New Seismic Design Criteria of Piping Systems in High口 Pressure

Ｓ
ｅ
Masatoshi lkeda
ユ百 Ｌ
on,
Toyo Engineering
Co「
poraは
TeChRO10gy Research and Development Center,
shi,Chiba,
ashino―
8,l Akanehama 2-chome,Na「
3 a p a n
Ｃ
ａ
ＥＦ
Ｓ
ａ
企ｕ
Makolo inaba
New Seismic Design Criteria of
Pressure
Piping Systems in High口
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[DOI:10.1115/1.1638789]
tain the propdety of design cttteria of piping systems with respect
to ground displacement,large defomation tests using several pip―
Scislnic design of high― pressure gas facilities such as towers
ing models were carned out by KItIK.
and vessels had Previously been carned out in accordance with
In this papeL wc introduce the requirements in the new seisHuc
Pressure
MITI Notiflcation 515 ``SeisHlic Design Code for lHigh―
design code,that is,the importance classiflcation of a piping sys―
Gas Facilities''established in 1981([1]).The Great Hyogoken― tem, the design base earthquake, response analysis, response
analysis against ground disPlacement and the evaluation method
nanbu Earthquake occurred in 1995 and the ground acceleration
of the Ll―RSR Then,we introduce the evaluatlon method of the
much beyond that ofthe Design Base Earthquake in the code was
L2-RSP proPosed in the guideline, and report the results of the
rccordedo Some piping systems were damaged due to ground dis―
large defomation tests.
PlaCement(Settlement and/or lateral movcment)induCed by lique―
faction. Having learned from the expedcnces of the Great
Hyogoken― nanbu Earthquake, the seisFliC design code was
阻iC Design Code
2 Requirements in New Seis】
amended in 1997([2]).
In thc amended code, both Level l and Leve1 2 carthquakes
2。l lmportance(Classiflcation of PiPing System
were considered,and the seisllic design of a piping systern was
れC 夕C a rg ビ
newly included within the scope ofthe code.A Level l earthquakc
2 . F . Fβ
rθr″惚
ヮ ザ P , , gれ. H i g ph r―e s s u r e
g a s
θ
cllities are classined into four categones,Ia,I,II and III,accord―
is a probable strong earthquake occurnng in the service life of the
ing to three factorsi the typc of high―prcssure gas,the inventory,
facllities,and a Leve1 2 earthquake is a possible strongest earth―
and the distance frorn the outer surface of a facility to the bound―
quake with an extremely low probablllty of occurrence.Facilities
ary of the plant grounds. When the importance of a tower or a
are required to remain safe without plastic defomation and with―
vessel(collectively called a vessel hereinafter)iS higher than that
Out gas leakage against the ground acceleration of a Level l earth―
of connecting piping,the importance of the piping is adapted to
quake.In addition,they are also required to rcmain safe without
that of thc vessel. This is based on the idea of preventing thc
gas leakage against the ground acceleration and possible ground
contents of a vessel from leaking through damaged piping of
displacement of a Leve1 2 carthquakee r)lastic defomation is al―
lower importance.
lowed in the case of a Leve1 2 earthquake.These seisIIllc PerfOr―
協 ルタ・
2.ア.2 筋 ?θ r勉れc夕 効 姥gοヮ て
mances are called the “ Level l Required Seislmc Perfomance"
研
ゲ 丘″れ?″αた夕 Sん″r―
is installed in a piping systcm
o3「valve
When
an
earthquake
shut―
Leve1
2
Required
Scismic
Perfor―
RSP
hereinafter)and
the“
(Ll―
connected to a vessel and the importance of the valve is adapted to
mance''(L2-RSP hereinafterl,respectively.The latter evaluation
that of the vessel, the importance of the piping after the valve
is applied only to facilities in the high importance category.
necd not be｀adapted to that of thc vessel.This is based on the idea
An evaluation method of Ll― RSP for each structure is specined
that shutting off the piPing right after an earthquake can funda―
in the amended cOde,On the other hand,the evaluation methods
mentally elirninate the possibility of the release of the contents of
of L2-RS■ including the estimation method of ground displace―
the vesscl through the piping after the valve.
mcnt, were investigated by corlmttees organized in the IIigh…
of a dc…
P r e s s u r e G a s S a f e t y l n s t i t u t e o f J a p a n (2.2
K I Design
t I K )Base
, a nEarthquake.
d t h O S Seislnic
C m e t coefacients
h o d s
sign base earthquake at the ground surfacc are desc五 bed by Eqs.
wcre proposcd in a guidelinc published by KIIK([3]).To aSCer_
l
lntroduction
(1)and(2)in the COde.
Conthbutcd by thc Pressure Vesseis and Piping Division for publication in the
JOURNAL OF PRESSURE VESSEL TECHNOLOGY.ManuscFipt received by the PVP
Division September 26,2003;revision rcccived October
G.C.Siagis.
Journal of Pressure Vesset Techno!ogy
Copyright()2004 by ASME
【〃=0。150μた
2β3
βlβ
13,2003.Associate
てy=0.075μた
βlβ
2β3
(1)
EditoE
FEBRUARY 2004,Vol,126/ 9
(2)
f
Wherc【″and【y are the horizontal and vertical seisllic
2.4 ResPonse
Analysis Against Cround Displacement
coefn―
cients of a design basc earthquake at the ground surface,and
β
l,
2.イ
. アR で w θ れs 夕A れαウS な ザ F 9 ″れがαr J θ
れA g αれs r C 門″れ冴 D F s ―
β2,β3,and μk are the importance category factor(1.0-0.5),
′
αc夕れcれA In evaluating the L2-RSP of a foundation,it is nec―
s e i s m i c z o n e f a c t o r ( 1 . 0 - 0 . 4 f o r L e v e l βl e a r t h q u a k c s , 1 . 0 - 0 . 7 f o r
essary tO caFy Out rcsponse analysis by an adequate method tak中
Levc1 2 earthquakes), site amplincation factor(2.0-1.4), and
ing into consideration liquefaction―
induced ground displacement
carthquake level factor(1,O fOr Level l earthquakcs,2.O or over
(Called“ ground displacement"hereinafter).It is also specined
for Lcve1 2 earthquakes),rcSpectively.Response magnincation
that the effect of ground shaking and ground displacement rnay be
curves are prepared corresponding to each seislnic zone and soil
evaluated separately,
pronle type.
It was observed in Past earthquakes that tilne lags occurred
between the mttor grOund shakings and the ground displacements.
2.3 ResPonSe Analysis
It、vas also obscrved during the Hyogoken― nanbu Earthquake that
the ampllication of acceleration frorn the basc rock was relatively
sC
Aれα
rytsJs`メ
S“
ο
rr′
ぇ
2.J.F Rで wθ れ
Pβ
g srttc物 ″.seismic
small in the surfacc soil where large― scale liquefaction was in―
rcsponses of supporting stmctures such as towers, vessels, and
duced.Thcse arc background data of thc judgment of
steel structurcs are analyzed by the modined static coefacient
chteria.
method or the response spcctrurn method. The static coefflcient
ver
impOrtance
categorics
method is applicable for structures in lo、
2.イ
.2 P"jれ g FJで克うど
JJ伊 ょ〃 C的 ″れど Djッ Jα
c2秘ゼれr.It is
the design
specined that the piping connected to a vessel with an earthquake
shut―
off valve shall be flxed to a supporting structure after the
2.J.2 R2学 っ″s夕 Attα ゥsな り
g SySrゼ 砲。 Seismic re―
valve on a coHllnon―
foundation with the vessel,C)therwise,it shall
sponses of piping systems are analyzed by the modined static
be conimed that the piping system is sufaciendy nexible t。
、
vith…
coeficient method or the response sPectruFn method. Response
stand ground displacement.This design critenon is based on the
spectra given in the code are those for the seisFliC design of struc―
idea that, if a piping is nxed to a supporting structure on a
tures standing directly on the ground. い江any piping systems are
common― foundation,relative displacement does not arise between
supported by supporting stluctures. Consequently, the modined
the nozzlc and the nxed point even though ground displacementis
seislnic coefacient lnethod is usually applied to piPing systems.
induced by liquefaction around the foundation.
(II and III)and relatively small in sizc.
'P"れ
2.J.J S夕 な初,c Fθ/c夕 qデ Pゥ jれ
g ttSr夕初 メ,r〃 θど茅ビ冴 SビjsttJc
タサ
んοtt Seismic coettcients of a supporting struc―
″ 舟″
Cθて
新'CJ夕
ture in thc horizontal and vertical directions at suppoiing
a pipe‐
point are obtained by using
2.5 Stress Calculation and A1lowable Stress for the Level l
Required SeisHlic Performance Evaluation. Strcss calculation
methods and allowable strcsses for the evaluation of Ll―RSP of
piping systems are sumHlarlzed in Table l.
Stress calculation fomulas are fundanentally the same as those
of ASWIE B31,3“ Process Piping,''except that the effect of axial
【〃y=β6【7
(4)
force is considered in calculating longitudinal stress. A stress
range of doublc the yield point is allowed for cyclic loading.
where μ【〃″ and J【
材y are the supporting stnicture's horizontal
In addition to the evaluation method by analysis,an easy sub―
seisHlic coefncient and vertical seisIIllc coefaCient at a supporting
stitutive method is prepared for piping in a lower importance cat―
re the horizontal response magnincation
6d , aβn d a μ
p o i n t 5a ,n β
factor,vertical response magniflcation factor,and hoぶzontal scis― e30ry(II,III).ThiS easy lnethod includes a support span check
against seislnic force and a displacement― absorbing―capacity
rnic coefncicnt distribution factor, respectively. When the re―
sponse spectrum method or the static coefacient rnethod is applied check against relative displacement(detail explanations are omit―
to thc supporting structure,the ratio of response acceleration at a ted here).
μ【材″=μβ5【″
(3)
supporting point to the acceleration of gravity or the seislnic co―
3 Evaluation of Level‐
2 SeisIIlic Performenve
cfncient at a supporting point is substituted for the value of
The cvaluation mcthod of the L2-RSP of Piping systems is
μ【〃″.
AssuHling that double the rcsPonse acceleration of a structure at established to conform to the basic concept of the code and in
a supporting point is induced unifomly in a piping systern,scis―
consideratlon of the consistcncy with that of the RSR
Ll―
rnic force which acts on the piping systern is exprcssed as
F〃″=β8μ【〃″W″
F〃y=β9【材yWy
3.l
(5)
(6)
SeisHlic Load
J.ア
.F D2s,gれ ずがsれJC Fθ/c夕
.Design seismic force is given
by Eqs.(5)and(6).
where F〃″and F〃v are a design modined horizontal seismic
J.F.2 Cα ′
c″Jar′
θれ 9β Rcspθれs夕 D為フ′
αご￠初夕れrてデ S叫7ο /rJれ
g
forcc(″
act. In the evaluation of the L2-RSP of a facility,the
り and a design modined vertical seismic force which
Srr″
cr"″
on the piping system(瑚
,β8and β
timate Design Method is usually applied(Shibata,[4]).In this
9 are the horizontal and verti―
Ul―
cal acceleration amplincatiOn factors(2.O for both),and w″ and
evaluation method,the yield ratio(the ratio of plastic deforlnation
uFy are piping weights in the horizontal and vertical directionsto yield deforlnation)is calculated for each failurc mode.There―
(り,reSpectively.
The seislnic forces of a piping system in the modined static
coefncient inethod are described by Eqs.(5)and(6)in the code.
For valves,the acceleration amplincation of l.O to 3.O fronl the
fore, fundamentally, it is possible to obtain the maximum dis―
０
μ
e r e,ら
ら〃″, μ
【
″a r e
″, る, a n d〃
＞
″
〃
杭， ０
仰 ら
ヤ ル
10/ Vol.126,FEBRUARY 2004
〓
quake even if it resonates with the response wavc of a structure.
ら
piping is considered.
Piping systems generally havc the structural charactenstics
such as being supportcd at a number of Points and high ductility.
0、ving to these characteristics,much damage in past earthquakes
was due to relative displacement between supporting points while
there was little damage due to the inertia force of the piping itseli
On the basis of the c貞teria,it is considercd that a piping system
designed by considenng an acceleration amplincation of 2.O from
the supporting point will not be senously damaged by an earth―
Wh
ｒ
物ゲ
ユ
placement at each elevation by investigating evcry fallure mode of
the facility.】
Iowever,this method is not convenient,It is consid―
ered that the displacement expressed as Eq.(7),in whiCh the
distttbution curve of Plastic defomation is approxirnated by that
of elastic defomatlon,rnay be used as the design disPlaccment of
the L2-RSP cvaluation of a piping system.
the
disPlacement at a supporting point(Fnm),reSpOnsc ho占
responsc
zontal dis―
Transactions of the ASME
ho
PIPhg
Longatuthdい
geSsdc rore
Stress calculation and a‖
owable stress for evaluation of Leve1 l Seisrnic Perforrnance
臣配RC―
dOn alld dlowable stHg
due to lnte― lp― -9 wdght and desngn
q=
+陽
BHSCal側
Vdve
山tacn md al10wable stHs
glgn getsmにfoNe When the wdghty d紳 山唯
説配N due to dと
1忠対
「 SS nOt SuPP。
島= 警 れ
n valve body tt
揮a betw∞
軸:鵡親総ど
群胡糾
軌
●輸研of
、
銅。
nal tta崎
。
弱
獄灘黙靴 研
警1:銭
e側
-2)
d五
宙
鮮縄盟掘品如
鮒
ぃ苺
脅:盟
￨
〕 m
銘ばJr(前
比縄 監 撒釘
A■owable tt―
HIBge duc to deslgn seStt forte and
Res― t sほ
movement ofsupPort
T阿●ofvalve
『valve
uake shute。
Allow
0.5S
stress
Other valves
EIP皿
―
ston
30ht
中
温辞総 穐電
孟襴 鞘瑞器盟営
韮il
tti品
盤'提
想鮒協湧鞘 s°
胡1+翌
猟
掛ど
COrreSDOndn2to desin cvCle number 500.
Allovrable strss
Tvpe Of昼笠oSS
Allowable stress
hnEttanal stess
Cyclic sttsS range
(い
Ia.I
O的
薔闘轟勲鑑鰐盤盟器撤
Pressure
=P+鳥
亀『
亜 ress lntensitv
Aliow st―
v Eentt meコ nbrane stess mtensitv
Primry local membrane plus tt bendmg
stress antensitv
_
Direrence cf maxlmum and malmum value at
1.5S
罷緒だ。
終戦魚盟 ど
濫出描l盟
品ri叫
2Sy
fmtenal
■抑●。
A l l o t■t e s s
Radius streSs in aan野
Cimmal ttSSintlanRe
2Sy
the
鮮 態
駈時
比
Allowable g―
The smallest of
foliowings
研詢 r e
room te叩
(1)0.6St(2)0.9Sy
Austmite mmess steel and highcnckel d I L o
加町es hner than
alloy used tt temPα
(1)0.6SuO
room t叩 匂臣tu『●
(3)0.9Sy。
d田
にo
Oth鶴
(1)0.6Suc
(3)0.9Sy。
餓背錯縦8鞭
００
の
部
毘緊魁慰ゴ輩魁認躍習品魁略m)
!樹
押温
lR肥
ぬsdal strtts in hub
o t t D
Allowable st―
Hi allowable邸臣超Hg S ibrtheョdLHdc design oF
駐alld■
=券・
え
挙
●ss
Type cF S位
Node
(い
13.I
F h n g e
r
」
闘鑑縄齢翻勝艦灘!濫l鞘
銘
６，
０時
り０
￨
Tab:el
説
Movement ofsuppoi:MoVementofStppOtt point due tt resPonSe disPlacement ofsupPcttng smcture
placemcnt of the structure at a supporting point corresPonding tothree meterst T■lis value is nearly equal to the actual displacement
t h e d e s i g n m o d i n e d h o d z o n t a l c o e f a c i e n t ( m m ) , p l a s t i c r e s p o n s ecaused by the Great Hyogoken― nanbu Earthquake.The amounts of
ratio ofthe mode,wherc the plastic response ratio is the largest of settlement, irregular settlement and horizontal displacement of a
all the failure modes,the yield seisHlic coefflcient,and the design foundatlon are calculated taking into consideration factors such as
modifled horizontal seisHlic coefncient,resPectively.
the existence of plles,length of piles,the depth of liquened layer,
is obtained and liqucaed soil properties,and the distance froFn the quay wall.
For a steel structure,the displacement of eachOra。
ng the
by adding the layer displacement, calculated by considc点
Fronl the results of response analyses of the foundation with re…
spect to ground disPlacemcnt,the displacement of thc structure at
plastic defomation,to the displacement of the lower floo丘
the pipe support point can be calculated.
れ Dげw′αc夕初ビれ, Duhng the
′
αガθ兄 ザ 乃 ″れ滋 r'ο
J.ア.J(効 Fc″
Great Hyogoken― nanbu Earthquake, large scale liquefaction ?c―
curred at reclailned land near the scaside and subsequent ground
settlement extended to 70 to 80 centiineters. At the seaside,
3.2 ResPonse Analysis
type quay walls moved several rneters toward the sea and
gravity―
the liquened ground landward ofthe quay walls aowed toward the
J,2.F 〃 ゼ滋ο冴 げ AttαウsJS,Nonlinear FEM(anite element
e ettct of the movemcnt of the quay
sea at the same tiine. 恥
method)analysis is very effective for analyzing the plastic re―
、
valls extended to the land nearly one hundrcd meters froln the sponse behavlor of a piping system.HoweveL this lnethod is not
sea, though the alnount of ground displacement decreased with popular in ordinary piPing design.A sirnPlined methOd called the
incrcasing distance.
modined aexibility factor inethod was investigated for designers'
After this earthquake,the method of estilnating the amount of convenlence.
ground displacement and the response analysis method of a foun―
θユ An elbow,pre―
'′
′
ゥ 乃 Cわr〃 ゼrん
dation were investigated by a cornlltlltteC Organized in the KIIK J.2.2 〃 ο冴"夕冴 用 α Jう
cisely spettng,a comer composed of an elbow and attacent
and some methods werc proposed in their guidelinc([3]).Accord―
short parts of straight pipes, has plastic defomation capabilities
ing to the results of this investigation,the amount of ground dis―
such as absorPtion Of large angular displacement with relatively
PlaCement depends on the soil conditions,the type of quay wall
small local strain under a bending moment smaller than the fully
and the coniguration around the quay wall.Finally,the estiIIlated
maximum value of ground displacement in the 、 vorst case was
plastic moment of a straight pipe.This implies that the nonlinear
Journal of Pressure Vesse:Technology
FEBRUARY 2004,Vol.126/ 11
behavior of piping systems can be analyzed,as long as the straight
pipc shows allnost linear behavior,by tttng into consideration
thc nonlinear characteristics of only elbows.
Modined flexibility factors of the elbOw in the plastic dcfoma―
tion range and an approxirnate fomula、 vhich shows the relation―
ship bctwecn angular displacement and equivalcnt plastic strain
have bcen dettved at KHK(Mukaimachi,[5]).
Flexibility factors in the three bending directions differ from
each otheL and the restoring moment of opening in―
plane bending
is thc highest among them.Average nexibility factor seems to be
reasonable for the analysis with respect to seisIIllC fOrCe and re―
sponse disPlacement at a support point,which are applied rcpcat‐
edly to the piping system.The nexibility factor of the cottespond―
ing bending direction is adequate for analysis with respect to the
ground disPlacement,which is not loaded repeatedly.Adoption of
the nexibility factor of opening in―Plane bCnding is conservative,
but a reaction force may be ovcrestimated.The modined flexibil―
ity factor mcthod is considered to be applicable,keeping in rnind
these characteristics.
There is another matter to be considered in the piPing design
and nexibility analysis for ground displacement.When a straight
9. Plastic defomation of extens10n rod of shut― off valve and
valve malfunction
To prevent these fallures in the event of a Leve1 2 earthquake,
allowable limits are established for each component,as shown in
Table 2.
An allowable plastic strain range of single amplitude 2% for
cyclic loading is proposed in consideration of thc extremely 10w
probability of occurrence of a Leve1 2 carthquake.This proposed
value still lcaves room for further study. An a1lowablc PlastiC
strain range of single amplitude 5% for ioading of ground dis―
placement, which has some margin for single cyclic 10ading, is
proposed to prepare for unexpected bchavlor of ground disPlace…
ment and also to cOntrol dettmental movement of a piping
system.
The a1lowable angular displaccments dettved from case studies
by FEM analysis at KItIK(Mukaimachi,[5])are considered to be
acceptable, The fomula for evaluating leakage from a nanged
joint denved from experimental studies at KHK(Ando,[6])is
also considered to be acceptable. The evaluation of the valve is
considered unnecessary becausc the allowable stress for a Level l
carthquake is 10w and also because the reliability of earthquake
p i p e
w i t h
a
l e n g t h
o f
l
t i l t s
a t
a n
a n g l e
o f
a
t h e
e n d
m o v e s
t o
a
off valves was verined by a sedes oftests conducted by KItIK
shut―
point of different coordinates and the length of the component in
in
1996.
the odginal axial direction decreases by .This
l(1-coSの
ettect,
due to geometrical nonlineanty,om piping
so long as the angle is sHlall and it is
tional analysis method.HoweveL it cannot
angle is large.A piping system must
absorb a relative disPlacement due to this
largc defomation.This must be keptin lnind
method is adopted.
aexibllity is negligible .3.5 Substitutive Method. It is specined in the code,、
vhen
disregarded in a conven―
considehng ground acceleration, that the evaluation of the Ll―
be neglected when the RSP for seislnic coettcients vhich
、
are half those of a Leve1 2
have sufacient nexibilitt
to can be substitutcd for the evaluation of the L2-RSユ
earthquake
efFect in the case of
This is a sirnplined lmethod based on the
l」
ltirnate
Design Method
whichever analytical
considering the energy absorption capability of a structure.This
3.3 Securing Piping Flexibility fo「 Gttund Displacement.
Generally, it is not easy to secure high Piping nexibility while
providing supports to reducc the effect of weight and seisrlllc
force.Itis known that a time lag occurs between the main ground
shaking and ground displacemcnt. Based on this experience, an
acceptable design method is to allow some supports to lose their
restraining functions with the progress of relative displaccment
due to ground disPlacement, in ordcr to guarantee the required
piping aexiblllty for large relative displacement.
Figure l shows an actual cxample of piping observed after the
Great Hyogoken‐ nanbu Earthquake.Thc combination of a straight
method is consistendy applicable to a piping systcmo When this
method is adopted,the Ll―
RSP is evaluated against the supporting
structure's seislnic coefacients and response displacement ob―
tained by the substitutive method.
4
SeisIIlic Performance Test of PiPing System
4。
l Purpose of Test. Ground settlement extending several
tens of centirneters or lnore was not considered in the past piping
design.Horizontal relative displacement extending several tens of
centimeters or rllore due to lateral ground movement、
vas also not
considered, 恥e purposc of the present tcsts is to conarln the
feasibllity of piping design airned at absorbing large relative dis―
pipe perpendicular to the direction of forced displacement(for―
placement duc to ground displaccment, the propdety of design
ward the riglt)and elbows at the both endsお
sorbcd a large
critena against ground displacement and the proPriety of the gen―
amount of relative displacemcnt. Furthemore, elevating the on― eral idea of the modined nexibility factor rnethod.Wc also ailn to
ground straight pipe after the elbow enabled accompanying rela― cOnam the movement of Piping in which an expansionjoint(uni―
tive disPlaCement in the vertical direction to be absorbcd. This versal typc)is included,under the loading condition that a r
actual examplc suggests an ettective design concept to prepare for
displacement excceding the absOrption limit of the joint is
ground displacement and also shows the feasibility of the modi― llnposed.
ied nexibility factor mcthod.
3.4 A1lowable Lilnit. The following fallure modes of a pip―
ing system due to seislnic force, response displacement of sup―
4。
2 Testい にodel
イ. 2 . P S を J 夕
cr,θ
れ。′P , ど″g S レ S r 夕
れybr ttsr.A typical example
of piping in a high importance category is the rcceiving piping
connected to a low― temperature double― wall flat―
bottoln tank con―
1. Largc plastic defomation of elbow and cracking of elbow
taining a large amount of liquened gas.This type of tank is usu―
due to fatigue or large strain
ally constructed near the seaside for the convenicnce of unloading.
2. Cracking at local discontinuity in a tee duc to fatigue or
This receiving piping was selected as a test rnodel.The nozzle for
large strain
this type of tank has the characteristics that it moves in the axial
3. Cracttng at local discontinuity in straight Pipe at supporting
direction with cOntraction of the inner shell during the initial cold
point duc to fatigue or large strain
operation and then inclines downward with the swelling of the
4. Ratcheting due to cyclic load under intemal pressure
lower part of the inner shell under a liquid head load.These char‐
5.Lcakage from nanged joint duc to excessivc bendingactcdstics
rno… are also considered in deteIInining thc shape of the
ment
piping model.
6。Cracking of bellows due to fatigue or large strain
The following threc types of systems are considered as means
7. Cracking at local discontinuity around nozzle due to fatigue
of elilninating or rnitigating the effect of ground displacement.
or large strain
8. Collapse,buckling or excessive defomation of support due
1.Cθ 確秘θれ電鋭 ″冴αrど
θれ 鱗 c冴―
SttpOrr sys姥 ″: The ettect of
porting stmcture and ground displacement are expected.
to reaction force and damage to pipc resulting froln loss of sup―
POrting function
12ノ
Vol.126,FEBRUARY 2004
ground displacement is elilninated by prcparing a nxed_
support point on a common― foundation and installing an
Transactions of the ASME
Auowable―
Allowable Lmt
t
mi
Se13dC fONe md inovement of
HPhg
bketcomnt
苦 激
rettre,wttiいし 'dSmic force and
帥
ｍ
Ｗ
￨
Table 2 AHowable li『 nit for evaluation of Leve1 2 Seisnlic PerfoHnance
fsuPPortb
符鰍 品。
縦鷺紺盟鎗鮮鷲瑠驚留
盤賊:甘
Nozle
盟
吼 :瑠
群靴 路 鍬 :鷺 船 螺 幣
“患
『絆 to mttt"ed鴫
AHnw iimit
並 ess lntens的
―
bgttng
輸にミS inttnsi的
min mge due to seismic force and
る
eOfmxね lum md mmmum value at
萌
縄押JFs淵野
紹鑑岱院
軸,ss range due to seismic force and
SuPPolt
Allowable Lnt(Cmund atsplacerElent)
I杓口●ofsmln
Allo‖
lim孟
Allowable HHttt
SuDDOrt
F<F,
Fix support
G u i d e s u P P o FR < 賄 ,
d■e to即側nd displtternent
破怠
m_
孔:促
即1鮒1錨
艦隅朽:器
磐錨
Release
support
ge
e戯:
4Sy
Allowable limit
に
述mぉ
F<Fyj総 品後f愉
に
Fく
Fu 母
呂
生
ギ
:皆
盟
獄
庁
革
摘〕
競
n抑
旧
側
:!軸
麒鱒撚塩縄舗
F>Fl,
怖
ず的 eq・iVal亜
acemnt)
Allowable mt(setsdC mtt and HPc― dlg「
Pri_local membmne phsぷ
輸
鑑
飾 ∝ N/m7n2D
m evdundoll
″ + 宅 わ ≦q β
for gound dsplacement
・
血 ess method
Evaluatton is aDDliCable.
e to resPonse dsPlacement ofsupporting m血 陣
Movement ofsuPPcrti MovemeIIt of suPPort POint d■
each typc of Piping Systeln, l to 3 descttbed above, are called F
port.To rnitigate the rcaction force to the support,the piping series(F―LF→ Hl,F―H2),NF series(NF― LNF… Hl,NF― H2),and U
system after the support is so designed that relative displacc―
series(U…LU― Hl,U― H2),respectively.
ment due to ground displacementis absorbed by a combina―
The dilnensions of test lnodcls are shown in Fig.2.One end of
tion of elbows and straight pipes.
each test inodel is axed to the support on a cornlnon―foundation
れ:Relative dis―
れ れθり統夕かSttpθrrり sr夕
れて
協rJο
2.Cθ 初初οれナ ,″
for F scdes,and to a vcssei nozzle for NF and U series.The other
placement duc to ground displacement is absorbed by the
end is the arst support point for the F…V model(settlement of the
same inethod as in the above systeHl,while providing a loop
foundation of local support is smaller than that of the vesscl),the
to assure nexibility for ordinary operationt The loop is sup―
V models(ViCe versa),the
arst tuming point for NF,V and U―
ported vcrtically or horizontally at points on the coFnlnOn―
second tuming point toward the quay wali for Hl models(F―
foundation for each cXpected ground displaccment direction
Hl,NF… Hl,U… H2),and an intemittent point toward the quay wall
so that little bcnding moment caused by ground displace―
for F2 models(F― H2,NF‐ H2,U― H2).ConSequently,the second end
off valve, while taking carc
ment is transferred to the shut―
in F―
Hl,NF― Hl,and U― Hl modelsis assumed to be an clbow and
not to restrain the free movement of the loop under ordin叩
earthquake shut―off valve between the vessel and the sup…
operatlon.
初:Relative disPlacements due
″族ガ sysr夕
″C′
3.巳 中 αぇsJοれブοれすど
to both nozzle movement and ground displaccment are ab―
is expected to be nearly a hinge point at large defomation.Each
piping system is assumed to be restrained in the axial direction by
a supporting structure near the quay 、 vall. The ends of piping
type expanslon joint included models
in theare
sorbed by a universal―
piping system.
Schematics of these piping systems are shown in Fig. 2. A
tical direction is assumed betwcen
relative displacement in thc ve「
the vessel foundation and local support foundations, and that in
the hodzontal direction is supposed betwreen the vessel foundation
and the foundation of a supporting structure near the quay wall.
The amount of settlcment of a tank foundation without piles de―
pends on factors such as the level of sand compaction, bottom
area,and weight(1lquid level at an earthquake),and iS nOt neccs―
sarlly greater than that of 10cal foundations.
the loading points in the tests,A short pipe is con―
nected to the cnd of each H2 model for convenience of test.
A nanged valve and a flanged duHllny valve or two dummy
valves, rcprcsenting a block valve and an earthquake shut―
off
valve,are installed near the axed POint for NF and U sehes.For F
series, cach piping model is welded to the nxed point with no
flange.
No test lnodcl is restrained ho五zontally at thc release support
point under thc assumption that thc support would lose its re―
straining function against reaction force as expected,No U series
modcl is also restrained at the support Point near the expanslon
t s c considettng
Pa―
す
〃θ
彦′
・ T e s t s w e r e c a r n e d o ujoint
確ざ
tsゲ
s jtθ
the pHmary ottect Of test.Movement of
イ
.2.2 DJれ
解
included system with is restraincd vcrtically at
rately for the threc relativc displacement directions.The modelseXPanSiOnttoint―
of
Journal of Pressure Vessel Technoiogy
FEBRUARY 2004,Vol.126 / 13
was loaded monotonically using a hydraulic jack.Intemal prcs―
sure was held constant at O.2 Mpa.A pin joint was used at the
loading point. 】VIovement of the loading point in the direction
perpendicular to the loading direction
ing a long rod(5-7.5 m in lcngth).This
acceptable for tcst purposes,thOugh it
on the restnctive condition around the
shows the setup of the test.
燕 ￨“轟 姦 !務革
茂静鉱縄 輝塩姦五姦‐
was restncted by connect―
boundary condition is
varies in practice depending
loading pOint. Figure 3
イ.J.2 ∬ θれ′
Jれ
でα/F温 ど
″ ど′
夕れでれrAれ αゥsJS.TO Support the
evaluation of the test rcsults,physically and geomet占
cally nonlin―
ear analyses were perfomed by using the nonlinear anite element
analysis code“
ABAQUS"fOr F and NF series piPing models.
Elbow A,B,C,and the attaCent parts of straight pipes(max.5
times the pipe diameter in length)were mOdeled by three―
dilnenslonal shcll elements, and other sectiOns were modeled by
beam elements. Nominal thickness was used in models of pipes
and elbows. Properties of elbow material,deterrnined by tensile
結蘇唱
ぷ乱品:智
1船解晩『
i,品
澄唱
域品珊締
and O,3,respectively,and the engineettng stress― strain cuttc is as
shown in Fig。 4.
Fig.l Piastic defoHnation of piping systems which absorbed
―The Great Hyogoken‐
iarge relative displacements―
nanbu
Earthquake(photo by Mr.Tanoue)
4。
4 Test Result. DeFonmation shapes of piping systems with
main ineasured data at the anal stages of tests are shown in Fig.5,
Analytical results are also shown.Transitions of the defomation
of U― sedes models are shown in Fig. 6. Force―
displacement
curves(二 N■ and U series),relatiOnships between forced dis―
placement and principal strains at the measured Point(F and NF
settes)and relationships among displacement,intemal pressure
support point ncar the expanslon joint under relative disPlacement
and axial forces of aange b。 lts(U―Hl,U― H2)are shown in Fig.7.
load in vertical direction can nearly be conarmed byH2model
U―
test.
4.イ.ゴ髭 sr R夕s″ル乃 rFα れ冴NF挽 ガタsP″ れgル ″
θ姥 ′
.
Piping speciacations are 6 B(150A,Do=165.2mm),STPG370
1. No lcakage was observcd in any test rnodel.
2.Plastic defonmation was cOncentrated at comcrs(elbows and
attaCent short connecting pipes)and was nOt fOund anywherc else
The expansion joint is a standard type,2000 mm in length,which
on the straight pipe.DefomatiOn modes of piping systems were
is designed to absorb a relative displacement of 200 mrn for de―
sign cyclic number of 500. 1「
he model size is half that of the as expected.
3. Little effects of forced displacement、
vere recOgnized in the
receiving Plpmg system of a 4 X 104 kl_class storage tank.
part around the earthquake shut―off valve in the case of NF sedes
(CarbOn steel pipe),PT370(carbon steel elbow),schedule 40(t
=7.lmm),and class 15(沖
in aange pressure―
temperature rating.
4.3 Test Procedure
イ.J.F 7移
sr Pttθ
cでど″万
夕
. Displacements,strains,reaction forccs
and intemal pressure werc measuredぅ 、
vhile forced disPlacement
colnlnon‐
「oundatlon
FixedtSOoFt Systm
Piping models.
4. irhe results of the nonlinear FEAtt analysis,such as displace―
ments of representative points,reaction force Of piPing mOdel at
the loading point,and Plastic srains at rneasured pOints,coincided
LXp_?艦
Sお
m
隠酬器
CO― on―
Foundatlon
Nodxed― Suppolt Svstm
並 hernatias
ofP地
Systm
(Cコ ●1)
/
お、 To Qぃ
yW」
(Ca四 2)
タ
耐 menttnnl
ofTest
Model
句
Fig.2 Schematics of piping systems and di『nensions of test rnodets
14/ Vol.126,FEBRUARY 2004
Transactions of the ASME
ｏ ｏ
ｌ
ｍ ｍ ｍ ｍ 知 ｏ
り
ｏ﹂
Ｅ
Ｅ＼
や
の
〓︶
の
︵
Ｎ
Fig.4 Engineering stress‐
20
25
strain curve of eibow material
Fig.3 Setup oftest
sttdes
F‐
V‐
model
NF―setts
U‐sαies
れ
D-794EIn
/
(〔
:) 耗
〕
C)') D-1001mln
(〔
Hl‐
model
↑
勝赦
￨
10
:5
Strain(%)
↑
aOを
悌 981■lm
D:Forced dtsPlacement(Ilm)
N)
F:Restthg force ofPiPl噌 symm agalド t disPtacetllent ioadは
0:Angular displacem価 l of elbow whBch showed maxlmum valuo(not
indudhg component of● onnedng Pipe cottibttng to global angular
dsplacement ofccmg)(deFee)
atneasuredPdEtOfeibowcゅ
的,●ど所 nc,d minl,2■
n t p cl a m壺i n i n e l b o w ( 0 / O j
fe 却
●: M a x l n u m v d u e直vo』
1,min gages were adh卸 胡 to the four poi強o■oよ類村bence at the“der of
maJor elbows 飼
a n如
d Po 8n P■C C i O S e t o t h e S x e d いP o t t A d o t i n 研
section indicates the Point where the ttmum value as a「 ■
acIPd的 なn研
sress was m類
1血 g side.As fbr elbo、
和、thH"鋪 n gages
,Viewed飾
w e r e a d h e r e d t o e a c h P c ms aotF ainn ta―n g l e o f 1 0 d e F e e s a n d t h e e x a c t
赳障d is atso ncted by cl∝
kwise angl●
Postton where ttmum value tt me■
h dettes from the belly ofan dbo叫
2.駈 cause ofthe価 ― 。
●臨 w●en reRonng forces in test and atalysis at id
age of F‐ V moこ ●
i test was dte to the lo■
dng住 dce.ERef古 to Nde(1)h
Fi2.コ
的he Sxed
a measured Point
of tt doS・
・
'い辞 艦 1'2江
宇
織
標
鞠
oentwc
ends(mm)
減blejol五
b“
ve dⅢ
lacement ofa●
△:Rel』
直
Fig.5 Resuits of:arge deforrnation tests and comparison with analyticat resuits
Test
Model
S伍に l rlnit』
ぉ
T醐 ぷ血
State 2(TranSieno
State 3何 h』 )
ExP駒 田回止On
1.From mate l的 gtate 2.forced displacement w西
n g 1R 0e na 」
ホ o r b e d b y a n e x Poa血
ttcn force
was relttively mall.(Figr 7(14),(15),
2.Anerthe e甲面 。
nj。血 reached itt me命
甑血
ホ OWiOn l面 t(Stale 2)re主《
●
施 宮 fOr●
suddenly ttHeased and ab8四
西On Of fOrced
dsPlacemed was押剛 ySmedto tt byth●
nexittlⅢofpわ
7(10,(10〕
hg itSdi tFig。
3.Wm the sudden h磁 な●of確 車胡ng fore,
蕊 al force Ofboltg of a valve nange nei to the
ixed Pcht― d hcreasingr The ttging ctrve
ofU‐
H2model was stett co叩
亜 d Wtt hatof
U‐
Hl model.中
iom the nanged j。
血t
w a s o b s r e d w oh ee dn 飯d i s p l a c e m l r r e a c h e d
6 0 0 m m h t h e c aHs2em oOdfeUl‐a n d 7 5 0 m m
品t h e c a s e H ol f Um ‐
o d e l . ( H g t 7 ( 1}6 ) , ( 1 つ
U‐Hl
U―H2
Fig.6 Transition of deforrnation of exPansion可
ointoincluded piping system
Journal of Pressure Vesse`Technoiogy
FEBRUARY 2004,Vol.126/ 15
Sedes
Hl‐model
V‐model
Ctte
病
3 1 2
Forcet
dsplace‐
ment c叫
:
8
8 1 5
二l o
二t
/4:ど
多
どどどすすす
ン
グ
0
あ 1。
Cenmt(口 )
D18,1●
(5)Stra3n3 at measured
３
Ｓ ︶●一
営
︵
２
１
４
０
D i 3 p l " 的t l ロ
d i s p l B c e c―u r v e t H F H 2 )
t9,Fo―
41,
FttcerdisPLcement curve tMFキ
48〕
コリ
︵
よ︶Ｅ ●、
t 10
O i 3 , ! t8 い
C ―
)
l,
能 酬 部 h高 ぃF韓 )
Strah掛
l t t ' S t r a ml en a3 S求u r e d P o l R ( N F H1421
０
恥
― ‐FB
一 Pi
∞
的
01 =
0 25
０
５
0 2 s
3 4 0
g 3 0
と2 0
= 1。
O i 3 , 1●
●
― t的
Foに erdLHcerHWR curve tuHH2)
ｍ
。
fle=ble ici証
一
ｔ〓
￡こ ８ ヽこ 一
aangedjoint
0 2鴫i8糾
ほ撫 辞 lm
Forcerd,3plaCement cuFVe tuHHl,tlD
t14〕
”
e
IIII″=■″=
1/1/111i
F ― ‐
印加ｍｍ仰抑抑口ｏ
０
１
●
8 1 5
二I I
一
▲
卸 抑 的
０
２
Nol鞄
3 2 0
F 一
ｍｍ ｍ抑仰 ｏ
０
３
、
.煮 車
、
1_…
/
各こ ”Ｓ ８ 常 ■ ●富
”
ド卿
E15 …
こ1 。
g
g拘
:i!:%i:iii:!!i!iiii!i:￨
3 ■5
Hcmenchture
a
8ured polRげ報 ,
P c lい〕
r tmaln3■
t F H l )確 白
-31-'32(Elbow C)
Dieplac●
●●
nt (H)
(13)ForGd38P3-ment curve tW〕
k
《理 型
iiii:i
1lii!!i!i!iii!lii!:!!!ii!i!i!!i!亥
一
L a
tom
c)
。 ８遇 ｔｆ ０
１
市
11%I!yI
―' F - O E D b o r r
コ
︼ ．卓
０ ３︵
１
確 生 ２ ０
B)
Dl,pl●
ment は )
●
t10)SFah3宝 meaSured pdnt(NFew
U‐
陥 tF判
―口
31‐-32(Elhw n
iiii::iiii:i:ii空.…
:iiiii:iii:!:″
JE翠
一 el -82 (Elbow B)
Force‐
dttlace‐
mentcwe
回Forc甜踊
!!ill!!!ii:!iil'''1::::二
ii!!!iiiiil
:ii:i:iii!ii::!iii!::!i!!i:〃
:
V)
‐ement Curve tNF・
t7)Forcsd38「
Smin斑
measred
po血
1こ
長
0 200 400 600 m 10oo
1000
じ こことり
︵
●一
●﹂あ
lbOW
4=
Ｏ知的∞
ａ
巾如
３
。
。
．“ 的
抑距２、１
NF‐
200
400 600
300
Di●
p l “― t l m j
せlo
己
一 εl-32(Eibow C)
===Z!==III
一 F-0導
s4
!!!i!!!￨::i!i!!!!夕
=タ 6 こ
喜1 5
(2,Forcerd33PlaCenent curve l)
tFⅢ
-31--32(Elbow A)
nttF=り
t4)Stratnt at mea8ured口
Force―
dsplace‐
Inent we
i8t
夏
IIII1/1身
喜2 0
4営
阻鞘品ヽ
配「e tFevl
(1,Forcetd韓
smin at
meastred
point
25 弾
:!!i111liii!!ケ
Z:,そ
lii!!lii!!:
:ii:iii:!ユ
/“ i:i:i:i:i:i:::ti
:/あ在II
―
…
//イ を,一々土=二Ⅲ
F‐
H2‐model
A)
伊
nt(コ 〕
D13,taC"●
卜HH〕
Bkagefrom m■ 9edj03nt t田
t16〕Lた
0 200 400 600 800 1000
Dipl●●“ nt(同 )
( 1 7 1 L e a n g e t O m m n g e d 1 0陀
i〕
nttu附
ぉ hcrease of restonng force tt fuced asPlaoemeHt exceeded 600 mm
(2)t ZemO retOring●betw―
for● dgPLcemed O and 200 mm―
(1)i Sudと
t m t tt h te h ee n pd l 距
of
force bywttch
■
vas dte to the eDtenston of Elbow B,wttch wag id
caused
anぷ d u t●o t h e t e s t t t e d l l脇w
fleltible joht and icading pom―k軒蔦1回
泣。
五d using
wag gmded becauscthe loading aPP-3 00uld act ttlly fouow the alovemest
a
n
o
t
h
e
r
d
i
j
a
c
k
u
a
t
t
t
f
r
c
e
d
d
i
s
P
l
a
c
t
t
r
e
n
c
h
e
d
2
00 mm
t
offrced
displacenc配
、
山
OfDiDint inthe dttdm pFpendiculart6山
Fig.7 Forcぃ
disp,acement curves and other disP,aCement‐
well with the test results.恥
e maxilnum value of equivalent plas―
うby
tic strain in the elbow was 4 to
6ワthe nonlinear FEM analysis,
which is at a comparable level with the allowable plastic strain
(5%)recOmmended in the guideline.
dependent data
the same direction leakage from the aanged joint nea
ixed Point was observed soon after forced displacement
reached the mechanical absorption lilnit of the expansion
J01nt・
2. In the casc of H【-l model, whcre the axial direction of the
4.イ
. 2 脅ざr R 夕ざ
ガぉ ザ 」 最ケ′
夕S P " J t t g 〃ο冴夕F .
exPansion joint corresponded tO that of forced displacement
and Piping after the expanslon joint had some nexibility in
1. In the case of H2 model,where the effective direction of the
the same direction, axial load due to forced displacement
eXPanS10n joint corresponded to that of forcedwasdisplacement
Hlitigated by piping flexibility but forced displacement
and Piping after the expanslon joint had llttle rlexibility
in by lateral and angular displacement of
was accompanied
16/ Vol.126,FEBRUARY 2004
Transactions of the ASME
piping at the cOnnection of the expanslonjoint.And,leakage
sible within the a1lowable
of the same pattern with U…
course of tllne.
4.S
H2model was observed in thc
COnclus,ons oF Test Results
l. Both dcsign conccPts Of a coHllnon― foundation ixed― support
systerll and a conllnon―
foundation nonaxed… support system are ef―
fective in protecting an irnPortant part Of a piping system against
plastic strain lirnit of 5%. It was also
conamed that the general idea Of cOnsidettng only elbow's non―
linear charactettstics in the modined aexibility factOr method is
reasonable. Also, supplementary piping nexibility is recom―
mended for a piping system in which an expanslon jOin
cluded,to leave a margin against grOund displacement.
Acknowledgments
A draft of seislnic
designsyst
ctt
a for piping
盤縦 精 鞘督縄 樹鮮品岳
:艦継轡謂機
8】
,::群
塩鑑暗乱総辞転踏淋撤S肘
:盟鮒賛
ground displacement.
2. Designing a piping systeFn tO absorb large relative displacc―
ment due to ground displacement is possible、
vithin the rangc Of
the a1lowable plastic strain lirnit of 5%,by utilizing a cOmbination
of straight pipes and elbows and adopting release supports as
neededt
3. The general idea of considedng only nonlinear characteHs―
Suzuki(TOkyo WIetropolitan Univ.),ProfessOr N.Shimizu(IWaki
tics of elbows in the modincd aexibility factOr lncthod is reason―
Meisei Univ.),Associate Professor■ Sawa(Yamanashi univ.),
able.The elbO、 v's characteristic includes the effect of Oval defor―
・
mation of the shOrt part of a connecting pipe,which cOntHbutes to
群 Ъ鯖 艦 盟 出 賠 と魚 tざ 撒
岱 :嵩 簡 建 :盤 済 品 瀞
the increase of angular disPlaccment of the comett HOwcvcL the
effect Of gcometttcal nonlinearity must be considered separately
in the case of large defomation.
4.When an exPansion joint is included as a means of absorb―
ing large displacement duc to ground displacement, it is rccom―
mended leaving margin by providing supplementary piping aex_
ibility to prepare against relative displacement which Hlight
The authOrs express their sincere gratitude to Profcssor Emeri―
excccd the absorption lirnit of the joint.
tus Heki Shibata(Univ,of TOkyO)and PrOfessor Kohei Suzuki
5
Conclusions
ln the aFnendment of the Seisrnic Design COde for High…
Pressure Gas Facilities of Japan after the Great】
Iyogoken…nanbu
Earthquake, seisHlic design of a piping systcHl was included
within the scope of the cOde.Basic requirements and the evalua―
tion methods of the Level l Required SeisEliC Perfomance for
Lcvel l earthquakes were specined in the amended code. The
evaluation methods of the Leve1 2 Required Seisrnic PerfOmance
for lし
eve1 2 carthquakes wcre propOsed in the guideline,Possible
ground displacement duc to liquefactiOn is taken into account for
Leve1 2 earthquakes.A design that al10ws sOme supports t0 10se
their restraining functions against relative displacemcnt due tO
ground displacement was considered tO bc acceptablet Largc de―
forlnatiOn tests、
vere carned out using several modcls Of the re…
ceiving piping of a low―temperature nat―bottonl tank.Tests cOn―
who directed us to establish the design criteria and Associate Pro―
fessor Toshiyuki Sawa and Associate Professor Tetsuo Watanabe
who promptcd us to cany out a series of tests.
ReFerences
Trade and lndustry of Japan),1981.“
[1]MITI(Mittsttt ofmatlonal
lnに
Sdsmic
醜 弱唖 Gas Fお mギ
Mtt Notln銅 。
n筑 5 Gn
裾 需]sSre ttr mg卜
On tt amcndmett Of
□巡品ど
‖
ど
『
絆lri為
燃3.Ntti鋼
[3]KHK(High‐ Pressure Gas Safety lnstitute of Japan),20tXl,“
Guidehne of Seis_
e逆
｀
品
監i駐
竜
総 i鷲
苫
紆I播
古
阿獣
FM!猛
紹温1増
よ路品
ま
3縦
器
ビ麒艦鑑靴慾路路
a d , " 能なれた 駒 g れで
c r rg″
1,Volumc l,pp
, A S M E P V P ―V o l . 紹5 ‐
l l ; 境よ翠
□
3謂
。:昔 盤 d塩 離 c撚 鮮 :デ盟 掛 警 号協 品 献 :盤 撤 t艦
is efFective and that the design of a piping systenl,which absOrbs :草帯苦古品 虎3号【と魚 s拠 盤 ゝ 古鑑 ぜ ￡ 離 古譜吊ド器 銘針 堤 緒 者嫌
配'"ざホ ″た ど″
L紹 5■,覧 hnc l,pp4
g筋筋 ″
g,ASME PVP,沌
iarge relative displacement duc to ground disPlacement, is pos_
!‖錨 貯
Journal of Pressure Vessel Techno,ogy
FEBRUARY 2004,Vol,126/ 17