L-15-310, C-CSS-099.20-069, Rev 0, Shield Building Laminar Cracking Limits
| ML15280A312 | |
| Person / Time | |
|---|---|
| Site: | Davis Besse  |
| Issue date: | 05/06/2015 |
| From: | FirstEnergy Nuclear Operating Co |
| To: | Advisory Committee on Reactor Safeguards |
| Shared Package | |
| ML15280A293 | List: |
| References | |
| L-15-310, TAC ME4640 C-CSS-099.20-069, Rev 0 | |
| Download: ML15280A312 (43) | |
Text
Page i CALCUI.ATION tfOP-CC-3002-01 Flev. 03 cALCULAnOil NO.
C.C$S.O3O.20{69 INMANilG I'OCUMEHT 2588+00o.TCGAM-m00s I I VcNDOR CALC SUilnAFY VENDOR CALCU LATIOI{ T{O.
f] BVl fI BVz DB IPY TltlailSubiocl:
Shield Buildng Laminar Craddng Limib Calrgory E Active E Histon:at EI study Claseiflcellon E Tier 1 Cabulation El Satety-Retated/Augmented Aralty I
Nonsafeg.Fetatad Opcn Aasumptions?
EYes ElHo lf Yes, Enter Tracking Number
$yrtem ilumbar DB-SUB 099.20 Fungtional Locetlon lvA Gommitmonts:
None (Perry & Davir.Beaae Odyl Calculation Tvpe: l.l/A Hefererrcad In Atlas? B YeB El No (PerryOnlYl Referenced In USAR Validetion Databass I Ves fl t'to GompstGr Progrem{al Program Name VErsion / Fevbion Category Status Deecdption ANSYS 13.0 c
Aclive Finite Element Analytis, validated undar Bechtel's QA Program MathCAD 15.0 c
Aclive Mathematlcaf compdation Rev.
Affctd Pages Originator (Prtnt. Sftn I ogltell Rgdemr/Design Verifter Pdrrt. Sffi? i Date)
Approtrur
{mnf SnI Danl 000 All Jevild A. Munshi (Bechfel)
HerJfun L.qF' &1n 4n*
vv{G, f ltltr Hmgcfiun Uu (8ofitel) I h
tl6lr Descripliwr of Changn: Inilial issrp Initiailrg Doctrnont 25884-00GTc'GAit-m0os Describe where ths calcufa{on willbe evaluated for 10CFR50.59 apdicaHlfty: l'l/A Rev.
tJfoctd Pagoe Odginaor FinL Sfrrn I EJg,tel Revlewsr/Dad gn Vadfier lPrinl Sbr? t Datel Appmwr (Prlnt, S@t
- Dab.)
001 Ilescdplim of Chango lnitiatlng Docncrient Describe rfiers the cabllation will be evalualed h'r 10CFR50.59 spdbability.
Rev.
Affected Pages otl$nabr lPrint. Skrn Dalta)
Reviev*erltleslgn Vef ft er PrtnI$itr1 A Date)
Approver Pililt. Sront Oatel 002 Descriplion ol Ghanga Inlfiatlng Docunent:
Describo tdtero lhe cabdafion willbe avduated tur 10CFR50.59 eppficability.
Page ii CALCULATION NOP-CC-3002-01 Rev.03 CALCULATION NO.
C-CSS{199.20-069, Rev.000 I I VENDOR CALC SUM]IlARY VENDOR CALCULATION NO.
TABLE OF COI{TENTS COVERSHEET:
OBJECTIVE OR PURPOSE SCOPE OF CALCULAT]ON
SUMMARY
OF RESULTS/CONCLUSIONS LIMITATIONS OR RESTRICTION ON CALCUI.ATION APPLICABILITY IMPACT ON OUTPUT DOCUMENTS DOCUMENT INDEX I
iii iii iii iii iii iv GALCULATION COMPUTATTON (BODY OF CALCULATTON):
METHOD OF ANALYSIS ASSUMPTIONS ACCEPTANCE CRITERIA COMPUTATION RESULTS 2
2 2
3 1 7 ATTACHMENTS:
A. ANSYS lnput and Output B. Memo from Prof. Mete A. Sozen C. Memo from Prof. David Darwin 1 3 3
2 SUPPORTf NG DOCUMENTS (For Records Copy Only)
DESIGN VERIFICATION RECORD CALCULATION REVIEW CHECKLIST DESIGN INPUT RECORD DESIGN INTERFACE
SUMMARY
DESIGN INTERFACE EVALUATIONS 50.59 DOCUMENTS OTHER:
1 Page 3 Pages O PAcCs o Ps'oFs 0 ereFs
,{tA N I A EXTERNAL MEDTA?
(MlCROFlCHE, ETC.) (tF yES, PROVlDE LlST tN BODY OF CALCULATION) n YES aNo TOTAL NUMBER oF PAGES lN CALCUTATION (COVERSHEETS
+ BODY + ATTACHMENTS) 39 Pages NOTES:
CALCULATION I I VENDOR CALC
SUMMARY
VENDOR CALCULATION NO.
CALCULATION NO.
C-CSS-099.20-069, Rev.000 OBJECTIVE OR PURPOSE:
The purpose of this calculation is to identify and define the limits of crack propagation and crad( widths that ar acceptable under the DIN 1 and ib associatad tedtnical basis induding the testing program canied out at Purdue University and the University of Kansas. The intent is to establish limits in terms of crack prcpagation and widths, to ensure that the Shield Building (SB) continues to meet and is in compliance with the dsign basis reouirements.
SCOPE OF CALCULATION/REVIS ION :
The scope of this calculation is listed below:
Performing an analytical upper-bound modal analysis of the shield building to estimate an approximate extent of cracking, for which the seismic loads derived from the original designs still remain valid. This was accomplished by reviewing
/ re-evaluating Attachment A of the DIN 1.
ldentifying and defining the acceptable limits of crack propagation and crack widths based on testing carried out at Purdue University and the University of Kansas to define a conservative upper-bound cracking threshold both in extent and width.
Review and update of previously established effects of laminar cracking on stiffness, strength, serviceability, ductility and long-term durability in view of bounds (of cracking) established in ltem 2.
Review and update of the previously established "Code Compliance" review (DlN 1, Att.L) in view of bounds (of cracking) established in ltem 2.
SUMMARY
OF RESULTS/CONCLUSIONS:
Based on the above discussed scope, a conservath/e upper-bound crack c-riterion has been stablished in this calculation, which can be usd as a basis to verif, compliance of the Shild Building against ongoing crack monitoring program. With considerable margin presented in DIN 1, the limit of crack width is concludd as 0.02 inches, and the limit of crack propagation has been established as following:
Upper-Bound Limits for Crack Propagation Reoion-1 (EL 801.0 - 812.75): No crad( (Dome region)
Reoion-2 (EL 774.5 - 801.0): 100% of the alea is cracked, # of efiec{ive (unqacked) flutes: 0 Reoion-3 (EL 643.0 - 774.51: 50% of the ara is cracked, # of efiective (uncracked) flutes: 0 Reoion-4 (EL 565.0 - 043.0): 20% of the area is cracked, # of efiec{ive (uncracked) flutes: 1 Furthermore, it is verified that the bounds of cracking establishd herein do not change the previously established code compliance of the Shield Building (DlN 1, Att.L).
LIMITATIONS OR RESTRICTIONS ON CALCULATION APPLICABILITY:
N/A 1.
2.
3.
4.
IMPACT ON OUTPUT DOCUMENTS:
No system descriptions are affected by this calculation.
Page iv CALCULATION NOP-CG3002-01 Rev.03 CALCULATION NO.
C-CSS-099.20-069, Rev.000 I I VENDOR CALC
SUMMARY
VENDOR CALCULATION NO.
DOCUMENT INDEX oz z
o Document Numberffitle Revision, Edition, Date o{)
- cEeog,
- 'o.
c 3o.
3o 1
FENOC Calculation No. C-CSS-099.20-063, Shield Building Design Calculation Rev. 01 tr a u 2
Original Calculation No. VC01/801-01, Shield Building -
Thermal Stresses - Shield Wall Rev.0, Approval Date 10/0111976 n
EI tr 3
Bechtel Report 25593-000-G83-GEG-000 1 6, Effect of Laminar Gracks on Splice Capacity of No. 11 Bars based on Testing Conducted at Purdue University and University of Kansas for Davis-Besse Shield Building 2012 tr B
tr
Page 1 CALCU LATION COMPUTATION NOP-CG3002-01 Rev.03 CALCULATION NO.
c-css-099.20{)69 REVISION:
000 BODY OF Calculation List of Sections Sections Page no.
- 1. Method of Analysis 2
- 2. Assumptions 2
- 3. Acceptance Criteria 2
- 4. Computation 3
- 5. Results 17
Fh#netrru
-t Page 2 CALCU LATION COTUIPUTATION NOP-CC-3002-01 Rev.03 CALGULATION NO.
c-css-099.20.069 REVISION:
000 1.0 llethod of Analysis The method of this calculation is listed below:
- 1. Performing an analytical uppEr-bound modal analysis of the shield building to estimat an approximate extent of cracking, for which the seismic loads derived from the original designs still remain valid. This was accomplished by reviewing / re-evaluating Attachment A of the DIN 1.
- 2. ldentirying and defining the acceptable limits of crack propagation and crack widths based on testing canied out at Purdue UnivEity and the Univesity of Kansas to define a conservative upper-bound cracking threshold both in extent and width.
- 3. Rvielv and update of previously established efiec'b of laminar cracking on stifriess, strengfth, serviceability, duc'tility and long-term durability in viem of bounds (of cracking) established in ltam 2.
- 4. Review and update of the previously stablished
'Code Compliance" review (DlN 1, Att.L) in view of bounds (of cracking) established in ltm 2.
2.0 Assumptlons Thero is no open assumption applied in this study calculation. In modal analysis conduc,ted in Section 4.1, the criterion for slecting an acceptable assumed upper-bound cracking scenario is that the new fundamental frequencies and model shapes are approximately within 5% differences from those determined in the original FE analysis (DlN. 2). This limit of 5olo difference is based upon widely used practic in enginering.
3.0 Acceptance Crlterla The acceptanc criteria of this calculation are established by defining limits of acceptable crack propagation and the crack widths based on testing caried out at Purdue University and the University of l(ansas, for ufiich the cunenty established design basis in DIN 1 remain valid.
Page 3 CALCU LATI ON COTTI PUTATION NOP-CG3002-01 Rev.03 CALGULATION NO.
c.css-099.20-069 REVISION:
000 4.0 Computation 4.1 Upper-Bound Modal Analysis In this section, an upper-bound modal analysis of the shield building has ben canied out to estimata an approximate extent of cracking for which the sismic loads de.ivd from the odginal designs still remain valid.
This was accomplished by using the same methodology adopted in Attachment A of DIN 1.
As discussed in DIN 1, Attachment A, Figure 1 shows the Finite Element (FE) model used in the original seismic analysis and design of the SB. As shown in this figure, the SB was modeled as a simple cantilevertpe beam shucture consisting of 13 beam elements and 14 nodes from EL 565'to EL812.75'. In DIN 1, Attachment A, the same methodology and the same modeling parameters were used except for the sec'tional properties. The sectional propelties of each beam were calculated considering difierent levels of cracks in the following three different FE models:
Model-l: No laminar crackinq This model was used as the baseline of the original FEA results and verifies the FE models with different cracking levels developed in DIN 1 Model-2: Laminar crackinq in all flutes/shoulders This model assumed that all flutes / shoulders are cracked while no cracking between flutes was considered.
llodol: Laminar crackino based on the crack mao Four different regions with difierent cracking levels werc considercd based on the crack map, i..
Reoion-1 (EL 801.0 - 812.75): No crack (Dome region)
Reoion-2 {EL 774.5 - 801.0): 70016 of the area is cracked, # of efiective (uncracked) flutes: 2 Reqion-3 (EL 643.0 - 774.5): 20% of the area is cracked, # of effctiv (uncracked) flutes: 1 or 2 (depended on elevation, se Attiachment A of DIN 1 for detail)
Reoion-4 (EL 565.0 - O43.0): No crack, # of efiactive (uncracked) flutes: 2 Also Note that each flute has two shoulders. In this calculation, in order to find out an upper-bound extent of cracking, for which the seismic loads derived from th original designs still remain valid, various assumed cracking-configurations of th shield building have been investigated. lt is concluded that the following case (Model4) can be defined as an upper-bound scenado, for which the extent of cracking propagation iE struclurally acceptable.
Note that the critorion for selecling such an acceptable assumed upper-bound cracking scenario is that the nenf fundamental ftequencies and model shapes are approximately within 5% differences from those determined in the original FE analysis (DlN. 2). This limit of 5% difference is based upon widely used practice in engineering.
Model4: Postulated laminar clackino scenario (Uooer-Bound)
Reoion-1 (EL 801.0 - 812.75t: No crack (Dome region)
Reqion-2 (EL 774.5 - 801.0): 100o/o of the area is cracked, # of effective (uncracked) flutes: 0 Reqion-3 (EL 643.0 - 774.5): 50% of the area is cracked, # of effective (uncracked) flutes: 0 Reqion-4 (EL 565.0 - 643.0t: 20o/o of the area is cracked, # of effective (uncracked) flutes: 1
Page 4 CALCU LATION COTUIPUTATION NOP-CG3002-01 Rev.03 CALCULATION NO.
c-css-099.20.069 REVTSTON:
000 S H I E L D. B L D G.
Region-3 Region-4 Figure 1. The Finite Element (FE) model used in the original SB seismic analysis
Page 5 CALCULATION COMPUTATION NOP-CC-3002-01 Rev.03 CALCULATION NO.
c-css-099.20.069 REVlSTON:
000 Dryis Besse SB stick FE modeling parameters fr/um,ber Gf nodesj Nrrodel= 14 IUumber of members:
Nelmnt:= I i Secfionaf pmperfies.
Second momenf of inertia of S8:
ORIGI\\:= I i := I..Nr,ode I " s.lmnt Rirr:= 69.5ft (lnner face radius)
Routr= T;ft (Outer face radiusl Ag :-.3 l.+5fr:
(Flute cross section area. VS01IB1-31
\\, := I I t0.r ? # 1SA wall cross section eree* VS01/81-31 h s{n}:= \\-
+- I I 10.; ifr-Ag + 2l.{Jftl Io.+:?$t:83.3 lfrJ
{vs01tB1-3}
Ri' e 69.5ft R.q, *
{\\+
n.Afl}
7r
- Ri,i
-+1 T
Y T r i J
r \\
- i'r}tq
- Ri",r Note that the same methodology in the original seismic analysis calc (VS01/81-3l is utilized to calculate the Znd moment of inertia of the flute (i e.. using an equivalent radius considedng flute areas!"
-icorl l= l50Pcf fc := +000psi E c_used:= -\\ l.t ? 5 *d[
Gc used:= 30990tkf
{VS01/81-3}
Numhr of l?sles considered in the ongina/ seismicanalysrs calc (V501/Bl-3):
E.;t*hrt,,r$ Flt-tes;l (s*a b*5. c'til)
EL 5{ 5 {p HL 6;3 -- ?. trl-rtca Gl{ e}
EL G o3 *,r FL.6+1 - a,Flu\\et (*lre/t)
EL6+3tp EL cio: *trr*.+ (*r,i,s,tq)
El-L{s {,, E tBol-ob-B r4*rtc+- ( r\\.1)
Page 6 CALC U LATI O N COTUI PUTATI ON NOP-CG3002-01 Rev.03 CALCULATION NO.
c-css-099.20-069 REVlSlON:
000 t1 l3 IT l l r0 I
I
?
I 6
J 3
1 f
t
{Elevf lr of Flt}
Elcr. :-
FL. :-
t l tEfrect
- of Fh afur crachl
{Node #}
!$odr" :*
t besed on the crack the crrck is deternunsd
$l?"?Jft 80Ift
?71.Jft
?48ft
?Ioft 692ft 660ft 6f6.Jft 613ft 609tr 603ft Jm.tft t?0.7Ift J6Jft Note that the efrectlus number of frutes afler rH8p.
llodel-l: ilo crugk lorlglnrl SB dechnl Ax fftr}
An r $r* + ru;Ag Ay tft'I Ay.,- +
I lftlf I. :- ln +- n, If t-n(a
Page 7 CALCU LATION COilIPUTATION NOP-CG3002-01 Rev.03 CALCULATION NO.
c.css-099.20-069 REVTSION:
000 Alr {fir}:
Ay {ltr}:
l {ftr}:
Arl := 1554ftI fut*:= 0ft1
Page 8 CALCU LATION COMPUTATION NOP-CC-3002-01 Rev.03 CALCULATION NO.
c-css-099.20.069 REVISION:
000 ModelJ: Cracls in some flutes and elsewhere (based on dre crack map. rnore accurmel Bssd on the cracft map. the SB 'vrnll is divided into the follo,rdng 4 regims havirg different levels of cnacks and/s clifferent effective run$en d flutes.
Resim-l tEL 801-0 ^ 812.75): Fb crack Regint-2 tEL 774.5 - 801.01,: 7Wo ot the aea is cr*ked @ OF rcbar lqyer Resim-3 (EL 8f3.0 ^ 774.5I ilI% of the aea is cr*ked @ OF rebar layer Regim4 tEL565.0 - 813.0l: l'lo crck Cross sectisrs are linearly prorated by usirg a factol Fck. lpsed m the cnack map-Fck,.= Oct (Regkm-l
)
Fctrr;= ?04i (Regim-2) j := 3..8 Fck, := l0P,i (Reglm-3) j.= 9..14 Fc\\ := 0.qir FeOim.ll Reductr'ons of lhe secfrona/ a,a and f,he Znd rar,tent of nertia drc to fhe cmc* aiorE tire OF rebelr layer AA:=
c{ F Sirl dtt F l'4lin
&. hRu$ -,.* - + ;
Ao* F,ri &.1 - *-tt tu-\\"
A [ : =
rro = (ongind Elev. =
t cc ts 3if, dt t + l.4lir R*.*Rnu-i*.*!
L.
- Tin.*-q^*;
L L 4 '
h -k.
AI = 3-59? " 105 S4
- of fldesl FI*. :
{Effective # sf fiutes, wtrere no creckl 1
e{ = 138-8tJ fr-B 12.75 801 774.5 748 7?0 693 fr60 646.5 tr3 60s 603 5S9.5 570,75 565 0
I I
B I
I 4
4 3
3 2
2 2
0 14 13 12 11 10 g
B 7
6 5
4 a
J 7
1 E
e 7
7 2
e x
1 2
2 e
7 2
0
Page 9 CALCU IATI ON COTI PUTATION NOP-CG3002-01 Rev.03 CALCULATION NO.
c-Gss-099.20.069 REVTSTON:
000
\\,= 29$1468fr4 It4,= OA4 t
.rt:r. r i: Oft-I+
fu*fuergy E-:t Page 10 CALCU LATION COTII PUTATI ON NOP-CG3002-01 Rev.03 CALCULATION NO.
c-css-099.20,069 REVISION:
000 ffigde l 4 : Assu.mgd, f pmi rlar crqctin g _Sce na rio Region-1 (EL 801.0 - 812.751:0%
of the area is cracked @ OF rebar layer Region-2 (Et 774.5 - 801.0): 10006 of the area is cracked @ OF rebar layer Region-3 (EL 813.0 t 774.51: 50% of the area is cracked @ OF nbar layer Region4 (EL 565.0 - 6a3.0f: 20% of the area is cracked @ OF rebat layer Cross sections are lineady polated by using a hctor. Fck. based on the crack map Fch I :! F.'t (Region-l)
Fck* ;= l00o,'1 (Region-z'
- 3.. I t*j :* 50g.ir (Region.3)
- - 9.. t-f ft
- !09'a (Region4)
Rductions of lhe secliaral area and the Znd moment of inerlta drc to the cnck alwg tlrc QF rebar layer:
A A p cc +- 3in dlt
- t.llin R..
- Ro*rt -
t I
t -
Acc
- t\\R..
\\ - A *
- 1 lIA
- 138.8t2.ft-Eltv. =
812.75 801 774.3 748 724 692 660 646.5 o43 609 603 589.5 579.75 565 AI.-
Ei - (onginal cc e 3for dI I
- l.{lin R..
- Ro,rt -
- {
{
Icc
- i,(*.*
L'- I"a At-3,59?x tO5.R{
- of frutes!
Nodt. =
I FLc.-
t 0
I I
I I
I 4
4 3
3 2
2 2
0 l4 13 L2 1 1 10 I
I 7
6 5
4 3
2 I
0 0
0 0
0 0
0 0
t I
I 1
1 0
E-t Page 1 1 CALC U LATI ON CO]UI P UTATI ON NOP-CG3002-01 Rev.03 CALCULATION NO.
G-CSS-099.20.069 REVTSION:
000 Ax {ft2}:
Av {fizf:
r fft!l:
Axr:- \\+
F[cr'.\\ - FdiAA Arl :r lt5{ft-1 Ar.. :- Oft-
- - t d It - I99l{6m4 l*
- 0fr4 Model4 has been simulated using ANSYS version 13.0, and results are then compared with those of Models 1-3 as well as the available original modal analysis results, which are presented in DIN 1, Attachment A.
As discussed in Attachment A of DIN 1, only the natural frequencies and mode shapes in the lateral direction are available from the original seismic analysis calculation as shown in Figure 2, so Model-l represents the original SB design condition and is considered as a reference/baseline for comparing with mode shapes from Models 2, 3,
&4.
Table 1 shows the naturalfrequencies and Mass Participation Factors (MPFs) calculated from the four FE models and the natural frequencies from the original seismic analysis, and the conesponding mode shapes are also presented in Figure 3. As shown in Table 1, the natural frequencies for Model 4 (upper-bound case) have good agreements with the original ones. For the first and second modes having significant (MPF is 74o/o and 160/o, respectively) contributions to the dynamic behaviors, the natural frequency difference with the original one is 4.0%
and 5.1olo, respectively. The natural fiequency difference for the third mode is 5.9%. However, the associated MPF of this mode is only 4.0%, which is considered insignificant based on its potential influence on the dynamic behaviors/
response of the SB. Similarly, the corresponding mode shapes are also calculated for Models 1,2,3 and 4. All the mode shapes for the first four modes are compared and the comparison shows good agreements between all four models. lt is then concluded that the assumed crack propagation scenario considered in Model4 can be used as an "upper-bound" condition, for which the structural evaluations performed in DIN 1 remain valid.
Page 12 CALCU LATION COM PUTATION NOP-CC-3002-01 Rev.03 CALCULATION NO.
c-css-099.20-069 REVISION:
000 Table 1. Comparison of the dynamic characteristic between the model including different levels of laminar cracking & the original model used for the seismic analysis Mode no.
Natural frequencies and mass participation factors Frequency differences with respect to the original calculation (Yrl Original Calculation (Ref. A3)
Model-l (baseline)
Model-2 (all flute crack)
Model-3 (more accurate)
Model4 (upper'bound)
Freq (Hz)
MPF
("/")
Freq (Hz)
MPF
('/")
Freq (Hz)
MPF
(%)
Freq (Hz)
MPF f/t Freq (Hz)
MPF (T")
Model
-1 Model
-2 Model
-3 Model
-4 1
2.97 Not Avail.
2.97 74 2.86 73 2.90 73 2.85 73 0.0
-3.5
-2.2 4.0 2
10.52 10.55 1 6 10.09 1 6 10.20 1 6 9.99 1 7 0.2
-4.1
-3.1
-5.1 3
20.65 20.70 4
19.57 4
19.65 4
19.42 4
0.3
-5.2 4.8
'5.9 4
29.02 29.10 2
27.72 2
27.87 2
27.53 2
0.3
-4.5
-4.0
-5.1 SUM 96 95 95 96 lJ\\oJe* I N\\oAe.* 2 Ntooer. g iviocie*' 4 Fne X.reNcr=Z.:aB F*eX,," wc.r = lO.:i24 Fro5te uc'i' Za.r"48 F.UXue xcY* 29.O?0 Figure 2. Natural frequencies and mode shapes calculated from the original seismic analysis
Page 13 CALC U LATI ON COTII PUTATI ON NOP-CG3002-01 Rev.03 CALCULATION NO.
c-css-099.20-069 REVISION:
000 P
r{-
tn g
o
+t(u o
E
-0.5 0
Normalized modal displr a) 1't mode (MPF: 73o,
,5 tcement to-74o/ol 1 5 o 4 E t lt ltl l lt t t lt tt " _ _ _ " I P(ts tnco P
(!
o IJ.J
-1
-0.5 0.5 Normalized modal displacement (b) 2nd mode (MPF: 160/o-17%l o,l tr
.f fi lnco P(o o
lrJ
-0.5 0.
Normalized modal disple (c) 3'd mode (MPF:
5 rcement 4Yo) 1.5 II l
Ij 1I
-L 5
-0.5 0.5 L.5 Normalized modal displacement (d) 4th mode (MPF:2o/ol Figure 3. Mode shapes calculated from the four FE models for the first four modes 4.2 Limits of Acceptable Laminar Cracking
Page 14 CALCU ISTION COTPUTATION NOP-CC-3002-01 Rev.03 CALCULATION NO.
c-css-099.20.069 REVISION:
000 The permissible extent and width of cEcking is evaluated based on the testing canied out at Purdue and the University of Kansas (DlN 3). This testing canied out independently by two different industry experts evaluated the efiect of laminar cracking at the most critical location i.e. the lap splices of the Shield Building. To be conservative and to get lower-bound strengths, tested beams simulatd two splices next to each other and in some cases (Kansas testrs) at only 6 days of strength for concrete. Note that the Shield building splices ar6 staggered and the actual in-place strcngth of concrete is much higher than what the test samples wr at when tested. Despite these aggressive test conditions, the lower-bound rssults from testing were determined to be well above the worst-case expected design basis forces/strsses in the Shield Building with adquate margins.
As indicated in the aftached Memo's from Profs. Sozen and Darwin (Attachments B and C), by testing the bond and development at the weakest location (lap splices), the testing carried out and the resulb thereof can be interpreted to be conseNatively applicable to the whole circumference of the Shied Building. Therefore, any laminar crack propagations from thqge observed previously would be covered and bounded by the rcsults of this tsting up to and extending the full cirorrference of the Shield Building.
The testing canied out at Purdue University and the University of Kansas also gave clear insight8 on th widths of laminar cracks at which the splices were still adequately able to perform their intendd function of full load transfer. These crack widths were observed to be in excss of 0.03 inches as reported in the attached Memo's by Prof. Sozen and Prof. Darwin. Based on th6se test results and as confirmed by the attached Memo's, a conservative upper-bound crack width limit of 0.02 inches can be safely used as the limiting criterion for crack widths for which the test results are deemd to remain valid.
In summary, based on the test results and as confirmed by Prof. Sozen and Prof. DaMin, any progression of the existing laminar ctacking around the circurference of the Shield Building is rcpresented and bounded by the results of the tests. Also, both experts have independenfly confirmed that the test results can be deemd to remain applicable as a basis for design compliance for observed crack widths of up to 0.02 inches.
Page 15 CALCU LATION COTI P UTATION NOP-CC-3002-01 Rev.03 CALCULATION NO.
c-css-099.20.069 REVISION:
000 4,3 Code Compllance Revlow of Accopteble Lamlnar Gracklng A detailed Code Compliance review had been caried out as part of the (DlN 1, Attachment L) and the obrved laminar cracking at the time. This review had indicatd that the Shield BuiHing still met all of the specific provisions of ACI 31863.
In this calculation, this Gode Compliance study was re-evaluated in light of the new cracking bounds detined in Sections 1.0 and 2.0. All the specific provisions of ACI 31843 in DIN 1, Attachmnt L were found to still rmain valid, as a result of which no revisions to Code Complianc is wananted. lt should be recognized that the Shield Building has safely ben able to perform its intended function so tar and the observed cracking is not expected to impac't its overall structural integrity or future func,tionality as confirmed by Prof. Sozen in his Memo (see Attachment B).
Page 16 CALCU LATION COMPUTATION NOP-CG3002-01 Rev.03 CALCULATION NO.
c.css-099.20.069 REVISION:
000 4.4 lmpact of Acceptable Laminar Gracking Efiect of laminar cracking on stifiness, shength, serviceability, duc'tility and long{em durability was discussed in detail as part of the design basis calculation (DlN 1, Section 3.0). This calculation had mncluded that thete was no appreciable impact to any of these paEmeters that would result in altering the expec{ed bhavior or performance of the Shield Building as a result of th observed laminar cracking.
In this calculation, this evaluation was revaluated in light of the new bounds of cracking established in this calculation. This review indicated that what had been discussed in OIN 1, Section 3.0 remained valid and thre was no impac't on these parameters or any additional issues expec'ted to be associated with the extended or progressing laminar cracking for crack widths within 0.02 inches.
Page 17 CALCU LATION COMPUTATION NOP-CC-3002-01 Rev.03 CALCULATION NO.
c-Gss.099.20.069 REVISION:
000 5.0 Results This Calculation defines acceptable limits of cracking for variation in modal frequencies and mode shapes, for which th original design basis seismic loading are deemed to rcmain valid. Based on this criterion, extent of acceptable cracking is stablished for the Shield Building as described belovv.
Upper-Bound Limits for Oack Propagation Reoion-1 (EL 801.0 - 812.75): No crack (Dome region)
Reoion-2 (EL 774.5 - 801.0'l: 100% of the area is cracked, # of effective (uncracked) flutes: 0 Reoion-3 (EL &13.0 - 774.5): 50o/o of the area is cracked, # of effective (uncracked) flutes: 0 Reoion4 (EL 565.0 - 643.0): 20% of the area is cracked, # of effective (uncracked) flutes: 1 This calculation also addresses the limits of acceptable crack propagation around the circumference and the crack widths based on testing caried out at Purdu University and the Univrity of lGnsas, and defines a conseruative cracking threshold, for which the cunently established design basis Emain valid. lt is concluded that the Shield Building will continue to meet its design basis as long as the obsrved cracking remains within the bounds defined below, especially crack width of 0.02 inches.
Attachment A: ANSYS Input and Output Calc. No: C-CSS-099.20-069, Rev. 000 Sheet No: 1 of 13 Sheet Rev.: 000 PROJECT
- DAVfS-BESSE 2013 SB new desiqn-basis calc ORIGINATOR
- SHEN WANG CHECKER
- HONGCHUN LIU SUBJECT
- Seisnic analysis evaluation considering lami.nar cracking on SB J O B N O
- 2 5 8 8 4 Examine the natural frequencies, MPFs, and mode shapes of SB considering t h e d i f f e r e n t l e v e 1 s o f th e la min a r co n cre te cra cks.
Her e, 3 differ ent cases are examined as follows:
! (1 ) C a s e - 1 :
O r i g i - n a 1 d e sig n (VS 0 1 /8 0 1 -0 3 ) - No cr ack, used as r efer ence data point
! (2 ) C a s e - 2 :
C r a c k s in a 1 t flu te s
- co n se rva tive since not al-l f]utes ar e cr acked.
! (3 ) C a s e - 3 :
C r a c k s in so me flu te s a n d e lse wh e re
- m or e accur ate, based on cr ack m ap
! (4 ) C a s e - 4 :
P o s t u l a te d u p p e r-b o u n d limits fo r crack pr opagation.
! Note that all modeling parameters are taken from the original seismic analysis calc
! except for the cross sectionaf propertj-es of the beam in the cracked area.
FINI SH
/CLEAR, START n_Case :
4 fname=STRCAT ( I SB_case', CHRVAL (n_case) )
,/FILNAME, fname,l
/PREP'7 (1) GEOMETRY
- DIM, ELEV, ARRAY, 1.4 I r t r T l I N O D E # :
I 2
3 4
5 t 1 E L E V ( 1 ) : 5 6 5, 5 1 0. ' 7 5, 5 8 9. 5, 6 0 3, 6 0 9, 6 4 3, 6 4 6. 5, 6 6 0, 6 9 2, ' 7 2 0, 7 4 9, ' t 1 4. 5, 9 0 1, g I 2. ' 7 5 t - - - - - - - - -
- NUMSTR, LINE,1
- DO, r, 1, l_4 K, I I O ' E L E V ( I )
- I F, I, G T, 1, T H E N T T 1
- ENDIF
- ENDDO K, 1 0 1, 1 _ 0, E L E V ( 1 )
( 2 ) M A T E R I A L & S ECTION # #
- DrM, AX1, ARRAY, 13 l [FT^2]
- DrM, IZI_, ARRAY, l_3
! [FT^4]
- D I M, W T I -, A R R A Y, 1 3
![K IP ]
- if, n _ c a s e, e q, 1 -. t h e n l ---------
tSLSt *,
1, 2
3 9
1 0 1 1 T 2 1 3 A X l - ( 1 - ) : L ] - 5 3. ' 7, 1 1 5 3. 7, 1 1 5 3. 7, l _ 1 7 5. 1, 1 1, ' 7 5. r, 1 1 9 6. 6, 1 1 9 6. 6, 1 2 8 2. 4, 1 2 8 2. 4, 1 2 8 2. 4, t 2 8 2. 4, 1 2 8 2. 4, 1 5 5 4. 0 IZL(L\\=
289283'
- 289283, 289283,
- 294883, 294883, 3004E3, 3004E3, 3228E3, 322883, 322883,
- 322883, 3228E3, 299L83 W T l ( 1 \\ = 2 1 2 0. 0 ' 2 7 9 L. 0, L 6 9 7. 0, 3 5 2 6. 0, 3 3 1 1. 0,
' J, 5 2 6. A, 4 2 9 A. 0, 5 7 7 1,. 0, 5 3 8 6. 0, 5 2 4 4. 0, 5 L 0 2. 0, 4 6 8 7. 0 t 4 0 3 5. 0
- e ls e 5 - f, n _ c a s e, e q, 2, t he n I E L E M # :
1 9 1 0 1 1 I 2 1 3 A X 1 ( 1 ) : 1 1 1 0. 8, 1 1 1 _ 0. 8, L 1 1 0. 8, 1, 1 L 0. 8, 1 1 1 0. 8, 1, 1 1, 0. 9, 1, 1 1 0. 9, l, 1 l - 0. 9, 1 1 1 0. 8, 1 1 1 0. 8, 1 1 L 0. 8, l _ 1 1 0. 8, 1 5 5 4. 0 rz 1 (1 ):2 7 8 1 8 3,
2 '7 8 ] - 8 3, 2 ' 7 8 L 8 3, 2 ' 7 8 1 8 3, 2 ' 7 8 1,E3, 2 ' r9 183, 2'79LE3,2791E3, 2'79LE3, 2781E.3, 2"181E'3, 218LE3,2991E3 w r l - ( 1 r : 2 1 2 0. 0, 2 7 9 L. 0, L 6 9 ' 7. 0, 3 5 2 6. 0, 3 3 1 1. 0, L 5 2 6. 0, 4 2 9 0. 0, 5 ' 7 7 L. 0, 5 3 9 6. 0, 5 2 4 4. 0, 5 1 0 2. 0, 4 6 8 7. 0, 4 0 3 5. 0
- e ls e if,
n _ c a s e, e q, 3, t h e n l - - - -- - -- -
I E L E M # :
I 2
9 1 0 1 1 L Z
- L J A X 1 ( 1 ) : 1 1 5 3. 7, l - 1 5 3. 7, L 1 5 3. 7, 1 1 5 3. 7, 1 L 5 3. ' 7, 1, 1 0 4. 5, 1. 1 0 4. 5, L 1 2 5. 9, L r 2 5. 9, L 1 2 5. 9, 1, 1 2 5. 9, 1 0 5 6. 5, 1 5 5 4. 0 rz1(1):289283, 2892E3,289283, 2B92E3t 289283, 2?6583, 2'76583, 282083, 282083, 282083, 282083, 264083, 299183 w T ], ( 1 ) : 2 1 2 0. 0, 2 7 9 1,. 0, 1, 6 9 1
. 0, 3 5 2 6. 0, 3 3 1 1. 0, 1 5 2 6. 0, 4 2 9 0. 0, 5 ' 7 ' 7 1. 0,
5 3 9 6. 0, 5 2 4 4. 0, 5 l - 0 2. 0, 4 6 8 7. 0, 4 0 3 5. 0
- e ls e if
, n _ c a s e, e q, 4, t he n I E L E M # :
1.
2 9
1 0 l 1 1,2 1 3 A X l - ( 1 ) : 1 1 0 4. 5, 1 1 0 4. 5, 1 1 - 0 4. 5, 1 1 0 4. 5, 1 1 0 4. 5, 1 1 4 1. 4,
! r 4 I. 4, I I 4 r. 4,
L 1 4 L. 4, 1 1 4 L. 4, 1, 1 4 1
. 4,
9 ' 7 2, 1 5 5 4. 0 r z r ( 1 ) : 2 7 4 5 8 3, 2 7 4 5 8 3 t 2 7 4 5 E 3, 2 7 4 5 8 3 t 2 7 4 5 8 3, 2 6 0 1 _ E 3, 2 6 0 L 8 3, 2 6 0 1 E 3, 2 6 0 L 8 3, 2 6 0 1 E 3,
2 6 0 1, 8 3, 2 4 2 1, 8 3, 2 9 9 1 8 3
! { T l - ( 1 ) : 2 L 2 0. Q, 2 ' 7 9 1,. 0, 1 6 9 7. 0, 3 5 2 6. 0, 3 3 1 1. 0, 1, 5 2 6. 0, 4 2 9 0. 0, 5 7 ' 7 1. 0, 5 3 8 6. 0, 5 2 4 4. 0, 5 L 0 2. 0, 4 6 8 7. 0, 4 0 3 5. 0
- endi-f M P, E X,
l,
5 2 4 7 5 7.
! k s f M P, G X Y, 1, 2 0 9 9 0 0.
l k s f M P, D E N S,
L, O.
1 3 1_2 t_0
Attachment A: ANSYS Input and Output GRAV: 32.L'7 4
- D O, r, l _, l _ 3 I f r
/ < a r ^ 2 Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-069, Rev. 000 2ot 13 000 R, I, WT 1 ( I ) / G R A V,, W T 1 ( I) /GRAV
- ENDDO (3 ) E L E M E N T # #
ET, l_, BEAM188 E T, 2, } 4 A S S 2 I,,, 2
- D O, r r 1, 1 3 SECTYPE, I, BEAM, ASEC SECDATA, AX1 ( I ), IZI ( r ), 0. 0, IZI ( I ),, 100 s E c c o N T R o L S, A X l, ( r )
- 2 0 99 0 0. 0 / 2. 0,,AX 1 ( r ) *2 0 9 9 0 0. 0 / 2. 0 sEcNUM, r
- ENDDO
- D O, r, L, L 3 L S E L, S, L I N E,, I 1, A T T, 1,, 1,, 1, 0 1 -,
, r
- ENDDO ESIZE, 100 LSEL, ALL LMESH, ALL
- n n T
1 t ?
V V
L L
L J
NN=NODE ( O, ELEV ( I+ 1 ), O )
T Y P E, 2 REAL, I E, NN
- ENDDO N N = N O D E
( 0, E L E V ( 1 ), 0 )
D, NN, A L L ALLSEL,ALL EPLOT
( 4 ) A N A L Y S T S + #
/SOLU N_FREQ:20 ANTYPE,MODAL MODOPT, LANPCG, N-FREQ ALLSEL,ALL
/ O U T P U T, f n a m e, 'O U T r SOLVE
/ P O S Tl
- D O, I, 1 r N _ F R E Q c t r T I T PRNSOL, U, X
- ENDDO SAVE F T N I S H ANSYS SOLVE COMMAND *****
N O T E * *
- There is no title defi-ned
- *
- N O T E * *
- C P :
f o r t h i s a n a l y s i s.
4. 6 6 4 T I M E : 1 8 : 0 2 : 3 0 4. 6 6 4 T I M E : 1 8 : 0 2 : 3 0 No modes are being expanded (MXPAND command) and therefore the element resul-ts wifl not be written to the mode file.
For more efficient calcul-atj-on of element results ln the expansion pass of any downstream mode superposition
- analyses, expand al-l-modes during the modat a n a ly s j - s.
- sElEcilo* o:-::l#-3r;ff3il?133'5fi";:R-APPLTcABLE ELEMENTS ELEMENT TYPE 1 IS BEAM]-88 KEYOPT(1):1 IS SUGGESTED FOR NON-CIRCUI,AR CROSS SECTIONS AND KEYOPT(3):2 ]S ALWAYS SUGGESTED.
ELEMENT TYPE 1 IS BEAM1BS KEYOPT(15) IS ALREADY SET AS SUGGESTED.
S O L U T I O N O P T I O N S PROBLEM DIMENSIONALITY.
.3-D DEGREES OF FREEDOM.
. UX UY UZ ROTX ROTY ROTZ ANALYSIS TYPE.
.MODAL EXTRACTION METHOD.
.PCG I,ANCZOS
Attachment A: ANSYS Input and Output NUMBER OF MODES TO EXTRACT.
20 GLOBALLY ASSEMBLED MATRTX
.SYMMETRIC L O A D S T E P O P T ] O N S LOAD STEP NUMBER.
1 Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-069, Rev. 000 3of13 000
- *
- N O T E * *
- The PCG solver has automaticallv set mo d e l t o 5.
C P :
4. 6 8 0 T I M E :
th e l-e ve l o f difficultv for 1 8 : 0 2 : 3 0 t h i s CENTER OF MASS, MASS, AND MASS MOMENTS OF INERTIA CALCUI,AT]ONS ASSUME ELEMENT MASS AT ELEMENT CENTROID T O T A L M A S S :
1 5 3 8.1 CENTER OF MASS x c :
0. 0 0 0 0 Y C :
' 7 0 2. 2 6 z c :
0. 0 0 0 0 TYPE NUMBER ENAME 1
13 BEAM188 2
L3 MASS21 MOM. OF INERTIA ABOUT ORIGIN I X X =
0. 7 6 7 2 E + 0 9 r Y Y :
0. 0 0 0 I Z Z :
0. ' 7 6 ' l 2 E + 0 9 r x Y :
0. 0 0 0 r Y z :
0. 0 0 0 r z x - -
0. 0 0 0 MOM. OF INERTIA ABOUT CENTER OF MASS I X X :
0. 8 6 5 4 E + 0 7 I Y Y =
0. 0 0 0 r z z :
0. 8 6 5 4 8 + 0 7 r X Y :
0. 0 0 0 r Y z :
0. 0 0 0 r z x :
0. 0 0 0 4. 6 9 6 MASS
SUMMARY
BY ELEMENT TYPE ***
TYPE MASS 2
1 5 3 8. 0 7 Range of element maxj-mum matrix coefficients in globar coordinates Maximum : 3.900'742325E+11 at element 6.
Min im u m : 4. 3 3 5 1 - 7 0 7 5 7 E + 1 0 a t e fe me n t 5.
ELEMENT MATRIX FORMULATION TIMES TOTAL CP AVE CP 0. 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0. 0 0 0 0 0 0 Time at end of element matrix formulation Cp : 4.68002987.
F o rm P r e c o n d i t i o n e r
- 0 Cu m.
Ite r.:
1 Cp = 4.6 9 6 Load Step:
1 Mode= 1-.
curEqn:
1,4 totEgn:
84 Job CP sec:
F a c t o r D o n e :
l-8 Fa cto r Wa Il se c=
j' 7 0 6.8 8 4 r ate=
0.0 M flops Iteration=
12 Number of eigenvalues converged:
5 Wall=
0.0 Iteration
22 Number of eigenvalues converged=
10 WalI:
0.0 Iteration
29 Number of eigenvalues converged=
17 Wall:
0.0 Iteration
32 Number of eigenvalues converged:
20 WalI:
0.0 Iteration=
33 Number of eigenvalues converged:
20 Wa1l=
0.0 fteration
34 Number of eigenval.ues converged:
20 WalI:
0.0 Iteration
35 Number of eigenvalues converged=
20 WatI:
0.0 Iteration=
36 Number of eigenvalues converged:
20 Wall=
0.0 Iteration
37 Number of eigenvalues converged=
20 Wall=
0.0 Iteration
38 Number of eigenval-ues converged=
20 WaIl:
0.0 Iteration
39 Number of ej-genval-ues converged:
20 Wa11:
0.0 PCG LANCZOS EIGENSOLVER HAS CONVERGED SUCCESSFULLY THE REQUESTED 20 MODES HAVE BEEN FOUND SUCCESSFULLY ANSYS - ENGINEERING ANALYSIS S Y S TEM RE L EA S E 13.0 ANSYS Mechanical 0 0 2 0 3 2 3 6 V ERS ION:WINDOWS x6 4 1 8 :0 2 :3 0 JAN 27, 2015 Cp:
FREQUENCIES FROM PCG T,ANCZOS ITERATION *****
MODE FREQUENCY (HERTZ)
I 2. 8 5 0 1 7 8 7 5 4 2 8 3 2
2. 8 5 0 1 7 8 7 5 4 2 8 3 3
9. 2 6 2 6 4 5 5 5 5 4 3 1 4
9. 9 9 1 9 1 4 3 8 4 5 8 3 4.'7 2'7
Attachment A: ANSYS Input and Output Calc. No: C-CSS-099.20-069, Rev. 000 Sheet No:
Sheet Rev.:
4ot13 000 5
6 1
8 9
1 0 1 1 1.2 l - J I 4 1 5 1,6 L 1 1 8 1 9 2 0 9. 9 9 1 9 1 4 3 8 4 5 8 3 1 9. 4 2 2 6 0 0 9 8 8 5 0 1 9. 4 2 2 6 0 0 9 8 8 5 0 2't.5269959519"7 2'7.526995951_9'7 2'7. 98 4L'7 669L7 6 3 3. 5 1 1 4 2 4 5 3 9 3 7 33.51L42453937 4L. 293'7 623 48 4 4 4L.293'7 6234844 4 6. 1 5 4 4 6 5 4 8 3 4 1 4 8. 8 3 2 6 s s 8 1 8 7 6 4 8. 8 3 2 6 5 5 8 1 8 7 6 5 9. 0 4 1 1, 1 _ 1 4 9 5 9 7 5 9. 0 4 1 1 1 1 4 9 5 9 7 63.2389I'724720 ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 13.0 ANSYS Mechanical 00203236 VERSION=WINDOWS x64 1 8 : 0 2 : 3 0 J A N 2 7, 2 0 1 5 C P :
4.'72'7 FREQUENCY X
DIRECTION RATIO EFFECTIVE MASS PART]C. FACTOR r
2. 8 5 0 1 _ 8 2
2. 8 5 0 r, 8 3
9. 2 6 2 6 5 4
9. 9 9 1 9 1 5
9. 9 9 1 9 L 6
1 9. 4 2 2 6 1
7 9. 4 2 2 6 I
2'7.52'70 9
27.52'70 1 0 2 7. 9 8 4 2 1 1 3 3. 5 1 1 4 L t J J. 5 - L l - 4 1 3 4 L. 2 9 3 8 1 4 4 L. 2 9 3 8 1 5 4 6. 1 5 4 5 1 6 48.832'7
[t 48.832'7 1 8 5 9. 0 4 1 1 1 9 5 9. 0 4 1 1 _
2 0 6 3. 2 3 8 9 3 3. 4 9 2 1. 0 0 0 0 0 0 1. 8 4 4 1 0. 0 5 5 0 6 2 0. 2 0 9 8 3 E - 0 8 0. 0 0 0 0 0 0 0. 8 ' 7 4 2 9 0. 0 2 6 L 0 4 15. 961, 0.4'7 6569 0. 4 7 9 6 2 0. 0 1 4 3 2 0 1.6323 0.22'788r 5. 6 ' t ' 7 3 0. 1 _ 6 9 5 1 2 r. 2 0 0 2 0. 0 3 5 8 3 5 0. 1 8 0 3 6 E - 0 8 0. 0 0 0 0 0 0 3. 7 9 ' 7 5 0. 1 1 3 3 8 4 0. 4 2 9 4 0 0. 0 1 2 8 2 1 0. 9 5 7 0 0 0. 0 2 8 5 7 4 0. 9 8 0 6 8 E - 0 1 0. 0 0 2 9 2 8 0. 1 7 1 0 4 E - 1 1 0. 0 0 0 0 0 0 0. 2 ' t 3 7 8 0. 0 0 8 L 7 4 0. 6 7 0 8 4 E - 0 1 0. 0 0 2 0 0 3
?. 2 3 9 6 0. 0 6 6 8 6 9 0. 3 0 6 s 7 0. 0 0 9 1 5 3 0. 3 2 5 0 1 8 - 1 0 0. 0 0 0 0 0 0 r t z r. 1 4 3. 4 0 0 8 6 0. 4 4 0 3 0 0 E - 1 7 0.'7 643'7 6 254.'7 6"7 0. 2 3 0 0 3 7 58.2517 3 2. 2 3 2 2 1. 4 4 0 5 0 0. 3 2 5 3 0 6 E - 1 7 1 4. 4 2 1, I 0. 1 8 4 3 8 4 0. 9 1 5 8 4 8 0.96I"1298-02 Q.2925358-23 0. 7 4 9 5 3 9 E - 0 1 0. 4 5 0 0 2 9 E - 0 2 5. 0 1 5 ? 8 0. 9 3 9 8 5 3 E - 0 1 0. 1 0 5 6 3 2 E - 2 0 PERIOD 0. 3 5 0 8 6 0. 3 5 0 8 6 0. 1 0 7 9 6 0. 1 0 0 0 8 0. r _ 0 0 0 8 0. 5 1 4 8 6 8 - 0 1 0. 5 1 4 8 6 E - 0 1 0. 3 6 3 2 8 E - 0 1 0. 3 6 3 2 8 E - 0 1 -
0. 3 5 7 3 4 E - 0 1 _
0.2984LE-01_
0. 2 9 8 4 1 8 - 0 l _
0.242]-7E'-0]-
0.242L7E-0L 0. 2 1 6 6 6 E - 0 1 0. 2 0 4 7 8 8 - 0 1 0. 2 0 4 7 8 E - 0 1 0. 1 6 9 3 7 E - 0 1 0. l _ 6 9 3 7 E - 0 L 0. t _ 5 8 1 3 E - 0 1 CUMUI,ATTVE MASS FRACTION 0. 7 5 1 0 5 7 0. 7 5 3 3 3 4 0. 7 5 3 3 3 4 0. 7 5 3 8 4 6
4. 9 2 4 4 2 5 0. 9 2 4 5 7 9 0. 9 6 3 5 8 1
0. 9 8 5 1 6 2 0.986L2'7 0.986L27 0.995'782 0. 9 9 5 9 0 6
0. 9 9 6 5 1 9 0. 9 9 6 s 2 6 0. 9 9 6 5 2 6 0. 9 9 6 5 7 6 0. 9 9 6 5 7 9
0. 9 9 9 9 3 7 1. 0 0 0 0 0 1. 0 0 0 0 0 RATIO EFF.MASS TO TOTAL MASS 0.'7293L2 0.221,11,LE-02 0.286267E'-20 0. 4 9 6 9 6 9 E - 0 3 0. 1 6 5 6 4 0 0. 1 4 9 5 6 1 - E - 0 3 0. 3 7 8 7 3 1 _ E - 0 1 0. 2 0 9 5 6 2 E - 0 1 U. Y J b S O Z I ! - U J 0.2L15028-20 0. 9 3 7 6 0 6 E - 0 2 0. 1 1 9 8 8 0 E - 0 3 0. s 9 5 4 s 1 E - 0 3 0. 6 2 5 2 8 1 8 - 0 5 0. 1 9 0 1 9 6 8 - 2 6 0. 4 8 7 3 2 3 8 - 0 4 0. 2 9 2 5 9 3 E - 0 5 0. 3 2 6 1 0 8 E - 0 2 0. 6 1 1 0 5 8 8 - 0 4 0.686780E-24 sum L 4 9 3. 5 4 0.9'7104'7 FREQUENCY PERIOD 0. 3 5 0 8 6 0. 3 5 0 8 6 0. 1 0 7 9 6 0. 1 0 0 0 8 0. 1 0 0 0 8 0. 5 1 4 8 6 E - 0 1 0. 5 1 4 8 6 E - 0 1 0. 3 6 3 2 8 E - 0 1 0. 3 6 3 2 8 E - 0 1 U. J 5 i J 4 T ! - U I 0. 2 9 8 4 1 E - 0 1 0. 2 9 8 4 1 E - 0 1 0.2 4 2 1,7 8 -0 1,
0. 2 4 2 L ' 7 E - 0 \\
0. 2 r. 6 6 6 8 - 0 1 0. 2 0 4 7 8 E - 0 1 0. 2 0 4 7 8 E - 0 1 0. 1 6 9 3 7 E - 0 1 0. 1 6 9 3 7 E - 0 1 0. 1 5 8 1 - 3 E - 0 1 CUMUI,ATIVE MASS FMCTION 0.3322848-20 0. 3 8 2 7 5 6 E - 2 0 0. 8 6 2 5 6 s 0. 8 6 2 5 6 5 0. 8 6 2 5 6 5 0. 8 6 2 5 6 5 0. 8 6 2 s 6 5 0. 8 6 2 s 6 5 0. 8 6 2 5 6 5 0. 9 4 8 0 2 3 0. 9 4 8 0 2 3 0. 9 4 8 0 2 3 0. 9 4 8 0 2 3 0. 9 4 8 0 2 3 0. 97 9503 0. 9 7 9 5 0 3 0. 9 7 9 5 0 3 0. 9 7 9 5 0 3 0. 9 7 9 5 0 3 1. 0 0 0 0 0 RATIO EFF.MASS TO TOTAL MASS 0. 3 1 8 6 1 3 E - 2 0 0. 4 8 3 9 5 7 E - 2 1 0.82701'7 0. 6 9 9 3 4 8 E - 2 1 _
0. 1 1 3 0 8 6 8 - 2 2 0."7060028-20 0. 3 1 5 0 3 7 E - 2 1 0.66L233E-22 0.1,3'7 4568-24 0. 8 1 9 4 2 1 _ E - 0 1 0. 1 8 0 5 1 8 8 - 2 4 0. 7 3 3 4 2 1 E - 2 2 0.309'7 648-22 0. 2 0 0 8 8 5 E - 2 3 0. 3 0 1 8 4 3 8 - 0 1 0.3347868-25 0. 5 8 3 2 6 6 E - 2 3 0.244'1908-24 0. t - 8 4 0 9 9 E - 2 5 0. 1 9653 9E-0 1 Y
DIRECTION PARTIC.FACTOR RATIO EFFECTIVE MASS L
2. 8 5 0 1 8 2
2. 8 5 0 1 8 3
9. 2 6 2 6 5 4
9. 9 9 1 9 1 5
9. 9 9 1 9 1 6
1 9. 4 2 2 6
' t L 9. 4 2 2 6 B
2'7.5210 9
2 " 1. 5 2 1 0 t 0 2 '7. 9 8 4 2 1 1 3 3. 5 1 1 4 1 2 3 3. 5 1 _ 1 4 13 4r.2938 t 4 4 t. 2 9 3 8 1 5 4 6. 1 _ 5 4 5 1 6 4 8. 8 3 2 1 L'7 48.832"7 1 8 5 9. 0 4 1 1 1 9 5 9. 0 4 1 1 2 0 6 3. 2 3 8 9
- 0. 2 2 I 3 1 E - 0 8 0. 0 0 0 0 0 0 0. 8 6 2 7 6 8 - 0 9 0. 0 0 0 0 0 0 3 5. 6 6 7 1. 0 0 0 0 0 0 0. l _ 0 3 7 1 E - 0 8 0. 0 0 0 0 0 0
- 0. 1 3 1 8 8 E - 0 9 0. 0 0 0 0 0 0
- 0. 3 2 9 5 3 E - 0 8 0. 0 0 0 0 0 0
- 0. 6 9 6 1 0 E - 0 9 0. 0 0 0 0 0 0 0. 3 1 8 9 1 E - 0 9 0. 0 0 0 0 0 0 0. 1 4 5 4 0 E - 1 0 0. 0 0 0 0 0 0 1, 1. 2 2 6 0. 3 1 4 7 6 1 0. 1 6 6 6 3 E - 1 0 0. 0 0 0 0 0 0 0. 3 3 5 8 7 E - 0 9 0. 0 0 0 0 0 0
- 0. 2 1 8 2 8 E - 0 9 0. 0 0 0 0 0 0
- 0. 5 5 5 8 6 E - 1 0 0. 0 0 0 0 0 0
- 6. 8 1 3 6 0. 1 9 1 0 3 7 0. 7 1 7 5 8 E - 1 1 0. 0 0 0 0 0 0 0. 9 4 7 1 6 E - 1 0 0. 0 0 0 0 0 0
- 0. 1 9 4 0 4 8 - 1 0 0. 0 0 0 0 0 0
- 0. 5 3 2 1 3 E - 1 L 0. 0 0 0 0 0 0 5. 4 9 8 1 0. 1 5 4 1 5 3 0. 4 9 0 0 5 0 8 - 1 7 0.1 44362E-18 L 2 1 2. I I 0. 1 0 7 5 6 5 E - 1 7 0. 1 7 3 9 3 5 E - 1 9 0. 1 0 8 5 8 8 E - 1 6 0. 4 8 4 5 5 0 E - 1 8 0. 1 0 1 7 0 3 E - 1 8 0.2I]-4t88-21, I I O. U J J u. z t t b 5 u t l - l J _
0. 1 1 2 8 0 7 E - 1 8 0.4'76441E'-]-9 0. 3 0 8 9 7 7 E - 2 0 4 6. 4 2 5 6 0.514 9268-22 0. 8 9 7 1 - 0 6 E - 2 0 0. 37 650 6E-2 1 0. 2 8 3 1 5 8 8 - 2 2 3 0. 2 2 9 2 sum I4'7 4.19 0. 9 5 8 8 5 7
Attachment A: ANSYS Input and Output Calc.
Sheet Sheet C-CSS-099.20-069, Rev. 000 5of13 000 PARTICIPATION FACTOR CALCULAT]ON *****
Z DIRECTION MODE FREQUENCY r
2. 8 5 0 1 8 2
2. 8 5 0 1 8 3
9. 2 6 2 6 s 4
9. 9 9 1 9 1 5
9. 9 9 1 9 1 o
J - y. q z z o 7
L 9. 4 2 2 6 I
2'7.52'70 9
2 '7. 5 2 7 Q 1 0 2 1. 9 8 4 2
). 2 3 3. 5 1 _ 1 4 1 3 4 r. 2 9 3 8 1 _ 4 4 r. 2 9 3 8 1 5 4 6. 1 5 4 5 L 6 4 8. 8 3 2 7 1'7 48.832'7 1 8 5 9. 0 4 r. 1 l - 9 5 9. 0 4 1 1 2 0 6 3. 2 3 8 9 PERIOD PARTIC.FACTOR RATIO 0. 3 5 0 8 6
- 7. 8 4 4 1 0. 0 5 5 0 6 2 0. 3 5 0 8 6 3 3. 4 9 2 1. 0 0 0 0 0 0 0. 1 - 0 ' 7 9 6
- 0. 3 0 2 0 8 E - 0 9 0. 0 0 0 0 0 0 0. 1 0 0 0 8 1 5. 9 6 1 0. 4 ' 7 6 5 6 9 0. 1 0 0 0 8
- 0. 8 ' 7 4 2 9 0. 0 2 6 1 0 4 0. 5 1 4 8 6 E - 0 1 7. 6 3 2 3 0. 2 2 ' 7 8 8 r 0. 5 1 4 8 6 E - 0 1 - 0. 4 ' 7 9 6 2 0. 0 1 4 3 2 0 0. 3 6 3 2 8 E - 0 7 - 7. 2 0 0 2 0. 0 3 5 8 3 5 0. 3 6 3 2 8 E - 0 1 5. 6 ' 7 ' 7 3 0. 1 6 9 5 1 2 0. 3 5 7 3 4 E - 0 1 - 0. 4 ' 7 2 5 5 8 - 0 9 0. 0 0 0 0 0 0 0.29841_E-01 -A.4294Q 0.012821.
0. 2 9 8 4 1 _ E - 0 1 3. ' 7 9 7 5 0. 1 1 3 3 8 4 0. 2 4 2 1 " ' t E. - 0 1
- 0. 9 8 0 6 8 E - 0 1 0. 0 0 2 9 2 8 0.2421.'18-01 0. 95700 0.028574 0. 2 1 6 6 6 E - 0 1 _ 0. 1 1 1, 7 0 E - 1 0 0. 0 0 0 0 0 0 0. 2 0 4 7 8 E - 0 1 _
- 0. 6 7 0 8 4 E - 0 1 0. 0 0 2 0 0 3 0. 2 0 4 7 8 8 - 0 1 0. 2 1 3 ' 7 8 0. 0 0 8 1 7 4 0. r _ 6 9 3 7 E - 0 1 - 0. 3 0 6 5 7 0. 0 0 9 1 5 3 0. 1 _ 6 9 3 7 E - 0 L 2. 2 3 9 6 0. 0 6 6 8 6 9 0. 1 - 5 8 1 3 8 - 0 1 0. 3 1 3 4 1 E - 0 9 0. 0 0 0 0 0 0 EFFECTIVE MASS 3. 4 0 0 8 6 112]-.7 4 0. 9 1 2 5 4 8 E - 1 9 254.'7 67 0.7 643'7 6 5 8. 2 5 L ' 7 0. 2 3 0 0 3 7 1. 4 4 0 5 0 3 2. 2 3 2 2 0.223304E-L8 0. 1 8 4 3 8 4
).4.42L).
0.96]-"7298-02 0. 9 1 5 B 4 8 0.1_247'7'78-21 0.4500298-02 0. 7 4 9 5 3 9 E - 0 1 0. 9 3 9 8 5 3 E - 0 1 5. 0 1 5 7 8 0.9822628-L9 CUMUI,AT]VE MASS FRACTION 0.22'7704E-02 0. 7 5 3 3 3 4 0. 7 5 3 3 3 4 0. 923 913 0. 9 2 4 4 2 5 0.96342'7 0. 9 6 3 s 8 1 0. 9 6 4 5 4 6 0.986L2"t 0. 9 8 6 1 2 7 0. 98 6250 0. 9 9 5 9 0 6 0. 9 9 5 9 1 2 0. 9 9 6 5 2 6 0. 9 9 6 5 2 6 0. 9 9 6 5 2 9 0. 9 9 6 5 7 9
0. 9 9 6 6 4 2 1. 0 0 0 0 0 1. 0 0 0 0 0 RATIO EFF.MASS TO TOTAL MASS 0.22Lr1,3,8-02 0.72931_2 0. 5 9 3 3 0 6 E - 2 2 0. 1 6 5 6 4 0 0. 4 96969E-03 0. 3 ? 8 7 3 1 - E - 0 1 u. 1 4 y 5 b I t l - u J 0. 9 3 6 5 6 2 E - 0 3 0. 2 0 9 5 6 2 8 - 0 1 0. 1 4 5 1 8 4 8 - 2 1 0. 1 1 9 8 8 0 E - 0 3 0. 937 60 6E-02 0. 62528 1E-05 0. 5 9 5 4 5 1 _ E - 0 3 0.8L125'7E'-25 0. 2 9 2 5 9 3 E - 0 5 0.48'73238-04 0. 6 1 1 0 5 8 8 - 0 4 Q.3267088-02 o.6386318-22 sum 1 4 9 3. 5 4 0. 9 7 1 0 4 7 PARTICIPAT]ON FACTOR CALCUI,ATION *****ROTX DIRECTION FREQUENCY PERIOD PARTIC. FACTOR RATIO EFFECTIVE MASS 0. 1 9 0 1 - 0 4 E + 0 7 0. 6 2 7 0 3 9 E + 0 9 U. 1 9 ' J I Z E - T J 0. I 64 34 3E+08 2s9329.
0. 1 9 6 3 8 1 E + 0 8 7 7 5 5 1. 1,
4 6 4 8 9 3.
0. 1 0 4 0 2 3 E + 0 8 0.'7326328-1"3 6 0 0 8 4. 6 0. 4 6 9 9 3 5 E + 0 7 3 0 5 5. 4 7 2909"7t.
0. 4 0 6 9 5 9 E - 1 6 148'7
.96 24'782.5 3 0 1 4 6. 3 0. 1 6 0 8 8 4 E + 0 7 0. 3 1 2 0 6 1 E - 1 3 CUMUI,ATIVE MASS FRACTION 0.2524848-02 0. 8 3 5 3 1 8 0. 8 3 5 3 1 8 0. 9 5 0 1 1 4 0. 9 5 0 4 s 8 0. 9 7 6 5 4 1 0. 9 7 6 6 4 4 Q. 9 ' 7 7 2 6 r 0. 9 9 L 0 7 7 0. 9 9 1 0 7 7 0. 9 9 1 1 5 6 0. 9 9 7 3 9 8 0.99'7 402 0. 9 9 7 7 8 8 0. 9 9 7 ? 8 8 0.99'7'190 0. 9 9 7 8 2 3 0. 9 9 7 8 6 3 1. 0 0 0 0 0 1. 0 0 0 0 0 1,
2. 8 5 0 1 - 8 2
2. 8 5 0 1 8 J
t. z o z o 3 4
9. 9 9 1 9 1 5
9. 9 9 1 9 L 6
1 9. 4 2 2 6
' 7 L 9. 4 2 2 6 8
2'7.52'70 9
27.52'70 1 _ 0 2 7. 9 8 4 2 1 T J J. 5 - L I 4 1 2 3 3. 5 1 1 _ 4 L3 41-.2938 t 4 4 1. 2 9 3 8 1 5 4 6. 1 5 4 5 L 6 4 8. 8 3 2 " t 1'7 48.8327 1 8 5 9. 0 4 1 1 L 9 5 9. Q 4 1 " 7 2 0 6 3. 2 3 8 9 0. 3 5 0 8 6
- 7 3 7 8. 8 0. 0 s s 0 6 2 0. 3 5 0 8 6 2 s 0 4 1.
1. 0 0 0 0 0 0 0. 1 0 7 9 6
- 0. 1 7 1 8 5 E - 0 6 0. 0 0 0 0 0 0 0. 1 0 0 0 8 9 2 9 ' 7
. 0 0. 3 7 ] - 2 7 5 0. 1 0 0 0 8
- 5 0 9. 2 4 0. 0 2 0 3 3 7 0. 5 1 4 8 6 E - 0 1 4 4 3 1. 5 0. L ' 7 6 9 ' 7 I 0. 5 1 4 8 6 E - 0 L - 2 ' 7 8
. 4 8 0. 0 1 1 1 2 1 0. 3 6 3 2 8 E - 0 1 - 6 8 1. 8 3 0. 0 2 ' 7 2 2 9 0. 3 6 3 2 8 E - 0 ] -
3 2 2 5. 3 0. 1 2 8 8 0 0 0. 3 5 7 3 4 E - 0 1 - 0. 2 1 0 6 7 8 - 0 6 0. 0 0 0 0 0 0 o. 2 9 8 4 L 8 - 0 1. - 2 4 5. 1, 2 0. 0 0 9 7 8 9 0. 2 9 8 4 1 8 - 0 L 2 L 6 ' 7. 8 0. 0 8 6 5 7 1 0.2421"'7E'-01" -55.2'7 6 0.00220'7 0.242I'7E.-0L 539.42 0.021542 0. 2 1 6 6 6 E - 0 1 0. 6 3 7 9 3 E - 0 8 0. 0 0 0 0 0 0 0. 2 0 4 7 8 8 - 0 1 - 3 8. 5 7 4 0. 0 0 1 5 4 0 0. 2 0 4 ? 8 E - 0 t L 5 7. 4 2 0. 0 0 6 2 8 7 0. 1 - 6 9 3 7 E - 0 1 - 1 7 3. 6 3 0. 0 0 6 9 3 4 0.16937E'-03.
L268.4
- 0. 050653 0. 1 - 5 8 1 - 3 E - 0 1 0. 1 7 6 6 5 8 - 0 6 0. 0 0 0 0 0 0 sum 0. 7 52 935E+0 9
1 _
2. 8 5 0 1 8 2
2. 8 5 0 1 8 3
9. 2 6 2 6 5 4
9. 9 9 1 9 1 5
9. 9 9 1 9 1 6
1 9. 4 2 2 6 7
1 9. 4 2 2 6 I
2 't. 5 2 7 Q 9
2't.52"10 1 0 2 't. 9 8 4 2 1 1
? ?
q, 1 1 / t r 2 3 3. 5 1 - 1 4 13 4L.2938 1 4 4 1. 2 9 3 8 1 5 4 6. 1 5 4 5 PARTIC]PATION FACTOR CALCUI.ATION *****ROTY DIRECTION FREQUENCY PARTIC.FACTOR RATIO 0. 0 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0 0. 0 0 0 0 0 0 PERIOD 0. 3 5 0 8 6 0. 3 5 0 8 6 0. 1 0 7 9 6 0. 1 0 0 0 8 0. 1 0 0 0 8 0. 5 1 4 8 6 E - 0 1 0. 5 1 4 8 6 E - 0 1 0. 3 6 3 2 8 E - 0 1 0. 3 6 3 2 8 E - 0 1 0. 3 5 7 3 4 E - 0 1 0. 2 9 8 4 1 E - 0 1 0. 2 9 8 4 1 E - 0 1 0.242L7E-0L 0.242L'78-07 0. 2 1 6 6 6 E - 0 1 EFFECTIVE MASS 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 CUMULATIVE MASS ERACTION 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0
Attachment A: ANSYS Input and Output Calc.
Sheet No:
c-css-099.20-069, 6of13 000 Rev. 000 I O I'7 l_8 1 v 2 0 48.832'7 48.8327 5 9. 0 4 1 1 5 9. 0 4 1 1 6 3. 2 3 8 9 FREQUENCY 2. 8 5 0 1 8 2. 8 5 0 1 8 9. 2 6 2 6 5 9. 9 9 1 _ 9 1 9. 9 9 r _ 9 1 1 9. 4 2 2 6 L 9. 4 2 2 6 21.52'70 27.52'70 2 7. 9 8 4 2 3 3. 5 1 1 4 33. 511_4 41.2938 41.2938 4 6. 1 5 4 5 4 8. 8 3 2 ' t 48.8321 5 9. 0 4 1 1 5 9. 0 4 1 1 63.2389 1. 0 0 0 0 0 0 0. 0 5 5 0 6 2 0. 0 0 0 0 0 0 0. 0 2 0 3 3 7 0. 3 ' 7 I 2 ' 1 5 0. 0 1 1 1 2 L
0.t'7 69'7I 0. 1 2 8 8 0 0 0. 0 2 ' t 2 2 9 0. 0 0 0 0 0 0 0. 0 8 6 5 7 1 0. 0 0 9 7 8 9 0.021,542 0.002207 0. 0 0 0 0 0 0 0. 0 0 6 2 8 7 0. 0 0 1 5 4 0 0. 0 5 0 5 s 3 0. 0 0 6 9 3 4 0. 0 0 0 0 0 0 0. 6 2 7 0 3 9 E + 0 9 0. 1 9 0 1 0 4 E + 0 7 0.L42462E-LL 259329.
0. 8 6 4 3 4 3 8 + 0 8 7 7 5 5 1. 1 0. 1 9 6 3 8 1 E + 0 8 0. 1 0 4 0 2 3 E + 0 8 4 6 4 8 9 3.
0. 1 0 4 3 4 5 E - 1 1 0. 4 6 9 9 3 5 E + 0 7 6 0 0 8 4. 6 2 9 Q 9 ' 7 L.
3 0 5 5. 4 7 0. 9 4 5 6 1 4 E - 1 8 24'782.5 1 4 8 ' 7. 9 6 0. 1 6 0 8 8 4 E + 0 7 3 0 1 4 6. 3 0. 3 3 5 6 5 9 E - 1 5 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 CUMULATIVE MASS FRACTION 0. 8 3 2 7 9 3 0. 8 3 s 3 1 8 0. 8 3 s 3 1 8 0. 8 3 5 6 6 2 0. 9 5 0 4 5 8 0. 9 5 0 s 6 1 0. 9 ' 7 6 6 4 4 0. 9 9 0 4 5 9 0. 9 9 1 - 0 7 7 0. 9 9 1 0 7 7 0. 9 9 7 3 1 8 0. 9 9 7 3 9 8 0.99't'784 0. 9 9 7 7 8 8 0. 9 9 7 7 8 8 0. 9 9 7 8 2 r 0. 9 9 7 8 2 3 0. 9 9 9 9 6 0 L. 0 0 0 0 0 1. 0 0 0 0 0 0. 2 0 4 7 8 E - 0 1 0. 0 0 0 0 0. 2 0 4 7 8 E - 0 1 0. 0 0 0 0 0. 1, 6 9 3 7 E - 0 1 0. 0 0 0 0 0. 1 6 9 3 7 E - 0 1 0. 0 0 0 0 0. 1 5 8 1 3 E - 0 1 0. 0 0 0 0 PERIOD 0. 3 5 0 8 6
- 2 5 0 4 1.
0. 3 5 0 8 6
- 1 3 7 8. 8 0. 1 0 7 9 6
- 0. 1 1 9 3 6 8 - 0 5 0. 1 0 0 0 8
- 5 0 9. 2 4 0. 1 0 0 0 8
- 9 2 9 ' 7. 0 0. 5 1 4 8 6 E - 0 ] -
- 2 1 8. 4 8 0. 5 1 4 8 6 E - 0 1
- 4 4 3 1. 5 0. 3 6 3 2 8 E - 0 7
- 3 2 2 5. 3 0. 3 6 3 2 8 E - 0 1
- 6 8 1. 8 3 0. 3 5 7 3 4 E - 0 1
- 0. 1 0 2 1 5 E - 0 5 0. 2 9 8 4 t 8 - 0 L
- 2 1 6 1. 8 0. 2 9 8 4 1 E - 0 L
- 2 4 5. r 2 0. 2 4 2 I ' t E - 0 1
- 5 3 9. 4 2 0.2 4 2 L ' 7 8 -0 1,
-5 5.2 ' 7 6 0. 2 1 6 6 6 8 - 0 1
- 0. 9 7 2 4 3 8 - 0 9 0. 2 0 4 7 8 E - 0 t
- 1. 5 1. 4 2 0. 2 0 4 7 8 E - 0 1
- 3 8. 5 7 4 0. 1 6 9 3 7 E-0 1
-L 2 6 8.4 0. 1 6 9 3 7 E - 0 1
- 1 7 3. 6 3 0. l_5813E-01
-0.I832rE-07 0. 0 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0 0 0. 0 0 0 0 0 0 0. 0 0 0 0 0 PARTIC.FACTOR RATIO EFFECTIVE MASS PARTICIPATION FACTOR CALCUI,ATION *****ROTZ DIRECTION 1
2 J
5 6'7 8
9 1 0 1 1 L 2 1 3 I 4 1 5 1 6 L'7 r Y 2 Q 0. 7 5 2 9 3 5 E + 0 9
- *
- N O T E * *
- Solution is done !
AI{SYS BINARY FILE STATISTICS BUFFER SrZE USED: l-6384 0. 0 6 2 M B W R I TTEN ON 0. 0 6 2 M B W R I T TE N ON 0.062 MB WRITTEN ON FIN]SH SOLUTION PROCESSING c P =
4. ' 7 2 ' 7 T I M E = 1 8 : 0 2 : 3 0 ELEMENT MATRIX FILE:
SB_caseT.emat ELEMENT SAVED DATA FILE:
SB_caseT.esav MODAL MATRIX FILE:
SB case?.mode 4. ' 7 8 9 INTE RP RE TATION (POS Tl) *****
ENABLE GRAPHIC D]SPLAY LEAVE POST1 1. 0 0 0 0 T o 2 0. 0 0 0 B Y 1. 0 0 0 0 A N S Y S RE S UL TS ENTER
/SHOW, DEV]CE-NAME TO ENTER FTNISH TO
- DO LOOP ON PARAMETER= I FROM USE LOAD STEP 1
SUBSTEP SET COMMAND GOT LOAD STEP:
TIME/FREQUENCY: 2.8502 T T T T T -
1 FOR LOAD CASE 1
SUBSTEP:
1 0
CUMUI,ATIVE ITERATION:
PRINT U NODAL SOLUT]ON PER NODE POST]. NODAL DEGREE OF FREEDOM LISTING *****
LOAD STEP=
1 SUBSTEP:
l-FREQ=
2.8502 LOAD CASE:
0 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM NODE UX 1
0. 0 0 0 0 2
0. 5 5 4 9 7 E - 0 3 4
0. 2 6 5 4 6 8 - 0 2 6
0. 4 4 1 8 8 E - 0 2 I
0. 5 2 6 3 8 E - 0 2 1 0 0. 1 0 6 3 3 8 - 0 1
Attachment A: ANSYS Input and Output 1 2 0. 1 1 2 2 5 E - 0 1 7 4 0. 1 3 5 7 7 E - 0 1 1 - 6 0. 1 9 4 6 8 E - 0 1 1 8 0. 2 4 7 9 0 E - 0 1 2 0 0. 3 0 0 6 2 E - 0 1 2 2 0. 3 4 8 4 5 E - 0 1 2 4 0. 3 9 4 3 6 E - 0 1 2 6 0. 4 1 1 9 6 E - 0 1 MAXIMUM ABSOLUTE VALUES NODE 26 V A L U E 0. 4 1 1 9 6 E - 0 1
- ENDDO TNDEX: T POST1 NODAL DEGREE OF FREEDOM LISTING LOAD STEP=
l-SUBSTEP=
2 FREQ:
2.8502 LOAD CASE:
0 THE FOLLOW]NG DEGREE OF FREEDOM RESUL?S ARE IN THE GLOBAL COORDTNATE SYSTEM NODE UX 1
0. 0 0 0 0 2
0. 3 0 5 5 7 E - 0 4 4
0. 1 4 6 1 7 E - 0 3 6
0. 2 4 3 3 1 _ E - 0 3 8
0. 2 8 9 8 3 E - 0 3 1 0 0. 5 8 5 4 9 E - 0 3 1 2 0. 6 1 8 0 7 E - 0 3 t 4 0. ? 4 7 5 5 E - 0 3 1 6 0. 1 0 7 1 9 E - 0 2 1 8 0. 1 3 6 5 0 E - 0 2 2 0 0. 1 6 5 5 3 8 - 0 2 2 2 0. 1 9 1 8 6 E - 0 2 2 4 0. 2 1, '7 L 4 E - 0 2 2 6 0. 2 2 6 8 3 8 - 0 2 MAXIMUM ABSOLUTE VALUES NODE 26 VALUE 0.22683E-02 POST1 NODAL DEGREE OF FREEDOM LISTING *****
LOAD STEP:
1 SUBSTEP:
3 FREQ:
9.2626 LOAD CASE:
0 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE TN THE GIOBAL COORDINATE SYSTEM NODE UX 1
0. 0 0 0 0 2 - 0. 2 5 5 1 6 8 - l _ 0 4
0. 6 4 7 1 3 E - 1 0 6
0. 1 1 9 9 1 E - 1 0 I - 0. 9 6 0 6 2 8 - 1 1 1 0 0. 3 I 2 0 I 8 - I 2 L 2 - 0. 3 4 9 1 9 E - 1 2 1 4 - 0. 8 5 6 4 6 E - 1 1 1 6 - 0. 1 8 s 0 6 8 - 1 0 t 8 0. 1 9 1 5 4 E - 1 0 2 0 0. 9 1 - 9 0 1 _ E - 1 1 2 2 - 0. 1 2 3 3 0 E 0 2 4 0. 1 5 5 1 9 E - 1 2 2 6 0. 2 0 7 6 6 E - 1 1 MAXIMUM ABSOLUTE VALUES NODE 4
V A L U E 0. 6 4 ? 1 3 E _ 1 0 POST1 NODAL DEGREE OF FREEDOM LISTING *****
LOAD STEP:
1 SUBSTEP:
4 FREQ:
- 9. 991-9 LOAD CASE=
0 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM NODE UX 1
0. 0 0 0 0 2
0. 1 7 1 5 1 - E - 0 3 4
0. 7 2 6 5 0 E - 0 3 6
0. 1 0 9 5 1 E - 0 2 8
0. L 2 4 4 9 E - 0 2 1 0 0. 1 8 8 1 - 2 E - 0 2 Calc. No: C-CSS-099.20-069, Rev. 000 Sheet No: 7 of 13 Sheet Rev.: 000
Attachment A: ANSYS Input and Output
).2 0.I9L628-02 1 4 0. 1 9 9 6 0 E - 0 2 1 6 0. 1 8 0 4 9 E - 0 2 18 0.L22528-02 2 0 0. 3 6 5 1 0 E - 0 3 2 2 - 0. 5 6 0 2 6 E - 0 3 2 4 - 0. 1 5 0 6 7 E - 0 2 26 -0.r'7 9298-02 MAXIMUM ABSOLUTE VALUES NODE 14 V A L UE 0. 1 9 9 6 0 E - 0 2 POST]- NODAL DEGREE OF FREEDOM LISTING LOAD STEP:
1 SUBSTEP:
5 FREQ:
9.9919 LOAD CASE:
O THE FOLLOWING DEGREE OF NODE UX 1
0. 0 0 0 0 2
0.313128-02 4 0. 1 3 2 6 3 E - 0 1 6 0. 1 9 9 9 2 E - 0 1 I
0.22'7288-0L 1 0 0. 3 4 3 4 4 E - 0 1 1_2 0. 34 98 3E-01 L 4 0. 3 6 4 3 9 E - 0 1 1 6 0. 3 2 9 5 1 E - 0 1 18 0.2236'78-0r 2 0 0. 6 6 6 5 4 E - 0 2 22 -0.I0228E-0L 2 4 - 0. 2 7 5 0 8 E - 0 1 2 6 - 0. 3 2 ' 1 3 2 E - 0 I MAXIMUM ABSOLUTE VALUES NODE
)-4 VALUE 0.36439E-01 POST1 NODAL DEGREE OF LOAD STEP:
1 SUBSTEP=
FREQ=
L9.423 LOAD Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-069, Rev.
8of13 000 000 FREEDOM RESULTS ARE TN THE GLOBAL COORDINATE SYSTEM FREEDOM LISTING 6
CASE:
O THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM NODE UX 1 -
0. 0 0 0 0 2
0. 3 5 s 3 6 E - 0 3 4
- 0. t-4 6208-02 6 0. 2 0 3 3 7 E - 0 2 B 0.220098-Q2 1 0 0. 2 0 3 0 0 E - 0 2 1 2 0. 1 9 1 5 5 E - 0 2 1, 4 0. 1 3 1 3 3 E - 0 2 1 6 - 0. 8 0 2 4 5 E - 0 3 18 -0.20607E-02 20 -0.795268-02 2 2 - 0. 6 4 5 3 9 E - 0 3 2 4 0. 1 3 3 8 9 E - 0 2 26 0.I"7582E.-02 MAXIMUM ABSOLUTE VALUES NODE 8
VALUE 0.220098-02 POST1 NODAL DEGREE OF FREEDOM LIST]NG LOAD STEP=
1 SUBSTEP=
1 FREQ=
L9.423 LOAD CASE:
0 THE FOLLOW]NG DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM NODE UX 1
0. 0 0 0 0 2
0.56549E-02 4 0. 2 3 2 6 5 E - 0 1 6 0. 3 2 3 6 3 E - 0 1 8 0. 3 5 0 2 4 E - 0 1 1 0 0. 3 2 3 0 4 8 - 0 1 t 2 0. 3 0 4 8 2 E - 0 1 1 4 0. 2 0 8 9 8 E - 0 1
Attachment A: ANSYS Input and Output 1 6 - 0. 1 2 7 7 0 E - 0 1 1 8 - 0. 3 2 7 9 2 8 - 0 L 2 0 - 0. 3 1 0 7 2 E - 0 1 2 2 - 0. 1 0 2 7 0 E - 0 1 2 4 0. 2 1 3 0 7 E - 0 1 2 6 0. 2 7 9 7 8 E - 0 1 MAXIMUM ABSOLUTE VALUES NODE 8
V A L U E 0. 3 5 0 2 4 E - 0 1 POST1 NODAL DEGREE OF FREEDOM LISTING *****
LOAD STEP=
L SUBSTEP:
I FREQ:
21.52'7 LOAD CASE:
0 THE FOLLOWING DEGREE OF FREEDOM RESULTS NODE UX 1
0. 0 0 0 0 2
4. 8 4 2 4 9 E - 0 2 4
0.32982E-0I 6
0. 4 0 2 9 1 - E - 0 1 B
0. 4 0 0 8 9 E - 0 1 t 0 - 0. 7 4 4 9 2 8 - 0 3 L 2 - 0. 4 8 4 2 4 8 - 0 2 1 4 - 0. 1 9 7 8 1 E - 0 1 l - 6 - 0. 3 2 8 8 3 E - 0 1 1 8 - 0. 1 7 9 6 5 E - 0 2 2 0 0. 3 1 0 8 0 E - 0 1 2 2 0. 2 6 8 2 8 8 - 0 1 2 4 - 0. 1 2 5 8 9 8 - 0 1 2 6 - 0. 2 0 7 3 8 8 - 0 1 MAXIMUM ABSOLUTE VALUES NODE 6
V A L U E 0. 4 0 2 9 1 E - 0 1 C-CSS-099.20-069, Rev.
9 of 13 000 000 ARE IN THE GLOBAL COORDINATE SYSTEM LOAD STEP:
1 SUBSTEP:
9 FREQ=
21.527 LOAD CASE=
THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM NODE UX 1
0. 0 0 0 0 2
0. 1 7 8 L 0 E - 0 2 4
0. 6 9 7 2 6 E. - 0 2 6
0. 8 5 1 _ 7 6 E - 0 2 8
0. 8 4 7 5 0 E - 0 2 1 0 - 0. 1 5 7 4 8 E - 0 3 L2 -0.1023'78-02 t 4 - 0. 4 ] - 8 1 't E - 0 2 1 6 - 0. 6 9 5 1 5 E - 0 2 1 8 - 0. 3 7 9 7 8 E - 0 3 2 0 0. 6 5 7 0 5 E - 0 2 2 2 0. 5 6 7 1 5 E - 0 2 24 -0.266L3E-02 26 -O.43841,E.-02 MAXTMUM ABSOLUTE VALUES NODE 6
V A L U E 0. 8 5 1 7 6 E - 0 2 POST1 NODAL DEGREE OF FREEDOM L]STING *****
LOAD STEP:
1 SUBSTEP:
10 FREQ:
27.984 LOAD CASE:
THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE NODE UX 1
0. 0 0 0 0 2
0. t I 4 9 0 E - l _ 0 4
0. 4 5 5 8 5 E - 1 0 6 - 0. 3 0 3 8 7 E - 1 0 B - 0. 1 8 6 9 2 E - 1 0 1 0 0. l _ 2 4 6 9 E - 1 0 1,2 0.224298-IL 1 4 - 0. 5 8 5 0 5 8 - 1 1 76 0.432'7'7E'-12 1 8 0. 8 5 2 7 8 8 - 1 2 IN THE GLOBAL COORDINATE SYSTEM
Attachment A: ANSYS Input and Output THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE NODE UX 1
0. 0 0 0 0 2 0. 9 4 4 9 9 8 - 0 3 4 0. 3 5 6 3 6 E - 0 2 6 0.381,94E-02 I
0. 3 4 5 7 7 E - 0 2 10 -0.35042E-02 12 -0.37250E-02 L 4 - 0. 3 6 5 1 4 E - 0 2 16 0.242518-02 1 8 0. 3 2 1 1 1 E - 0 2 2 0 - 0. 1 - 6 4 4 8 E - 0 2 2 2 - 0. 3 5 0 4 8 E - 0 2 2 4 0. 8 8 5 3 4 E - 0 3 2 6 0. t - 7 8 7 0 E - 0 2 MAXIMUM ABSOLUTE VALUES NODE 6
V A L U E 0. 3 8 1 9 4 E - 0 2 Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-069, Rev.
10 of 13 000 000 2 0 - 0. 1 0 4 3 8 E - 1 1 22 0.87 669E-1.2 24 -0.'7'7049E.-]-2 2 6 0. 4 5 4 2 0 8 - 1, 2 MAXIMUM ABSOLUTE VALUES NODE 4
V A L U E 0. 4 5 5 8 5 E - 1 0 POST1 NODAL DEGREE OF FREEDOM LISTING *****
LOAD STEP:
]-
SUBSTEP:
11 FREQ=
33.511 LOAD CASE:
THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM NODE UX 1
0. 0 0 0 0 2
0.835'728-02 4
0. 3 1 _ 5 1 6 E - 0 1 _
6 0. 3 3 7 7 8 E - 0 1 I
0. 3 0 5 7 9 E - 0 1 1 0 - 0. 3 0 9 9 0 E - 0 1 L 2 - 0. 3 2 9 4 3 E - 0 1 l-4 -0.32292E-01 t 6 0. 2 1 4 4 1 E - 0 1 1 8 0. 2 8 3 9 9 E - 0 1 2 0 - 0. 1 4 5 4 6 E - 0 1 2 2 - 0. 3 0 9 9 6 E - 0 1 2 4 0. '7 8 2 9 7 E - 0 2 2 6 0. 1 5 8 0 4 E - 0 1 MAXIMUM ABSOLUTE VALUES NODE 5
V A L U E 0. 3 3 7 7 8 E - 0 1 POST1 NODAL DEGREE OF FREEDOM LISTING *****
LOAD STEP=
1 SUBSTEP:
12 FREQ:
33.511 LOAD CASE:
IN THE GLOBAL COORDINATE SYSTEM LOAD STEP:
1 SUBSTEP:
]-3 FREQ:
4L.294 LOAD CASE:
THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM NODE UX 1
0. 0 0 0 0 2 0. 3 1 9 2 5 E - 0 2 4 0. t _ 1 1 8 9 E - 0 1 -
6 0. 9 1 7 3 1 E - 0 2 B 0.654L'78-02 l _ 0 - 0. 2 2 3 1, 1 E - 0 1 t 2 - 0. 2 0 6 3 2 E - 0 1 1 4 - 0. 6 6 0 4 6 E - 0 2 1 6 0. 4 1 7 5 8 E - 0 1 1 8 - 0. 3 4 8 6 2 E - 0 1 2 0 - 0. 1 9 1 9 2 E - 0 1 2 2 0. 4 2 3 4 0 E - 0 1
Attachment A: ANSYS Input and Output Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-069, Rev. 000 11 of 13 000 24 -0.423308-02 2 6 - 0. 1 5 0 9 5 E - 0 1 _
MAXIMUM ABSOLUTE VALUES NODE 22 V A L U E 0. 4 2 3 4 0 E - 0 1 POST1 NODAL DEGREE OF FREEDOM L]STING LOAD STEP:
1 SUBSTEP:
14 FREQ:
4L.294 LOAD CASE=
O THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE NODE UX 1
0. 0 0 0 0 2
0.32'7t58-03 4
0. L I 4 6 6 E - 0 2 6
0. 9 4 0 0 1 E - 0 3 8
0. 6 7 0 3 6 E - 0 3 10 -0.22863E-02 12 -0.2].1428-02 1 4 - 0. 6 7 6 8 0 E - 0 3 1 6 0. 4 2 7 9 2 8 - 0 2 18 -0.35'724E-02 2 0 - 0. t 9 6 6 7 8 - 0 2 2 2 0. 4 3 3 8 7 E - 0 2 2 4 - 0. 4 3 3 7 8 E - 0 3 2 6 - 0. 1 5 4 6 9 E - 0 2 MAXIMUM ABSOLUTE VALUES NODE 22 VALUE 0.43387E'-02 POST1 NODAL DEGREE OF FREEDOM LISTING IN THE GLOBAL COORDINATE SYSTEM LOAD STEP:
1 SUBSTEP:
15 FREQ=
46.1-54 LOAD CASE:
0 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM NODE UX 1
0. 0 0 0 0 2
0. 1 1 7 5 5 E - 1 3 4
0. 3 2 2 6 8 8 - 1 3 6 - 0. 1 3 8 7 7 E - l _ 2 8
0. 1 4 3 8 9 E - 1 3 1 0 0. 1 9 6 7 1 - E - 1 1 1 - 2 - 0. 5 0 1 0 7 E - 1 1 L4 0.28'7028-]-2 1 6 0. 5 1 8 1 0 E - 1 4 1 8 0. 9 3 6 3 1 E - 1 4 2 0 - 0. 9 6 8 4 5 8 - 1 4 2 2 - 0. 5 5 2 9 9 8 - 1 4 2 4 - 0. 3 9 9 5 7 E - 1 5 2 6 0. 6 7 8 5 1 E - 1 4 MAXIMUM ABSOLUTE VALUES NODE 1-2 V A L U E - 0. 5 0 1 0 7 E - 1 1 POST1 NODAL DEGREE OF FREEDOM LISTING LOAD STEP:
1 SUBSTEP:
1.6 FREQ:
48.833 LOAD CASE=
0 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE NODE UX 1
0. 0 0 0 0 2
0. 1 2 8 0 6 8 - 0 2 4
o. 4 t ' 7 L 4 E - 0 2 6
0.22'731E-02 8
0. 8 4 2 9 3 E - 0 3 1 0 - 0. 9 4 9 5 6 8 - 0 2 L2 -0.'7'7 988E-Q2 1_4 0.2'731_'78-02 1 6 0. 1 8 2 7 7 E - 0 1 1 8 - 0. 4 0 0 7 6 8 - 0 1 2 0 0. 4 9 6 6 5 E - 0 1 2 2 - 0. 3 4 0 8 4 E - 0 1 2 4 0. 3 6 3 0 5 E - 0 3 2 6 0. 1 0 2 5 2 E - 0 1 IN THE GLOBAL COORDINATE SYSTEM
Attachment A: ANSYS Input and Output MAXIMUM ABSOLUTE VALUES NODE 20 V A L U E 0. 4 9 6 6 5 E - 0 1 POST1 NODAL DEGREE OF FREEDOM LISTING *****
LOAD STEP:
1 SUBSTEP:
I'7 FREQ=
48.833 LOAD CASE=
0 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE NODE UX 1
0. 0 0 0 0 2
0. 3 1 3 7 9 E - 0 3 4
0.r022L8-02 6
0. 5 5 6 9 9 E - 0 3 8
0. 2 0 6 5 4 E - 0 3 1 0 - 0. 2 3 2 6 7 E - 0 2 1 2 - 0. 1 9 1 1 0 E - 0 2 1, 4 0. 6 6 9 3 6 8 - 0 3 1 6 0. 4 4 7 8 6 E - 0 2 1 8 - 0. 9 8 1 9 9 8 - 0 2 2 0 0. 1 2 1 6 9 E - 0 1 2 2 - 0. 8 3 5 1 8 E - 0 2 2 4 0. 8 8 9 5 9 E - 0 4 2 6 0. 2 5 t 2 I 8 - 0 2 MAXIMUM ABSOLUTE VALUES NODE 2Q V A L U E 0. 1 2 1 6 9 E - 0 1 POST1 NODAL DEGREE OF FREEDOU LISTING LOAD STEP:
1 SUBSTEP=
18 FREQ:
59.041 LOAD CASE=
0 THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE NODE UX 1
0. 0 0 0 0 2
0. 1 5 2 8 3 E - 0 1 4
0.423258-0I 6
0. 2 5 4 8 5 8 - 0 2 I - 0. 1 - 6 1 3 8 E - 0 1 1 - 0 - 0. 4 8 9 5 9 E - 0 1 -
L 2 - 0. 3 1 7 8 4 E - 0 1 L 4 0. 5 7 8 2 7 E - 0 1 1 6 - 0. 1 4 3 8 2 E - 0 1 l-8 0.4'79328-02 2 0 - 0. 1 6 8 3 3 E - 0 2 2 2 0. 5 3 0 0 5 8 - 0 3 2 4 0. 1 8 4 4 0 E - 0 3 2 6 - 0. 2 3 0 3 7 E - 0 3 MAXIMUM ABSOLUTE VALUES NODE 14 V A L U E 0. 5 7 8 2 7 E - 0 1 POST1 NODAL DEGREE OF FREEDOM L]ST]NG *****
LOAD STEP:
]-
SUBSTEP:
19 FREQ:
59.041 LOAD CASE=
0 THE FOLLOWING DEGREE OF NODE UX 1
0. 0 0 0 0 2
0.20920E-02 4 0. 5 7 9 3 8 E - 0 2 6 0. 3 4 8 8 6 E - 0 3 8 -0.2209LE-02 1 0 - 0. 6 7 0 1 8 E - 0 2 1 2 - 0. 4 3 5 0 8 E - 0 2 7 4 0. 7 9 1 5 8 E - 0 2 1 6 - 0. 1 9 6 8 6 E - 0 2 1 8 0. 6 5 6 1 2 E - 0 3 20 -0.230428-03 22 0.7255'7E-04 24 0.252428-04 2 6 - 0. 3 1 5 3 4 E - 0 4 MAXIMUM ABSOLUTE VALUES Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-069, Rev.
12 of 13 000 000 IN THE GLOBAL COORDINATE SYSTEM IN THE GLOBAL COORDINATE SYSTEM FREEDOM RESULTS ARE IN THE GLOBAL COORDINATE SYSTEM
Attachment A: ANSYS Input and Output NODE
].4 V A L UE 0. 7 9 1 5 8 E - 0 2 POST1 NODAL DEGREE OF FREEDOM LISTING LOAD STEP:
1 SUBSTEP:
20 FREQ:
63.239 LOAD CASE:
O THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE NODE UX 1
0. 0 0 0 0 2
0. 5 7 4 3 8 E - 1 3 4
0.645L18-L2 6 - 0. 8 1 8 7 8 E - 1 2 I
Q. s 8 s 2 8 E - r _ 2 10 -0.6'76LLE-L2 L2 -0.8225'78-L2 1_4 -0.239348-L2 1 6 0. 1 4 0 2 9 E - 1 1 18 -0.LI622E-II 2 0 - 0. 6 5 5 3 9 E - 1 2 2 2 0. 1 4 2 8 8 8 - 1 1 -
24 -0.I4L94E-12 2 6 - 0. 5 0 9 0 6 8 - 1 2 MAXIMUM ABSOLUTE VALUES NODE 22 V A L U E 0. 1 4 2 8 8 E - 1 1 NO T E * *
- cP :
DELETED BACKUP FILE NAME: SB case4.dbb.
- *
- N O T E * *
- c P :
NEW BACKUP FILE NAME: SB case4.dbb-ALL CURRENT ANSYS DATA WR,ITTEN TO FILE NAME:
FOR POSSIBLE RESUME FROM THIS POINT EXIT THE ANSYS POST1 DATABASE PROCESSOR R O U T I N E C O M P L ETE D CP :
Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-069, Rev. 000 13 of 13 000 IN THE GLOBAL COORDINATE SYSTEM 4. 8 0 5 T I M E : 1 8 : 0 2 : 3 0 4. 8 0 5 T I M E : L 8 : 0 2 : 3 0 SB_case4. db 4. 8 2 0
To:
FROM:
RE:
Calculation C-CSS-099.20-069, Rev. 0, Aftachment B, Page 1 of 3 Mr. Javeed Munshi Mete A.soz*n,5E
{filinois} [{.tc *,i{a" u-*
On The Effect of Laminar Cracks Observed in the Shield Structure of the Davis-Besse Nucfear Power Station DATE:
25 March 2015 Not having made the crack-width measurements in person, let me start with a iummary of what I know about the distribution and development of laminar cracks observed in the shell of the structure.
As documented in Table I of this note, a totaf of 15 bores have been subjected to repeated crack width measurements over the course of 2 to 3 years. None of the repeated measurements identify an appreciable trend of increasing crack width.
Crack widths reported in 2011 range from 5 to 13 mils. Those made in 201? and ?013 range from 5 to 10 mifs.
In the data reported in Table 1, there is no trend that would be inferred to suggest a change in the strengfh of the structure.
This conclusion is in agreement with the standard expectation that, unless there is a serious disturbance in its surroundings, a reinfurced concrete structure that has been built decades ago should not have criticaf change in its properties within its expected life span.
Results of experiments carried out at Bowen Laboratory in 2012 focusing on the effect of laminar cracks on strength of unconfined lap splices of #11 reinforclng bars provide a basis for understanding the strength state of the Shield Structure at the Davis-Besse Nucleaf Power
- Station, The question to be ansrfi,ered is simple and direct. Given that the observed laminar cracks in the Shield Structur were not caused by bond stress, the questinn is "What fraction of the yield stress of the relnforceme nt can be developed by a splice with an existing laminar crack of a Biven magnitude?"
Eight of the twelve tests reported were focused on that questionr. Test girders with 120-in. and 79-in. spfices (Figure 1 & f l were loaded to develop laminar cracks,
- unloaded, and then loaded to failure ts determine the effect of "existingl' cracks. Their results in relation to the question to be answered are sumrnarized in Table 2. The glrders measured L7 518 by 30 in. in cross section.
In the tests with 120-in. spfices (Series Al, it was observed that a splice with an existing crack as large in thickness as 120 mils developed 120% of the measurd yield stress of the reinforcement.
ln the tests with 79-in splices (Series B), it was observed that a splice with an t M. A. Soren and 5. Puiol, 'An Investlgation of The effects of Laminar Cracks on $trength of Unconfined Lap Splicer of *11 reinforcing bars,' e report submitted to First Energy Nuclear Operating ComBany, Oak Harbqr, Ohio, Xl July 2012.
Calculation C-CSS-099.20-069, Rev. 0, Attachment B, Page 2 of 3 existing crack width of 30 mils developed 105% of the measured yield strers of the reinforcement.
In both cases the existing crack widths exceeded those measured in the Shield Buitding.
The mea$urements made in the tests at Bowen Laboratory confirm that the reported laminar cracks in the Shield Building sf the Davis-Besse Nuclear Power $tation will not prevent the structure from fulfilling its design mission of ductility in the event of impulsively applied internal or external forces.
It is relevant to note the ACI 318-63 document states in Article 805 "Splices at points of maximum tensile rtress shsuld be avoided wherever possible; such splices where used shall be welded, lapped, or otherwise fully developed."
In the tests made at Bowen Laboratory wlth faminar cracks, the 120-in. splices developed a minimum ot77 ksi and the 79-in. splices developed a mlnimum of 59 ksi. The minimum reinforcement stress developed in both types of splice exceeded the nominal yield stress (60 ksi) as required by ACt 318-63..
Recommendetlon Based upon the study of the tests performed at Bowen Laboratory, 0 conservative lswer bound erack-width can be establlshed. lf the measured laminar crack width does not exceed 0.0?
inches, the splices wif l continue to satisfy thelr original design objective.
TABUT ml TU l0t3 ID Cncklttidth Date Cnd Wdh Drte CrdWldth Date Cn*lilifth Oate CnckWidthDate 0ffilin.
0.Ol ln.
0Olin.
0"filtin.
$ffiiil.
$tmil.s lUtUt0ll efiutsH 5+ea$$
1$2ff20'11 NoCl6 t/illou u$/lCI$
s773.16
u2unfi lt 9fi5/Ifi!
s665.S&
10/2sil11 s5rul!
s7-6$',t.S25 xonryro}r e/sn0$
5S653.$9 1T5/trynu tloCllG uz{eu t{oC}lG ffiunu INe/u/st:
5$666.$11 ilrumll sltw ifoClG USm: f'loCl6 ilvlot3 e$/$t!
tln5.?a5 {0 10/3U20u(I0 5NWlt lloCllG wlffi2 ilo [tf6 g#mu el34l?ou tu-5617'1)il0
$fi{m:
elluHs 511"569.$l?
10[6/mil e/u/m$
5U-666S4 10124/r0trtio Cl6 iltVmu ililm:
1l elluilu 5lt66S8 1Uyt01t lt u$nfit 9ls613.$46s10
$/251rur No CHG u$/nu r{ 9H4lt01 r+n4,o3.5
<lll EB/NU erulslr flnt${
131u4l0u
!{o CHG uB/40il t{o CtlS g3/101:
1(elB/mu
Calculation C-CSS-099.2S069, Rev. 0, Attachment B, Page 3 of 3 TABTE Z L{t cd flrE 3ffi-I L, t
I I'
?r Eomr Tr Sarrn
,, L_,u It
-r Ir I
'.J l-,oJ 3
l-Figure I Test Girder Series A rg q
I 1' Er$r.f
$lH Rcd Test Girder lD txlrtlng Crack Wldth 0,001 In.
Tesile Stress Developed in Reinforcment ksi Yield $tress ksi A1 150 79 66 A2 80 7g 66 A5 80 79 65 A6 60 77 66 B2 30 69 65 B3 15 7A 66 B5 25 72 66 B6 15 72
$6 s-a 3" _l I L.
f.r (Llp Sprat tmdrr Figure 2 Test Girder Series B 3a'{'
rl 3, L-s4 s'--l r'.r
Calculation C-CSS-099.20-069, Rev. 0, Attachment C, Page 1 ol2 DAVID DARWIN, consuftins Eneinesr Struc'tu ral E ngineering Engineedng Matefials 1901 Camelback Drfve Lawrence, l(ansEs 66&t7 78ffi6+3827 78S41-2888 Cll 785-764-9922 MEMORAT{DUM TO: Javeed Munshi FROM; David Darwin DATE: March 24,2A15
SUBJECT:
Potential Limits 611 lqminar Qs6[iag in Davis-Besse Shield Building This memo is in response to three questions addressing the laninar cracking in the Davis-Besse Shield Building.
- l. Do the testing and results reported ia University of Kansas Center for Research, Inc. SL Report 12-2, dared Juoe mlz, in any way place a limit on the laniaar cracking around the Shield Building? In other words, if tbe laminar cracking is p,resent thtougbout the Shield Buildin& are the rcsts and test results valid?
Response
The t$ts and test results reported in SL Rport l2-2 cover the conditioo of firll del"'niqation in the vicinity of splices, and thus, conespond to laninar cracking throughout the Shield Building.
2, Is there a limit to the crack width that can be allowed based oa tbe tst results rcported in SL Rport r2-2?
Response
Five of the six test specimens described in SL Report l2-2 were fabicded using a cold joint (obtained using two colrcrctc placements) to simulme a laninar crack Three out of these five specimens were preloaded to obtain la"'ina' cracks in the plarc ofthe spliced bars with wi&hs in the nnge of20 to 35 mils (0.020 to 0.035 in.). Those specimens were subsequently reloaded lo failure - a ftilure that was governed by splice shength. One of the tbree preloaded specimens had a splice lenglh of79 in" Ils initial l6qding resulted in a laminar crack width of 20 mils (0.020 in.). Upon subsequent reloading, a sbess of 57,000 psi was obtained in the spliced bar. Prior to Gaching this stress, a l+'ninr crack wi&h of 35 mils (0.035 in.) was measured The other two preloaded specimens had splice leogths of 120 in-These specirnens were preloaded to produce laminr crack widths of 35 and 30 mils (0.035 aod 0.030 is),
respectively.
Upon reloading, the specimens achiwed respective bar stresses at splice failme of 67,000 and 69,000 psi. Given that all tbree beams achiwed a laminar crapk width of at least 30 mils (0.030 ia.), a crack width of 20 mils (0.020 in.) would be a prudent upper limit for the Shield Building.
- 3. Assumhg ifu4 the Shield Building has laminar cracking around its firll cfuumference aod that the cfiack widtbs are maintained within the limits to your rsponse to Erestion 2, how does this situation in the Shield Building meet the provisions of ACI 3 I E-63?
Response
Splice design in accordance with ACI 318-63 rcquires that qplices fransfcr the entire oomputed shess from bar to bar without exceeding tbree-quarters of the permissible bond values (expressed as an ultimate bond sbess). The lap length must be increased by 20% for contact splices speced lderally closer than 12 bar diameters or located oloser than 6 in. or 6 bar diamaers tom m ouside edge. these critaia were considered for the initial de"igrr of the Sbield Building. Neither ACI 318{3 nor any other ACI code
Celculation C-CSS-099.2G069, Rv. 0, Att8chment C, Page 2 of2 Javeed Munstd I{arch 24,2015 Page2 addrcsses the presence of lanrinar cracts in the plane of the einforement. That said, the tests and rsults described in SL Report l2-2 demongtrate that bar stresses of 57,000 psi and grearer cn be provided by splices in the p,resence of laminar cracks with widlhs of 20 mils (0.020 in.) or gIaler, Thus, lhe dcsign forces in the bars can be maintainc4 even for concrete that has mdergone significat laminar cracking with crack widtbs cqual to or greater tban the recomncnded upper limit of 20 mils (0.020 in).
Page I of 1 DESIGN VERIFICATION RECORD NOP-CC-2@i-01 Rev.00 DOCUMENI(S yACTrVfTy TO BE vERTFlED:
Shield Buiklinq Laminar Crackinq Limits, C-CSS499.20{69 Rev 0 El SNrEW RELATED fI nUcUENTED QUALITY f] NONSAFETY RELATED SUPPORTING/REFERENCE DOCUMENTS Refer to the body of the calculation.
DESIGN ORIGINATOR:grtnt and Sr'gr Name)
ShenWang W DATE 0lft*/ug VERIFICATION METHOD f0necl ono) 8 OeSrcN REVIEW (Comptateoes,gn EI ru-fenNATE CALCULATION il OUru-tflCATlON TESTING Review CDeclr/isf u Calculation Review Chacklisl)
J USTI FICATION FOR SUPERVI SOR PERFORM I NG VERI FICATION :
APPROVAL: (Print and Srgn Name)
DATE EXTENT OF VERIFICATION:
Verified using Galculation Review Checklist
- COMMENTS, ERRORS OR DEFICIENCIES IDENTIFIED?
E VCS A
NO RESOLVED BY: (Print aN Sign Name)
DATE VERf FIER' (Print and Srgn Nane)
JaveedA.Munshi Fforr,lthurr
[:a {nr IaUg&t lt4,lnflr', do.
DATE or /ob /wlt APPROVED BY: (Pfint aN Sign ft/ame)
Hongchun Liu DATE o5fo6l"ou
E F ! oss 8R 0oI; s?
?efi E =E J
g F
? o 3 -
L'. ur.':
J > O =
< i u o z o E < : t
=
ltj I
ultrzIF J3C)
J t t vB (f,s Fc)
C)sl d
O d.oz o 4 Q r o
---t O
- o q E bp 6 : i c')
c nco
.9 cCD tn 0)
D EcIE sfp o
Eg rt o
oo8o ql
.o (U
o o.
CL
(!
E'5 ooc(6 Eo (J
(t(U
.E es E O s-8 coo ll o
a.>
GtrG tro) ho os a C
( ) u o o r ) r drg 3H l\\,
(l) z g TH G -
v 0 }
- f c ' c L u l gE E!
v o ' i 3 c-tr rE T ' 3
( J 5EE 3eS 6Ep b g; EEfi
< o E E$E co
.9, otro(t Eg
(!
-g tloc 0oGI o
c.o
-g:
C'(lt TJ oE o
ttc
.q ctE 33n{,(t ^.
= i t l l, o c,.rly')
q ( l l rt
.Cl ts I t o
= - og*
FE C ' g EH E6 8.9 f;E q r 3 SE o P oEE F-S t r - g 3 (, l
! ? ss9 58 88
- 5 ( E 9E O ( o
- o a I c o rPO e5 9 - o C r.,
p o E (, :
o =
8E
- (, '
' - c ctt o c o SE
= o
'E>
EE E8 o. '
' g a (r,o t r o.
J ^sf,
!F Fg
$Eg
- frE o E 8
( 6 o.
E*
.EE o P 8E 5,;
h t t l g G 6 ( l,
g ? t EE r [ o EFe,E gE tl tr 5 :o: '
o 5
CL
.g EE, G ' E s
.3p O E r r Eee E O ' E xeBiE E$
E o o
> \\ c
,8 s'3
. c S r t,
o b EE fis t s E
. $ c F r !
o " oFiE s8E
-E E8 w t !
H a o -
I t 0 'P.E E3 SR F o b l 9 gE a ( )'3'r E.E g 6 o =
.F.E E8
- 96=
. o8s 6 8sFHfi E!sE
$$g o >
E cocto aG co qt E
IEco(,
o
(!
o E
^g es E
TE o
o o
5CL
.E H
o E.9 E'
p u,
co()
O)
.E t!
o CL o
-!P
.cl G'
.9 a.
ES G -: a l
!t C(E E
.9 gop E
6
.g(,
coo It at o
-o cr0 o,tr E
o Eoo.
o as slo(t ocEEag ol.s o-o
.9 co c
ll(!
IJ o
33 o.o C)oott ooct oooo=
CL o
.Jo tto tto G
o o.c aooo
- o N c lss flRs
?
3l'3n I
= ;8 7 xt E 3e i;si
(, G < 3 zotr 3
Joolr,tr p
2UJ E
Eo()
Fa IJv O
llJ
()-
=
ltj I
uJ trzo IF J
=o J
O; G+
F oI0-oz oz x
cto x x
x x x x x
x x
x x x x x
x x
X
(=
x x
x zo
- Fou, fo o
o3 Es oa
.g
.ooa)
Oozut IL o
E co I'c'
.g E
ll,o3 cl, tr oo tn EE ole o.
o 3
CLtr E C \\
5 g 9 ' 6
! o 9 E oi N
t,.e5 9"8 5
E EE EE
>E Q ogs Sa o E Eg
( U 6 g-E EE 6 crt
= o E 9 T bs..
- ' e -
- o
= O u i gE B b8E eaE tt.lP.i; gEE rt p
fo(t TE E
oog) au, o=
(5
=z G
3 o(Eo E(f u.l tro oe oco(t, CL rr.
r(' ra
= e
= o v @
E E o. o tr.c R o ar (0
F T I
- a u 5E I
N
(\\.
tto ooIo oo, (E-c3 T'cto o:o.
.g o
tt ooEo()
cos
?
.9 o
Gg ooTE o
fo.:'o o
f CIEo(t o
E I
rrt
$l
!ltr G
o ue o.
cl, c'c oo
.gc't to Eo N
cE r o(,
E E
3 Eo ln'a co(,
x 6
- t o u o J G o oEe 6 ' 6
,- e6
- o. g 6 o S E.E F e 9
- ( f ! t Ie c t t, al
.g oc oc
.9 G=e, o
co o
ooat J
l1' E
e
!to!t o
CL tro o
(J'-
a,t ltoco Q e P O s r g l o t r o o o t r E C o $
ltst roe
(,
oqt o
tao oE Itco EIe CI ttoE o
Eoo ac,o e
ooo iio
.;F C'E o
E
(!
E
.8 o
o3
{i GI
.9o oco o
E
.E Eoo:'
(J o
oco
.gots o
IJ-rU.e
'a E
o sto E,g
(!co C'c5 6
O i r E.E
- o
= O F T E F >
Ets 4 t s
! r o w c t 1 9 c
. o
_ g o I. ( t ot sl
(\\otg o
E
!t Co Q
c5 oog o
G tto cooEo=
5oE
.t g
cio r.
- t Et
.tr c
tnooco Eo 6E o
a o
I o
ag oo EIo o-o o
E d,
E 2
to Ico.lctl cott c.9 Es oco(,
Ie o
ao-CO s.o=oc.;
DE 6ctE oo cos3 Eo 6og o
ttc6 o
.oocoa 6E
- t oo oc o
o!t c
E n E Z E 9 o Es d l a zEs s.o'c o
'g (J
oI{6 c\\o()
C'o oc, Eg nc
.9 o
ott o
E$
g o
co G
.g=
,h 5.;
-oo Coo(B E
G E
a}
,,8 ll,)
t.
l(?
tc)
(\\.
(n t=,
3oE g
.9 o=o rEo oE co
!!oo(0
.o
-g
.o IU 5
o.:.
qc.9 o
oc'oo Ito t!
g, o
q()
co 1A E
!,cTE c.9
{I E
IJ(E(,
E
.E o
c,E ootG c
oc(0 ItIo.oE 3c Fr!
co:(too oo Ctl8.r
- O 6
a r E E :
- ( C I
d (vl s.
-0D D'6 3o oE oco
.g g
E
.g c
.9
.U Eo
.E r[
g (o
(t, o
o o
!roog g
G 5o,c't os(U lt$r b.e 9E d c s E E k5 g 6EE E ' E
-IJ (E E E 5!
Eb aE 5:E E5 r-E.E o -
o o 9 - g IEH l.
tf\\
i(9 E
7 o(,
c(6 E
o goo c s
. E 3 F5 C E P
Eg IJ G' c t o
- c )
E 9 oc)
E Q t'
rr'FE o -
g o q C 6 g F CH8 o ca
?i -g E 3 F O o o
- ( t te
'jt (It o T t
= cgs 1 6 ( ' '
e r 6 9 E rO (r) o
- tt ag TE E
T' r!
ao Cgt
.A g
!to rU E c.
. E C
- o h 3 d. g
-ct >
- o b :Eg FF i Ef i =
6 ( E o ! t
. E { d
- o
_ s o EF 9E H o
= o G s a r O 5. C
= ffo
- t I r !
i.o, (n
(\\. I wl o
oE]
tUl fiq o
IAo.o cI g
oco(J tr
.gs T'
ol c
.t2 xo
.E 3
Eo o
ttt o
5U'o Co
-gt o g
- o d o Z =
u f 6 8 e J >>a 9. r -
an
! r o trt st o.
F.o (6
cle aoo ao 1'o E
o c l l n f ( D t t l G
-.{=
c D c
.E',=
P d 8..8
':i o
= ( !
E :
! g D
_ - o c t : l
, o
.9, tr o o
{ g FF 6 0 9 o J O L ' O 6 ( / )
o E 9. o Q ' -
6 o 9 t r Y A F T L tt
(!
o aocoo(U E
o!tco o
co oE E{'s l0 c\\i t
U' troEo'5 cr E
co 6E o
.g c
.gl tho E
g
$C'E rg t0 Eo lt, f
E oCLE o.
c.g g
f(!E*
9 d
! E r a )
d i g I O (v)\\'
$ o }$s f;R oior Io 6Io
< =
d 2; Z,
- ! g i,iE
.si
[=*g
'5 r{
8l-1\\c' (v)r\\a rt
- t}
lll go oo(!
te to-Fa JvouJ Ec) 3 UJ I
nJ Ezo F
J3 C)
J o;
G g$
- N:
EI; EE;iei C L ! -
EgE o o E EEg
$Eg
- - 5 9 88 iii o-t ie E
- - c L f
C r-oeH E
- o o
-tl
.o SeE
} F E;EEg
!g$E 9 4 6 0
. E E G O
. 9 ( )
F U J 6 =
e ag;
' 6 >
o t t o o o c iP s r 5 a o fl sg c o t 5 c l c ( U
( l
- o ' -.
.eS cE 6*
tror*
.s.g SE 5a e a E *
- )o P
( 0 =
F 5
. J r r ! $
i i o EcrE o
oE'6 co()
cooo co
-(!5 IJ(!(t
$g 5
o t, '
{ oE6 E
- q
{ t t 5 o tt' r{f gr EJ F5 q{
\\l
-tl C
rtJ A c F If
.9oo.o c
CD
.Ao!t
.g Eo(,
c,E o
o o(U 3
c
.9(o El,(!()
o o
g.E o
olt o
Go, E
o-c.9 dErJ 6o oE p(]