ML18081A895
| ML18081A895 | |
| Person / Time | |
|---|---|
| Site: | Salem  |
| Issue date: | 04/19/1979 |
| From: | Dingwell I ARTHUR D. LITTLE, INC. |
| To: | Noonan V Office of Nuclear Reactor Regulation |
| Shared Package | |
| ML18081A894 | List: |
| References | |
| NUDOCS 8001140536 | |
| Download: ML18081A895 (29) | |
Text
.April 19, 1979 Hr. Vincent S. Noonan, Chief
~,gineerinb Brnnch Division of Operating Reactors T.;.S.
~J'uclear :;2~gul:itor;* Com::iission Washington, J. :.
20;_=:::
Dez:- H:-. ~oonan:
98705
! a~ enclosing a rn~~orandum which confi~s :he in:on::ation furnished at a meeting ;.;i th you and o c.: *.::::.* :.:;e:::=-:::::-.s ;;f the ~l'RC Staff :ionday af:=rnoon, April.16, 1979.
I a= sencing a copy of this letter (and its ilttach~ents) to John G. Davis, Acting Director, Office o~ l~~~~~tjon and Enforrencnt, U;."laer CO\\.'e-!' Of t::::-ans:nittal, a copy of \\."ni=ii is at::ached for your
- .::.£or:::3 tion.
A copy of this letter and its attac::1::icnts.:ire hcin£ sent to the c-:-;ani::.ations listed i:i Appendix II, ~ho are ADL?:i:.F::: licensees.
As disc~ssed at: our A?ril 16 ncetin;, 'l."e '..:ill verify t:ie five bench r::.::rk problem solur:ic:1s (.af::er l"l:C:".!ipc o; r:nc probl,':::s fro::i N?.C) ?uolishcd in ENL-:.1.Jr:!:":G 2.!.2£.l-l~S.:ind 3:~L-NCi\\..SG-236Z;5 ur:.li::.i.ng
.::.e p:-esen;: ve::::sion cf.AD!...!'I?::,
Fe.b::-~ary 197i. Ve::-sicn JC.
If you desi::-e any net r.~si;:ate c~ c~ll.
8001140 s 3"
1967 1968 1969 l9i0 1971 l9i2 1973 1974.
"I:,.....,,,.
~--:I 0 1977 1978 T,\\Bl.i~ I -
Dl:..'"VELOP!*IB1"f UF Al>LJ>.il'E Develop~ent of static load version Delivery of static version Delivery of prototype dyn:1mic vcrsiun Delivery of stntic dyo~mic BJl. 7. vcrsiun Inclusion of ASHE Section III Class 1 Inclusion of,
C..;.O:::S :..i,y spaced ::iodes*
Inclusion of ASlfE Section III Cl<iss 1 u-- "'tQ
.:.-~- factors Inclusion of 1-!etric ur.its Inclusion of ASHE Section III Class 2 a~c. 3, B31.l Revised in?ut organization Force time history analysis Transient ther.;ial ar.alysis (n~e-di~ensj~~~~)
Inclusion of 1.92 modal s~ation (~ro~? =ec~oc)
I:i:lclusion of post-processor inr new 1. ~2 :\\;..-=:aticn Revised =a=rix storage and solution
A ~rief Histo~ of ADLPIPE (see table 1)
Arthur D. Little, Inc., first prepared a program in 1952 to co::ipute the flexibility and ther:na.l defor-....ations of piping systems for a private firm.
An. ASME paper vas delivered in Apr;l 1956, "The 6X6 Matrix Method of Piping Sys t2tt1 Stress Analysis".
!..: ::er during the li~uid oxygen fueled ballistic missile program, Ar~~~r D. Little,
!nc. 1 adapted this program ta make dyriamic analy$C5 of ~issile fuel!ng syste=:s.
A ne~ program, ADLPIPE, Yas developed in the period 1967-1968, first for the static (deadweight, ther-...al, exte~al force, applied displace-ment) analysis of elastic piping syst~~s.
The prog~arn ~as ~ritten in FORTRAN and designed to ae independent of the particular computer syst~~ used.
The second develo~ment--also.in 196S~(raocificati~n one)
- .:as for the dynamic (modal) analysis of l~:::ped :nass ;ii?in:; systems.
rne transient loading was described as a res?onse spectra.
Fo:low-ing a prot:otype development rieriod, a v.::.rsi.:m ;.;as delive::-ed in Au~"t:St: 1970 which enabled the user to i:::;".'le::::ent A:\\SI BJl. 7 "Nuclear
?m:e-::- Piping".
This version could not produc~ a iull stress report bu: gave strcsse~ for particular loadings.
I:1 1972 a ve:.rsion 1.;as rel~sed
~hich enabled the user to produce a partial st:-ess r2~0rc to meet the
- -e:;:.!i:-ernem:s of ASHE Section III.
In 1912 -this vcrsicin 1.::1s rel~.:!scd to ControL.Dat.:i Corpo:-<Jtlc,;n Cybt.!r.l~L.
- 11 197J LliL*
cr~::;;.*ut-::io;'l of :*~=l~:.ie usa;e factors was compl~ced.
In 1974 a version ~as released for the ut:liz..ir:ion of AS'Hi: Section III, ':"l.:!s:> 2.
- n 19i5::. force c:::n~ his::ciry analysis o;.,;as included for the calcul.:iti..:m of hyd.-~ulic tr:insil.!:-d:s.
Ar.
the sa=e time a one-dimensional ther.nal t=ansient ~~alysis ~~s d=veloped fo:- t:he requirements of ASHE Class l.
In 1976 the auto;:-..atic. cornpt.:tat:ion of ~-:::..s:::ic u~r11.yses iz:.t1,:corci.-:nc~ \\,.*i!:h R=;::l;:itory Guide 1.92...:~s developed ::::C: c:iccke:..!.
T'r:e co;-::jlletc r.:.=:::-ix anc.lysis por:ion of the prog:-ar.i was re\\*:-i:ten b2sec ;enerally on t:ie
~a::.::-.iques 0£ SAP IV "With so~e improveraen:s in the ::at:-i::-; storage ::=r:1:::-ds.
-:1 acc:iition, a pose-processor -;;as develo;::ec ::!::::":-: w.llo\\,*eci the :..!5Cr CCI r::.:;k12 loc:ici se: cc:-:.bi:iut:i::'ns for !.!Se i:--.
- ~
- .:.:.:::.!... :::::
~:;':i;:-
- ~::.:=i R.:;~:.:~::r~*:**
1::*~::.~e 1. 92.
in~s version ""!as released
- .~ ?e~:-ua:--y l.9i! and up;:-.:ided in
- ~c==~e:- 1977 and Septe=ber 1978.
!n :he period 1968 to 1973, ADL?II'E \\,,":':S che only cr:::::iu:e:-
pro~r;:::n (1.*hich
- .:.'.l~
- rv~i.l~ble to the public) for CDi.1p11tir.::; pipin;; rc:;;ionse tu vaz-inus s l:::: i c
~n c!
~:-:ins l c n t 1 o ~ d.s
- t Jt: h c r r :-* *
~.*.; ::.:-: s,..,, '-' r P
.! ;i
~! r-::.:: ~ h t1 t c o r. u r l::-:,:*.. ;le~:.;c..
th~!-=e '\\...'ere.: pr:>pr i l!L.J.ry a:i1.1 lh1t:
- .v~
- i l~~bj l!
- i.q**
- _;L.
- n~r;1 l use.
ir:s ince~:ion. ADLPI?E could be ~:il~zcd for 3 ~~~i2:y nf s~~ess c~:.::.i::irions _noc i:ivolving nuc~c~r ;'n**~r ~:ir=n;.
!~ 1~75.Ji"lrli::zitions
- ~*c.-~*:* l!:*::2nGcd tci :::c>ct the rc*<J11i:-c::1c:1~.s ro:" c!iL'::dciJ i<::::: ;in;J r.:-!i.ncry
~:?.:.:-:.;;.:nd :>e:ralt.=u::l t:.=c:iz~.:~*,ur=~t.ion !*ipi:-:;.
..\\r:li::: ill J:tic. ln,*
I J
In t:.his pt.!riod of ti::ic, ADL!>IPE w.:is liccnscJ to se*.:a:ral clients and released bc~inning 1~ 1972 to sever.:ll nationYide cc=?uter service bure.:lus.
A listin;:; of ADI.PIPE versions and docurn~:i:ation is given in /l.ppcndb: 1.
Tiu: n:n:ics uf Anf.1'1 l'E U c~sces."lnd the cff cctivc d.:it1.*~ o C Lhc l iccnse a;;rcc1:icn t:.s arc.: i;ivcn in AppendU: II.
The dcvclop::::ient of th.e seismic: <ln:Jlysis method was guidf?d by av:iilabli:
l itcr~1turc ;mu the.: dcsi~~n ~cquircmcnt-s of our c:l:icnts.
,\\method of
- in.
- llys is..,.;.:.is dc\\*c] opci.l which,.:is cxpl:iined hy two documents published in 1969.
'!he.:se are enc:li.Jsed.is Appendix III. ".Modi!'ic.a:ion One-Response to Grounc Shock. Spectra" and Appendix I\\', "Development of Moci<il Pan:icip.:ltion H.:ltrb: for Cene:ral Thre:e-Dimension Shock Input: -to Lumped Dyn:Jc.ic: System".
In Appendb: III on page _r;-_::;
T st:a te "the
!:lOcfal ai:iplitude, q, is thus cvalu.::ited as a scaiar su=r-_a:::ion of the prod~c::s of :he ncPi v~ctor of the rnod.:ll p~rcicfpa:::icn-i:itr~x and the spe:c::ra :!mplitudE.! (D.) ".
The "spi.:ctra a::~.!.irude" ~eilns the spcccra 1 dis?lac!:!::ent cor-pone~t~ in the princi?al coordinates of the piping l sys::=.
F~o~ these modal amplitudes,.i set of dis?:ac~~encs for e..ach I
', moce o! res?onse is c:or=?uted.
At e;:ich point: in th.: ?i;:-ing system,
~ three modal ~ocent co=poncnts are then co=?uted, one of each princi?al
'.axis.
t:ach co;r.?onen: i.*.'.ls then squared and then the sg'l.!are root: of the
- su~ of squ3res ~as taken to combine :he effect of all c~~es.
inis c~~=e~c ~~s used to ~odel earth motion ~!en~ a vec:~r ~~ich was not ncce=sarily aligned *..rith a principal axis *but 'Was s~:*: anc was decc:::-
?csec co three components.
The reilscin for this deYel_op::~:'lt is sl"ic...,-:1 in.Fig~re 1 C:-ia~e 4) \\o.*bere a scruc:turt: is not: aligned *~*ii:.11 a glo=._1 coordi:::ate system.
An ear<:hquake is assu::ned to ac: ?e=-?encicula:- to one *.:all of che structure.
Ha the.!ll.a tically, the ske.-..* a:*: is of ;:he earthquaxe is deconposed into tvo horizontal co~ponents in :he global
~xes.
A user could calculate earthquake res~onse with a vertical cornponen:
a.:-id a si~gle horizont.:.2. c.:..*::;;Jonenc i...
~~,a tt*.':J c..:xe:s
'--*=r~
- .:t.:L.:.Jil?~E:d (.;.;:::-
bining several such analyses to create a vorst case effect.
A user could ~~ke three or more a1::erent analy~es, one for e.a=h princi?al axis ag~in combining the r~sults.
~se:-s ~~o =ade a single an3lysis using a cri-direc:io~a: earthquake
- Jlc
- :.:*:e ;:-:-inted oi.:t.::; single set: of r::odal m=imencs.
e.:.c~ :-esi'cnse s1*i.:ct:-;i cc:nponent: by a sep.'.l:-ate anillysis r: one isola.::C se:s cf individual :::c:::e~t co~ponents, the resultant f:-o= the si::.gle cri-cire:::ional analysis woulc be the algebraic St!::l of each incividua~ cc=::?an:::::c
'.;;;: e:ich e.a::-thqunke dir.:cti0n;il co:::;-ionenc.
T:it: U?~=r :e*:e:l vould ':le ::ie absclu:e sc= of the ic=~=-~o~~! co~~o~~ncs.
The :c~e= ::~:l cou:d be
- e:::--o *...:i:.h:in a i.lCd~.
Hc:""ever, it is my vie~: -:hat i::-.=
- ~~=:"-:::0C22.
su:.-_-:-:.::.~:-i
- .:s:..=-:£ t.hC:!
s~uare: root s:..:..~ of :.:ie squ.3.:-es **.:ii.!!.C. not. *::e===C' an:i.,
i~ :..:.=:.,
- ~.... c~lC :10C *.. w..:.=:-~ ;:--e.:1:ly C.=33
?C~ce:-:~)
- r~!':"..:; square :-c~t St!::. a: sqt;ar:s (5?.. SS) :.:1:::-2-:::oG.Jl sc==:!::ic-:i.
- ..
- -:u::e:-:..c.:;.:
~=-:.ar::ple
- .~
- .*2~ i
- l..!.~?=::.=:.:-:
I 1r*.,. I*\\.
llo
I I
C1*n<l.i:iunin~. \\~l,L.Jm~.:.). 19;1, A:ul:;sis" (i<efercncc !5).
~. '
!he co~?Ut-tion of intra and inter mod~l ~~~cnt c~:::~~n~nt su:m:lation h~s been ve:-ified by a separate computer pro;:-ci::: for tha: ;:iur*;iose.
A report "ADL:Prr:E: Modal Response Combination for Clossly.Spaced nodes", is available as ADL?I?E reference 24.
Various ~lc:ul nti.nn procedures required b:* ASHE Section.LI! verc verified in AD!..?I?E references 10, 11, and 13 entitled ";.J!..PI;"::: Co:::putation of Be~tlini; Stress in !ees and Branch Connectior.s, ;.s::-::= Section III, Class 1 Pi;:iing", "ADL!'IP?: Cc-:::iput<ition of Resul t*mt Ho::cr. :.s for s,*ction III Class 2 and 3 Str2sses", and "ADLPIP::: Stress Coc;mca::ion of Pipini; Co:-:po-nents:
A Comparison._..ith Hand Calculations for A!\\SI B.31 and ASHE Scc::ion III."
In 1978 an indepe.'1dent third party re*~rie"..* of ADL?I?"':: (Sectio':l III, Class l).,.as pe.rfor;::ed "Verification of ADL?I?=:.
/,~!"E Se.:::.c~ ~II. Class l Piping Stress P"::'ogram", Teledyne E::lgineeri:.g Ser-:i.:es, ;::.:?port No. TR-2884=1, ~ugust 11, 1978.
A.DL?I?E Develoo=ent Folicv The follo~ing policies have been in effect
.ADL?I?E:
- 1.
The details of calr:ulai:ion p:-ocesses are ~"*.:.:.:.:ible to the public by fret.: di~:cri.buti:i::.;: :jl*.!::"a:...i.:...; ::-..* :-::;.:.2.., :me.! re:f _:-.::;nc!?s.
These are tabul.:it:ed in J\\ppcndi:-: !.
F~,c:-: ~uj er nei.~ f ear:ure of ADLPIPE is doci;r:icntcd for U'-<!r :-cvic*.;.
Pro!;:-am listings are i::.:ide avc:ii.!.ab:e to :L:e~sees.
are not restricted from w~King ?r~g~a~ ~~a~~es.
. 3.
ADLPIPE is periorii..:ally i-:7.'.'r,,*~e,:.:.nc *Ji-::.::!::::,: ;:;.:-::' } i.:e~>=e,.. :
are not:ified c: :11c rnodificaL:io:ls
~=
- },~
- .:.::: u~ :.i2~ :re.leas=
of the modified version.
- 4.
ADLl'!?E is hand checked..,herever -;--ossi!:.:.e.
- .;;e
- -: t:;l.s is net
?o:s~!:::le~,~L?:?~ :.~
che:.::~=.! :,::
~::;-.~::-:..:_..:.:-.::::
- -.~.:.::..:..::.5 or
~~z=
resul~s of OLher calc~lation ?~=c2~:;~es.
large. or sraall, is checkec.
.:.::::? :-::
Spcci41] vcr.sions or 1\\Dl.l'Tl'E t.:"iJl
- ... *.. :ri:t1*:1 ::" :l I il'.L'l1Sl'~**s Sj>t!cific::itjun.
!111wevL*r.
Li11.* vc::-si11:: ni :,::!_,*::-;: r*:lt:;1sc.;tl t" cG:::~t:C*~r service burezius
µc~~~i:.:.:~: d1."'e::
~..... :
- .:.",."£. !-=uch s;"'~i::..:.1 nJC:.::ions.
- 6.
Old vc!"sinns of ;dJJ.!'11'E :11*1.; n**C r, ~.1 inL*:.:
- .::.:.:::- !J.
Ll:::*~.
Prior to 1971 any corebination of loads or earthqu:.~~= h=~ :~ be ~~de by hand or by anot~er program.
In 19i2 I released ~ st=::.~:icn ~=-=ce dure '1..-hich enabled users to c:om'bi.ne lo.:ids in acc:ord.=:::e :::".:h E:il. 7 and Section III criteria.
In 1973 the computation of f~:igu= ~=~ge :~ctcrs
~as released, which included the cyclic effects due :o ~ar:".ous ea:-th-quake components.
If these summation techniques ;.*ere usa:c. the user could input several transient (earthqu;ika) loadings ~nd co::-.bine these loadings, one by one, with a sustained loading (dead~eis~:) to ac~ieve a "worst case" stress calculation.
!focal Analvsis bv ADL?!P~ Durinl? the Period 1977 to the P:-es.:nt A neY option was r::.ade available in ADLPIPE in Febru.:<:-y 15-77" for t~e ccn:putation of earthquake response in accordance,.*it:: Re;-:..:..:a::or;-.;uide
- l. 92, Revis inn l, !-~rch 1976.
In.:iddition, a posc:-process.:ir has hc~!n clc.:v~*lo1H-'u 1*iiiL<1 L-:~ :;- :,_._.;
- ii~
user to make a nu:ber of com=inations of di=ec:i~nal e.:.r:~~~c.kes aff acts not included in Regulatory Guide 1.92.
Verifica:ion of ADL:?I?F:
Vc=ific:ati9_:n of ADLPI?E w;Js undert:ikc>~ i:i."J series ci:
f::::*:*-.-::::::1t."l~ c:iiccks.
In i=:?ortanc. ::iociifications a supporting document w~s ?re;:-.:.:-.:..: as ~.,.-illL?:!:?E refe:-ence.
7he veri.fic:ation ?:"ocedure 1o.*a.s as follows.
1°:'1e ther-~l and deadweighc. loadini;s *.icre checked by c.
Rc*:;.:~r= Ee::c and hand calc!.llated syste:::s given in "Design o:- Pipin£ S::.:;;:e::-.s", :-1.
!*.". Kellogg, Second Edition, 1956, and "For.nulas of S:::-c.ss :md S:::-~in". :::..J. r._:1ar:;.,
~!cG.:-a,...-Hill.
The dyn.:.::i.ic analyses... -ere checked by "R.esi'Pnse of Sr::.:-:.ic::.::-.:: Sys;::::-:s to Ground Shock", Shock and Structural :t2sj1c:-.se, AS:-::::, :?60.
- .~ ";.:;:_::::?;:
Results of Model Given by Young (ADLi'T"'E' R12fcre>nce t..::. u::= ":;::r:.:::.;::::..:
.Dehavior of a Foum:!<ition-T ike Sr::-uc::111°:0", :-l<-"'ch::r:ic;JJ I:'1.;i--.::::-:=-.:ncc* '*i*:c.hods,
..!.S:-1:::., 1958, in "E:qeriI!lenc.al Ve::::"ific.:icion of ;.DL.?::?£ :-:.:-d
~
(~\\.J:..:::?E.
?.ef.:rence 3)
- Tile time history an~lysis \\.*as checked by CJ scpilr:ite.:.::4l:::::..:=- sc:u:ion o[ the ?=oblem given in "Analyr:ic.:il i-h!:liods of Vibr;1: ;,_,~~. **
~*.--::.:~ 2;;;s.
L~~n~rC :*jeinovit:ch. ".:\\.DI..?!11!: Time Hl~t~1;*:* 1\\~sponse C::-:::=:--.. :*~~ *.::::1:.
SL*c:ond check ~*~s made: usi:-:;:.
"Pr~ssuri..: *:.\\.!ss....:*l :1nU
?:-:J~!'~ss \\'erific:atiQn", AS:-:.::, 1972 (i'roi.l:c::: 5;.
r.::: ::::..: -.. -
-:::~*..:.::::-
-: : : : : : i ' i :
~ : it.* I: 1;..
\\'/ -
UXID!RECTIONAL EART:-iQUAK:E ',.TITH S~E:; co:!ro::~;-rs r
f I
I I
f l s
(..:. -"'-)
- \\::: :: : * : * :. : t !c* ir~.
May 1974 April 1975 July 1975 April 1976 Rcferencci:;:
- 1.
.\\:>I.P::*r. ::.1:.h.. ::::.*:.~.::il
- ,*;~.-.:::c.l L11~ i **:1 l l'rnt.:vd11r..:
- 2.
s~*ct..i~*n 111.S:::::pl1..* Pr**:<.. ::.
J.
E..-.;pcrimcnr:.:tl rcri.:ic~:i.::'l 0~ * *.-.X.rI?E :*!OD l
- 4.
ADLP!?E Results a: ~mce: Give~ by D.
Young
- 5.
Generalized Piping Syste= Res?onse to Ground Shock Spectr~
- 6.
A ~Iethod of Co~?uting S:re,ss ?.ange and Fatigue D.a.::age in a !\\uclear Pipi::; Syste:n by ~. B. ~right <Jnd E. C.
Rociabau;~.
ADLPIPE ***** St<:itic. Thcrro.:tl, Dyn<:iI:lic Input Preparation dated ~L-1:: 1974 Pipe Stress Analysis Ne~ Features:
Codes - B31.l (1973): s~c:ion I:!, Class 3
. l, 2.
- 7.
- 8.
Ne._, 1'eferences:
Section III s~~?le ?r~ble=, Class 1, 3
,."0:sr B3l.1 (lS-73) S.::::;-;lc ?:-cblen:
ADL?l?=: *** S c:a tic =r.~ Dyn.::i:::i i;:. Pi ?a Z*esi;r: a::: S :ress
..\\nalysi.s:
In?ut Preparacion ~!..1~~a: Ca~=~ :ar..u~=-:- 197.S Ne._, Features:
Re'\\*isec input or~ani~ati~~ (~ec~e:ry a~~
execution ci.:cks)
~e~
Reference:
- 9.
ADLPIP~ Avril l975 ~=l~ase ADLPI?~... Static.::inc Dyna~ic Pipe ~esi;n a~= S:ress Analysis:
In;:iut Pr!:'pr.:-a ti0r. ~-~.::nua: d.:.::'::
_*.:;:a:.;-~: 1976 Ne._. ?eatures:
Section III Cl.::i.ss 1. 1, 3
(:~1.:.:.; :orce time histor~ dyn.::i=ic an~lys~s
~ew ~eferences:
~.
Docu~en:acion uf ~D~?!?~ :~r ~:a:~=
Sr.q te::ibcr 19 7 3.
ti.
,*, Mct:h0d C'f Cci::ru::.::..:. St:-"'.;:;s r:~n~=
- !nd F~tiµue Di:i;:-:.:.;:: :.n
~1
~:;..:..:l~~:-
?:~in; Nuclea:-
E..":;:.:-:t2~rir:;.J.::cJ J:si;;::~
.::~
- 7.
- 8.
- q.
A2~?I?~ S~e~ C~rd T~st R~~.
1\\:11.!'T:'E,\\prn i 9iA r..,'i c':1-.r*.
-:~ - **5
.:...~1;;.
Ill. /.i>LI'll'l: C:<>11q*11t:1l i1111,,;* J:,*:;.iini: SLrvs!; in T1*1*s :111d i:r:111,.i1 C:i:1111.. r*L ;.* ;;-_;. :.:-::-:E Sl**:l ion 111, c.!. ~~ 5 5
~
!' : ; : i. ~~:.:..
_; *,;; ::.: : :-s.
i l.,\\:11..:*: ~,r..
C,,.*::::1t:t..:1~ it'":~ :*.** i:1.*..:: ~ t:int ~!w::1ents
,*,,r S\\,.
0 l 0
i.q\\
r i 1 c:.1~s ~ :,::.:
i
- "'\\L7"t"SS..:::s
. It: ! ~: : t.' "/ -: *
- ... : :: ll ! ) : :: 11,. l: 1.
1-.
\\'ersion April 1968 August 1970 Jdy 1971 Sep::er::::ie:-. 1971
,;ove:uoer Dece::ibe:- 1971 June 1972 July 19i2 Dece.=ber 19i2
- \\! 1f'i*::-;;) i :\\
A:>L::'Il'E \\'ERSlO:\\S A:\\il 1Jo1:~-:::::;:-.-.::..
ADLPIFE The~l. Static, Dyn.::=~= ?i?e Stress Analysis Operating ~..;inual, undated.
- Th~:-:-:~:. 5::.:i:ic, Dynoimic ?ipe Stress Analysis:
~!arch 26. 1969.
Operatin; ~:~:r..:a:, first version dated Features:
7:-:;~~:. deaci;.*ei~ht, external, acceleration :md slroci~ lo:1t.ls;
.... ~:1:.::i..: lo::d st n.:ss ;:naly.o.;is; code - B3l.l (1955).
ADL?IP~ **** Static-The~l-Dynz=~c ?ipe S::ress Analysis dated August 15, 1970 Ne~ Features:
Code - 531.l (:?=7:; equa:ior.s 9-13, 331.7 ADL?:?~.... 5:atic-The=:nul-D~.~~==-= ?i?e S~:-as£.;r.alysis dated January 15, 1971 New Features:
Four r::od.::l si:.=..-::.z:ic:;
te=::r.:~ues:
r.:ax1=.ir::,
ca.::-:il:lu:: c:.nc s~:.:~=:? :-cic:.;;;:.;:: :: squa::-es of re~ai....~in; ~~ci~=. sc~~re root su~ of squares, absolute; s~ua=: ~c:: s~= o: sq~a~es for stress c~lc~:a:~::::.:
ADL?I?E **** Stat:ic:-The:::::~l-)y':':.:.:::~: ?i?e S::-~ss A:::.alysis d~ced A~ril 1, 19~1 Ne'.W Features:
S::ress st..:..7_-::"1r*:
lcacls 3Jl. 7 for r::ul::.ple ADL?!PE ***** St.:itic, Tber:-::;;.l, ::*:-.s:-:-.:'..c ?:.;"le St:::-ess Analysis Input Preparation dated,\\p:-i: :. :?7:
Ne'..*.Fe.at~res:
AS~-!E Sec:::iC":'l I::. C:as: l (:971). suw:::.:iry scress re~c:-: :~ =~:::=:e loa~s; closely Sf'tiC:~d
~r.'c.!.::l S.. -*.-~::..,~
References:
- 1.
Logical F=ccec~r~
Scc:~a~ I:! ~:~~:~ ?:-=~:2::i 3 *
[:-: i) c ~ i r: ~ i: :. ; ~
....... -; ~ : c ~ :.: : I * ~,
1* ~ f I\\ n i. !' T ? ~
- 4.
,\\DL?!!'::
- ~
- .?s:.;.:.:~
~: :*:~C.:=:2. c;.:.ve:1 Cy D.
'You.,.~g;
- 5.
ADLPL?~ ~~~:.:~:~::c~ :, ~es~o:::.se to G=ou~~
- ipl.!.*:r.:i
- 6.
iJcvC'lc*;'::i~*!1t
.~: :-:.:-..:.'.11 i'.:r::ic";*.::it:ion H:1trix for C~t.:nt!:-~.J 7~ri..:-=. : ::--..:.:is.i.\\..~n Si1ock Inp~t to
,\\DL?!.?!:......... S:.,t:ic. Tlit.!:*:::::.:. : :*:*.-:-:=
1
~;*,...:
S:..r,~ss /\\r:~lysi.s
- ~:.::
P:-?!J~::-::.t:i~:-: C.::t::-C :.:-:*:*:.:
- --~
- r::-::.:2.:'..s:. ::::::: :::. ::-:..:
~::: :.:.::::.:::;::::::.::.:-::
s~:-css
- 1 J~ ** ! *:s:....._
I 1
- 1,...
- .*:... :.:... l 111:Lj>11C:
l,:-.:d::u_*t :- !. :-.
- \\; tl1tr1* J j i
r.::Jint.:iins all p.-:st fl!.'.lCurc::; whir.:i1 h.:ivr::
- it=~:-. :::.:;.:..:::
- ~
- 1~::.le:
~o thC! users during the period !9il to :~JS-.
)WJ)£A.t;~
!. 101.
Din~*.. :ell
/\\r:hur fl. 1.i tt:l c. Inc.
C.:imbr.idge,
~!.:\\
0:!140 April 19, l9i9
Blac:k &
Veatch
'5rot:.'"1J. & -Root Bur:is & Roe Cooision Federal de Electricicad Gibbs & Hill
~-l. W. Kellogg Co::::pany P.O.
l 1
l 2
1 Charles T.
Main, Inc.
P.O.
Montreal
- ='.ngineering Co:r.;;any &
Ho:lenco S.:i:::;:iut-ing Sen*ice L:d.
1 Utilities Service Co~;1:rny 10/04/i4 10/0:0/67 11/07/75 7 /22/77 8/19/77 p2;nr:~c 7/ /i4 2/23/75 11/29/72 11/16/75 7 /20/76 2/20/70 7 /06/7:.
11/01/iB 5/12/70 11/19/i.:i io125r:,
4/lS/72 6/25/75
?
= J/Ol /77 5/!.'2/70 i ; -.
1"'11*--
..J.""\\i.-
pe=?e:.:.:al per;oe:ual per~ec:i.;al per;ctuill auco=<J:ic e~cen~ion per;::~tual au:c=~=~c e~:c~s~on ll/H '76
.-.r.--c:i-**-:
1
- 1
. I
. \\: : : ~ ~ ! : :
I
! [ ! l ~. : ~.
Sencr Ingeniera y Siste::as 9 S.A.
1 2
3 4
Unit:!d r:n;inccrs
& Cons true to r-s
';.;estin&house El2~=ric Cor~o:-;Jtion E?"FECTn*::
0:~1::
2/0l/72 10/01/73 6/l&/75 5/0l/i7 11/01/78 5/20/70.
ll/27/6i j ! - *.
p~r;:-?tU.:l~
I I
I o
. \\f : : " : ~ '
I :
~: ~ j:
0
,\\i'i'i:::;ii:*: l: l
~_1_(_1 :_i_l_F_*.:..I..;;;C.:..;'.:..1:....;;.J...;;)...;;_. _...;l...;: _
_.:..R...;l.:..*::;_; i'":;;: i. *; l
- I:~:.:~~'- _' ~. _.:...* _. _; ~
~ ~ *~
TI1c b:tsic npprn:H"h tn hC' ui:;C'u in C".t1mp11l in~ t!ll' ::"***:;*
0 1:"::;l' of rirdn1~
systci:::s to i:;round shock inputs in trrm~ ni tli:q>l.,,-,.::.*r:: (**r v*:l11<ity or
<Jccclcr;:ic.ion) spt*ctra consists of l~"1wr:1l in;~ 1111' d*:1;.1:: j,* pr**p**rtit:~* ni rhe syste:n.:md ;;pply!.:'l):: a codi'll supcr-posiLil*n l'!t.:tho~ (:ir 1wr.:i<Jl cod!!
octhnd) to c.h:iinc the struc.c.ur.,l r1*:;pnma* tu ti11.:
- .!1111*i~ i:q*11t<;.
Tlw for-
- iul.lcion in tt!'I"OS of nurm.:ll modes fnlln1.'s r.t*nc*r:Jlly :ih' :"iir.:: discus~ed by Young~l) As fo'CTllul.:itcd in this rC'icn~n~l', the cc:it:-:i:rnt i1ins from tile individu<il norr.ial modes :ire defined in l*.:r::i:: rof *' ~r,;:.i j*:trl idrn-ti on faci:or t.thi ch depends upon the nC'r.:::Jl.;;;.*:*..: (r:i ::~*::*;,*:tnr) ;me the distribution of U1c 1..-.:...i over chc: slructun*.
- ... i:-
- :-.1:::::.iu11 ls aprU-cable, ho.,evcr, to syst:i?l':lS exciced by one-l:i:-:...:n:-;i. :1.-.. :,.;... _,,._; c*nJ::. i.e.,
For the general chrce-ciiu;en.sional shock inpul <md rc~pc;::~l' c:::~**. t;JC: cont:ribu-sponse cue to g::-ound shock is given in tile [011,-,*~*in~ p.:.:-.:::r.::;"ilS.
bi1i::y or 5::iffri~ss ::i;:c1 i.x rcl:icin;:
- .,;-ct*:~ :1::.:.* j;,. :.:.
~.;,...;:~
points in ci1e syslc~ must: be ~~ner~L~d.
for ~ syscc~ of ~ ~c:~nr~ pnints.
6 x 6 subsets.. )
uic f11J l,1-.:i11;: pri.. ri Ly:
fir::I, ll11* :n:1:;:; p**i::f*;; *,,*.;i.., 1:,,. i11!**ri11r iir:m1:l1 pof11L:;; *;111J ( i11:il ly, Ilic ;111.-111*1 l"'i :11 *..
!i1 1
- I 1 o!
I.
! **:*1*.
- nJ !:::..i*11c: ~i1*:1l
!\\"*'..;pdf1~c*, A::u*rit*.111 :;,,, ~.-: *: 1*: **
- ~. Y., ; ~'UU.
r i 1-1 l"I 1
- ** 111 **
"! ;:.:::*: IJL't" rs, Anl1* *r r '\\I ;t* I,. J.....,-
- -:* L-'LJ
.._.~*-
,\\
\\.
Lim!> !urccJ-will la: urt.h:rctJ :m i1uli1*.11**1l lu-1**~::
A B *. D. E Ii c:
]
J~
1-*
II I
m."lS.S poinL.!' suh-111;1l rtY-incerinr pllints suh-.:i.'1t ricL'S i\\S shown, the m~trix is p:irtjcionccJ inln tf1t~ Li1r\\*1*
~-.,IC!l~nrit*1' n( rwt~nrk points.
The formation of chc cri:.~lctc m.'.lcrix is r~1rril*d t*11l 1.J::,\\l>L!'ll'E.
The rows c:rnd colu.."llns corres?c'.1din!?: to anciior roints.::r.rc m*"'* deleted from the.stiffness matrix. lcnving a r.1:1trix ch."lr:1.:tL!rizin~ :::."ls;; j'IOints nnd interior branch p~ints only.
r ('...,. *.: * ~ * -
I " " 1 cc:-
1 1*
\\.
\\,.... a~
- l. \\.....
ti 0 rcp:-esents deflccr:ions at the m.::r.ss point!',.incl
- imi1
- irl*:. i" rt*;*r***. r;: *; !tr.!*:<; :11*
II tions.::r.t the interior br;inc:l1 puinti:>.
the mass points, and f 1 louds &it the in::cricJr h:-;.rnch poi.:~c~.
ln tile coise of free vibration, the.londs r-0.::r.re inc.:r!:icil l11:1d~ elm.~ 1;,, t:w :::.::i;:s points and the loads F 1 are zero si:..:e intr::riur nctt-:C"lr:: ;-'.ol:1ts ;.r*.* ::.:.:: lrJ:.Jcd.
Tile equat:iiJns then become A.
+ I:.
I (J
.* (I I~
+-
r-:. '
II II Fn*m tl11.: sccont.I cqu.:ic.i on. -,,
-1
= -E I'
I I I-:~
Anhur Q Unle i:i=.
~.. \\.
IJ J *, "
F II
. J"*f 1 c:ct i uns 01t m;a.s.s poi nLs.
llds 111;1l ri x i :o ;an n x n :arr:1y whc.: n* 11 f s the number o( mass points:;.
J-"nr inc.*rti;a ln:ul::. lhi:; m:1Lri~ c.**111oaLinn nwy be written as 2 'I.
- "0 (ol.. *
- \\ ()
where (A -
li E-I ll)
E.
CalculF.::ic-. of ::c-rrd Modes nae ei~<?nvcctors. ho* ::md the c.*i1:1.*nval111::;, *.
I fCJr t*.,rh of Lile
- 1 n
nonual modes arc computed by solvini~ Lhc m;alri::-: 1.*.111.,tinn
~
- t.. 0
- s i..
- -t i 0 for CClch.. of iL.s n c:h;irac:tc:rislic snl11t,il*n:.;~
Tiii~~ 1**p1:1Li1111 ra:17 Ill'
. solved by iterative procedure when put i~co tiic fClr.:i AV n
- 7.
s w--v n
n This transformation is pcrfnrmcd !Jy d1.*finin;:
- md M "" !'11 / 2 }11 /.
- ?
1/2
=M
- \\U v n 11 thu_!;
dcfinin~ Lhc -matrix A ai:;
It
.""1SS11rt*s tli:1L tl11* itcr:aLinn 1Ji1l 1*1111*.***r;:** :111*111.,*11* rc*::l :1111! l"";ith*c-1 (2) 1.* 11~Pnv;1 llL'S
- 2.
'"'.id.:.i.,
H. !>(iffn,*c;:; M:1tri:~ :;t:-11,1111.ii,*,;i.1_!..:.:_*_'_*.'.,jcl P:-1,pn]:.iun L.,hnr.,tnry. Tc*1*itnic-al f\\,*p11rt 1:*--;*:,. 11.-:.. i.,-r "ii. l'H*'*.
I I I -
~
Arth.ur D Little. Jr.::.
'l.!i&h Liu* m;alrix c.*ri11;1li11n in tlai!. l11r*111, rlw ii* 1.111*.**
l'r**11**.*. will
,*nnv&:r~,. ams L r&.**uli I y m1 Lill' "' i 1~t*uv;al m* la;1v i 111: r Ill' I** n:***: 1 m*u:n i 1 uut*.
Fnr s:rnund shoC"k 1'.'l.$p011SC: **1111lic:ttiuns~ it i:; r:iurt* 1l1*!dr.1hh* rnr th1*
process to c:onvcrJ.:C most rc;idily to the* sm.,11,*st iJ:&*nv;ilm*.
Cnm.;c-qucntly. the moic.rix c:qu&itions oirc put in Lht! inv,*rlcd furm where
.. c v * ; v n
n
- n C
- A -l ilmI l e
n l/..,-
11 and ilpplicilCion of an itcriltivc mclhnd, sud1 :as tlw SL1 1'111l:1 mt:t.l111d, will produce thl? sucC'cssivc r.tn<lill fn*c1u\\!nc-k:.;
(L-i;:1.*uv;1lu~s) ;ind modal columns (eigenvectors) oi ci system in ;isn*ndi1.r. orJcr.
An alternative solution tcchniq1u:, 1.1hid1 h;1~ l..h 0cn uLiliz1*d in ADI.PIPE MOD l is the Jacobi mcchod(j).
In ti1is prrwc*cl11rl!, :111 nf the eigenvalues and eigenvectors are prot!uced. ~dmul r.1n1*nusly \\,*i tii c1u;il accuracy.
This :ncthod may, ciicrcfon*, cmpJ.. 1y th'-
1:1;1t:-i:-~ l'1p1.,ti1111 in either for:: (i.e., with eigcnvalu<.>!" J /,} o~ * ).
In :*!C..1:J l, ti1c SL;cond n
a for::i, in ti:f::-::lS of l., has been used.
TI1a m1,d:d (n!qucnci~*lO :ire scored n
in a ".frequency vecr::or", and the mod:il column~ arc st.ore<.! ~n r.:odified f oL.D as colut:1ns in a "modal matrix".* Tile moi..lul colu::ms an* modified by first converting the Vn.back to mod."ll deflection~ ". 0 and t:1t:n by nor-malizin~ the column.
Each of che s.-*t with in ;1 m111l:1 l coJ 1:-::i. *.., no\\.'
l 11 rcjlr~scnts a nurmcilized dL~flect.i.on oi mass* i in r.iucli: n.
C.
CalcuL;tion of Eouiv:ilcnt Scacir* !Jcfh.*c-t i1111~
As indicar::ed" in chc* appendix, U..:.: mod;il m::pl.itu<lc ci1:
io.; sliu*.:n tc* u_,
given by the expression
'111 :: i. j' (IJ
)
- g.
II ;
'I.
11 J.
Grcc.:nst.:iclt, J. "TI1c U1*t*'nT1in:tli.. n* ** r 1i11* 1:11.1r;wt**ri~:i 1
- R11o*t:; 11f
.'.i l1atriA hv [hl* Jac:nbi l'h*tluui", 1:i1.1pl 1*r i "' :*!.11 i1**1**:11 i.. 1 I
~-11*1 i111d:;
for Dj.. it.,} C1*mu11CL*rs,.lnhn \\..'i}1-::. :':1*1.: Y.. rk. l'l°>'J.
Arthur D !.Jttle In::.
~
whc.*r"* 'I' is Lhc muJnl* p01rt.idp:1t.iun m;1t.ri;.; ;1ml (U.J i!; tlll" :;luwk in-nt
- II put displacement for each coordinate.ind fur \\!;ic:h mt1CJt:.
This 1:cn~ral thrcc-dimcnsiono:il fonn rcducc.*s to tlw i:;iznplt..*r fnrna;alarion q
IJ n
n a
i.n the r'il!'C: that the inruL :-;hn<*k. mul inn ;al 111** h:1:a* i:* tlu* :;:1111t* in every C't,nrdiniltt".
It" ii; this latt1.*r f,1rm whirh i,.; &1.*vt*l*'ld hy Youn~ (l).
For this onc-dimc.*nsinnill r.;z:;c. :1i; &liscus:;,*,I in R**fC'rt"'IH"*' 1, t:he modill participation factor is dc.:I inl!d fl'r t*<1d1 c11dc 1.-idle for Lhe I
general three.-ci.i.:i~nsi.;~*~~-
c:ai:;e, *the moJill p;1rt i<* i'a:.inn is dc:-finc-d for 1!3C:h :n.:i.ss for cuch mod~, and thus i:o in :i stpwn.* ;irr.1y fnr.:: r:llhL*r than in a linear array form.
T'nt: amplitudes (De.)n iirc obtainl.'d from tlu* dvc*n input shark. spec-tra (e.~., Housnc::r spectra (or earthquake lo:nlin;::i:;).
In tiu.:se SfH!ctra, thl? OI:lplitudcs arc defined by the rr.oJ.:il rn:rp1cnC"y ;inJ h\\*
till~ coordiniltl!
ar.is.
Fo~-~*&J<:h V."J*lllC' nr r..* LhPrcf1*rr< ;111.! fur.. :..-Ir rur*rd::i:rU* :1:ds in n
which there is a prescribed input sp*"'Ctr.:i. ~,. lwvt* ;i vLIJ u1: c-f (ii.)
- 11 The ccdal amplitude q is then evaluated as th..: scalar.!'u:::wation of the n
products of the nth vector of the mncl;il* parti.-ip.;tiun :::atrix :md the sp<!ctra <0.-:iplitude {D 1 ), or. as i:iven pr!!Viliusl::,
n q
.. i:
n t
I n...
7he r:.ocal ;:;:::plitudcs are now crmvcrtcd ro Limplituut.*s in Llrl" oriJ..:inal co-ordinate system by.the relation II
-. *I*.
'I l
Jll II
- 1.
Yu1111:~. ll:1n:1 11Rt*s11111i:a: r*r :;1rnct111;,I :;,*:.1**111:: l" c;,.,.,.,..:. ::iJ,.,*;:", !:l1ru*k
."lnd Str11t*tur;ll !h*soons..:, A.':leric111 Soc-i**t::,,r :*h*t-'1;lnic.,1 En::inc.:crs.
?~. 'i., ElbU.
J r, _ -.
Anhur D Little. In=.
'firr.*
.1..
1lais now 11ri*v i 1lt*~* ;a :a*t ul 11 i :. p I *&n"lln"ll l :.
- I 11 I
- i1..,
I 111* ll II *
- I mout"S.
TiacSC individu;:il sets of displ;1cc-m1*nls \\illl 1111:.: h'"* ;1ppli1*cl to th'"*
system ;i.c; cquiv:ilcnt i:ttottiC" cJr.flt-r.t.iuns; 111** rnrrw:pun1lin:! 1wlwnrk fnrc\\!S.;ire ubt;iiraL*J hy Lhc usual pru1*cdur1*:*..,.,\\Ul.l'IJ'I-..
It slumlJ he.*
nuLcd th:it the sLiffncss nzatLrix to 1..- u:;l*d fur tlai:; 11rru*
1*tl11rr* musl ht" that resultins:: when thr: rnwi;,~nd Ct"lum.ns ("1*rrt*spC111dinr. Lo ;mdanr ('letint~
A I.I IJ 1-:
-J TI1e reduced stiffness matrix (A-BE U) camwc la, us..:r.!. s;nc:e int\\!rior points (branch points) must be c:onsiu..:rcd in tlic process of transferrins interior loads and deflections from pt"int co pc.*i:ic.
ADLI'IP!:: util izcs Che ncLwork furr.c st*t.S 111 l!l"lll.!r.,l..: sl rross1*~: for each code.
TI1e upper bound for the scrc:ss h*v1.*ls <JC at:y point jn Che system is given by chc OJbsoluc~ surnm;1tiun of LilL~ sl rTs:o:..:,.:
1!~*11..:rntL'U for each mode.
Such ;i summation.assumes tl1ilt Liii' c;nntrib11tjo:-:s from l~;ich mode reach their m<Jxi:num value at Chl* point in CJUL*s ti<"'n.1i. the s~ml!
tirnc. *Ocher methods of surnrn.,cion m.,y he ui=:... *J,,,f *our~..:. r!.*;wnclini: on ti1c degree of conservatism 1.ksin::d i11 t:,c ~naJ*,-:;i;;.
,; s*:.:::**:*l**d ;JILcr-nacive, for exo:::nplc, might be che sui:i,,f ChC' cont:-ibution of the funda-mental mode and che rms su:::mndon of thi? hii.:iu.:r mode.
I I 1-t, Anhur D Llttle.lnc.
e e
Al'l'J::.~I>l;~ I\\'
Ur:Vl:J.OT'Ml:..'-'T m* HOU.i\\L PART IC: ll'Al IO;: !'11\\'rl: n: J-"ClH c:1::E1:;,J.
TliRl::E-U lHl*~SION SllOC~. UiI"LIT" 1U LU~!Pl-JJ uv::,\\:-i IC SY!>I 1*:'*1*
TI1c dcvC'lopmcnt of Che mud~l p.:irt icipal i1;;1 (:ic-Lur jn th1* 0111;dysis of the rcspons~ of.:i lumped dyn:uni c,;ystc:n tn,--; 1101.-J im~ns i cmoal shock input is coirr icd oul by Yuun1~. £0 R1.*f **r~*nc** I lay "l'I' l i 1*:1L i 1111,,f l.;1i:r:m~r' s eqm:ition W\\.th tlu: sys_tL'tll kinc.'ClC ;JIW pULl'nti;aJ 1°11L'r1:i1*s l'Xpr1*s*;**tl in tCtiDS of nnt'1D.:il cnoruin:itcs.
In this ;11*1wndi:-:. this 1h*v1*l1*111111.*nt js 1.*x-cc:ndcd to includL* Cht" J:t"ncrill lu:iclini: c*:isc* in wliicli 1liff1*r**11L :;luu-k in-puts are allo*.*=-= :.n each of Lhc -syst*-m c:ourpin:1t**.,:,.. s.
TI11.* t1.*nninljlOJ;Y utilized by Young hOJS been fnllo:.;.:c.J t11 Lia* r*:*:I r*nl pu:;!'i ihl**.
For the lumped systl!m tlc!'in:::cl h\\' th1.* sv::::m*Ld,.
i.111.~rt. i;1 m.,tr i.x m..
l J and by the stiffness matrix k.., let u. be tlh* cl:ist!c d~splCJccmcnc in
'lJ l
the it 11 c:oordinc:icc,* and let u. + s. h..: th!! ;ih*;nlutc-displ;11TmL*nt.
1ia*
1 l.
elc:nentS U. and S*. il1"C, in the hcner:il C'<!Sl~ *...;ix *.*J.*:-i1*nt.
\\'*'C"'tC't"~ f,ir e;11.*!1 L
l rn~ss po.int.
n1e kinec.ic encr~y r of Lhc syst... *m is s: i \\.'I'll b*:
L T * -
.t 2 ij 1
- r.
2 "ii m ** {u. + s.) (i1. + s.)
lJ J
J I
l (m j.i u. u. + rn.. u. s. +m.;
1 l_J J
l l.J The potential cner~y v i~ given uy v = l -
2 ~. ;;,ij ui u j
. l.J
- u. s. + m *. s. ~.)
I
.J I i l
.J Wl* iutruch11:1* ll1L' nurm:il r*rn1nl i11.111*:: *,,
(1).111rl I' (I l
),,. I Iii* I i111*:11*
!I II l r:111:;fun11.1lj un:;
la *
( L).. i:
J.
n
'1 I 11 II
( l )
s. i (L) = ~ ~-
p (t)
Jn n
n
- Scpte~ber 30, 197k I\\"- I Anhur D Lttlelnc.
I*
~
(wlll"r&." *'*
- 1r** Liu* 1n111laJ ru I mun:; "I.,... 11........
111.1 l r i *. 1 :111*1,,,.. I
- I I I I*~* I H 111 *
.. Ill din~ Lr.in:;; C urm:J Ll uns U!!lWt.:t.:ll u. mad 'In' ii. ;1111 I 'In*
1 I
p
- We further c.!c!inc th~ p.ener:Jlizt"tl.inert i.'1 hy n
- uni
... :11111 I' '
- 11111
- r...
II J
lh*C:JUSC o( orthOJ!UllOJI ily, tfw* J~c*nr."r:JI i:l:r*d irll'rl i.1 m:rl rix i:; :I cli:11~1111:if moitrix., nnd hcnc:c ~Y. be wri ttC"n ois
~here okt a Kronecker delta.
Because of the symmetry of cha incrti~ ::.:1Lrix. m...,
lJ ij m *. u. s.
iJ J
i becomes r
ml.*J* ?i.*k.* qk +J." Po
-... ij kt
.r..
.r..
and the bilinear term r m ** u. s. *also
~*
ij l.J l
Similarly, the quadratic for::u; z m *. u.
l.J l
becomes
- u. ant.I -
J (p,.) ~.
- a.
The kinetic energy m<lY, therefore, be wri-nc-n ilS T
r (M
i..
- 1.,,.,
L k k
- . I:
k
- . mk qk
- 1.
r.: *. 5.
11 l
i: I' I. l tlu: bil i nc:ir form pk
- s. become
.1 l-'rm:i Liu.: dc[iniLiun of nur.:m.,J mm.lr:s, \\."l' ii:1v..
c :. i j k ;:; i j): i : u
.i is :m ci~cnvcc:tor (r.1od~il C"~>lu:::nJ :1111!
j I\\'-.'
1:; 1i1" i:r:rrr~p111ic.lin~
- i.
Anh~r D [Jttle. ln::.
l For the nth muu;d column o'lnd thl! nlh t*i1:.. nv:1lm*. this hcct~ml'S *
.or
- r.
k.. i:-.
l.J Jn ij Now the potential energy
>: lk.. -
(~ )- m.'. J j
l.J n
t.J
- j*
~ u jn
- r. k.. ~*.
j I I JO
'Ii. ** (w JS is given 2
- <*** )
n r m
)- r.
n ij by \\' =
i j
- jn j
m.*..*
l.I
.I 11 I,...
1 I k..
- r
- u.
2 i.i 1 l J
l
~
=*t n
- u.
.I 2
.I..i
... in qn ijns 1
c:
k..
=
- i.
2 11S l..
- z 2 '*
ns 1,.
z: -.. *'
2 11 Ihc <ippropri.'.lte form of I.agr:m~c: 's cr;u~tion ji-;
- ,\\'
+ -.-.- = 0 aqk
-i i u* - l:
n n
- ? :--
n 1.:li i ch i;.1. Vl;.S Ll11.: cq1J:1Li uns ol ruoLion, 'I. + ***
t r
1.I 0 n
. in Ti1l: so 1 ul i11n cl LI
- s ll.
cqu:1l LOii I ur tit<' ra.1d:il
.111:p i j r 11d1* 'I*
1 :.
'I.
(t") =
K i.;k f jik (Tl
~:in **,_
(t-T).r;*
Cl 1*:- I n
n n!'>
qs J.S js qn a *5 )
Arthur D. Little. !nc:.
Frum 'Lhc Lr:insfurm.-itiun L"qu;1l iun. till" v'*c*t111* jik i~; r**l;it.. *I '" r lu* v1*1*L11r gk which describes the ilCCclcr:itions of th<' u;1sr nf thL* sylHL'm.
Thi's I
l
,., -1,.
n*,OJL ll &ff l'k. *
- _ **kl.* f.
t Hence. qk (t) * :k i.£ ~*;! !:1 (T) sin "'k (L-T)dT.
1 lic* i 1lc*nl i l y m.;1( r ix.
IC [RC (t) ]k Iii 1 f sl Cc) sin... k (t-T)1IT ;mcf t"hc shock inpul l:Jk 0
displ.:icemcnt (D,,)k
- iIR (t)]kj"
- th~ input spt*ctr:1 nrt" 1h:fim*d ;is Q
C."lX the m.'.lXil:lum modulus of the response v:d uc 1' ~. l l}.
Tiu: mud;Jl amp I i l mies
-1 b
~ r Z.
(D )
or q
'(Jl )
"-"11crc *r i.s.:in 1.*lemcnt now eeoee qk..
- k.2.
1 k' k
~ '* 'k:.
- k "ki' t
~
cf the modal participation matrix for mode k, mass point ~ 0 In the special. case in which al 1 uf the c*lL*r.iPnLs of s.. ;ire lhc S.'.llnC' and all of the (D;) '* are the same, this exrrc:-osic.*n reciuc.:~ co l....
ll
.. 'i' k~.
~
T'nis is an alternative expression"for Young's re~ult since i: can be shown th~t tlie mod;iJ :'*Jrt::icip.,th1n i~cto:-, "f,_, is c-rpi;il to : *:*' r A
K<.
Ihe rnod~l particip:itiori fnccor is ;ippropri;itc, however, only for rile ~pcci;il c;:isl~ when :ill nf Liii' 1*l1*111('nl~: nf rlw h.,S*' ;11*n*l,*r:11ion tlirn.:11sio11.:11 siioL:k mocjons with diff1.'r1*11l sii... *i.:l; input:;
(sp~**:tr:l) in the
~~rious coordinate axes.
1** *
.- I Arthur D Uttle. lnc.
The tcsc for the closely sp~ced moJcs is:
(£2 fl) if--...--
£1
< k, then the bandwidth factor (k~ for thes~ modes
~
cause the program co form an absolute sum.
(This c:ype summacion must be requested of the progt'am by the analyst.
At present. the factor Kin percenc is entered in the Z2 field on the SHOCK ~rd. If Z2
- o.*
then.equation 2 is utilized.)
ALTER.~T!VE SOLUTIONS A cons~cive assumption is that the vibratory energy in an earthquake is random and the component moments along each axis are independent of one another. Realistically, the earthqu;ike acts as three different earthquakes. with the axis orientacion a variable.
Therefore. since phase relationships are unknown. a mean solution is taken independently-for each shock direction..
In mode n, 1/2 (M
)2) kjn (Equation 4)
Follcving the square root su:n:na.tion fer the modes " to n max.
(Equation 5)
Since the absolute sum is overly conservcitive, an altern.a=i**e is to take the maximum modal response plus the square root su:n of the square of the remainir.s ::.omen ts.
!M. j" I)
IC m 1:1aX Tl max - 3
_ 1/2
+er.er ~it*)")
n*l j*l Jm (Equci tion Ii)
Eac.h of these al.ternative solut:ion su=:mtion schemt*!i or v~r::i.:l Lions there-on can be insereed, t:~on request, in to the ADLPlPi:: proi:r=.
rne resultins s::ress an;ilysis i~ dependent on the s~..:i ti on of the
~od~l ::O~ent:S.
Tile eT.a=ple Siven here is not a Statistic~l ~~~n but certainly indicates chat the presen:.versio~ of..;DLPI~! is unconscrvative but re11lis::ic.
As a consensus is r.:-:ichcd.
- o Lhcr 5,,--1 L.i::~ r~.,chniques vill be introduced.
Artl~url) I.ml<! Inc
--*--~- -- ------------------*_,,---;---::"'"------;-*-* *- -----**------------.--,.-.
-~----.-------- --------
~-.- --- ----- --
a*
- t lk
- where k
- orthogonal ;ixi8 (X, Y, Z cnurtlinatc) j *earthquake direction (X, Y, Z axis response spect~a) n
- mode
- With a normal mode an.olysis, <:111, coupling and ph:i.!;c.* rcl~tionships between modes are unknown. ** However,* since the!ie moments have algebraic signs and refer to a consistent position on the piping surf~cc, the quescion of hov to sum the modal moments oiriscs.
!he presenc version of ADLPIPE assumes that earch motion is oriented along ~ single veccor and i~ compose~ by ~ spectra vith co~ponents in the three orthogonal axes.
Therefore, in ** single mod~. che piping responds "in phase" 3
M
- t nk Mkjn (Equ01don l) and the algebraic sum is t:iken of the mot~on which results from the single e-:irthquake.
The response is independent of ~xis oric~tation.
(Equ;1 tion 2)
T:'iere is an alcerr.a t:ive technique \\."hi ch impl.: es that closely spaced
- odes are couple~ and are taken. to he in phase.
TnereiC're, when that occurs, the square root sum of s ~uar~s is takE'n of the ahsolucc sum of the closely spaced moc.lal n1'nent!'i.
For in:;t.inc:e, modes l and.:?. *ffc cloi;cl:** spa~cd J
3 J
! I.
" - ((
l!-\\j l i +
.,. i,.
I ): +
(V I* )
(!:q un ti"" 3)
.. k
- 1 *..
- -. i,
.. J.*
j=l j=l j=l V-.2 Anl1t1r I ) I !((IL-l1x.
- -*-----.-----*------*---** ---- - -- - - --------- ---~---~-----*---*-
1\\1 'I' i:.* I' * :*. \\'
UYNA1"1C S'rRE~S A:i,\\l.YS IS lli'.\\1>1.1' 11'1~
hy I. W. Dinl,,"VCll Arthur D. Little. Inc.
On page S of the reference an expression for a sec of displacements is developed for each masa degree of freedom and for each ::iode:
- These displacemenU are developed from the normalized set of displace-ments q, as transformed by the modal matrix ¢.
for mass direction i l.D and :iode n.
The displacements, xi. represent the zero to peak displacement of each mass degree c! freedom when subjected to :i shock lo;itling which is described by a {displ.:icement/velocity/accefor3tion vs. frequency) res~on:;;e spec~ra. The dis~~acements have a consist~r.t set* of algchraic signs
- hich define the mode shape of the deflected piping syst~m. Reversing the signs of the.displacements gives the opposite p~ak ~odal deflec-rions of the pipi.ng system.
From this see of i:;iod.al displace=ents, X., the displacements of the
- l.
non-mass points are calculated. There are t"'..10 types of non-cass points:
a) non-it.ass netvork points, and b) interior points 'iJithin a pi;>e section.
Since ADLPIPE uses a transfer mat~iT-technique for combining several pipe elc::ments in series to formulate the stiffoess of the section (a section is a series of connected elements), the non-mass network points
. are calculated first:, then those deflections are ut:ilizeJ to calculate reactions at the nec-.:ork points.
Fir.ally, internal forc~s; moments, and deflections are calculat:ed b>* transferrini; the initial boundary conditions across.each member in' a section.
Thus, for each mode, a set *ar carncnLi:; i:; c:alculaLt.>d:
""kjn Gener nli.z~~d Piping Sys t:cm Responi=:C' to I.round Slicit:k SpC':: !.. :*;1 hy irvins t-!. !Jing-,.rel.l, Arthur n. l.jt.tJP. Inc.* C:.1r:llirit!~:**, :*:1:;s:1C"h11sect:o;.
'.'-I Ar1lu1r I) I 1ttk: la *.
1\\
l I
1 I
- 1
'I !
I r *
- 1
- I I l
- /
j J
):.* a.
.... c:..,
'-J.
~
~
- .111... *11,
- .11 1.:... 1;.. pl,*
AL pul11l. zero 111.\\SM~ 'Section Ill Smaple l'l*Jblcm (C:las~ l, I: Jass 2)
Mx Shock l>l t'.
K
-47467 y
-153624 z
-27185 I
\\
alcl*bralc sum (Equation 1)
-228276 SRSS (Equation 4) 163071 Shnck x
-27J4J y
159117 z
-851446 "l~~hraic sum (Equation 1)
.. 7196 72 SR~!i (Equation 4) 866617 Shock Dir.
)(
101890 y
-29914
- 7.
-6862
,\\lr,**l*rah'. 1;11111 (l*'.q11;iLl1m l) 61114
~:n~;s (Equation 4) 106559
- t-r-=--1:*:-.~--* =~":"*~*:-~.... -:...2~=.==
lllT.\\I. mom~nt C01!1putcd by SHSS of alg. s11111 (Equation 2) 7576/tl 828241 5HSS of SRSS (Equation 4)
,\\huulutu ta1111 of alg. euiu
,\\h1,o l 11tc sum of SRSS Max * + SR SS of a 1 (:
- sum
. (Equatlo11 1)
(E1111at fun l)
(Equat 11111 1)
(F.111101t. l1111 6) 1011062 1136247 956512
)06116 Hy
-1297
-4199
-743
-6239 4~57
-5128 29843
-159690
-131,975 162535
'" l195
-938
-278 197~
lJ4l 135131 162630 143193 170333 141520 Hz 67221 217557 3M98 323276 230936 2882
-16174 89758 75866 91357 1426756.
-418883
-1211098 Uli:.1725 1492144 9411098 1512670 1282867 1814437 1215'/BJ 1218031 1761701 1639664 2147615
. 1551406 20115~1) 1.0
- l.44 1.34' 1....
- 1
.STONE 0 VlE.oSTEn
- -:**.-.~.
~--*.. -~ r-,_, ~----* J
, ~~
1875 EYE STREET N.W., SUITE 550
- ~ O\\'
BOS'TON N[W YORK CHERRY HIL.L, NJ.
DCNVER CHICAGO HOUSTON P'ORTLAND.OREGON SAN DIEGO WASHINGTON, D.C.
WASHINGTON. D.C. 20006 Honorable Morris K. Udall, Chairman Committee on Interior and Insular Affairs House of Representatives Washington, DC 20512
Dear Mr. Chairman:
OC.510N CONSTRUCTION Rl"PORTS l['ltAMl""'ATIONS CONSULTING CNGINCERING November 16, 1979 I have had occasion recently to read your letter of November 9 to your colleagues on the subject of the proposed Markey Amendment to the bill authorizing funds for the Nuclear Regulatory Commission together with the detailed statement enclosed with that-Jetter.
On page 2 of your detailed statement*, in the four th paragraph wherein you discuss "two precursor events" which raise questions in your mind about nuclear safety, the following sentence is included:
"Another unsettling event was the discovery of errors in calculations relating to the ability of several operating nuclear power plants to withstand earthquake forces."
On March 19, 1979, Mr. William F. Allen, Jr., Chairman and Chief Executive Officer of Stone & Webster Engineering Corporation, testified before your Subcormnittee on Energy and the Environment concerning this matter.
Notwith-standing the characterization by the Nuclear Regulatory Commission of the seismic calculations in question as "erroneous," Mr. Allen pointed out to the Subcommittee that the design was in fact adequate and that the systems involved would not lose their ability to function as intended were a postu-lated seismic event to occur.
Subsequent review by all parties involved has revealed conclusively that no error ~as committed, that the analysis method employed reflected conservatism in design comparable with more modern, current techniques, and that the design reflected the state of the art of seismic analysis at the time employed by a number of organizations on a number of plants.
In an October 25, 1979, letter to Senator Hart in response to questions propounded by the Senator, the Nuclear Regulatory Commission has again addressed this issue and I enclose for your information a copy of Question
?\\o. 4 and the response thereto by the NRC.
As you \\*>'ill note, the Co::miission has now concluded, based on a survey of other plants and the design proce-dures employed by other organizations, that the seismic calculations
~ :..
perforr.ied by Stone & Webster on the five plants in question were in accord with the state of the art of seismic analysis at the time.
I hope that this information will be of assistance in your further consid-eration of these issues.
Enclosure Very truly yours, Gerald G. Fain Assistant Manager Washington Operations
ANSWER:
Fle::se iis: each re:::c:.sr r.~.-ich hi!s b:::-t::1
- ""ou
- .~ :-... _:: ;-'..-=:-::::-:,.:,
includinc the five re2c~ors hhich w2re the s~~j~c: of the hearing, - to have had an error i_n the sei Sj;li c ar.c. lys es of pl ant design.
In your response, please include:
{a)
(b)
(c)
(d)
(e)"
whethe~ the reactor was shutdown because of thee-ror; whether the shutdown nas voluntary or by order; the systems involved; whether the systems are safety rehted or non-safety related; and the resulting corrective measurE if any.
At the time of the original safety revtew of the plants i11 question, specific HRC (then AEC) guidance on acceptable r.>ethods for combining seismic forces did not exist.
rluclear industry practice to combine seismic forces for piping systems varied; some design organizations used algebraic sum1~tion, others used square root sum of the squares {SRSS) and others used absolute sumT~tion Qethods.
It has thus developed that *a nu~ber of plants were designed using analysis techniques, which were accepted practice to a portion of the nuclear industry at the time (i.e., were state of the art) and are clearly unacceptable today.
In Decenber 1974, when Regulatory Guide 1.92, "Combining Modal Responses and Spatial Components In Seismic Response Analysis", was issued providing specific_
guidance on acceptable methods, the stafi did not review earlier plants to deter-*
mine if unacceptab 1 ~ methods had been_ e~pl oyed.
Our efforts to reevaluate the seismic analyses and design of piping systeT-s have*
been directed at only safety relcted systems since these are the systems which are of importance to assure the protection of the public health and safety.
The
.list of the plants which have been found thus far to have used the algebraic surrrnation technique for the combination of codirectional responses to multiple earthquake input components is contained in the accompanying tab 1 e. including wheth~r or not the reactor was shut down, whether the shut down was voluntary or by order:_, a general description of the system involved, and any cor*rective measures.
.