the internal work for the total collapse and soft first story collapse systems is equal and using Eqs

(6) (9) and (10) Eq(11) for pα can be expressed as

( ) ( )( ) ( )1221

121

minus+sdotminus

minussdot+==

μ

μ

α α

n

n

D

D

S

S p

Eq (11)

Fig 12 shows pα for buildings up to 20 stories when 05== micro micro The value becomes larger as the total

height increases As can be seen from the figure a value pα for a 10 story building with a soft story is

equal to 19～23 This means that the required lateral load resistance of the soft first story collapse

system is about 19 to 23 times as large as that of the total collapse system when ductility is to be limited

to 50

983088 983093 983089983088 983089983093 983090983088

983089983086983088

983089983086983093

983090983086983088

983090983086983093

983091983086983088

983091983086983093

α

983101983089983086983088

α983101983088983086983088

α

建物階数

αの値 983088983086983088 983088983086983089 983088983086983090 983088983086983091 983088983086983092 983088983086983093 983088983086983094 983088983086983095 983088983086983096 983088983086983097 983089983086983088

Fig 12 The relationship between pα and the number of stories

RESULTS AND DISCUSSION

The obtained results of the Ds- micro relationship for 14- 10- and 6-story buildings are shown in figs 13 14

and 15 respectively The scatter values present the results from the non-linear numerical analyses for the

seven input motions Plots presenting the variation of the coefficient α from 0 to 10 are drawn in the

figures Also the constant energy and constant displacement plots are included

00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

20

Constant

displacement

983107 983151983150983155983156983137983150983156

983141983150983141983154983143983161

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141983150983156983154983151

983112983137983139983144 983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983089983092983110

micro

Ds

Fig 13 D s-Ductility relationship for 14-story

00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

20

Constantdisplacement

Constant

energy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141983150983156983154983151

983112983137983139983144 983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983089983088983110

micro

Ds




00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

Constant

displacement

Constantenergy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141 983150983156983154983151

983112 983137983139983144983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983094983110

micro

Ds


For 14- and 10-story buildings for ductility 06= micro a value of Ds equal or greater than 06 is obtained

from the non-linear numerical analyses as shown in figs 13 and 14 respectively For a value of 06 orgreater the response becomes small enough however for a value Ds of 04 the response is much greater

and gets close to a value of pα of about 10 requiring as a result a high ductility In the design of new

structural elements (columns) of soft first story building it is recommended therefore that a value of Ds of

06 or greater to be applied to avoid a soft first story collapse

On the other hand for a 6-story building and for ductility 06= micro a value of Ds equal or greater than 055

can be applied in the design of new structural elements (columns) of soft first story building to avoid a soft

first story collapse The result from the non-linear numerical analyses presenting the relationship ( Ds ndash micro )

is shown in fig 15

Furthermore fig 16 below summarizes the Ds-Deformation angle relationship for 6- 10- and 14-story Itcan be seen clearly that the deformation angle decreases as Ds increases

Finally fig 17 shows the relationship between the number of stories and α p x Ds for 6- 10- and 14-story

As shown earlier the value of the required lateral load factor α p x Ds is 055 for 6-story building and

increases to a value of 060 for 10-story building or greater

04 05 06 07 08

000

002

004

006

008

010

012

014

016

D e f o r m a t i o n a n g l e ( R a d )

Ds

6F

10F 14F

Fig 16 D s -Deformation angle relationship for

6- 10- and 14-story



0 5 10 15

025

030

035

040

045

050

055

060

065

070

075

080

983124983144983141983151983154983141983156983145983139983137983148 983148983145983150983141

983123 983145983149 983152983148983145983142983145983141983140 983148983145983150983141

α

p

x D s

Number of Stories

Fig 17 Number of stories- α p x D s relationship

for 6- 10- and 14-story

CONCLUSIONS

A new seismic design procedure that could secure the structural safety of soft first story buildings during

severe earthquake motions by allowing column sideway mechanism at the first story has been proposed

A relationship between the required design strength of the soft first story and seismic response of ldquoPilotirdquo

buildings is clearly obtained by an analytical study

From the non-linear numerical analyses and for ductility 06= micro a required lateral load factor α p x Ds

equal to 055 is obtained for 6-story building and increases to a value of 060 for 10-story building or

greater

ACKNOWLEDGEMENT

Dr Kheir-eddine Ramdane expresses his appreciation to the Japan Society for the Promotion of Science

(JSPS) for the two-year post-doctoral fellowship at the Building Research Institute Tsukuba JapanSpecial thankfulness is also extended to his colleagues at the BRI Dr Kusunoki Dr Teshigawara Mr

Kato Dr Fukuyama and Dr Fukuta for their uncountable assistance and support

REFERENCES

1 2001 Technical Guidelines for Building Structure (in Japanese) The Building Centre of Japan

2 Architectural Institute of Japan (1991) ldquoStandard for Structural Calculation of Reinforced Concrete

Structuresrdquo 19914

3 Housner GW (1952) ldquoIntensity of Earthquake Ground Shaking near the Causative Faultrdquo The

Third World Conference on Earthquake Engineering New Zealand 94-115

4 Otani S et al Analysis of the Full Scale Seven Story Reinforced Concrete Test StructureEarthquake Effects on Reinforced Concrete Structures US- Japan Research Publication SP-84

ACI pp 203-239 1985

5 Takeda T Mete A Sozen N Norby Nielsen (1970) ldquoReinforced Concrete Response to Simulated

Earthquakerdquo Journal of Structural Division Vol 96 ST 12



Generally soft stories have less stiffness than the upper stories Together with a lack of ductile capacity in the

reinforced concrete columns beams and joints these soft stories can cause many brittle failures during an

earthquake ground motion The 1978 Miyagi-ken Oki Earthquake caused brittle and severe damage of the

columns of the first floors to RC buildings which had shear walls except in the first floors This type of

damage was more noticed in the 1995 Kobe Earthquake Based on this fact a design procedure which does

not allow column side-sway mechanism (soft first story collapse) was recommended in the Japanese Seismic

Design Guidelines

On the other hand soft first story collapse might be permissible even in Piloti buildings if the maximum

response deformation angle of the first story can be kept to the level of the maximum response deformation

angle supposed in beam sideway mechanism (total collapse) buildings And since soft first story buildings

have fewer andor no shear walls to absorb the energy generated by an earthquake than those total collapse

buildings thus in order to hold the maximum response deformation angle of soft first story buildings to the

same level as that of total collapse buildings and according to the energy constant law the horizontal load-

carrying capacity required in the soft first story buildings must be increased in comparison with total collapse

buildings

In this paper a procedure to determine the failure modes of a building with a soft first story from the failure

modes of columns and walls at the soft story is demonstrated This will be used to develop a designprocedure to secure the safety of those buildings allowing the soft first story collapse mechanism Then a

strength increasing factor pα which represents the capacity demand for the soft story in order to get the

same total collapse of the system is determined based on the energy constant law so that the ductility factor

for buildings with a soft first story collapse micro is equal to the ductility factor for buildings with total

collapse mechanism micro

The buildings considered in this study are designed according to the specification prior to the 1995 Japanese

code The values of the base shear coefficient C b divided by the vibration factor Rt are 043 046 and 043

for the considered RC buildings of 6- 10- and 14 stories with soft first story respectively Then the base

shear is varied with respect to the original value and the stiffness of the first story is assumed as constant

OUTLINE OF THE SEISMIC DESIGN CODE IN JAPAN

Significant developments occurred in the Japanese Seismic Design Code since the restoration of Meiji period

in 1968 Following the 1923 Kanto Earthquake the Urban Building Law which concerned only six major

cities in Japan required the use of a seismic coefficient of 01 in conjunction with a materials safety factor of

3 on ultimate stress These requirements were revised from time to time following devastating earthquake

disasters

The first Building Standard Law applicable to all buildings in Japan was revealed in May 1950 The

purpose of the law is to safeguard the life health and property by providing minimum standards concerning

the site structure equipment and use of building The Law requires that a building owner must submit

before construction work an application to building officials to confirm that the building plan site structure

and equipment satisfy the provisions of the law This requirement made the code prescriptive because

building officials must be able to judge the conformity The structural design was based on the allowable

stress design

The 1978 Miyagi-ken Oki Earthquake which caused serious damage led to accelerated implementation of the

revised Building Standard Law in 1981 The Building Standard Law included a seismic coefficient that

varies with structural vibration period and introduced a two-level design procedure The first level design















iiseS un

W C F F DQ Eq(2)




























(a) (b) (c)











983122983145983143983145983140 983138983141983137983149983122983145983143983145983140 983138983141983137983149

983127983137983148983148

983127983137983148983148

983127983137983148983148

983127983137983148983148

983127983137983148983148

983107983151983148983157983149983150983107983151983148983157983149983150

983122983145983143983145983140983085 983152983148983137983155983156983145983139 983155983152983154983145983150983143983142983151983154 983142983148983141983160983157983154983137983148 983138983141983144983137983158983145983151983154

983122983145983143983145983140983085983152983148983137983155983156983145983139 983155983152983154983145983150983143983142983151983154 983142983148983141983160983157983154983137983148 983138983141983144983137983158983145983151983154

983116983145983150983141983137983154 983155983152983154983145983150983143

983142983151983154 983155983144983141983137983154

983116983145983150983141983137983154 983155983152983154983145983150983143983142983151983154 983137983160983145983137983148 983138983141983144983137983158983145983151983154

983109983148983137983155983156 983145983139 983138983141983144983137983158983145983151983154 983109983148983137983155983156 983145983139 983138983141983144983137983158983145983151983154






stiffness of 5



INPUT MOTIONS






Record PGA (cmsec2)

El Centro NS 44812

Hachinohe NS 27791

Kobe NS 44405

Wg60 48430

Wg61 46733

Wg62 52292

Wg63 51004

983088983086983088 983088983086983093 983089983086983088 983089983086983093 983090983086983088 983090983086983093 983091983086983088

983088983086983088

983090983086983088

983092983086983088

983094983086983088

983096983086983088

983089983088983086983088

983089983090983086983088

983089983092983086983088

983089983094983086983088

983122

983141 983155 983152 983151 983150 983155 983141

983105

983139 983139 983141 983148 983141 983154 983137 983156 983145 983151 983150

983080 983149

983087 983155 983141 983139

983090 983081

983120983141983154983145983151983140 983080983155983141983139983081

983109983148 983107 983141983150983156983154983151 983118 983123

983112983137983139983144983145983150983151983144983141 983118983123

983115983151983138983141 983118983123

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983089

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983090

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983091

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983092






by Eq(4) given as

12

1

minus

=

micro s

D Eq(4)








983088 983089 983090 983091 983092 983093 983094

983088983086983088

983088983086983093

983089983086983088

983119983150983141983085983149983137983155983155 983155983161983155983156983141983149

983127 983080983088983086983091983081

983127 983080983089983081

983080983088983086983091983081

983080983088983086983093983081

983080983089983081

∆983089983161

983123 983156 983154 983141 983150 983143 983156 983144

983080 983111 983081

983108983145983155983152983148983137983139983141983149983141983150983156 983154983137983156983145983151 983080 ∆983087 ∆983089983161

983081











expressed by Eq (5)

S

S p

D

D

=α Eq(5)





( )

( ) ( )1214

1

12

1

1



μθ

θμθ

yS

n

i

y yS in

h Dmnn

h Dsmih DmiW Eq (6)






μ

983108983155

μ 991257

983108983155991257







( ) 1

2


where




983145983149983108983155

983144θ983161

μ 983144θ983161









)1(

2






弾性限界 α 983101983088 α 983101983089983088983100α 983100983089



( )

( )



2

11

4

1

12

1

2

1

1

μθ

θμθθα

α nh Dmn

h Dmnh Dmnh DmiW

yS

yS yS

n

i

yS in

Eq (9)


obtained

S

S

y

y

D

D

=

θ

θ Eq (10)

983145983149983108983155991257

983144θ983161

983145983149983108983155

983144θ983161

991257

α 983145983149983108983155991257

α 983144θ983161


rsquo





( ) ( )( ) ( )1221

121

minus+sdotminus

minussdot+==

μ

μ

α α

n

n

D

D

S

S p

Eq (11)





to 50

983088 983093 983089983088 983089983093 983090983088

983089983086983088

983089983086983093

983090983086983088

983090983086983093

983091983086983088

983091983086983093

α

983101983089983086983088

α983101983088983086983088

α

建物階数

αの値 983088983086983088 983088983086983089 983088983086983090 983088983086983091 983088983086983092 983088983086983093 983088983086983094 983088983086983095 983088983086983096 983088983086983097 983089983086983088







00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

20

Constant

displacement

983107 983151983150983155983156983137983150983156

983141983150983141983154983143983161

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141983150983156983154983151

983112983137983139983144 983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983089983092983110

micro

Ds


00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

20


Constant

energy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141983150983156983154983151

983112983137983139983144 983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983089983088983110

micro

Ds




00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

Constant

displacement

Constantenergy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141 983150983156983154983151

983112 983137983139983144983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983094983110

micro

Ds










is shown in fig 15





04 05 06 07 08

000

002

004

006

008

010

012

014

016


Ds

6F

10F 14F


6- 10- and 14-story



0 5 10 15

025

030

035

040

045

050

055

060

065

070

075

080

983124983144983141983151983154983141983156983145983139983137983148 983148983145983150983141

983123 983145983149 983152983148983145983142983145983141983140 983148983145983150983141

α

p

x D s

Number of Stories



CONCLUSIONS







greater

ACKNOWLEDGEMENT




REFERENCES







ACI pp 203-239 1985

















iiseS un

W C F F DQ Eq(2)




























(a) (b) (c)











983122983145983143983145983140 983138983141983137983149983122983145983143983145983140 983138983141983137983149

983127983137983148983148

983127983137983148983148

983127983137983148983148

983127983137983148983148

983127983137983148983148

983107983151983148983157983149983150983107983151983148983157983149983150

983122983145983143983145983140983085 983152983148983137983155983156983145983139 983155983152983154983145983150983143983142983151983154 983142983148983141983160983157983154983137983148 983138983141983144983137983158983145983151983154

983122983145983143983145983140983085983152983148983137983155983156983145983139 983155983152983154983145983150983143983142983151983154 983142983148983141983160983157983154983137983148 983138983141983144983137983158983145983151983154

983116983145983150983141983137983154 983155983152983154983145983150983143

983142983151983154 983155983144983141983137983154

983116983145983150983141983137983154 983155983152983154983145983150983143983142983151983154 983137983160983145983137983148 983138983141983144983137983158983145983151983154

983109983148983137983155983156 983145983139 983138983141983144983137983158983145983151983154 983109983148983137983155983156 983145983139 983138983141983144983137983158983145983151983154






stiffness of 5



INPUT MOTIONS






Record PGA (cmsec2)

El Centro NS 44812

Hachinohe NS 27791

Kobe NS 44405

Wg60 48430

Wg61 46733

Wg62 52292

Wg63 51004

983088983086983088 983088983086983093 983089983086983088 983089983086983093 983090983086983088 983090983086983093 983091983086983088

983088983086983088

983090983086983088

983092983086983088

983094983086983088

983096983086983088

983089983088983086983088

983089983090983086983088

983089983092983086983088

983089983094983086983088

983122

983141 983155 983152 983151 983150 983155 983141

983105

983139 983139 983141 983148 983141 983154 983137 983156 983145 983151 983150

983080 983149

983087 983155 983141 983139

983090 983081

983120983141983154983145983151983140 983080983155983141983139983081

983109983148 983107 983141983150983156983154983151 983118 983123

983112983137983139983144983145983150983151983144983141 983118983123

983115983151983138983141 983118983123

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983089

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983090

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983091

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983092






by Eq(4) given as

12

1

minus

=

micro s

D Eq(4)








983088 983089 983090 983091 983092 983093 983094

983088983086983088

983088983086983093

983089983086983088

983119983150983141983085983149983137983155983155 983155983161983155983156983141983149

983127 983080983088983086983091983081

983127 983080983089983081

983080983088983086983091983081

983080983088983086983093983081

983080983089983081

∆983089983161

983123 983156 983154 983141 983150 983143 983156 983144

983080 983111 983081

983108983145983155983152983148983137983139983141983149983141983150983156 983154983137983156983145983151 983080 ∆983087 ∆983089983161

983081











expressed by Eq (5)

S

S p

D

D

=α Eq(5)





( )

( ) ( )1214

1

12

1

1



μθ

θμθ

yS

n

i

y yS in

h Dmnn

h Dsmih DmiW Eq (6)






μ

983108983155

μ 991257

983108983155991257







( ) 1

2


where




983145983149983108983155

983144θ983161

μ 983144θ983161









)1(

2






弾性限界 α 983101983088 α 983101983089983088983100α 983100983089



( )

( )



2

11

4

1

12

1

2

1

1

μθ

θμθθα

α nh Dmn

h Dmnh Dmnh DmiW

yS

yS yS

n

i

yS in

Eq (9)


obtained

S

S

y

y

D

D

=

θ

θ Eq (10)

983145983149983108983155991257

983144θ983161

983145983149983108983155

983144θ983161

991257

α 983145983149983108983155991257

α 983144θ983161


rsquo





( ) ( )( ) ( )1221

121

minus+sdotminus

minussdot+==

μ

μ

α α

n

n

D

D

S

S p

Eq (11)





to 50

983088 983093 983089983088 983089983093 983090983088

983089983086983088

983089983086983093

983090983086983088

983090983086983093

983091983086983088

983091983086983093

α

983101983089983086983088

α983101983088983086983088

α

建物階数

αの値 983088983086983088 983088983086983089 983088983086983090 983088983086983091 983088983086983092 983088983086983093 983088983086983094 983088983086983095 983088983086983096 983088983086983097 983089983086983088







00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

20

Constant

displacement

983107 983151983150983155983156983137983150983156

983141983150983141983154983143983161

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141983150983156983154983151

983112983137983139983144 983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983089983092983110

micro

Ds


00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

20


Constant

energy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141983150983156983154983151

983112983137983139983144 983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983089983088983110

micro

Ds




00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

Constant

displacement

Constantenergy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141 983150983156983154983151

983112 983137983139983144983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983094983110

micro

Ds










is shown in fig 15





04 05 06 07 08

000

002

004

006

008

010

012

014

016


Ds

6F

10F 14F


6- 10- and 14-story



0 5 10 15

025

030

035

040

045

050

055

060

065

070

075

080

983124983144983141983151983154983141983156983145983139983137983148 983148983145983150983141

983123 983145983149 983152983148983145983142983145983141983140 983148983145983150983141

α

p

x D s

Number of Stories



CONCLUSIONS







greater

ACKNOWLEDGEMENT




REFERENCES







ACI pp 203-239 1985







(a) (b) (c)











983122983145983143983145983140 983138983141983137983149983122983145983143983145983140 983138983141983137983149

983127983137983148983148

983127983137983148983148

983127983137983148983148

983127983137983148983148

983127983137983148983148

983107983151983148983157983149983150983107983151983148983157983149983150

983122983145983143983145983140983085 983152983148983137983155983156983145983139 983155983152983154983145983150983143983142983151983154 983142983148983141983160983157983154983137983148 983138983141983144983137983158983145983151983154

983122983145983143983145983140983085983152983148983137983155983156983145983139 983155983152983154983145983150983143983142983151983154 983142983148983141983160983157983154983137983148 983138983141983144983137983158983145983151983154

983116983145983150983141983137983154 983155983152983154983145983150983143

983142983151983154 983155983144983141983137983154

983116983145983150983141983137983154 983155983152983154983145983150983143983142983151983154 983137983160983145983137983148 983138983141983144983137983158983145983151983154

983109983148983137983155983156 983145983139 983138983141983144983137983158983145983151983154 983109983148983137983155983156 983145983139 983138983141983144983137983158983145983151983154






stiffness of 5



INPUT MOTIONS






Record PGA (cmsec2)

El Centro NS 44812

Hachinohe NS 27791

Kobe NS 44405

Wg60 48430

Wg61 46733

Wg62 52292

Wg63 51004

983088983086983088 983088983086983093 983089983086983088 983089983086983093 983090983086983088 983090983086983093 983091983086983088

983088983086983088

983090983086983088

983092983086983088

983094983086983088

983096983086983088

983089983088983086983088

983089983090983086983088

983089983092983086983088

983089983094983086983088

983122

983141 983155 983152 983151 983150 983155 983141

983105

983139 983139 983141 983148 983141 983154 983137 983156 983145 983151 983150

983080 983149

983087 983155 983141 983139

983090 983081

983120983141983154983145983151983140 983080983155983141983139983081

983109983148 983107 983141983150983156983154983151 983118 983123

983112983137983139983144983145983150983151983144983141 983118983123

983115983151983138983141 983118983123

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983089

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983090

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983091

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983092






by Eq(4) given as

12

1

minus

=

micro s

D Eq(4)








983088 983089 983090 983091 983092 983093 983094

983088983086983088

983088983086983093

983089983086983088

983119983150983141983085983149983137983155983155 983155983161983155983156983141983149

983127 983080983088983086983091983081

983127 983080983089983081

983080983088983086983091983081

983080983088983086983093983081

983080983089983081

∆983089983161

983123 983156 983154 983141 983150 983143 983156 983144

983080 983111 983081

983108983145983155983152983148983137983139983141983149983141983150983156 983154983137983156983145983151 983080 ∆983087 ∆983089983161

983081











expressed by Eq (5)

S

S p

D

D

=α Eq(5)





( )

( ) ( )1214

1

12

1

1



μθ

θμθ

yS

n

i

y yS in

h Dmnn

h Dsmih DmiW Eq (6)






μ

983108983155

μ 991257

983108983155991257







( ) 1

2


where




983145983149983108983155

983144θ983161

μ 983144θ983161









)1(

2






弾性限界 α 983101983088 α 983101983089983088983100α 983100983089



( )

( )



2

11

4

1

12

1

2

1

1

μθ

θμθθα

α nh Dmn

h Dmnh Dmnh DmiW

yS

yS yS

n

i

yS in

Eq (9)


obtained

S

S

y

y

D

D

=

θ

θ Eq (10)

983145983149983108983155991257

983144θ983161

983145983149983108983155

983144θ983161

991257

α 983145983149983108983155991257

α 983144θ983161


rsquo





( ) ( )( ) ( )1221

121

minus+sdotminus

minussdot+==

μ

μ

α α

n

n

D

D

S

S p

Eq (11)





to 50

983088 983093 983089983088 983089983093 983090983088

983089983086983088

983089983086983093

983090983086983088

983090983086983093

983091983086983088

983091983086983093

α

983101983089983086983088

α983101983088983086983088

α

建物階数

αの値 983088983086983088 983088983086983089 983088983086983090 983088983086983091 983088983086983092 983088983086983093 983088983086983094 983088983086983095 983088983086983096 983088983086983097 983089983086983088







00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

20

Constant

displacement

983107 983151983150983155983156983137983150983156

983141983150983141983154983143983161

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141983150983156983154983151

983112983137983139983144 983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983089983092983110

micro

Ds


00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

20


Constant

energy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141983150983156983154983151

983112983137983139983144 983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983089983088983110

micro

Ds




00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

Constant

displacement

Constantenergy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141 983150983156983154983151

983112 983137983139983144983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983094983110

micro

Ds










is shown in fig 15





04 05 06 07 08

000

002

004

006

008

010

012

014

016


Ds

6F

10F 14F


6- 10- and 14-story



0 5 10 15

025

030

035

040

045

050

055

060

065

070

075

080

983124983144983141983151983154983141983156983145983139983137983148 983148983145983150983141

983123 983145983149 983152983148983145983142983145983141983140 983148983145983150983141

α

p

x D s

Number of Stories



CONCLUSIONS







greater

ACKNOWLEDGEMENT




REFERENCES







ACI pp 203-239 1985





INPUT MOTIONS






Record PGA (cmsec2)

El Centro NS 44812

Hachinohe NS 27791

Kobe NS 44405

Wg60 48430

Wg61 46733

Wg62 52292

Wg63 51004

983088983086983088 983088983086983093 983089983086983088 983089983086983093 983090983086983088 983090983086983093 983091983086983088

983088983086983088

983090983086983088

983092983086983088

983094983086983088

983096983086983088

983089983088983086983088

983089983090983086983088

983089983092983086983088

983089983094983086983088

983122

983141 983155 983152 983151 983150 983155 983141

983105

983139 983139 983141 983148 983141 983154 983137 983156 983145 983151 983150

983080 983149

983087 983155 983141 983139

983090 983081

983120983141983154983145983151983140 983080983155983141983139983081

983109983148 983107 983141983150983156983154983151 983118 983123

983112983137983139983144983145983150983151983144983141 983118983123

983115983151983138983141 983118983123

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983089

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983090

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983091

983105 983154983156983145983142983145983139983145983137983148 983127 983137983158983141 983092






by Eq(4) given as

12

1

minus

=

micro s

D Eq(4)








983088 983089 983090 983091 983092 983093 983094

983088983086983088

983088983086983093

983089983086983088

983119983150983141983085983149983137983155983155 983155983161983155983156983141983149

983127 983080983088983086983091983081

983127 983080983089983081

983080983088983086983091983081

983080983088983086983093983081

983080983089983081

∆983089983161

983123 983156 983154 983141 983150 983143 983156 983144

983080 983111 983081

983108983145983155983152983148983137983139983141983149983141983150983156 983154983137983156983145983151 983080 ∆983087 ∆983089983161

983081











expressed by Eq (5)

S

S p

D

D

=α Eq(5)





( )

( ) ( )1214

1

12

1

1



μθ

θμθ

yS

n

i

y yS in

h Dmnn

h Dsmih DmiW Eq (6)






μ

983108983155

μ 991257

983108983155991257







( ) 1

2


where




983145983149983108983155

983144θ983161

μ 983144θ983161









)1(

2






弾性限界 α 983101983088 α 983101983089983088983100α 983100983089



( )

( )



2

11

4

1

12

1

2

1

1

μθ

θμθθα

α nh Dmn

h Dmnh Dmnh DmiW

yS

yS yS

n

i

yS in

Eq (9)


obtained

S

S

y

y

D

D

=

θ

θ Eq (10)

983145983149983108983155991257

983144θ983161

983145983149983108983155

983144θ983161

991257

α 983145983149983108983155991257

α 983144θ983161


rsquo





( ) ( )( ) ( )1221

121

minus+sdotminus

minussdot+==

μ

μ

α α

n

n

D

D

S

S p

Eq (11)





to 50

983088 983093 983089983088 983089983093 983090983088

983089983086983088

983089983086983093

983090983086983088

983090983086983093

983091983086983088

983091983086983093

α

983101983089983086983088

α983101983088983086983088

α

建物階数

αの値 983088983086983088 983088983086983089 983088983086983090 983088983086983091 983088983086983092 983088983086983093 983088983086983094 983088983086983095 983088983086983096 983088983086983097 983089983086983088







00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

20

Constant

displacement

983107 983151983150983155983156983137983150983156

983141983150983141983154983143983161

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141983150983156983154983151

983112983137983139983144 983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983089983092983110

micro

Ds


00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

20


Constant

energy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141983150983156983154983151

983112983137983139983144 983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983089983088983110

micro

Ds




00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

Constant

displacement

Constantenergy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141 983150983156983154983151

983112 983137983139983144983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983094983110

micro

Ds










is shown in fig 15





04 05 06 07 08

000

002

004

006

008

010

012

014

016


Ds

6F

10F 14F


6- 10- and 14-story



0 5 10 15

025

030

035

040

045

050

055

060

065

070

075

080

983124983144983141983151983154983141983156983145983139983137983148 983148983145983150983141

983123 983145983149 983152983148983145983142983145983141983140 983148983145983150983141

α

p

x D s

Number of Stories



CONCLUSIONS







greater

ACKNOWLEDGEMENT




REFERENCES







ACI pp 203-239 1985










983088 983089 983090 983091 983092 983093 983094

983088983086983088

983088983086983093

983089983086983088

983119983150983141983085983149983137983155983155 983155983161983155983156983141983149

983127 983080983088983086983091983081

983127 983080983089983081

983080983088983086983091983081

983080983088983086983093983081

983080983089983081

∆983089983161

983123 983156 983154 983141 983150 983143 983156 983144

983080 983111 983081

983108983145983155983152983148983137983139983141983149983141983150983156 983154983137983156983145983151 983080 ∆983087 ∆983089983161

983081











expressed by Eq (5)

S

S p

D

D

=α Eq(5)





( )

( ) ( )1214

1

12

1

1



μθ

θμθ

yS

n

i

y yS in

h Dmnn

h Dsmih DmiW Eq (6)






μ

983108983155

μ 991257

983108983155991257







( ) 1

2


where




983145983149983108983155

983144θ983161

μ 983144θ983161









)1(

2






弾性限界 α 983101983088 α 983101983089983088983100α 983100983089



( )

( )



2

11

4

1

12

1

2

1

1

μθ

θμθθα

α nh Dmn

h Dmnh Dmnh DmiW

yS

yS yS

n

i

yS in

Eq (9)


obtained

S

S

y

y

D

D

=

θ

θ Eq (10)

983145983149983108983155991257

983144θ983161

983145983149983108983155

983144θ983161

991257

α 983145983149983108983155991257

α 983144θ983161


rsquo





( ) ( )( ) ( )1221

121

minus+sdotminus

minussdot+==

μ

μ

α α

n

n

D

D

S

S p

Eq (11)





to 50

983088 983093 983089983088 983089983093 983090983088

983089983086983088

983089983086983093

983090983086983088

983090983086983093

983091983086983088

983091983086983093

α

983101983089983086983088

α983101983088983086983088

α

建物階数

αの値 983088983086983088 983088983086983089 983088983086983090 983088983086983091 983088983086983092 983088983086983093 983088983086983094 983088983086983095 983088983086983096 983088983086983097 983089983086983088







00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

20

Constant

displacement

983107 983151983150983155983156983137983150983156

983141983150983141983154983143983161

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141983150983156983154983151

983112983137983139983144 983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983089983092983110

micro

Ds


00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

20


Constant

energy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141983150983156983154983151

983112983137983139983144 983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983089983088983110

micro

Ds




00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

Constant

displacement

Constantenergy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141 983150983156983154983151

983112 983137983139983144983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983094983110

micro

Ds










is shown in fig 15





04 05 06 07 08

000

002

004

006

008

010

012

014

016


Ds

6F

10F 14F


6- 10- and 14-story



0 5 10 15

025

030

035

040

045

050

055

060

065

070

075

080

983124983144983141983151983154983141983156983145983139983137983148 983148983145983150983141

983123 983145983149 983152983148983145983142983145983141983140 983148983145983150983141

α

p

x D s

Number of Stories



CONCLUSIONS







greater

ACKNOWLEDGEMENT




REFERENCES







ACI pp 203-239 1985





μ

983108983155

μ 991257

983108983155991257







( ) 1

2


where




983145983149983108983155

983144θ983161

μ 983144θ983161









)1(

2






弾性限界 α 983101983088 α 983101983089983088983100α 983100983089



( )

( )



2

11

4

1

12

1

2

1

1

μθ

θμθθα

α nh Dmn

h Dmnh Dmnh DmiW

yS

yS yS

n

i

yS in

Eq (9)


obtained

S

S

y

y

D

D

=

θ

θ Eq (10)

983145983149983108983155991257

983144θ983161

983145983149983108983155

983144θ983161

991257

α 983145983149983108983155991257

α 983144θ983161


rsquo





( ) ( )( ) ( )1221

121

minus+sdotminus

minussdot+==

μ

μ

α α

n

n

D

D

S

S p

Eq (11)





to 50

983088 983093 983089983088 983089983093 983090983088

983089983086983088

983089983086983093

983090983086983088

983090983086983093

983091983086983088

983091983086983093

α

983101983089983086983088

α983101983088983086983088

α

建物階数

αの値 983088983086983088 983088983086983089 983088983086983090 983088983086983091 983088983086983092 983088983086983093 983088983086983094 983088983086983095 983088983086983096 983088983086983097 983089983086983088







00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

20

Constant

displacement

983107 983151983150983155983156983137983150983156

983141983150983141983154983143983161

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141983150983156983154983151

983112983137983139983144 983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983089983092983110

micro

Ds


00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

20


Constant

energy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141983150983156983154983151

983112983137983139983144 983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983089983088983110

micro

Ds




00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

Constant

displacement

Constantenergy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141 983150983156983154983151

983112 983137983139983144983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983094983110

micro

Ds










is shown in fig 15





04 05 06 07 08

000

002

004

006

008

010

012

014

016


Ds

6F

10F 14F


6- 10- and 14-story



0 5 10 15

025

030

035

040

045

050

055

060

065

070

075

080

983124983144983141983151983154983141983156983145983139983137983148 983148983145983150983141

983123 983145983149 983152983148983145983142983145983141983140 983148983145983150983141

α

p

x D s

Number of Stories



CONCLUSIONS







greater

ACKNOWLEDGEMENT




REFERENCES







ACI pp 203-239 1985





)1(

2






弾性限界 α 983101983088 α 983101983089983088983100α 983100983089



( )

( )



2

11

4

1

12

1

2

1

1

μθ

θμθθα

α nh Dmn

h Dmnh Dmnh DmiW

yS

yS yS

n

i

yS in

Eq (9)


obtained

S

S

y

y

D

D

=

θ

θ Eq (10)

983145983149983108983155991257

983144θ983161

983145983149983108983155

983144θ983161

991257

α 983145983149983108983155991257

α 983144θ983161


rsquo





( ) ( )( ) ( )1221

121

minus+sdotminus

minussdot+==

μ

μ

α α

n

n

D

D

S

S p

Eq (11)





to 50

983088 983093 983089983088 983089983093 983090983088

983089983086983088

983089983086983093

983090983086983088

983090983086983093

983091983086983088

983091983086983093

α

983101983089983086983088

α983101983088983086983088

α

建物階数

αの値 983088983086983088 983088983086983089 983088983086983090 983088983086983091 983088983086983092 983088983086983093 983088983086983094 983088983086983095 983088983086983096 983088983086983097 983089983086983088







00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

20

Constant

displacement

983107 983151983150983155983156983137983150983156

983141983150983141983154983143983161

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141983150983156983154983151

983112983137983139983144 983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983089983092983110

micro

Ds


00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

20


Constant

energy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141983150983156983154983151

983112983137983139983144 983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983089983088983110

micro

Ds




00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

Constant

displacement

Constantenergy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141 983150983156983154983151

983112 983137983139983144983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983094983110

micro

Ds










is shown in fig 15





04 05 06 07 08

000

002

004

006

008

010

012

014

016


Ds

6F

10F 14F


6- 10- and 14-story



0 5 10 15

025

030

035

040

045

050

055

060

065

070

075

080

983124983144983141983151983154983141983156983145983139983137983148 983148983145983150983141

983123 983145983149 983152983148983145983142983145983141983140 983148983145983150983141

α

p

x D s

Number of Stories



CONCLUSIONS







greater

ACKNOWLEDGEMENT




REFERENCES







ACI pp 203-239 1985







( ) ( )( ) ( )1221

121

minus+sdotminus

minussdot+==

μ

μ

α α

n

n

D

D

S

S p

Eq (11)





to 50

983088 983093 983089983088 983089983093 983090983088

983089983086983088

983089983086983093

983090983086983088

983090983086983093

983091983086983088

983091983086983093

α

983101983089983086983088

α983101983088983086983088

α

建物階数

αの値 983088983086983088 983088983086983089 983088983086983090 983088983086983091 983088983086983092 983088983086983093 983088983086983094 983088983086983095 983088983086983096 983088983086983097 983089983086983088







00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

20

Constant

displacement

983107 983151983150983155983156983137983150983156

983141983150983141983154983143983161

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141983150983156983154983151

983112983137983139983144 983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983089983092983110

micro

Ds


00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

20


Constant

energy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141983150983156983154983151

983112983137983139983144 983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983089983088983110

micro

Ds




00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

Constant

displacement

Constantenergy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141 983150983156983154983151

983112 983137983139983144983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983094983110

micro

Ds










is shown in fig 15





04 05 06 07 08

000

002

004

006

008

010

012

014

016


Ds

6F

10F 14F


6- 10- and 14-story



0 5 10 15

025

030

035

040

045

050

055

060

065

070

075

080

983124983144983141983151983154983141983156983145983139983137983148 983148983145983150983141

983123 983145983149 983152983148983145983142983145983141983140 983148983145983150983141

α

p

x D s

Number of Stories



CONCLUSIONS







greater

ACKNOWLEDGEMENT




REFERENCES







ACI pp 203-239 1985






00 02 04 06 08 10 12 14 16

0

2

4

6

8

10

12

14

16

18

Constant

displacement

Constantenergy

983159983143983094983088

983159983143983094983089

983159983143983094983090

983159983143983094983091

983109983148 983107983141 983150983156983154983151

983112 983137983139983144983145983150983151983144983141

983115983151983138983141

α983101983089983086983088

α983101983088983086983088

983094983110

micro

Ds










is shown in fig 15





04 05 06 07 08

000

002

004

006

008

010

012

014

016


Ds

6F

10F 14F


6- 10- and 14-story



0 5 10 15

025

030

035

040

045

050

055

060

065

070

075

080

983124983144983141983151983154983141983156983145983139983137983148 983148983145983150983141

983123 983145983149 983152983148983145983142983145983141983140 983148983145983150983141

α

p

x D s

Number of Stories



CONCLUSIONS







greater

ACKNOWLEDGEMENT




REFERENCES







ACI pp 203-239 1985





0 5 10 15

025

030

035

040

045

050

055

060

065

070

075

080

983124983144983141983151983154983141983156983145983139983137983148 983148983145983150983141

983123 983145983149 983152983148983145983142983145983141983140 983148983145983150983141

α

p

x D s

Number of Stories



CONCLUSIONS







greater

ACKNOWLEDGEMENT




REFERENCES







ACI pp 203-239 1985



Documents

Non-linear numerical analyses to improve the seismic design method for soft first story RC building.pdf