ML20054G132
| ML20054G132 | |
| Person / Time | |
|---|---|
| Site: | Zion File:ZionSolutions icon.png |
| Issue date: | 05/10/1982 |
| From: | Hluhan R, Yu C WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
| To: | |
| Shared Package | |
| ML19268B006 | List: |
| References | |
| NUDOCS 8206210149 | |
| Download: ML20054G132 (130) | |
Text
-
ANALYTICAL ASSESSMENT FOR EFFECTS OF LOOSE PARTS ZION PLANT NO. 1 R. A. H1uhan l
C. Yu Ma 10,.1982 t
I 8206210149 820617 PDR ADOCK 05000295 p
TABLE OF CONTENTS (Con't.)
Section Title Page 2.6 Results of Wedged Parts Analysis 2-57 2.6.1 Parts Wedged in Lower Radial Support 2-57 2.6.2 Parts Wedged Beneath Seconaary Core Support 2-57 2.6.3 Discussion of Potential Problems and Recommended 2-66 Operating Procedure 2.6.3.1 Loose Part Configuration I D 2-66 2.6.3.2 Loose Part Configuration II D 2-71 2.6.3.3 Discussion of Loose Part Configurations 2-74 2.6.4 Recommended Operating Procedure 2-74 2.7 Summary Wedged Part Effects 2-80 2.7.1
~
Effects of Loads Induced in Core Support structures Due to Wedged. Parts 2-80 2.7.1.1 Parts wedged in Lower Radial Support 2-81 2.7.1.2 Parts Wedged Beneath Secondary Core Support Structure 2-81 2.7.2 Minimum Core Barrrel Flange To Vessel Ledge Load 2-81 2.7.2.1 Parts Wedged in Lower Radial Support 2-82 2.7.2.2 Parts Wedged Beneath Secondary Core Support Structure 2-82 i
2.7.3 Loads Induced in' Reactor Pressure Vessel 2-84 2.7.3.1 Parts Wedged in Lower Radial Support 2-84 2.7.3.2 Parts Wedged Beneath Secondary Core Support Structure 2-84 2.7.3.3 Local Stress in Vessel Cladding 2-84
3.0 INTRODUCTION
- IMPACT EFFECTS 3-1 3.1 Definition of Missile 3-1 l
3.1.1 Missile Geometry 3-1 3.1.2 Missile Velocity 3-2 3.1.3 Missile Energy 3-2 3.2 Target Geometry 3-3 3.3 Methods of Analysis for Missile Impact 3-3 3.3.1 Local Impact Effect 3-4 3.3.1.1 Punching Shear 3-5 3.3.1.2 Penetration (Denting of the Target) 3-6 3.3.2 Overall Structure Response Effects 3-8 3.3-2.1 Target Effective Mass 3-11 3.3.2.2 Coefficient of Restitution 3-16 3.3.2.3 Target Energy Absorption Requirement 3-18 3.3.3 Energy Absorption Capability of Targets 3-18 3.3.4 Core Barrel Analysis 3-22 0583E:1
TABLE OF CONTENTS (Con't.)
Section Title Page 3.3.5 Instrument Tube Analysis 3-24 3.3.5.1 Bending Strike 3-24 3.3.5.2 Shear Strike 3-25 3.3.6 Thermal Shield Flexure Analysis 3-27 3.3.6.1 Impact at Center of Thermal Shield Flexure 3-27 3.3.6.2 Impact Near Flexure Support 3-27 3.4 Summary Impact Effects 3-28 4.0 Reference 4-1 e
t 0583E:1
1.0 XNTRODUCTXON The purpose of this study was to determine the potential effects on reactor internals and reactor pressure vessel of loose parts generated by the steam generator nozzle cover left in the hot leg inlet plenum of the ID steam generator at Commonwealth Edison's Zion Unit 1.
These parts, assumed to have entered the reactor pressure vessel through an inlet nozzle, cause.two specific concerns.
The first is that a part may become wedged during cold shutdown and induce loads in core support structures during plant heatup.
The second concern is that loads on reactor internals may be induced by impacting loose parts.
This report describes in detail the work performed to address the above concerns.
1.1 DESCRIPTION
OF LOOSE PARTS An inventory of missing loose parts believed to be in the reactor pressure vessel is given in Table 1.1-1.
TABLE 1.1-1 INVENTORY OF MISSING LOOSE PARTS Part Description Material Number Missing 1 - 20 x 3/4 long flat head Stainless 21 assemblies plus one loose nut and one loose bolt, nut and washerTs'sembly Steel (Figure 1-1) washer l
l 3/4 x t x 0.06 Hinge Fragment Stainless 1
l (Figure 1-2)
Steel l
1 1/16 x t x 0.06 Hinge Stainless 1
l Fragment (Figure 1-2)
Steel l
1 x 0.1 x 0.6 Hinge Fragment Sta %1ess 1
(Figure 1-2)
Ss.l 1/8 x 1 x 0.06 Hinge Fragment Stainless 1
(Figure 1-2)
Steel 5/16 0 x t Long Hinge Fragment Stainless 2
(Figure 1-2)
Steel 1-1
P4. - 2.0 LANC FL.AT HEAT l
~ Ncaint scgEW
( iEE 30
'l> ETA tcl 3T r ~
t WASHER o.D =,$,
THICKNESS = h LL 3:20 uwe Nur ko ACRoSS FLArs
- t PotMT - To-PotNT TMickNEss. k "
4 ALL P AR.TS STAIN LESS STE.E.L oVERALL LENGTH
'4 INCH wEtsHT of ASSE.MBLY = 0.3 OUNCE r-y
- 37. N J
_--____-._Q y
g 37.
3_
+
loLT 3E. TAI L FIGURE l-1 LOOSE BOLT ASSEMBLY
\\ - ?-
pa
,d T,,
h 7@
@y
[z,,
2 w
a4-Tsicxstss = o.ccoo is.
L b
I i
$~
'd FIGURE l-2 HINGE FRAGMENTS 1-3
It must be assum:d that the bolt, nut and washer assemblies may oe either together or separated, since parts were recovered in both conditions.
1.2 POTENTIAL LOOSE PARTS WEDGING LOCATIONS I
A comprehensive study was made in order to determine possible loose part wedging locations along possible paths from an inlet nozzle to the lower core plate.
Based on the size of the parts and reactor internals gap sizes, two significant wedging locations were discovered.
The first location is the radial gap between the radial key and clevis insert.
A radial key that is Jamed due to loose parts may induce loads in the core barrel, radial keys and reactor pressure vessel during thermal transients.
There is also a potential to violate the minimum core barrel flange to vessel ledge contact load thereby increasing the likelyhood of undesirable flow-induced vibrations.
The second wedging location identified was the gap between the secondary core support and inside vessel head.
If relative motion of the reactor internals and vessel at this location becomes restricted due to interfering loose parts, loads are induced in these components.
In addition there is again the possibility of violating the minimum core barrel flange to vessel ledge load thereby increasing the likelyhood of undesirable flow-induced vibrations.
1.3 POTENTIAL IMPACT TARGETS Along with potential wedging locations for loose parts, possible impact locations were also identified.
Three significant targets were identified as requiring detailed evaluation. These targets are 1)
Core Barrel at Inlet Nozzle 2)
Thermal Shield Flexure 3)
Bottom Mounted Instrumentation Tube Penetrations The three targets identified were evaluated for potential perforation and denting, as well as for overall structural response due to impact loads.
1-4 I
\\
m..~..~~
2.0 INTRODUCTION
POTENTIAL WEDGED PARTS EFFECTS The following analysis was perfonned to assess the consequences of loose parts described in Section 1.1 being wedged at the two locations described in Section 1.2 and shown in Figure 2-1.
In the event that a part or parts becomes wedged during cold shutdown, loads are induced in the core support structures and reactor vessel during plant heatup.
Six areas were identified as the most sensitive for loads caused by wedged parts between the radial key and clevis insert and between the secondary core support and inside vessel bottom head:
1)
The secondary core support structure columns, or the energy absorbers; if yielding of an energy absorber occurs, the energy absorption capability may be reduced below the acceptable levels considered for postulated accidents.
2)
The contact force between the core barrel flange and the reactor vessel ledge; a spring is provided at the core barrel flange and reactor vessel ledge to maintain a compressive force between the core barrel flange and the vessel ledge; if the compressive force is overcome or reduced substantially, (a minimum of 100,000 lbs. is desirable), an undesirable flow induced vibration condition could result.
l l
l 3)
The membrane, shear and bending stresses induced in the reactor l
- vessel.
4)
Yielding of radial keys; a single jammed key also induces stresses in the remaining free keys.
5)
Core barrel stresses and critical buckling load.
6)
The local stresses immediately under the wedged part and the effect on the vessel cladding.
l 2-1 l
I
\\ b >m ni o s
r i!
i F. e.
P 13 N
i
!! W. a plgy %pW/e::..a ji ll N ih m
N gliMIiLii Wir!:iifMlksi li N
s N
ls i
i
/
a
- r
-s.
g
\\'
ls ii!Oililillidillll!!!!:1j.I MS[!$ $H,!b 77;ii;!!!M"L l1 1
4
!ifi i
\\
imimpmth mitmirG]%,e:
+F
~ **
2 ys jj
\\
~
s
\\
b !h h h m K M ll! $ 3 3 IE!I[E L
\\
's TEL mm A
.W1]
J, N_LFa52Stestw eeELe eeEJ F.
'\\
- J3 Lr.3W " VN iiE6119 + viv
" W / v O
\\
WD '
E N
'N 7,
JF- \\
i
\\
)
\\
l f E
( ('-~ N [
b:
\\
t :
l l
\\
N-E j ll l
y is E
l
,e
\\
l( )
d i L E
-YN! L hl
\\
X I; ',s
/
[s l
/ fl
)
l
~
\\
f i
3 sc r
[]
e i
h i,.
N
- V.
s1 et s
i
$f[]' 4f N
\\
I '-
/
s d4: "9 y* k;.{:[7 H
=
3
'l l-L j LOOSE P, i
_.2 s.
y 3
0
]
JAMMED A
(
\\
e
['
j 8
?
i 2
g j
e, g
l3
/
m f
d#
N-F:,-
3 RNN i
s t_
-i
)
_.3
~
vegw a.a
~
t sh SECONDARY CORE GAP - CO LD -
LOOSE PART t
SUPPORT BASE GAP - HOT WEDGE AREA J
PLATE s
Figure 2-1. CWE Reactor Vessel, Lower Internals s
9 s3 c'.
An analytical evaluation program was performed to address the above arens and to detemine heatup rates and pressures to preclude potential damage if parts become wedged.
A five-step program was develoceo as outlined belcw:
1)
Detemine the load-deflection relationship for potential configurations of wedged loose parts.
Since there are quite a number of possible configurations, testing was precluded due to a ccmpressed tire frame.
Conservative load relationships for loose parts were determined by the, analytical method outlined in Section 2.1.
2)
A reactor vessel and internals vertical stiffness model was developed.
The load deflection relationship for the specific wedged parts systems were used in the vertical stiffness model to estimate the loads induced by the :. edged bolts.
The allowable criteria used in the calculations for all cases is as follows:
'a.
No yielding of the energy absorbers is pemitted.
b.
The minimum net contact force between the core barrel flange nd vessel ledge must be at least [
.]i$$,
A reduced minimum value of the preload from the core barrel hold dcwn spring which considers the maasured permanent set in the spring of [
.]$$$hafterthehotfunctionaltestwasusedto i
detemine the existing contact force.
The stiffness model is discussed in Section 2.2.
The analysis to detemine the contact force is discussed in Section 2.6.
3)
A thermal analysis was performed to determine the minimum clearance between the rocctor vessel and core support base plate during heat-up transients and a power increase to 100 percent power.
The analysis and results are presented in Section 2.3.
4)
An analysis was performed to determine the effect of the wedged parts on the stresses in the reacsor vessel.
The analysis is l
l reported in Section 2.5.
l 2-3
5)
Various prcssure conditions and heatup rates betw;cn O'F per hour and 100*F per hour w2re ana!yzed to determine the acceptable combinations of pressure and heatup rate.
The analysis and results are presented in Sections 2.4 and 2.6, respectively.
6)
The summary is presented in Section 2.7.
\\
I 2.1 Determination of Wedoed Loose Part Load-Deflection Relationshios The stiffness of the wedged loose part configuration is an important parameter in the analysis to determine loads induced in the internals and reactor vessel.
The determination of this stiffness is a complex problem involving the prediction of both elastic and plastic behavior of the parts.
The problem is further complicated by the fact that there are numerous parts and they may tend to congregate and fill gaps by stacking up.
Therefore, the following conservative assumption is made in order to simplify this task.
Assumotion (1):
Since the parts are small and cannot sustain ~high loads elastically, they will deform plastically.
Since crush tests are not performed it must be conservatively assumed that the wedged parts sustain their ultimate load carrying capability for the wedging conditions considered.
An ultimate strength of 63.5 ksi is used for all temperatures.
2.1.1 Load-Deflection Relationshio for Wedoed Bolt Head The load deflection curve for the bolt head is determined by calculating its ultimate load capacity for given degrees of deformation.
The bolt head is conservatively idealized as a cylinder with the dimensions shown in l
Figure 2.1-1.
Conservatively assuming that the vessel and internals contact surfaces are rigid, the load deflection curve for the bolt head is developed in the following manner.
l 2-4 1
Assuming that both contact surfaces of the bo'l2 head doform equally,
~' '
the contact area of the bolt head is calculated for varying degrees of deformation (6) as shown in Figure 2.1-2.
6=i[4rf-w3)
(Eq. 2.1) 2 r
B 6=r8 - i[4r2,,2 t 3
(Eq. 2.2) l Solving for w:
w = [4 6(2r8 - 6)3
~
(Eq. 2.3) e 0
l e
4 9
2-5
..~
///////
g '= 15/64 inch r
v.
?P
- 2. = 1 inch 1
1 v
-m///
FIGURE 2.'l-1 IDEALIZED WEDGED BOLT HEAD i
l 6
y y
h
~
v
.2 E3 6
FIGURE 2.1-2 BOLT HEAD WIDTH AND DEFLECTION 2-6
E Since both contact surfaces of the bolt deform equally, the total compression of the bolt, 6, is equal to 23.
The load corresponding B
to this bolt compression is calculated by multiplying the bolt contact area by the ultimate strength of the bolt material.
Therefore, the load-deflection relationship for the bolt head compression is given by Equation 2.4.
g[ ULT [2 (2rB~
)3
=
or 6
P=1 ULT [26 (2r8 - - )]
(Eq. 2.4)
B 2.1.2 Load-Deflection Relationshio for Wedoed Nuts, Washers and Hince Fracments Since an area-deformation relationship determination for these parts is at best extremely complicated, it is assumed that these parts deform plasticly at constant area (constant load).
Again assuming rigid vessel and internals contact surfaces the maximum load due to wedged nuts, washers and hinge fragments is determined for each piece by multiplying its effective area by j
the ultimate strength of 63.5 ksi.
The areas and maximum loads determined for these parts are listed in Table 2.1-1 and the geometries of the wedged parts are shown in Figures 2.1-3 through 2.1-7.
4 2-7
TABLE 2.1-1 EFFECTIVE MAX. LOAD 2
PART SUB-C0f1 FIGURATION AREA (It1 )
(LB)
Nut I (Figure 2.1-5) 0.132 8382 Nut X (Figure 2.1-5) 0.1095 6953 Washer J (Figure 2.1-5) 0.3220 20447 Hinge Fragments B (Figure 2.1-3) 0.3308 21006 G
e s
e 4
I e
i 2-8
I' Su3 - CON AGURATioN A
onE act.T seAo AN D ONE WASWER.
/
///////
()
(. 53,2 i
/ /// //////
I FmAx = 7430 Lb
(.M o r)
Su% - CONFIGURATION 3
WlNGE FEAGM ENTS
//////
Y f
"2 (1) PARTS
//// /
5/4
/ ////
- }
l "r.
( 0 P Ae.T
/ ////
I
/////
[ *z.
(3) PARTS
'/ // //
- Sgg b CONTACT AREA = (1[.'i5 (.oLQl
- C.12.5 ( 042)l
- 3 b k (IG
.3306IN*
.3308 (,63 5co) Lb = 21 cob Lb FMAX Su3-CONFIGURATION C
TWO MUTS i
/ /// / / //////
U 5co H
r
////////////
Fsg = 8 3 8'2. Lb
(. hot) 2-9
EV E - CON FIGUR A
',o M O ONE C C LT
//////////
g O,750 I
////////
Fm Ay, = 1778 tb
\\
SUB - C.ON WlGUR Ai \\ ON E
E l GHT W AsHERS
/////////
a o.Soo y
/////////
FMAx= 20447 Lb SUB - CONflGURATION F
SEVEN WASMEES AN D Two NINGE eqMM:
//////////
d O.Fdo e
?
?
v
/// / // / //
Fmy, i I6733 Lb SUB - CONFIGURATIohl G
TM RE.E NOTS
/////////
[I D
O,750 M
/ // // // //
FMAX
- b3b2= bh EU B - CON FIGU ratio M H
TWO NUTS AND ONE HINGE FRA C, M Z t '~
/ / / / / // //
7 6
TT O. E(.O I
1
/////////
bAX h3h1 Lb 2-10
.e-e..e
- v. c.
v n s., 2 a v.
-v ~ r.. o. v n n.. v m 3
)
uB-coNri s u e ATio N I (si n ta NU-T l
//// / / / / ////
u E+
I
/// ///// /////
d6(lh' b/h # (.50.1R)?_- 3 (.RGY'j IN' CONTACT. AREA 3
7_
1
~. l31 I N Fnn =.132. (635oo3 Lb = 8382 Lb S us - cowisu n Arie 9 J S m G LE.
W h 5 H E R-
// / / / //
$ p' l
////// //
Y ( (%r,
-(.25Y IN
. 3220 IN*
CONTACT AREA 4
FMA%' 20467 lb 9
Sut-coo FeG u n. A rio d K.
5 IM G LE our
//////
a 7 O
/IG
// /////
couw u.E g =
o, 4 3 8 fo I s-) # =
- 0. Io 9 5 2
iu-Fmnw =
6953 u.
2-11
Fec u cir z. I-G e., c.
ras., r sv 3 - m 5. cot. % a L V
.CO rdlf D.Lkr10 9_b k.._[._6{&M__(._.M._.
- 5. n_ c.v.i.v. N. _..:
. I. M...
_ I.. f. ' I l. ~. W.. N.
Y..l.
//-/. *7 '..,.
/
w s..
- /
,cxm F'
?
s
_1 af.
s g
5 5
i
- s i,
i i
i si gu u;.. e
.y
/ i.,e
,a,
M J'b'lf./,LZ_./ /
'~
._ X g-.
,.f
,.. g-.
l t,
i
" "2, ~ 0 0 - -- -- - ' - -
j i y
_ j.
j l _ d k_J I'
) _
i i[ 8 t i '
r i i
l
}.;
.1.l I.v. [ _ J.
'a' f, M.f.
~"~
'-I i~ ; --
' ~ ' ' ' '
.,s
- t..
s I
l/l } -l
.! ! I i $ _ '
's
? i-
\\
i l -- * -
t-- t -
1 i [t
-f - i ik'I
/ i -k i '-
f
~
l
-i -
4--
8
}#! t N*d. I-, [., _,,
.;-_'. / 't.
, j./
1 4 w 1 7.,
g (.f ii. i ' y,
Ar- }
-~
I ' ?- -t T r%$
i_ _4.. _;_.
t i
l e
i i
.1 at,,
y, 4
.. t i 1
i
, g t
~.
1
T t h. " ~. Ql-i T [. i
$ i - $. s '-
}
t i -~
- 1. \\-., f.: a j,,, y : Tf )
u
.2 U
4. { m.-.- _;
F-i - it t 19 i i ;-i 'I ~ l ^ ) i i I._E --
I " '
//
t ;-
'--*i 4 {. j _\\ J. - j j..{. 1_ T. / ]..';V.g..} - J./ t f.
- f
- 4. {...{- ;. t.. :- -.
4
{...j W,' VQ j...{ --a,'; ' i'*
y..
- 7.., 4
\\ j iH tM I t e -i -t
/g
- ggp i :
i 1 t i -i
~L l
l l'i P --! / -
t-Y--i- + -i--t
-i -
f 2
i
- .. : _. - q : ;.,
- .;_ _ y_f..
_4
. _..._.._4
_2__..
...; 4
. _ g _
.2 c-
- Q.
=..g g p. ;. g.
. _ y _.
2 0X
.p 4
g e
e g,
g g
\\
\\.P. - -.;-; _-p.,
l.
i 70 P-i T7 f.i. J -i=F -4 Mcki.i# NLMc s in c rr-: ~ b. ; si sstiriB i.3 E s..
t
' s e
e a
s 4
i i f
I 2-12 i
s u u -s
- 2. t - T Lo a s t.
Yhe-:
S v2 -cou mcv m oas M-O SUB
.C.ou_Ei6 uanr_o.i>
M s
_._ N _ A. N \\ N.A __N. A.... :._ __.
^ ~ ~--_.-.1.?
' ~ l -._....
/4A ll - I
'~
~ ~ ~
- 3.
. ;a R
-.- - n H.EI6M = ~ Q.82 6
./cs
- .. d...
[
}.
L
.. 2,;.
.tsj(4
-- q i/ /
/ /
//
l/
F 933.y Lb i ns M-c.oN Fi c-iU R AT I O N N
SINGLE WASH ER
////////////,
ye t
~
sy Ife F
'////////////
4 CONTAC.T AREA ' ( I6 - 4)( Yb) IN*
0.02.73 is t
bu =.o2.73 (63,500) Lb. = 1734 lb (hot)
S V3 - codF Gu e.M7o9 O
S/9cLC 30L.r REA2
//////
v o
\\ J
////// /
^
I.qn 2-13
2.2 REACTOR VESSEL AND TNTERNALS STIFFNESS MODEL 2.2.1 Introduction The vertical stiffness model for the vessel / internals is implemented to determine forces and deformations resulting from bolts wedged between the secondary core support pla'te and vessel bottom head.
The spring model includes the cross-sectional stiffnesses of the various sections of the reactor vessel and lower internals.
Table 2.2-1 tabulates the spring constant values of each component included in the mathematical model.
The calculated spring quantities are known from previous work performed for Consolidated Edison in support of the loose part in the IPP-II reactor vessel in March 1978.II )
?
2.2.2 Stiffness Analysis The a'ssumption used to determine the stiffness of each sub-component of the reactor vessel and'internais is described in Reference 30.
The numerical values of the various springs are tabulated in Table 2.2-1.
The values in Table 2.2-l'are for 70*F and must be corrected for the actual average temperature assdciated with each transient or steady state condition analyzed.
The correction factor to be multiplied by each spring is the ratio of the modulus of elasticity at the average component temperature (through the component thickness) to the modulus of elasticity at 70 F.
Section 2.3 provides the average temperature distribution for the vessel and internals for various transient and steady-state temperature conditions.
Thus, in the analysis, the spring constants are variables that depend on the temperature condition being analyzed.
2-14
Table 2.2-1 VERTICAL SPRING CONSTANTS Element Descriotion K
Vessel a., s k
Nozzle shell course n
k Vessel shell course s
kh Vessel head Internals kcbf Core barrel flange kcbw Core barrel shell klsp1 Lower support plate (one absorber acting) k isp4 Lower support plate (four absorbers acting) k ac Energy absorber cylinder, e
Housing, and Guide Post k
Energy absorber Ligament ear k
Base Plate eap Bolt Systems KSB Bolt and local stiffness of base plate, vessel, and vessel clad as a system Refer to Figures 2.2-2 and 2.2-3 for correlation to actual parts.
0583E:1 l
2-15
Figure 2.2-1 and 2 show the spring system of the reactor vessel and internals, and the load paths asso,ciateo with a wedged bolt.
As snown, a compression load path exists in the reactor internals, and a tension load path exists in the reactor vessel (the stiffness calculations incluci shear ano bending distortions as appropriate in the vessel head, and other components in the load paths).
As shown on figure 2.2-1 the tension load path is comprised of the vessel barrel and the lower spherical head.
The vessel load path is comprised of three springs.
System Stiffness of Vessel
. t,b y
y
- y
}"
K 1/(k 3y k
k n
s h
(cold)
Corrected for lower modulus at 550*F,
_. L,b sv "
(hot)-
The upper internals load path can be viewed as consisting of two regions:
the upper internals structure load path, or the portion above the core support casting; and the lower support load path region, or the. portion below the core support cast %g.
Each region is discussed separately.
System Stiffness Above Lower Core Support Castina.
The upper load path region consists of two parallel load paths as shown on figure 2.2-1.
The load path indicated by a dashed line, composed of the fuel assemblies, and upper internals structure, has been shown by previous analysis to have a spring rate much less than the load path indicated by a solid line on figure 2.2-1, and has been neglected in the analysis.
The spring rate for OS83E:1 2-16
tho upper barrel region is th::n compriseo of the load path shown by a solio line in figure 2.2-1, and is given by:
Ky - 1/( k
)
k cbw cbf System Stiffness Below the Core Barrel The-spring system below the casting consists of three elements:
the core support casting; the energy absorber cylinders and the energy absorbers.
The spring rate varies and is dependent on the number of absorbers that are acting.
For four (4) absorbers the value is:
1 Kg 1/ ( g
=
+
k
- (
), and 1sp4 eac ear For one (1) energy absorber the value is:
K2" II(k
)
+
k 3
1spl where:
k3=k4+k5 k4 1/ ( k
)
=
k eac ear I
1 k5 1/ (2k
)
=
+
k
_4 eap Refer to Figure 2.2-3.
The overall system stiffness of lower internals is; fg K37 -
1jg 1j 2
For four (4) absorbers acting the overall system stiffness is:
_. a#
KSI =
- and, (cold)
_%b K37 -
(hot) 2-17
For one (1) absorber acting, the overall system stiffness of low:r internals is:
_ s.s K31=
- and, (cold)
K37 =
(hot)
Figure 2.2-3 shows the idealized final spring model for the system.
In the model, KSB is the stiffness for the wedged part system: and SBV " 1/K IIE SB SV The value 6 is the potential interference with the part.
o is the part p
p height, minus the gap between the reactor vessel and the lower support base plate calculated for each temperature and pressure condition evaluated.
Section 2.4 discusses the calculatica for 6 p.
Using the fact that the force (F) acting on the springs, K and 37 K33y, must be equal and opposite forces, and that 1 + A, then; o
-a 2
p F
F 3p" KSI kBV F = 6 / ( "1
)
1 P
+
^SBV Substituting the previously stated relationship for K in terms of K SBV SB and K results in 3y I
1 1
F-6/ (K
)
+
K K
Thus, the force (F) acting on the internals and the vessel can be simply evaluated for a specific value of h, the potential interference, and for a specified value KSB, the stiffness of the wedged part system.
The load deflection curve, as discussed in Section 2.1 is non-linear, and the appropriate value of K is initially unknown.
An iterative procedure is employed to SB datermine the appropriate value of K and the resulting force induced in the SB system for a specified 6.
p 2.2.3 Summary A comprehensive spring model was developed that considers the stiffness of the individual structural elements in the load path for the internals and vessel for forces induced by a wedged bolt.
The stiffness of the vessel structure elements arid internals structural elements are corrected for the average temperature for each thermal condition analyzed.
An iterative procedure is employed to account for the non-linear load-daflection curve of the wedged part system.
The force induced in the reactor vessel and the internals is determined for the potential interference that exists with the parts for any specific thermal and pressure condition.
The calculation of the potential interference that exists with the parts for any specific thermal and pressure condition (part height minus the gap between ths vessel and the lower core support base plate) is discussed in Section 2.4.
The forces calculated for various temperature and pressure conditions are discussed in Section 2.6.
2-19
COMPRESSION LOAD PATH OF THE FUEL ASSEMBLlES ANO UPPER INTERNALS IS NEGLECTED.
A
,d L.
A a
A 4%7 r}
3%
a h
b
% COMPRESSION LOAO y
k r
I PATH IN LOWER
\\
s 3
j p
INTERNALS Ag g
eld aw l
--+
t i
1F i l b
^h Y
Y j
k 3('
1 I
i CORE / UPPER TENSION g r1
~, a i; J,-
INTERNALS r,=
ms
,i
}
h oAo P 7H 1 P 4...9@
l g,g,
~
m m{!
4 g, g
--, 7 g g
!40 WiW R jr_)
p
\\.r a n
):
~
- :/
LOWER INTERNALS u p; c
l LOAD PATH ia i g L p,e s[.q J
REGION g
f x
l LOAD j
f.)
t' J p PATH L
NWg 6
s X /2 i
BASE PLATE WEDGED BOLTS FIGURE 2.2-1 LOAD PATH IN LOWER INTERNALS FROM WEDGED BOLTS 2-20
~
em
- 1) DIMENSIONS ARE USED IN CALCULATING AXIAL AL OF VESSEL DUE TO OPERATING PRESSURE-IN INCHES.
- 2) DIMENSIONS ARE USED IN CALCULATIONS FOR AXIAL THERMAL EXPANSION-IN INCHES.
Figure 2.2-2 Core Barrel Assembly-Vessel Mathematical Model (Four Energy Absorb,ers Under Load) 2-21
-.e
-w
u q) l i
e
- 1) DIMENSIONS ARE USED IN CALCULATING AXIAL AL OF VESSEL DUE TO OPERATING PRESSURE-IN INCHES.
- 2) DIMENSIONS ARE USED IN CALCULATIONS FOR AXIAL THERMAL EXPANSION-IN INCHES.
Figure 2.2-3 Core Barrel Assembly-Vessel Mathematical Model (One Energy Absorber Under Load) 2-22
19,178-34
. ~ sb Figure 2.2-4 Vertical Stiffness Model of Internals, Wedged Part, Vessel System 2-23
2.3 THERMAL ANALYSIS FOR TRANSIENT TEMPERATURE CONDITIONS An important parameter in the analysis is the relative growth that takes place between the reactor internals, (core barrel, support structure, etc) and the reactor vessel during temperature changes.
As shown on figure 2-1, the significant relative growth is that which takes place between the core barrel support ledge and the bottom of the vessel.
As shown on Figure 2.2-2, the core barrel is essentially a cylinder with an approximate thickness of 2.25 inches for its significant length and the reactor vessel is composed of three areas:
1) the bottom head which is 5.5 inches thick; 2) the cylinder below the inlet and outlet nozzles which is 9 inches thick; and 3) the cylinder above the nozzles which is 11.0 inches thick.
In addition, the core barrel is 304 stainless steel, while the reactor vessel is carbon steel.
Because of the differences in the thicknesses and the difference in material, the average temperature in the reactor vessel will always be lower than the core barrel during transient heat-up conditions.
Thus, the gap between the lower core support structure and the bottom reactor vessel head will be smaller during transient heat-up conditice,s, than during steady state conditions.
A thermal analysis was performed to estimate the average temperature difference between the core barrel and the reactor vessel to conservatively predict the minimum gap between the core support and vessel dur.ing the heat-up transients.
2-24 0583E:1
)
2.3.1 ANALYSIS MODELS - THERMAL Figure 2.2-2 shows the actual core barrel and reactor vessel configuration The core barrel is essentially a cylinder of constant thickness equal to 2.25 inches from the core barrel support ledge to the top of the core carrel support keys.
Below the support keys, the core support structure and core barrel is composed of materials of various thicknesses, which are greater than 2.25 inches.
Therefore, assuming that these lower structures are all 2.25 inch thick will over predict the internals average temperature, which in turn will conservatively over predict the closure of the gap between the vessel and internals structure during the transient.
The models considered in the thermal analysis are shown in Table 2.3-1.
As indicated in Table 2.3-1, an analysis was performed for each of the reactor vessel thicknesses.
Table 2.3-1 THERMAL MODELS COMPONENT INNER RADIUS (INCHES)
WALL THICKNESS (INCHES)
Reactor Vessel 86.5 5.5, 9.0, 11.0 (Carbon Steel)
Core Barrel 74.5 2.25 (Stainless Steel)
One-dimensional thermal models, using the WECAN(4 ) computer program were used to obtain the reactor vessel and core barrel radial temperature distribution during the transient heat-up conditions.
Each model consists of 10 elements through the wall thickness to estimate the radial temperature distribution.
A post processor, a modified version of ATEW35, was used to convert the radial temperature distribution into an average temperature.
ATEW 35 computes a weighted average, where the weighting function accounts for the increase in area associated with the increased radius of each of the 10 elements through the vessel thickness.
The one-dimensional thermal mooels correspono to assuming that the reactor coolant temperature is constant along the axis of the reactor vessel.
0583E:1 2-25
~
The heatup is from an initial temperature of 70*F to a final temperature of i
550*F.
Haatup rates ranging from 20*F/hr to 100*F/hr were consicereo.
A heat 2
transfer ccefficient, (h), of 3000 BTU /hr-ft _.F was applied to the ID of the reactor vessel and the OD of the core barrel.
At the ID surface of the 2
core barrel, a "h" of 500 BTU /hr-f t _.F was applieo.
The lower "h" for the 10 of the core barrel is a result of the lower coolant flow rate at the inside surf ace.
The OD surface of the reactor vessel was assumed to be adiabatic.
As subsequently discussed in Section 2.3.2, the data obtained for the heat-up from 70*F to 550*F can be used directly to obtain the temperature differences for a heat-up of 70*F to 350*F and 70*F to 450*F.
2.3.2 TEMPERATURE DISTRIBUTION FOR HEAT-UP TRANSIENTS The maximum temperature difference between the reactor vessel and the core barrel occurs at the end of the heat-up ramp when the coolant fluid temperature just reaches the 550*F temperature.
Figures 2.3-1 through 2.3-5 show the temperature time histories for the three reactor vessel thicknesses and the core barrel, for heatup rates of 20*F/hr, 30*F/hr, 50*F/hr, 80*F/hr and 100*F/hr, respectively.
The maximum temperature lag for heat-up to 550*F for the various thicknesses as a function of heat-up rate are shown on Figure 2.3-6.
As seen on Figure 2.3-6, the temperature lag as a function of heat-up rate can ba approximated as a straight line that intersects the temperature axis at 550*F for each thickness.
Therefore, the temperature lag for each thickness, for any heat-up rate can be read directly fron Figure 2.3-6.
As previously discussed, the maximura temperature lag for each thickness occurs at the end of the heat-up transient, when the fluid temperature just reaches its steady state condition.
The calculations were performed for a steady state temperature of 550*F; however, the temperature lags for lower steady state conditions can be read directly from Figures 2.3-1 through 2.3-5.
The appropriate temperature for each of the thicknesses is the temperature at the time when the fluid just reaches the desired steady state temperature less than 550*F.
See Figures 2.3-1 through 2.3-5.
0583E:1 2-26
N
\\
x m
Two other intermediate steady state conditions were also evaluated.
They are:
70*F to 350*F and 70*F to 450*F.
For both of these conditions, the temperature lag for each thickness versus rate of heat-up were developed.
The curves for the two conditions are shown on Figure 2.3-7 for the 70*F to 450*F condition, and on Figure 2.3-8 for the 70*F to 350*F condition.
The average temperature for each thickness of the reactor vessel, ano for the core barrel (internals) from Figures 2.3-6, 2.3-7 and 2.3-8 are used in the subsequent analysis to determine the relative thermal growth of the reactor vessel and core barrel (internals) for the various heat-up rates considered in this study.
2.3.3 STEADY STATE TEMPERATURE DISTRIBUTION FOR VARIOUS LEVELS OF POWER During increases in power levels, the outlet temperature (hot leg) and the inlet temperature (cold leg) are assumed to have a linear variation with the power level as shown on Figure 2.3-9.
The hot leg temperature (THL) and the cold leg temperature (TCL) at any power level can be calculated from P
THL - TH + TOU (THL,100 - T ); and, g
TCL " H 100 (TCL,100 - T ); and, H
THL + TCL TAVG "
2 The reactor vessel and internals are separated into three regions for the purpose of evaluating the average temperature in the internals.
The three regions, as shown on Figure 2.3-10 are:
1) upper barrel region; 2) middle barrel region; and 3) the lower core support assembly region.
0583E:1 2-27
The entire reactor vessel and the lower cora support assembly will tend to follow the colo leg temperature curing power increases.
Thus, the average temperature for the reactor vessel and lower support assembly is T1-TCL The upper core barrel is exposed to both the hot leg and cold leg fluid.
Therefore the upper barrel temperature (T ) will tend to be the average 2
temperature of the hot leg and cold leg, or T2-TAVG The middle core barrel is also exposed to both the hot leg and cold leg temperatures.
However, in the middle barrel region, there is a significant amount of gamma heating which raises the average middle barrel temperature by 35 degrees above the inlet temperature at one hundred percent power.
The middle barrel temperature at any power level is determined by proportioning the 35 degree increase at 100 percent power and the level of power (i.e. the average tsmperatures of the middle barrel at 10 percent power is 3.5 degrees above the inlet temperature).
The size of the gap between the secondary core support and thes inside vessel head is plotted as a function of power level at various pressures in Figure 2.4-2.
C l
0583E:1 2-28
. u.
ab l
E t
m e3 E
w 4.Iw
, D'=
wc mw>4 I
i i.
1
(
l
\\
t,
' TIME (HOURS) l l
l Figure 2.3-1 Thermal Response to 100 Degree Per Hour Heatup Transient 2-29 1
n -
t 10,178-42 e
i I
I l
Co
~
weC8>
c.
35
- E w
3O Z
w e
o D
8 o
a I
- Q
~
u8 o
2 W
P
.o
=
S e
Oh o
E
~5 Eu.c>
N t
M.
N 8
3 O.
L I
I l
Lio) HunivusdW313DvusAv 2-30 m___
6
- a.
C m
e "l1 W<
m m
IlL.2m i
TIME (HOURS)
Figure 2.3-3 Thermal Response to 50 Degree Per Hour Heatup Transient I
2-31
l
. _.c
-a e
C o_.
m C
3 m
Wa.2m wc<cw>
TIME (HOURS)
Figure 2.3-4 Thermal Response to 30 Degree Per Hour Heatup Transient 2-32
N E
. ?
mz3&<z w
A2m wc<zw><
~
~
TIME (HOURS)
Figure 2.3-5 Thermal Response to 20 Degree Per Hour Heatup Transient 2-33 O
.n
- mm
l T
~
en I
i i
=
e i
C m
CU m
W Q.2m H
w C<
at:w><
+
HEATUP RATE ( F/ HOUR)
Figure 2.3-6 4L Heatup Transient Temperatures at End of Heatup Ramp When C8/RV AT Occurs (70 F to 550 F) yg 2-34
ch C
W m
3 z
Es W
>=
W0<z W><
I
~
HEATUP RATE (*F/ HOUR)
Figure 2.3-7 4L Hectup Transient Temperature at End of Heatup Ramp When C8/RV AT Occurs (70 F to 450 F) ygx 2-35
.1 s,1 %n
/
=
=am C
Wmo.
p<
m W
Q.2mH W
0<
mw><
i HEATUP RATE (*F/ HOUR)
Figure 2.3-8 4L Hestup Transient Temperatures at End of Heatup Ramp When CB/RV aT Occurs (70 F to 350 F) s3gx 2-3G
/
~
..,/
4 Tat,1M
\\
T TEMP-HL Tg = HOT STANDBY TEMP.
l THL = HOT LEG TEMP.
T T
TCL = COLD LEG TEMP.
H CL I
l
--TCL,1CC g
I i
0 10%
100%
POWER (P) o Figure 2.3-9 Temperature versus Power Relationship 2-37
-s m
, as e
t 3
Sigure 2.3-10 Temperature Zones in Lower Intemals and Vessel are Given for 10% Power 2-38
2.4 Analysis to Predict Gao for Various Temaerature - pressure Canditions The gap between the secondary core support base plate and vessei bottcm head is in part based on relative growth that has taken place between the lower internals and reactor vessel during heat-up changes.
As shown on Figure 2.2-1 and 2, only the growth which takes place between :the core barrel vessel support ledge and the bottom of the vessel head is significant.
The magnitude of the gap is also a result of the operating pressure applied to the vessel wall and bottom vessel head.
The potential interference needed for the analysis discussed in Section 2.2, is the difference between the part height and the gap determined for each te.mera-ture and pressure condition.
After the gap and the potential interference are deter-- ::
the force applied at the vessel ledge, energy abosrbers, and bottom vessel head are calculated us1ng the stiffnesses determined in Sections 2.1 and 2.2.
The as-built readings recorded prior to hot functional test between the secondary core support base plate and reactor vessel gave a minimum gap of 1.030 inches.
These readings were taken prior to the addition of the fuel.
An analysis was performed to determine the reduction in the gap (additional extension of the core barrel assembly frcm the vessel ledge) due to the added buoyant weight of the fuel.
The analysis consists of loading t..e spring model shcwn en Figure 2.2-1 and 2 with the appropriate fuel weight.
The calculated i 'duced cold gap is [
.]a, b inches.
l 2-39
-.ece
. e mee..e..
e..~ -
2.4.1 RELATIVE THERMAL EXPANSION The differential thermal growth for the vessel and lower internals from the core barrel flange vessel ledge def.ines the reduced thermal gap as follows:
AL = aLy - AL2 ~ Al3 - 4'4 - Reduction in gap due to thermal condition alt = ay 1 (T1 - 70)
L 2"
2'2 (T2 - 70)
' AL AL3 " "3'3 (T3 - 70)
AL4=aL4 4 (T4 - 70) where AL y length of lower internals measured from the vessel ledge to
=
the bottom of the lower support structure (see figure 2.2-2)
T1 Indicated average temperatures of the internals structure
=
obtained from section 2.3.2 during heat-up transient conditions.
AL A'3^l4 - Refer to figure 2.2-2 for the appropriate lengths.
2 T
4 Indicated temperatures of the vessel obtained from section 2.3.2 during heat-up transient conditions.
aj Appropriate mean coefficient of thermal expansion
=
(Reference ASME code section III Appendix, 1977 Edition) from 70*F to indicated average temperature l
l t
l 0583E:1 2-40
In tha case of an increase to the 10 pcreent power. level, AL is given by 1
i = a1 1(T -70') + a2 2(T -70*) + a3 3(T -70*)
al 8
8 0
1 2
3 where T,T,T '0,8,8, are defined on figure 2-25, and 1
2 3 1 2 3 at,a2 and a3 are defined the same as a$
The actual values of, a, vary by approximately plus or minus 3 to 4 percent from the nominal thermal coefficient for a given material type.
In the present analysis, the magnitude of variation can have a significant effect on the estimated force induced by a wedged part.
In this analysis, a conservative approach was used.
The reactor internals are assumed to have an that results in the largest growth; while the reactor vessel is assumed to a,
have an a, that results in its smallest growth; thus, the analysis predicts the " absolute" minimum gap for the range of a.
A statistical approach, (eg.
using the SRSS method) would predict a more realistic and larger gap for each temperature condition.
2.4.2 PRESSURE EXPANSION i
The Vessel extension due to pressure was calculated in accordance with the formulation in Roark's Formulae For Stress and Strain, Table XIII, Cases 1 and 2, 3rd Ed., p. 268 as 2
a)
.7PR
' head " W b)
.2PRL 8 cyl(i) "
Et i The total expansion is then; Sr total 8 head + 'cyl(l) + 8 cyl(2) 5 cyl(3)
+
0583E:1 2-41
where:
P operating or heat-up transient pressure, psia
=
R Mean Radius of vessel or bottom vessel head, inches
=
L4=
Lan9%, of vessel of a specified thickness (figure 2.242),(in)
E,E =
tiodulus of elasticity, psi, correcteo for average g
temperature for cylinder length L, and the mcdulus of j
elasticity for the head.
t,t =
Vessel thickness, inches, for a given length of cylincer (see Figure 2.2-2) or the head thickness.
i segment nuir.ber of cylinder of length Lj and thickness
=
i 2.4.3' GAP SIZE COMSIDERING THIR!al GROWTH AND PRESSURE The final gap for any temperature or pressure is then given by e
-%h Gap =([
- til + cr) inches
+
i 0583E:1 2-42
Facu ex_ z. 4 - 1 G AP 512.t vs. HEAR ue RhTv 7,m s
O 9
O e
i 1
i 1
i t
'a 2-43
.t
Fl o u s.s.
2.+-2.
GAe s sa v5 pg g,. t w t Power
)
mi F
I d
I s
e B
e m
?-44
~
....-..-.~.._~.+s/
"~
2.5 Ooeratinq varcins The main areas of concern due to the lead transmitted by the wedging action of parts are:
1)
Hold down spring margin at the vessel ledge, 2)
Energy absorber yield strength margin, 3)
Vessel ' stress margins, 4)
Radial key yield strength margin, 5)
Core barrel yield and buckling margins.
2.5.1 Hold Down Soring Marcin (Uolift Resistance)
__ a,3b p.
The permanent set of CWE hold down springs was measured to be L and the preload of the 304 SS hold down spring is a., s lbs. (hot)..
From static equilibrium of vertical mechanical and hydraulic forces in the lower internals, the reaction, R, at the vessel ledge during normal' y
operation is given as, R
=F
+F
+ F,g - F (See Figure 2.5-1) y s
L
(+)Down
(-)Up where a,b F
= core barrel hold down spring force - lbsf=[
]
(hot)
F core reaction force on the lower core plates lbs and transmitted i
c f
down to lower core support plate l
2-45
The core reaction force, F, is calculated at a minimum value, in c
order to obtain a conservative hold down saring cargin.
Refer to Figure 2.5-1 Fc3-Fc4 I (nin) = Fc2 + Fc1(nin) c Where:
cl = Fuel Assembly spring Load (min at BOL)-lbsf F
Fc2 = Fuel Assembly weight-lbsf due to the drag force c3 = Fuel Assembly Lift Force-lbs F
f of the reactor coolant ficw c4 = Fuel Assembly buoyancy-lbs F
f
_ ab lbs F (nin)
- 7 e
ab 7
F = L wer internals weight (wet) - lbs =
lbsf u
1 i = Lower Internals Hydraulic (drag due to recctor coolant flow) li f t force - lbsf=
]au lb sf (up) on the icwer core plate
- Thus, ab 1bsf R
n y
an If a minirr;a value of lbs is naintained as margin against uncercaf ng, the reserve centact force at the vessel icdge becomes
- ab lbsf R
=
y Thus the induced load by the wedged parts must not exceed the above reserve contact force.
2-46
[ LOWER INTERNALS
,Fg l
W
/&
VESSEL UPPER CORE PLATE LEDGE RV fjff fjpp pp
- l l*
- UPPER FUEL
'F r-.l b..- - ---- - b. [
INTERNALS ASSY Y
o al si l
~
P FC (MIN) ;
l F
F F
a g
l
_l I/t k/t//
s
" li il
~~ p LOWER CORE lr
.3 "l
- l E
fl V
PLATE t
l C(MIN) 9 STATIC EQUILIBRIUM OF FUEL 3,
y
_ASSY FORCE COMPONENTS E
W WHERE:
F g
Fc gygyp = Fm+Fcy - Fcg - Fy STATIC EQUluBRIUM OF LOWER INTERNALS C(MIN) = MINIMUM FUEL ASSY F
VERTICAL MECHANICAL AND HYDRAULIC REACTION FORCE ON FORCE COMPONENTS LOWER CORE PLATE -
LBS.
WHEREj p
Ry=F3+Fw+FC (MIN)
- EL d = FUEL ASSY SPRING FORCE
~
Ry = MIN REACTION FORCE AT VESSEL C2
- N # N O N LEDGE - LBS.
F
- MIN HOLD DOWN SPRING FORCE -L83.
3
~
L F
= MIN FUEL ASSY RUGON FORCE -W.
C
~
(TRANSMITTED FROM LOWER CORE PLATE)
~
E W = LOWER INTERNALS SUOYANT WElGHT-LBS.
F
= LOWER INTERNALS HYD. LIFT FORCE-L88.
g FIGURE 2.5-1 VERTICAL MECHANICAL AND HYDRAULIC FORCE COMPO LOWER INTERNALS gn
2.5.2 ENERG;( IB ORSER YIEllD STRENGTH l%RGIH
'An analysis was performed which shows that maintaining the load on the
, 2 absorber belcw l lbs does not cause yielding of the absorber; and : 2 relaxation effects at temperature, caused by a deflection controlled 1c: 0, will not reduce the energy absorption capability belcw acceptable margins.
Even though it is believed that additional analysis would shcw that the absorber could be plastically deformed in excess of 0.1 inches without adversely affecting its energy absorption capability,, the load induced in 15?
energy absorber, due to wedging, is conservativaly limited to less ',han
>a
[]
lbs., to prevent plastic deformation.
1 2.5.3 Vessel Marcins, The stresses induced in the reactor pressure vessel by loads due to wedged loose parts were evaluated.
2.5.3.1 Vessel Battem Head Marcin A conservative vessel load was calculated assuming that all loose parts
, a.,.
beccme wedged at this location.
The maximum postulated load of Ikiss
]a,s
-4 wasassumadtobeactingoverabearingareaof[
square inches.
The calculated maximum membrane stress intensity due to wedged part and norral operating loads is 24,543 psi, which ccmpares favorably with tha ASME code allowable of(1.5 S ) 40,050 psi.
m l
The calculated maximum primary plus secondary membrane plus bending stress intensity under the load is 45,525 psi, which compares favorably with the ccde allcwable of (3 S ) 80,100 psi.
m l
2-4S
f
- -- ~'/
The local Hert;: contact stresses between the wedged part and the vessel cladding exceed the yield strength of the clad and some indenture will occur.
Of all possible loose parts, the threaded portion of a bolt has the greatest potential for clad indentation due to the sharp corners of the threads.
Assuming that a bolt head could be broken off from the bolt body, the bolt threads could be wedged against the vessel cladding.
Conservatively assuming that the bolt is rigid, the maximum depth of indentation expected would be equal to the height of the thread profile.
For 1-20 UNC external threads this height is equal to 0.031 inches.
The minimum clad thickness of the CWE vessel
- a., u is inch.
The minimum clad thickness minus the maximum expected ind nture is equal to the present minimum required cladding thickness of inch.
Therefore, the clad indentation which might be expected -
g due to wedged loose parts is acceptable.
2.5.3.2 yessel Core Block Marcin The loads for which the vessel was evaluated in this case were a a.>
- a., a radial load of
,kipsandanaxi.a.1loadofi
_ kips, the same loadr used for the radial key evaluation.
The stresses due to the wedged parts loads were combined with the normal operating stresses and were shown to meet the ASME code requirements for stress intensity.
2.5.4 Radial Key Yield Strenoth Marcin The bottom of the icwer internals assembly is restrained laterally by si: uniformly spaced key (304 SS) which are mounted cn pads on the lower support casting.
The keyways are counted on pads on the reactor vessel.
Each key is 5.0 inch wide and has a nominal contact area with its keyway of 2.2 by 15.0 in.
They side faces of keys are hardened by weld depositing Stellite No. 6 Alloy., The
-9 ncminal total cold clearance of each key in the keyway is in.
The keys are press fit laterally into a recess in the mounting pad on 1
the core support casting.
There are eight 0.875" dia. type 316 cold-worked stainless steel shear pins designed to take additional vertical loads and each key is clamped to the core support by ten l
2-M
1.250-7-UNC type 316 cold-worked stainless steel cap screws.
2.5.4.1 Loads From Jammine the Key The stresses in the radial key are calculated for the loads due to 26 bolt heads jaa:ted in the radial gap between the key face and the clevis insert.
It is conservatively assumed that the bolt neads beccme wedged cold and are crushed due to relative thermal expansion of the internals and vessel during plant heat up.
Since the lower internals and lower vessel are at the inlet temperature during heat up, the relative radial expansion is due only to the different coef-ficients of thermal expansion of the internals and vessel.
The calculated relative radial thermal expansion of the vessel and
]n.,u internals is[
inches.
Conservatively assuming that the lower support structure and vessel are rigid, the radial load g
in'duced in the key is calculated for a bolt deformation of[
inches using equation (2.4) frca Secticn 2.1.
The resultant radial
_ a., s load in the key is equal to kip,s.
Since the relative axial expansion of the vessel and internals is approximately 0.500 inches, either the jammed bolts must slip or be at their maximum shear load capacity.
Conservatively assuming the latter, the axial load in the key +is calculated to be equal to a
7 one half of the radial load, or
, kips.
u 2.5.4.2 Model and Analysis i
The radial key as shown in Figure 2.5-2 is modelad as a short built-in beam, its dimensions is conservatively calculated in Figure 2.5-2C.
The major concern is in the root of the key.
[%b a) tangentialload=[
lb f
-Nb
= 450 psi
=
_ a.,b
~
vc 1220 psi p
=
e
=
=
x
'z:
,g
FIGURE 2.5-2 RADIAL XEY AND ITS MODEL Nb
'e S
1 1
\\
\\
\\
\\
DEED 2-51
adjusted by stress concentration. factor of 1.3 [ 2 ]
ex 1220 x 1.3 = 2370 psi o
=
x b)
Radial load =
lbf (ccmpressive) a., b 1560 psi o
=
=
x
_%b c)
Axial load lb
=
f
_ s,b 773 psi T
xZ
_~
_ a., s
~
e
=
x
= 952 psi The maximum stress intensity produced is 5,200 psi.
In view of this relatively small magnitude and duration of this stress, safety is not a concern.
The next consideration is en the shear pins.
Since the majority of vertical leads are taken by the frictional capacity in the press ns o
fit, approximately lb-
,w r, very little load is on the shear pins.
Theverticalload,[.
_ lb, small in ccmparison with lb,
a., s f
to make the press-fit asse.Tbly to slip.
Thus, no safety probicm in the shear pins.
2.5.5 Cera Barral Marcin The major concern on the core barrel is the compressive stresses created when one of the radial keys is jammed by the loose parts and, thus, axial thermal expansion of the core barrel is constrained during heat up.
s 2-52
-2.5.5.1 Core Barrel Bucklina Marcin The portion of the core barrel affectec by the jsmming of the radial key is conservatively modeled as shown in. Figure 2.5-3.
Frca [ 2 2, the buckling stress is given by h
1 y2
[(12(1-W)(f) + (f) 3 +(f) a
=
Substituting gives 610,000 psi o
=
Compressive stresses in core barrel a, s 1,840 psi o-
=
=
Thus, the margin for buckling is very large.
G 2-53 J
23h I
l FIGURE 2.5-3 CORE BARREL EFFECTIVE REGION 2-59
.... _ / ~
~
m.
2.505.2 Core Barrel Flange Lifting Margin Due to the worst possible jar = ting of loose parts on one radial key, an adoitionai a,s upward lifting force, F '
- lb., could act on the core barrel flange.
u Sinceaminimumvalueof[
]Ibsshouldbemaintainedas'amarginagainst uncertainty, and the additional uplifting force is acting on part of the core barrel flange.
The equation is rewritten as:
R F
+
+F t) ~
2 et 2n t s
w c
~
where t = thickness in the radial direction of the spring-core barrel flange contact area.
t = length of are that uplifting force is acting r = radius of core barrel
_ Nb The criteria is that R Assuming, 1, the length of the arc equals y
to the length of the support casting which radial key is mounted on plus the length of arc 15 radiated frca the side of the casting, shown in the folicwing schematic drawing, on each side:
. a, b
,ag i c-
+2x x tan 15
? 196.8" which corresponds to
%h radians 2-53
, _/ '
~ ' - -
Simolify the above equation and substitute appropriate values.
2, R
F
+F
+p
_y r
~
y s
W c
u 2,55 u
_ a., b a
~
_Nb 114,770 >
=
Thus, the induced load by the janmed loose part does not exceed the above reserve contact force.
A N
edge of core bar l
l' I'Y1 f bll$:t:.T v>ilh V $ 0. {,
l Ir C 0Ye-ta j
- Satrel, n-)
II t I
1,m
.g I
/u 4
I
~
l I
k Yad.l. d 3
- v. 3
[
p Scherr.atic drawing of portion of the core barre 7 jar:ning acted upon.
0 2-56 a
2.6 Results of Wedged Part Analysis The results of the analysis to predict the effects of loose parts wecged at the. two postulated locations are summarized in this section.
2.6.1 Parts Wedged in Lcwer Radial Succort The analysis in the preceding-sections determined that the case of 26 bolts wedged in a single radial key-clevis insert gap was not critical for any of the concerns listed in Section 2.0.
2.6.2 Parts Wadced Beneath Secondary Core Succort Due to the potentially complicated gecmetry of icose parts configuration:
in'this location a more detailed study is required.
The gap sizes at this location are presented for various heatup rates and pressures in Figure 2.4-1.
Likewise, the gaps for various levels of power and pressures are presented in Figures 2.4-2.
Induced leads for varicus levels of potential loose part inter -
ference may be calculated using the stiffnesses of the icose parts as determined in Section 2.1 and the reactor internals and vessel system datermined in Section 2.2.
In order to facilitate this lo;d calculation, plots of potantial ctrt interference versus icad are made for 26 icdged bolt heads with varying constant v:cdging lord componencs.
This constant load ccm.:cnant is the total load induced by wadged parts other than bolt heads.
Thus for any loose part configuration and gap size, the potential induced load is found by calculating the constant load due to interfering nuts, washers and hinge fragments and then applying Figures 2.6-1 througn 2.5-3 for the appropriate degrec of bolt head interference.
If there is no potential bolt head interference then the total load is ecual c
the constant value P '
c 7.:-
VIG u G.E
- 2. G -I J.0 hh VS S tJ T t,L W t t. C N c t AA e
1 s
e 4
4 e
6 m
0 2-58
/
~ ~
~
FIGutE 2. 6 - 2.
Leo vs. TwTr.sstatus.
i. L.
a S5 e
2i G
T i
9 b
l I
I l
es.
m 2.- 59
I G u R E.
26-3
/ oA3 Y $.
O M T t R;EE.E M cE, A >h O
e G
4 O
e mi
- 2. - G o
/
m._
/
Assuming that all parts are potentially weoged in sne gao cenieen the secondary core succort and inside vessel head, the resultant maximum potential load is evaluated for four assumptions regarding loose parts gecmetries.
These fcur assumptions are listed as (A) through (D) belcw.
ASSUMPTIONS:
A)
Part assemblies do not separate and do not stack.
B)
Part assemblies do not separate but may stack.
C)
Part assemblies separata but do not stack.
D)
Part assemblies separate and stack.
An extensive study of possible loose part configurations for each assumption vis perferr.ed.
Figures 2.1-3 through 2.1-7 show some possible sub-configurations of single and stacked loose parts.
The maxinum loads due to loose parts are determined assuming that all the parts are wedged at this location in the worst combination of sub-configurations.
Tables 2.6(A) and 2.6(B) show the maximum potential load calculated for worst case configurations analyzed for assumptions (A) and (B).
The maximum loads are calculated in the follcwing manner.
MAXIMUlt LOAD CALCULATION FOR L_0OS PAP.T SUS-CONFIGURATIONS i)
Assume nuts, washers and hinge fragments are at their maximum load capacity.
This assumption is valid since those parts may sustain very lou defisctions elastically.
Also, the cross-sectional area for these parts as shown in Figures 2.1-3 through 2.1-7 docs'not very drastically during deformation.
ii)
For bolt head deformation, use the curves of Figures 2.6-1 through 2.6-3.
These curves were generated based on changing bolt head cross secticnal area, conservatively for 26 bolts, during bolt head deformation and the stiffness model of the reactor 2-6.1 i
' ~ ~ ~ ~ -.. -....
/~
~..
vessel internals.
The value of op on these curves is the original potential interference for a given gap size, or the total height of the stacked bolt head sub-configuration minus the gap size 'for which-the load is to be determined (no potential interference is possible for negative values of dp).
The value of Pc on the curves is the constant load ccmponent that exists for deforming nuts and washers.
0 6
e b
e e
2-62 no m
TABLE '. 6(A)
LOOSE PART C0!!FIGURATI0?l I WORST CASE FOR ASSUMPTION (A)
MAXIP.Uli NUMBER OF SUS-CO:lFIGURATIO:1 SUB-CO:lFIGURATIO15 B (Figure 2.1-3) 1 N (Figure 2.1-6) 22 0 (Figure 2.1-6) 21 P
1(21006) + 22(1734)
=
59154 lb.
=
c
_%b
_%h 0.469 -
a
=
inch
=
p 1,6 P
=
max as
_s
(
(Figures _2.5-1 and,,2, Interpolating between P
=_
=[
J and P l
for P
=
c 1
i t
1 2-63
TABLE 2.6 (B)
LOOSE PART C0tiFIGURATI0ft (II)
WORST CASE FOR ASSU!!PTIO!! (B)
IMXIMUM fiUMBER OF SUB-C0tiFIGURATIO!1 SUB-C0tlFIGUPATIOils L (Figure 2.1-5) 1 P
U'O c
il/A 6
=
p
_Nb l
P 98641 lb. <
=
_'b.
max l
l 2-64
Since the assucctions (A) and (S) are ve. lid, the aximun., o.
-3 allcwaele load on the secondary core sucact:
is not violated.
Since assumotion (C) is beunded by assumction (A) then there is no potential problem if assumption (A) is valid.
Assumption (D) hcwever, shcvis that potential problems do exist if separated loose parts somehow stack up.
This subject is discusscd in Section 2.6.3.
e 2-65 s
2.6.3 Discussion of Potential Problems ana :ecc=anE$a 5$ ruin $
Procedure From Sections 2.6.1 and 2.6.2 the only potential problem exists for loose parts wedged beneath the secondary core support and stacked according to Assumotion (D).
The source of this problem lies in the fact that separated loose part assemblies are assumed to st ck up in the worst possible conceivable manner.
Therefere, the bounding stacking configurations are describeo in this section in order to clarify the sources of potential problems.
The worst case loose part configurations are described and the method of potential interference load calculation for each case is presented.
2.6.3.1 Loose Part Conficuration ID This loose part confiouration is a combination of the sub-configurati ns showa in Figures 2.1-3 through 2.1-7.
The maximum number of each sub-configuration is based upon the assumption of 21 assemblies (latest ::..
The maximum load for each sub-configuration is determined in the following manner.
Itaxirtm Lend Calculation for Loose Part Sub-Ccnfiourations 1)
Assume nuts, washers and hinge fragmants are at their maximum load capacity.
This. assumption is valid since these parts cly sustain very low deflections clastically.
Also, the cross-scccic area for these parts as shown in Figures 2.1-3 through 2.1-7 does not vary drastically during deformation.
2-66 p
,,.mz+m-w w
m
~-
ii) For bolt head deformation, use the curves or Fig;res 2.6-1 through 2.6-3.
These curves were generated for 26 bolts caseo er changing bolt head cross sectional area during bolt head deform :i r and the stiffness model of the reactor vessel and internais.
~he value of 50 on these curves is the original potential interferen::
for a given gap size, or the total height of the stacked bolt head sub-configuration minus the gap size for which the load is to be determined (no potential interference is possible for negat: <e values of Sp).
The value of Pc on the curves is the constant load component that exists for deforming nuts and washers.
Table 2. 6.4-1 lists the sub-configurations that make up Configura-icr. ~
Table 2. 6.4-1 Maximum flumber Sub-Configuration of Sub-Configurations A
21 C
11 B
1
=
Thus, the value of Pc for Configuration ID may be calculated.
.P
= 11(8282) + (1)21006 = 113,208 lb.
c
_%b Potential interference for a gao size of inch is calculated " r-100 F/hr. heat up rate and 1000 psi.
_% g
_ Nb Sp =.5313
_ =_
_ inch.
2-67
- '../
Using the curve of Figure 2.6-2 for P
= 125,000 lb. and sp = 0. 363 c
inch shows that the total load is equal to approximately 220 kics.
Frcm the same curve it is seen that the interference for the allcwable r- ]9d' kips is approximately inches.
The cao size that
~ 2 d>
load of g
-mc wouldproducetnislevelofinterferenceisI which is greater than the height of sub-configurations (B) and (C).
Therefore, a different procedure must be employed in order to determine the allowable gap size for configuration ID.
Calculation of Minimum Gao Size For Conficuration ID The most direct procedure is to generate a plot of loa'd versus interference.
In order to determine the coordinates of points on the plot, the following procedure is used.
1)
Assume that sub-cenfigurations (B) and (C) behave elastically (valid if deformations of these sub-configurations are small).
2)
Determine the linear load-deflection relationship for sub-configurations (B) and (C).
3)
Determine the load-interference relationship for configuration ID using the wedged part and internals - vessel system stiffnesses.
Determination of Data Points for Lead-
_ Interference Plot for Conficuration ID As Fce interferences of less than
, inch, the plot for P
= 0 given c
in Figure 2.6-1 may be used.
This is true because sub-configurations (B) and (C) are not loaded for there levels of interference.
For 9
interferences greater than
_an additional stiffness due to sub-configurations (B) and (C) is acting.
Thus the load-interference plot will not be continuous.
The equivalent linear stiffnesses for sub-configurations (B) and (C) 6 are calculated assuming an elastic dodulus, E = 25.4 x 10 psi.
c.-
Sub - Configuration Area, A Height, L X, a. = I 4
2 (in )
(in)
(U/in) 6 B
0.3308 0.500 16.805 x 10 6
C 0.132 0.500 6.706 x 10 Since the sub-configuration (B) and (C) equivalent springs act in parallel, the effective spring constant is the sum of the equivalent spring rates.
6
".16.805 + llx(6.706)}
x 10 lb/in Keffective 6
90.57 x 10 lb/in
=
The non-linear load-deflection relationship of the bolt head is given by equation (2.4) of Section 2.1.1.
The resultant load-interference plot for configuration ID is shown in Ficure 2.6-4.
From this figure it is seen yh,at for an allowable load of xg
- kips, the interference is equal to
_ inch.
Therefore, the minimum a!:vaable gap, G, assuming that configuration ID may g
occur is calculated.
._ N b G
inch
=
A
_%b -
inch G
A 2-69
Ficuet z. c to o vs. ra--tuutoct 4,3b G
e e
b o
e N
l m
N 2 -7o
2.6.3.2 Loose Part Conficuration IID
~
This loose part configuration is also a combination of-the sub-configurations shown -in _ Figures 2.1-3 througn 2.1-7.
Again assuming tnat parts due fto all 21 assemblies are present the sub-configurations that make up Configuration IID are listed in Table 2.6.4-2.
Table 2.6.4-2 Maximum Number of Sub-Configuration Sub-Configurations D~
21 E
2 8
1-C 11 Thus, the value~of Pc for Configuration IID may be calculated.
2'(1778) + 2(20447) + 1(21006) + 11(8382)-
Pc
=
Pc
=- 191,440 lb.
CALCULATION OF f1INIMUM ALLOWABLE GAP SIZE FOR CONFIGURATION IID TO PAINTAIN MINIMUt1 CORE l
BARREL TO VESSEL LEDGE LOAD
\\
The minimum allowable gap size assuming configuration IID may occur 1
is calculated by accounting for the internals and vessel system and i
wedged part flexibilities.
l It is known that due to the large degree of deformation that occurs in sub-configuration (D).
Therefore, this sub-configuration is at its ultimate load carrying capability.
Sub-configurations (E), (B), and (C), however, will have limited deformations and may be assumed to be 2-7f j
,,,2
.v
..c #. J -
elastic for an initial iteration.
The ecuivalent spring constants for each suo-configuration is calculated. assuming an elastic modulus, E = 25.4 x 106 psi.
AE Sub-configuration Area, A Height, L Kgg = I 2
(in )
(in)
(lb/in) a B
0.3308 0.500 16.805 x 10" 6
C 0.132 0.500 6.706 x 10 6
E 0.322 0.500 16.358 x 10 Since the sub-configuration equivalent springs act in parallel, the ef-fective spring constant is the sum of the equivalent spring rates.
6 Xeffcetive 16.805 + 2(16.358) + 11(6.706) x 10 lb/in
=
6 123.29 x 10 lb/in
=
The load in the effective cpring, P, is equal to the maximum allowable g
load minus the constant load due to sub-configuration (D), Pcl*
Pcl = 21(1778) = 37,238 lb.
2, s g
,- 37,333) lb =
,]lb.
P
=
The deflectica of the effective spring, 6, is equal to the spring X
load divided by the spring rate.
a>b 6g =l123.T9 x 106 inch
[ inch r
6
=[
g 3
2-72
Check cssumption of elastic deformation in sub-configurations (3),
(C) and (E):
>h a, a, P
16.358 x 10 lb
lb.
t L.
l,b a
since[
j < 20,447 sub-configuration (E) deforms elastically
_ a,b
_sh 6
P
16.805 x 10 lb
lb.
B L
'6
.3 sinceJ
- < 21,005 sub-configuration (8) deforms elastically
_ '> h s
0
_a h PC = 6.706 x 10 lb =
_ lb.
_ a> b since;
< 8382 sub-configuration (C) deforms elastically ii..efore, the assumption of elastic deformation in sub-configurations (B) (C) and (E) is valid.
The deformation of the internals and vessel systems, a, due to the s
maximum alicuable load must be added to the deformation of the wedged parts in order to dettrmine the minimum allowable gap size.
_ a-> b 6
inch
=
s
_gb inch 6
=
s Thus the allowable interference, 6, is equal to the deformation of the d
internals cnd vessel system plus the wedged part daformation at the maximum allowable load.
6D=
6
+
6 g
s 16 3
Sg=
inch
,, 8 OD" 2-73
The minimum gap si n, G,.is equal to the minimum wedged part con-4 figuration height minus the allowaole interference.
. s.,b 7
p
-%b Gg = (0.500 t
inch =L
_ inch 2.6.3.3 Discussion of Loose Part Conficurations From the calculations of Sections 2.6.3.1 and 2.6.3.2 it is seen that the loose parts configuration that results in the most restrictive gap size is configuration IID.
Although configuration ID predicts essentially the same allowable gap size as configuration IID, the analysis of configuration ID is based ucon load-interference plots generated for 26 wedged bolt heads and is therefore overly con-servac.
The analysis, however, is useful in that it shows that configuration Ib is not as limiting as configuration IID.
Although there is no basis for determining that configuration IID absolutely may not occur, it is statistically unlikely that all 21 bolts would be standing on head and all nuts and washers arranged in vertical stacks.
Assuming that cnly half (11) of the bolts are standing on head reduces the maximum possible load due to configuration IID by 17,780 lb to a value of 173,660 lb.
Assuming that the stacking of nuts and washers may be precluded results in a maximum load of 37,333 1b.
The consequence of configuration IID occuring in its worst form is that the reaction at the vessel ggdge-core barrel flange interface isreducedtoavalueof[
l b or 65.6 percent of the recc= ended minimum value to preclude undesirable flow-induced vibrations.
2.6.4 Rece r.endnd Oceratina Procedure
)
Based on the results of Section 2.6.3, it is reccmmended that the l
plant be acerated in su h a manner as to not violate a minimum cap c
c-l of
_ inch between secondary core support and inside vessel g
l i
2-74 L
-. /
head.
In order to investigate any r'e hric.icns in heat up rate or power escallation, the minimum allcwable gap size is plotted as shown in Figures 2.7-1 and 2.7-2.
Figure ~2.7-2 shows that no restriction in power level is required for any of the plotted pressures.
Possible limitations on heat up rate are discussed in Section 2.6.4.1.
9 2-75
2.6.4.1 Effect of loose Parts on Heat Un ?Fo~ chin 6E From the analysis of Sections 2.3 and 2.4 it may be snown that heat u:
from 70 F to 450 F at a constant rate of 100 F par' hcur results t,s in a zero pressure gao ofi
_ inches at 450 F.
Therefore the
]w,nchesisnotviolatedforheatuo a
minimumgaprecuirementof[
i rates up to 100 F per hour at temperatures frca 70'F to 450 F.
Heat up from 450 F to 550 F, however, may cause the minimum recem-manded gap to be violated for certain heat up rate and pressure combinations, as shown in Figure 2.7-1.
The minimum pressure for given temperatures is obtained from Reference [ 3 ]
and is shown in Table 2.6.4-1.
TABLE 2.6.4-1 Temnerature (*F)
Minimum pressure (pSIG) 350 350 400 480 450 660 500 1060 550 1540 l
i Using the tcmperature-pressure relations in Table 2.6.4-1, the minimum gap size may be bounded for a 60 F per hour heat up rate.
Since it has teen shcun that the minimum gap requircmant is not violated for t:mparatures up to 450*F at heat up ratcs up to 1C0 F por hour, the range of temperature to be exanincd is frcm 450 :
to 550 F.
The vessel stiffness is evaluated for the temperature distribution that exists at 450 F.
The vessel expansion due to i
pressure, G, for this case is p
- hb G
P inch
=
p where P is th'e vessel pressure (psig) 2-76
Y
.n.
The minimum gap occurs at the end of the heat uo ramo wnen thermal lags in the vessel are the greatest.
The zero pressure cap for heat uc
- a., 6 to 550 F at a rate of 50 F per hour is[
_ inch.
Assuming the stiffest vessel (at 450 F) and minimum pressure (at 4E0 F) the r-
- 6b minimum vessel expansion due to pressure is equal.to _
jinches.
The minimum gap, Gmin, corrected for the vessel expansion due to pressure is ab G
=
inch min Thus, the minimum gap that occurs for the temperature range from 450*F to 550 F during a 60 F per hour heat up rate does not exceed the minimum gap requirement if the minimum pressures given in Table 2.6.5-1 are satisfied.
6 A
e 2-77
Fisues
? 7-t HEW up RR s Vs.
GAP S I s t.
~
3., %
e t
e t
l i
-i M
-M E
a
-+->
e-w-.e.,--
e.-
% e e==
Ficue.v-2.7-2 RRcEnv few t e.
vs. GAP sist M
em e
O 9
4 h
i i
l I
i
\\
mim.
Summuusi
1
~
i
~.
2.7 Su=rary Wedced Part Ef ects
' ~ ~ ~
"~" ~' " "
l A comprehensive review of the lower internals package was performed in order to determine areas where cojects could lodge and present Oossi le Two areas were determined as potential wedging locations tha:
concerns.
could cause concerns during heat-up' and operation of the plant.
These locations, shown in Figure 2-1 are tt._ gap between the secondary core support. plate and the vessel bottom head and the radial gap between the radial key and clevis insert.
The effects of the postulated wedging were evaluated for three items of concern:
1)
Loads induced in core support structures during plant heat-up and power escalation.
2)
Minimum cr.a barrel flange to vessel ledge load to preclude undesireable flow-induced vibrations.
3)
Loads induced in reactor pressure vessel.
The results of the three evaluations performed are summarized in Sections 2.7.1 through 2.7.3.
2.7.1 Effcets of Loads Indur.ed in Core Suncort Structurec Due to pedgyd Perts Tne effects of lotds induced on ccre support structures due to parts wedged at the two postulated locations are su:r.rarincd in Sections 2.7.1.1 and 2.7.1.2..
e 2-80
c./.i.6 car a Wedoca in Lower Radial Succorr The case of 26_ lcose bolts wedged _between a single radial' key and -
clevis. insert was evaluated.
The postulated wedging condition
- a., w was detemined to induce a, radial load of _.,
kips and an axial.
(vertical) load ofI kips on the radial key.
The maximum:
stress intensity induced in the~ radial key was determined to be-5200 psi.
The factor of safety for an allowable stress intensity of 48,600 psi (3 S,) is 9.3.
In addition to the radia1 key, the stresses induced in the core barrel were evaluated.
The ccmpressive stress in the barrel due to the wedged _part was determined to be 1840 psi.
The factor of safety for. an allowable stress intensity of 48,600 psi (3 S ) is 26.4.
Additionally, the core barrel was m
analyzed for potential buckling.
The analysis showed that this possibility is precluded.
2.7.1.2 Parts Wedoed Beneath Secondary Core Succort Structure The load path through the core support structures due to parts wedged in this location is shown in Figure-2.2-1.
Analysis of the affected structures sh0;as that the critical h
load for structural integrity is kips based on yielding of an individual column of the enercy absorber.
This load is greater than the[
@j kip critical load determined for main-fb
~
taining minimum core barrel flange to vessel ledge load.
2.7.2 Minimum Core Barrel Flance to Vessel Ledce Load The core barrel flange to vessel ledge load was determined for normal hot and cold conditions based on as-built drawing dimensions and operating loads.
The hot load was determined abs to be
_ kips.
The effects of wedged parts in the two postulated locations op the ability to maintain the minimum allowable load of
_ kips were determined.
The results are u
sumnarized in Sections 2.7.2.1 and 2.7.2.2.-
2-81
N 2.7.2.1 Parts'Wedced in Lower Radial Succort Since the comoressive-load in the core barrel is not uniform throughout all sections for this load case, the minimum load per.circumferential inch at the core barrel flange-vessel _ ledge interface-at the critical section is the I
governing criteria.
The analysis based on a vertical'.ccmaressive load of C ]Abkips and an effective core barrel region showed
.that the minimum requirement is not exceeded.
1 2.7.2.2 Parts Wedaad Beneath Secondary Core Succort Structure For this case it'was postulated that all parts were potentially wedged in this location.
The gap size for various heat-up rates and. power levels at various pressures was determined based on as-built drawing dimensions and coerating
. loads.
The results are shown graphically in Figures 2.4-1 and 2.2-2..
A comprehensive stiffness model of the vessel, reactor internais-and postulated loose parts'was used to determine the load induced by various degrecs of interference due to loose parts.
The model is shown in Figure 2.2-2.
l i
Four assumptions regarding possible geometries of loose parts i
wedged at this location were made and a ecmprehensive study was performed in order to determine the maximum possible _ load i
_for each assumption.
i The assumntions and maximum loads are presented in
{
Table 2.7-1.
Since the maximum allowable load is[_
kips, only assumption (D) indicated that a potential problem existed.
A critical gap size was determined based on this assumption and was plotted on Figures 2.7-1 and.2.7-2 as the dividing line between acceptable and unaccpetable gap sizes.
t i
l 2-82 1
4
_, ~
_, _ ~ - - _ _ _ _ _.
TABLE 2.7-1 POTENTIAL LOAD ON SECONDARY CORE SUPPORT DUE TO WEDGED PARTS MAXIMUM POTENTIAL LOAD ON SECONDARY RECOMMENDED CORE SUPPrAT PLATE OPERATING ASSUMPTION (KIPS)
PROCEDURE A
107.4 None B
98.6 None C
1107,4 None D
(See Section 2.6.3)
(See Section 2.6.4)
ASSUMPTIONS:
A.)
Part assemblies do not separate and do not stack.
B)
Part assemblies do not separa.te but may stack.
C)
Part assemblies separate but do not stack.
D)
Part assemblies separate and stack.
2-83
2.7.3
_ Loads Induced in Reactor Pressure vessel The effect of loads induced in the reactor pressure vessel due to wedged loose parts in the two postulated locations were evaluated.
2.7.3.1 Parts tiedged in Lower Rddial Suonort The stresses induced in the vessel due to the radial load
,s a,s of ; _ kips and axial load of _~
_ kips _were calculated and combined with normal operating stresses.
The resulting vessel stress intensities do not exceed allowable values.
2.7.3.2 Parts Wedoed Beneath Secondary Core Succort Structure
_ 2., b p
The stresses induced in the vessel due,to,the load of _ _
t kips distributed over an area of
_ square inches at the inside vessel bottom head were calculated and combined with normal operating stresses.
Tha resulting vessel stress intensities do not exceed allowable values.
l l
2.7.3.3
_Lecal Stresses in Vessel Cladding The potential for cladding indentation was considered to be greatest for a bolt body wedged in such a way that the bolt threads contact the vessel cladding.
The maximum po'stulated depth of indentation was such that the present minimum clad thickness requirement is not violated.
l 2-84
3
-3. 0 IMTRODUCTICH IMPACT EFFECTS-The following is a summary of the. work.comoleted-to evaluate the potential damage that may result due to-the. loose parts-impacting against the core barrel, thermal shield flexures and-bottcm mounted instrumentation vessel. tubes.
These targets'are the most sensitive structures for. impact loads in the flowpath of the missile from the pump to the bottom'of the reactor.
. vessel.
The current work is based on a conservative estimate of the damage that could result from the impacting of the largest loose-part found in-the' vessel.
The analysis considers both the potential for penetration by.the parts, as well as overall structure damage.
3.1 DEFINITION OF MISSILE 3.1.1 MISSILE GEOMETRY The largest loose part is the bolt-washer-nut assembly.
The part is shown in Figure 3-14. The mass of the assembly'is 2
0.582 x 10-3 lb. sec based on the weight of 304 stainless steel.
A second missile is the largest secment of a broken hinge.
The segment is the No. 4 piece in Figure 3-1 b.
3-1
3.1.2 MISSILE VELC; CITY The velocity of the missile was assumed to be equal to the veiccity of the fluid flow at the location of the target.
The flow rate considered was for normal operation mechanical design ficw.
The velocities, from POLAC Run APVQEMJ (4-2-82), at specific areas are:
a,b l
.l.
Inlet Nozzle [
]
d,b 2.
Thermal shield flexure [
]
a,b 3.
Instrument tubes [
]
The velocity used for the missiles is considered conservati-1.
These velocities are achievable if the missile is in the flow for the distance of approximately 20 ft. without impacting or rubbing against the sides of the pipe or thermal shield annulus walls during flow.
3.1.3 MISSILE ENERGY The energy of the missile upon impact is given by the equation:
o E = (1)mV" The E for the defined missiles are:
3-2
1.
largest plate missile a)
At Inlet E = 1.76 15. ft.
b) At Flexure E = 0.347 lb. ft.
c)
At Tube E = 0.693 lb. ft.
2.
Bolt Missile a)
At Inlet E = 1.88 lb. ft.
b)
At Flexure E = 0.370 lb. ft.
c)
At Tube E = 0.738 lb. ft.
3.2 TARGET GE0 METRY As previously discussed, three potential targets have been defined that constitute the most sensitive parts in the flow path of the missile from the pump to the bottom of the reactor vessel.
The targets are:
l a) core barrel; b) thermal shield flexure; c) instrument tube.
In all cases the material properties used in the evaluation are those for the appropriate target material at 650*F.
The core barel and analysis model are shown on Figures 3-2a and b; the flexure and analysis model are shown on Figures 3-3a i
1 and b; and the instrument tube and analysis models are on Figures 3-4a and b.
3.3 METHODS OF ANALYSIS FOR MISSILE IMPACT The two major considerations for evaluating missile impact are limitations of local damage and of overall response of the target structural" element.
Local damage may include penetration 3-3
or punching shear in the region of impact on the structure.
Overall response includes bending and reaction shear in 'the structure.
Criteria for penetration and local punching shear are discussed in Section 3.3.1 and the evaluation of overall response is described in Section 3.3.2.
The prediction of overall response is generally based on energy / momentum balance.
The criteria of acceptance is that the target can absorb the impact energy without deformation that would impair the operation of the plant.
l In all cases considered, the impact is assumed at an angl.e of strike normal to the target.
The angle of strike has a sub-stantial influence on the penetration depth and the' energy that must be absorbed by the target.
In some cases, such as the instrument penetrations, th,e probable angle of strike l
would appear to be substantially greater than 20*.
An impact at 20* has approximately 12 percent less energy than a nonnal strike, and an impact at 30* is 25 percent less than the normal strike energy.
Considering the actual flow conditions in the reactor, the normal strike assumption is considered very conservative.
3.3.1 LOCAu IMPACT EFFECT l
Two local impact effects have been considered for the targets.
The effects are:
1)
Punching shear; and, 1
2)
Penetration (denting)
The two are discussed in Sections 3.3.1.1 and 3.3.1.2 respectively.
3-4
'N. _._ _ _ m __ --
3.3.1.1 PUflCHIfiG ~ SHEAR The minimum energy required.for the missile to punch out a plug of plate in shear was also evaluated.
The failure mechanism is as shown on Figure 3-5.
The minimum energy required is given by:
h SR3 F (d-x) dx Ws"#o Where:
x is the distance traveled through the plate; R
is the perimeter of the missile; p
S is the yield of the target material in shear; and, s
d is the plate thickness.
I Evaluating the integral gives:
2 SRd W
sy
=
s 2
The value of 5 equal to one half the minimum yield stress at 3
650.
3-5
-m.T
- m..
The potential for perforation is given by the ratio:
R
- E /W 3 ""*r*
is the kinetic energy of the missile.
s M
s M
Table 3-2 provides a su mary of the. R calculated for the s
various missile and target ccmbinations.
TABLE'3-1 PERFORATI0t1 BY PUNCHING SHEAR Missile Tarcet W (lb.Ft.)
R s
s Lg. Plate Core Barre 1000 0.00083 Lg. Plate Flexure 27 0.0064 Lg. Plate Inst. Tube 94.5 0.0037 Bolt Assembly Core Barrel 1280 0.0007 Bolt Assembly Flexure 35.6 0.0052 Bolt Assembly Inst. Tube 121 0.0031 Based on Table 3-1 results, the potential for perforation by punching shear is really negligible.
The minimum factor of safety is 182.
3.3.1.2 PENETRATION (DENTING OF THE TARGET)
Conscrvative numd is used to estimate an upper bound of the potential denting caused by the missile impact, the method utilizes the postulated failure made in punching shear dis-cussed in Section 3.3.1.1.
The movement of the plug for a specified impact energy is estimated from the ecn.
X E=I Ss F (h-x) dx g
3-6
-.._.____. m - -.
d Where x is the movement of the plug or the magnitude of the dent.
S ' R, and d are the same as in Section 3.3.1.1.
s F
Integrating gives the energy required for the plug to move an amount X as:
2 E = S R (dx -
)+C 3p Using the initial condition that when E = 0 and x = 0, that C must equal 0; the equation for X is given by:
X - 2dx + 2:e
=0 2
SRsp X
= 2d -
4d2,g SR sg 2
The value of X estimated for various missile and target combinations is sun:narized on Table 3-2, 1
3-7
TABLE 3-2 POTENTIAL PENETRATION (DENT)
Punching Shear Missile Target Assumotion Lg. Plate Core Barrel 0.001 "
Lg. Plate Flexure 0.001 "
Lg. Plate Inst. Tube 0.001" Bolt Assembly Core Barrel 0.0008
~
Bolt Assembly Flexure 0.001" Bolt Assembly Inst. Tube 0.0008" As indicated in Table 3-2, the predicted dent is quite small.
However, as previously stated, it is believed that the actual values would be much lower than the predicted values because:
1)
They neglect that a minimum missiTe energy is required prior to initiation of denting or penetration; and 2) they neglect the energy dissipated in deformation of the target in regions not immediately under the missile, l
that will occur.
3.3.2 OVERALL STRUCTURE. RESPONSE EFFECTS In order to evaluate the overall response of the target structures for missile impact, the type of impact must be classified as either "hard" or " soft".
The softness of a given impact is obviously relative, but in general, soft impact is characterized by significant local deformation of missile or target in the region of impact; while local deformation under hard impact is neglected.
For soft impact, the deformation characteristics of the missile or target are used to develope an applied force time history, and the analysis of the structure is carried out as for an impulse load.
In the case of hard impact, energy and momentum balance techniques are used to predict maximum response.
3-8
While the conditions of hard impact rarely exist in "real" life, tha method is conservativa esith resp;ct to predicting overall structure response ano potential damage, because it neglects the energy absorption through local deformations.
The evaluation for potential damage was performed using the conservative assumption of hard impact.
Conservation of momentum and energy are used to determine the the portion of the kinetic energy of the missile that is transmitted to the structure to be absorbed,as strain energy.
Conservation of momentum for Impact of two masses is:
MVio=MV 1 y + M Y ; and e2 Conservation of energy is:
2 2 + 1/2M,V 1/2 M V = 1/2M V 1
y 2
Where:
My=
Missile mass; Me-Target effective mass; Vg-Velocity of missile before impact; V1=
Velocity of missile after impact; V2-Velocity of missile after impact; An additional equation can be written for the coefficient of restitution:
V2Y1 e=
y o
0583E'1 3-9
~
Solving the equation for e for V, and substituting into tha momentum 1
equation yields the expression for post-impact target ano missile velocity as:
My T
V Yo (1+e)
- and 2"
M 1+1 Me M
17-e Y
1" M
o y
1+7e For M /M, > e the missile velocity is positive after impact and the mis-y sile will move toward the target.
Thus, the kinetic energy of the missile' after imoact must be absorbed by the target, in addition to the kinetic energy imparted to it during initial impact.
The energy to be absorbed by the target is then:
E = 1/2 M,V2 3
e or 2 + 1/2 M,V E = 1/2 M V 11 2
l From the equations for velocities and the energy to be absorbed in structure strain energy, several observations are noteworthy:
1)
An underestimation of target mass results in a conservative estimation of energy transmitted to the structure; i
0583E:l*
3-10 l
2)
Tha uppsr bound of en:rgy ab' sorb d by the structure is thsn the target mass is assumed equal to zero (0), ths upper couno energy is equal to the total kinetic energy of the missile at impact 2
(E = 1/2 M V ); and 1
3)
The assumption that e = 1, or a perfectly elastic impact occurs, although unrealistic, is always conservative for estimating structural camage to the target.
3.3.2.1 Target Effective Mass The effective mass of the target when a missile strikes a concentrated mass is obviously the total target mass.
However, in the case of a distributed mass structure, the inertial resistance of the structure is actually a variable, changing during response and is dependent on tha magnitude and duration of the applied loads.
Typically for impact evaluation, the effective mass (M,) is that fraction of total structure mass determined based on the assumed static deformed shape of the structure due to the applied impact force.
The equivalent mass is derived to maintain equality of kinetic energy with the real system.
M m d(X) dx
=
e where m = mass per unit length; and, d(X) = assumed deflected shape.
In this regard; it is necessary to predict in advance whether the response will be elastic, elasto-plastic or plastic, because the deformed shape varies accordingly, as illustrated in figure 3-6.
Table 3-4 provides values for M e
for some typical structural shapes for the elastic and plastic assumption.
In some cases, to accurately define the M, an iterative procedure is required.
e 0583E:1 3-11 1
~
The Me predicted by the above method gen,erally participates in the final response of the structure.
However, it may not be effective during the time of impact when energy is being transfered from the missile to the target.
A structure subjected to an intense load for a very short auration will respond during impact only in the immediate area of the load, such that only a small portion of the structure mass participates in the energy transfer between missile and structure.
If the impact results in a less intense load applied over a longer duration, then a greater portion of the structure mass will participate in the energy transfer.
It is suggested in Ref. 9 that the mini-mum target effective mass is that included in an region within "d/2" of the periphery of the impact surface.
The value of "d" is the thickness of the target in the direction of impact.
This minimum mass must move if the struc-ture as a whole is to deform.
As discussed in section 3.3.1 failure within this area is governed by peforation or punching shear which have previously been shown to be a negligible possibility.
The actual determination of the mass is highly dependent on the geometry and elastic and plastic characteristics of both the missile and target.
- However,
{
it can.be bounded based on the duration of the time the force acts between the bodies.
By assuming the missile remains elastic and the target is rigid, upon impact, a compressive stress wave propagates from the point of contact towards the free end of the missile.
At the free end of the missile, the stress wave is reflected causing an expansion wave to return to the contact surface, such that the missile rebounds at the impact velocity.
The impact time (t )
is(10) d td-2W 0583E:1 3-12 l
Table 3-4 t
EFFECTIVE MASS (M;)
Beam Type Elastic Plastic Simple-Simple Span Center Concentrated 0.494M 0.333M Load Fixed-Fixed Span Center Concentrated 0.383M 0.333M Load Cantilever Span Concentrated Load 0.243M 0.333M At Free End M = Total Mass of Beam From Reference 8 0583E:1 3-13 1
Tho force during impact is given by P = aCV g
sx Where P = Contact pressure (psi) 4 a = mass density of missile (lb-sec /in )
C = Speed of sound in missile (183688 in/sec)
Vg = Impact velocity (in/sec)
L = Length of missile (in)
Thus the force time history applied to the target is a rectangular impulse load of constant magnitude for a duration of t.
The value of t fra d
d missile of length.75 inches is then
= 8.1 x 10-6 t
sec d=
The ability to mobilize the effective mass of the static deformeo shape, (1st mode of structure), can be evaluated based on the response of the structure to a rectangular pulse force time history.
Tha response in each mode of vibration for a uniform beam is(11)
[0 PI*)#n(x)dx X
(DLF)
=
2*0 6
(x)dx mn or Xn - B (DLF) s Where:
DLF = Dynamic Load Factor d (x) = normalized shape of mode n n
p(x) = load as function of x
= Circular frequency w
m = mass per unit length b = length of beam 0583E:1
The value B for a given mode is a constant and for simple shapes such as fixed
- fixeo beams and cantilever beams will be smaller for the higher modes than for the fundamental mode.
Figure 3-7 shows the Dynamic Load Factor (DLF) for a rectangular pulse load as a function of t divided by the period of vibration (T ) of the struc-d 1
ture.
From this figure it is seen that for t /T1 ratios greater than 0.5, d
where Ti is the period of the first mode, the predominent response will be in the first mode, or the assumptien for target mass based on the static deformed shape is valid.
Conversely, for t /T1 ratio less than 0.08, even g
if the term B for the first mode was two times that for the higher modes, the I
higher mode response could tend to dominate the total response; thus, the effective target mass assumption based on the minimum mass in the region of impact would be a better approximation.
The t /T1 ratio for the three targets are:
g Core Barrel t /Ty = 4.4 x 10-5 d
Themal Shield Flexure t /T1 - 0.0117 d
Instrument Tube t /T1 - 0.0024 d
From these values of t /T, and recognizing that the td predicted may be d
1 low by a factor of 2 to 3 times, general observation in regard to effective target mass can be made:
1)
Core barrel - The effective mass of the core barrel during impact is clearly that of a higher mode associated with local deflection of the core barrel shell in the region near the point of impact; 2)
Themal shield flexure-- The effective mass is also that of a higher mode associated with local deflection.
3)
Instrument tube - The value of t /T indicates that the d
1 minimum mass should be used for the impact.
- However, 0583E:1 3-15
as shown on figure 3-4b, a substantial portion of the cantilever beam is above tha point of impact on the beam.
For movement to occur at the point of impact, the top portion must also move; thus the portion of the beam above the impact point will tena to act as a concentrated mass at the point of impact.
Although the determination of the effective mass is a complex problem which requires testing and refined analysis to define accurately, the best assumptions regarqing the various targets are:
1)
Core barrel - M is the mass of the core barrel shell computed e
by the minimum mass criteria-for a missile cross section of 0.2" diameter the mass is 0.0174 lb sec2 in.
2)
Thermal shield flexure - The flexure mass should be the M, based on minimum mass criteria.
3)
Instrument Penetration - The instrument penetration M should be e
the mass above the impact point plus the portion of beam below the impact point for the mass coefficient from Table 3-4 for elastic conditions.
3.3.2.2 Coeff:cient of Restitution The coefficient of restitution, e, is a measure of the energy loss auring the collision of two bodies.
The collision when e = 1 is referred to as a per-fectly elastic collision, while when e = 0 the collision is classically refer-red to as a perfectly plastic collision.
Collision with e between 0 and 1 are referred to as inelastic collision.
Typically, the amount of permanent defor-mation in the bodies is used to illustrate the concept of the coefficient of 4
i 0583E:1
~
3-16
res*itution.
The typical discussion on codfficient of restitution is misl. S ng since it implics the energy dissipatea during collision is only aue to plastic deformation.
In fact, energy during collision is dissipated by many mechanisms such as a) internal material damping; b) internal vibrations of the bodies; c) stress wave propagation from the point of impact; d) friction at the contact surfaces; and e) local and overall plastic deformations.
In many cases, a substantial energy loss can occur, with "e" approaching zero, without plastic deformation of the bodies during impact.
An example is shown in fioure 3-9 for a footing.
In this case, a substantial portion of the input energy (by impact or vibration) is transmitted away from the point of contact
.by stress waves, which are losses during the energy transfer during impact, and thus do not participate in the overall deformation of the structure.
The actual coefficient of restitution is highly dependent on the size, shape, material properties and velocity of the bodies during collision.
These char-acteristics are not only important because they affect plastic deformation of the bodies, but also they greatly affect the energy dissipated by other mechanisms.
Reliable values for "e" must be based on tests of similar missile and target geometries, or by extrapolation of test data.
A conservative value of e = 0.8 is used in the analysis for determining damage to the target structures.
0583E:1 3-17 l
,w
~
3.3.2.3 TARGET ENERGY ABSORPTION REQUIREMENTS The table below summarizes the energy that must be absorbeo by the three oefineo target structures based on the assumptions for M from Section e
3.3.2.1 and a coeffcient of restitution (e) equal to 0.8.
Section 3.3.3 discusses the consequent effects on the target structures.
Target Structure E (in-lb)
Core Barrel 0.223 Instrument Tube 0.0887 (Bending Strike)
Instrument Tube (rigid target Assumeo)
(Shear Strike)
Thermal Shield Flexure (rigid target assumed) 3.3.3 ENERGY ABSORPTION CAPABILITY OF TARGETS After the energy that must be absorbed is known, the energy absorption capability of the structure is determined from the area under the resistance (force)-displacement curve.
Figure 3-10 shows a typical curve.
This area represents the strain energy absorption capability of the structure and must be equal to, or greater than, the energy of the impact discussed in Section 3.3.2.
When the strain absorption capability is greater than the effective impact energy, the amount of permanent deflection in the structure can be estimated from the curve by assuming that unloading will occur along a line parallel to the original elastic portion of the curve.
The intersection of the line with the deflection axis is an estimate of the permanent oeflection in the structure oue to impact.
i 0583E:1 3-18
Tha value R is tho static collapse load and is that valua of load that m
results in the formation of sufficient plastic hinges in the' structure to create an unstable mechanism which would collapse without any aoditional load.
The methods for computing the collapse load R are containeo in many m
standaro text books, and figures 3-11 and 3-12 pr7 vide the formulae for several comon structures.
The values in figure 3-11 and 3-12 are defined in terms of the plastic moment (M ).
The value of M is a function of the u
u asswr,ed stress-strain curve of the material and the geometry of the cross section of the beam or plate.
The most common assumption for the stress-strain relationship is that of elastic-perfectly plastic behavior.
This assumption is consistent with that used in ASME subsections NB and NG for computing the collapse loads C and g
L, respectively.
Therefore, the equivalent impact force to absorb th'e L
impact energy is comparable to the code limits for C and L.
The cross g
t section property, the plastic nodulus, which is needed to compute M is contained in many comon text books. (12) u The next parameter to be defined is the yield stress value for the material where perfect plastic behavior begins.
The yield stress is assumed to oe 1.5 S.
The yield value is then increased by a conservative factor of 1.2 to g
account for the increase in yield stress due to the rapia strain rate during impact.
The increase in yield stress and ultimate stress, because of rapid strain l
rate, is well documented.
In Ref. 7, tests were con-4 3
ducted with a range of strain rate of 10 to 10 per sec and for tempera-tures from about 25 to 600 *C.
At room temperature, the increase in ultimate stress was 40 percent at the highest strain-rate, and the increase in yield stress was 170 percent.
The normal rate of strain for tensile tests is about 2 x 10-3 per sec.
The strain-rates, based on the impact velocity for the missiles considered herein, would be between 1 x 102 2
to 5 x 10.
Thus the use of the comon impact yield stress increase factor of 1.2 is consioereo very conservative for this evaluation.
0583E:1 3-19
It should be emphasized that the collapse load calculated using these assump-tions is not the true collapse load of structures maoe from stainless steel.
The "true" collapse load should be baseo on the ultimate strength and an elastic-strain hardening model for tne material.
These assumptions will increase the collapse load and energy absorption capability 1.5 to 2.0 times those calculated using the elastic-perfectly plastic assumption.
The preceeding discussion provides the procedure to calculate the strain energy absorption capability for structures that are not subject to other loads during the impact.
In general, this is not the case, and the energy absorption capability of the structure must be reduced to reflect both sus-tained load and cyclic loads'that exist concurrent with the impact.
Figure 3-13a and b provide the energy reduction for a fixed-fixed beam for various potential concurrent load conditions for both the center impact and end impact loading.
Cases a and b on figures 3-13a and b are determined by calculating an equivalent load at the impact point (P') that results in an energy reduction equal to the indicated distributed or concentrated load.
The equivalent load is given by:
AP ' = ( b p(x) g) g Where:
a = the displacement at the point of impact p(x) = the concurrent load as a function of the length along the beam, and, d(x) = the elastic or plastic deformed shape as appropriate.
The value of P' varies as plastic hinges are formed during the impact, because the function 6(x) varies.
In the calculations herein, the largest P' was useo for the various elastic and hinge combinations that exist until the final collapse mechanism has been developea in the structure.
~
0583E:1 3-20
Concurrent loads such as load case c on figures 3-13a and b, do not in generai affect the collapse load; however, they do affect the available energy up tc the time that the collapse loao mechanism is formed.
Such loads increase er decrease the coment capacity at any beam location until a hinge is formeo.
The remaining moment ccpacity is:
MR"N
+M u
i 1
. Where:
M is the remaining moment capacity at a given location; R
M is the plastic moment; and u
M is the moment at a given location due to the concurrent loao.
j
'The remaining moment capacity at a location on the beam can change the applic load at which a hinge is formed and also can change the sequence that hinges are formed until the collapse load is reached. The reduction shown on figures 3-13a and b were determined by performing an analysis to determine the sequence of hinge formation for the indicated concurrent loao.
The equivalent force P' for several concurrent cyclic loads that are independent, (caused by different sources of excitation, or are a resuit of different modes of vibration), should 9 combined by the Square-Root-of-the-Sum-of-the-Squares (SRSS) method to obtain the total P to be considered for the energy reduction.
A cyclic load should be considered as a sustained icac, if the cyclic period of the load, divided by 4, is greater tnan the anticipated time of the impact (time to reach the deformed shape rcquired is absorb the effective impact energy in strain energy).
C583E:1 3-21
[
3.3.4 CORE EARREL ANALYSIS Figure 3-2b shows the model used to evaluate the effect of the postulated irrpact on the core barrel.
The loose part is assumed to impact the core barrel at the inlet nozzle at the inlet nozzle velocity.
The minimum value of target effective mass and a coefficient of restitution (e) equal to 0.8 were used in the analysis.
The equivalent force (F ) acting on the barrel, e
assuming elastic action of the barrel, is obtained by equating the energy (E) to be absorbed by the target (core barrel) to the strain energy of the barrel due to impact, or 2
E = (1/2) F a - (1/2) Ka e
where a = Oefle dian at point of impact K = Equivalent spring constant at point of impact The expressions for a and F are g
a - F IK e
F = (2EK)1/2 e
The value of K was determined based on the model shown in Figure 3-2b.
the analysis performed counsidered both the local deflection of the shell and the deflection of the core barrel as a beam.
The beam deflections are essentfa'ly negligible.
0583E:1 3-22 l
l
.s
.. _.... ~
The K, (K = F /a), is calculated frca the deflection a given by Roarx e
(5th edition, case 9b,/page 496):
5 3/4 1/2 -9/4
-1 L
t E
a =.0820 B F R e
g 2 1/8 where B = [12(1-u )3 R = mean radius of shell L = length of shell t = thickness of shell Eg = elastic modulus u = poisson's ratio The value of F is 652 lb.
e The stresses in the barrel were also evaluated using the equations provideo 'n Ro' ark.
The stress due to the impact, and the combined stresses for impact an normal operation are sumarized in Table 3-5.
The combined stresses are also compared to the allowables in Table 3-5.
As seen in Table 3-5, even using the most conservative assumption for energy absorption, the stresses are well within the allowable values.
Table 3-5 STRESS SLMMRY CORE BARREL SUXf&,RY OF APPLIED AlsD ALLO'JELE STPESS ItiTEtiSITIES FOR CORE EAPF.EL AT POItiT OF D'. PACT P
P +Pb m
P +Pb + Om + Ob m
m Applied Stress 2,799 2,806 13,178 Intensity Allowable Stress 16,200 24,300 48,600 Intensity (Sm)
(1.5 Sm)
(3 S )
m Factor of Safety 5.79 8.66 3.69 Stress Cue To Impact of the parts are considered as secondary stresses.
0583E:1 3-23
/
3.3.5 INSTRUME.1T TULE ANALYSI5 As previously discussed, the penetrations are evaluated for two postulatea hits.
The first case is for maximum impact height above the reactor vessel.
This is referred to as the "bencing strike".
The second case is for minimr height above the reactor vessel and is referred to as the " shear strike".
Th2
" bending strike" is discussed in section 3.3.5.1 anc the " shear strike" is discussed in section 3.3.5.2.
3.3.5.1 Bendino Strike Figure 3-4b shows the model used to evaluate the effect of the impact on the tube of the penetration.
The deflections of the tube at the point of impact includes both those due to bending and shear.
In addition, the local rota-tional stiffness of the 5.5 inch thick reactor vessel was included.
The overall bcnding stiffness of the reactor vessel was assumed rigid, and the rotational spring used in the cnalysis included the local stiffness of the vessel as an elastic half space.
The rotational stiffness of a rigid circalcr disk on an elastic half space is (ref 20):
3 SGr 0"
3(1-p) where:
r is the radius of the tube which is equal to 0.75";
p is poissions ratio; and the shear modulus G = E/2(1 + u)
The resistc"ce-displ;csent curve for the instrument tube is shown on fig.
3-14.
No other loads cct on the tube concurrent with the impact.
Thus the total area under the resistance-displacement curve is available to 63 sore energy of impact.
As previously discussed in section 3.3.2.1, the value ahia.
is appropriate for the target Mass (M ) o the instrument tube is that which e
includes the weight of tube above the impact point, and the effective stati:
deflected shape mass for the cantilever beem below the impact point.
It is expected that a value for the coefficient of restitution of between U ard 0.5 0583E:1 3-24
... _. ~. /
will exist for the actual missiles (part fragments) potentially involvec in the impact.
The actual part fragments are irregularly shaped and subst:ntil; local plastic deformation at the contact surfaces can be expected.
- However, there is little material in the literature that could be used to evaluate tr.c actual value for "e".
Thus, for the current evaluation, the conservative value of 0.8 is used.
Figure 3-14 shcws the load and deflection that would occur to absorb the required strain energy for the e = 0.3 assumption. As seen on the figure, the energy wou.ld be absorbed without exceeding the conservatively defined collapse load of 1.2 L.
In addition, the stresses predicted by elastic analysis as t
shown on the figure, are less than the value of (1.2) times 3 S.
The m
impact force is a self limiting load condition, analogous to thermal loads, where the deflection of the structure, as shown on figure 3-14, is limited'oy the energy that it must absorb.
Thus, secondary stress limits are applicable for the impact load condition.
Since the load is below the effective yield point of the tube, the permanent deflections are very small and neglected.
The effective yield is defined as the load and corresponding deflection when the first plastic hinge is formed.
This definition is, in general, more conservative than that normally used.
The normal assumption is that the. effective yield is the deflection bascd sa the clastic load deflection curve at the collapse load. (e.g. the intersection of the horizontal collapse load line and the clastic load deflection line).
3.3.5.2 Shear Strike Figure 3-4b shcus the model used for the assurei missile impact at the jur.c.-
4 tion of the penetration tube and the vessel.
Preliminary calculations inci-cated that the tube is essentially rigid for this assumed ir: pact conai".icn.
Thus, the bending strike model are not appropriate for the shear impact evaluation.
0583E:1 3-25
- ~ ~ '
An alternative trethod was used to conservatively predict the load cue to the shear strike.
The tube was consicered as a perfectly rigia body and the missile was assumed to remain perfectly elastic during the impact.
As cis-cussed in section 3.3.2.1, the constant contact pressure curing impact is tr.er given by:
P = aCV ;
g and the contact time is given by:
td = 2L/C; where The terms are as defined in section 3.3.2.1.
Since td/t is small, as seen in section 3.3.2.1, the maximum dynamic loading f actor for a rectangular force-tim.e history is 0.3.
The maximum force for shear strike is F = 0.3 AP 3
where A is the contact area during the strike The contact area for the potential strike is conservatively assumed to be equal to a wicth of.25 inches times a length equal to one half of the tLt-outside diarr.eter.
The contact area is then.1875 square inches.
For an impact velocity of 35.61 ft/sec, the force is then F = 0.3 x 0.1875 x 58.3 3
= 3.3 kips The average primary pure shear in the tu::e is then 2.27 KSI.
This strets small in cc.Tpariscn with AS:'.E Subsecticn NB allowable for pure shear v.hicn.:
0.6 Sm or 14 KSI.
0582E:1 3 26
~
-.--..a.'
3.3.6 THERM;;L SHIELD FLEXLRE rad.YSIS The thermal shield tlexure is analyzed for two postulateo impacts. The analysis is presented in sections 3.3.6.1 and 3.3.6.2.
3.3.6.1
^ Impact at Center of Thermal Shield Flexure Tne load due to impact for this case is calculated assuming the minimum effective mass of the target and a coefficient of restitution of 0.8.
The load-deflection relationship for a center load on the flexure is snown in Figure 3-17, corrected for the effect of simultaneous operating loaos.
For a minimum target effccuve mass of 7.21 x 10-5Lb-sec /in the energy that 2
must be absorced by the flexure is calculated to be 1.730 inch pounos.
From Figure 3-17 it is seen that the spring rate in the elastic range of the
-ap load-deflection curve is The load at which the requireo
- n.sa energy is absorbed is (
] pounds.
From Figure 3-17 it is seen that for tne t
center strike the flexure is able to withstanc this load elastically.
Therefore, no permanent set will occur and the flexure will remain structurally adequate.
3.3.6.2 Imoact Naar Flexure Succort For this case the minimum target mass is again assumed along with a coefficient of restitution of 0.8.
Figure 3-18 is the load-displacement curve for a strike 1.703 inches frcm the flexure support, correcteo for simult:.rscus operating loads.
From this figure'it is seen that the required energy is absorbed at a load of 2527 lb.
Under this load, a single plastic ninge is formed in the flexure.
The resultant permanent set in the flexure for a
(
single impact is 0.00062 incnes, which will not affect the structural integrity of the thermal shield flexure.
Subsequent impacts are not enec:cc to increase this permanent set due to material strain harcening.
0583E:1 af f
l t
a
l 3.4
$UPPARY IB: PACT EFFECTS The following is a summary of the work completeo to evaluate the potential damage that may result due to the effects of locse parts impacting against the core barrel, thermal shield flexures and bottom mounted instrumentation tubes.
The current work is based on a conservative estimate of the camge that could result frcm the impacting of the largest loose part found-in tne vessel.
The analysis considers both the potential for perforation by the parts, as well as overall structure camage.
The evaluations used the AShi cc!' properties of the various target materials at 650 F.
The missiles were assumed to be traveling at the velocity of the coolant at the target to estimate the missile kinetic energy.
The potential for perforation was estimated by assuming failure by local snear mechanism that results in punching out a plug of the targest material.
The energy required to punch out a plug of material and kinetic energy of missiles were than calculated. The smallest margin of safety calculated is 1E2.
The above method were also used to conservatively estimate the potential for penetration or denting.
The predicted dent is quite small.
The maximum depth of dent is 0.001".
In order to evaluate the overall response of the targets (structures) for missile impact, the evaluation for potential damage was performed using tnc conservative assur,. tion of hard impact.
Conservation of nementum and energy are usea to deterline the portion of tc kinetic energy of the missile that is transmitted to the structure te be absorbed as strain energy.
The strain absorpticr. capability of the structures was determined botn sy elastic analysis ard by plastic collapse load analysis.
(The core barrel w u only analyzed by elastic analysis and shown adequate) 0583E:1 3-28
~~.
f.
m _._ __
In the collapse load analysis, the assumption for the stress-strain relation-ship is that of elastic-perfectly plastic behavior.
This assumption is con-sistent with that used in ASME Sec. III, subsections llB and ilG for cc puting the collapse loads C ano L, respectively.
Tne yield stress value for L
t the material where perfect plastic behavior b'egins is assumed to be 1.5 S.
g The yield is then increased by a conservative factor of 1.2 to account for the increase in yield stress due to the rapid strain rate during impact.
The energy absorption capability of the structure was reduced to reflect both sustained load and cyclic loads that exist concurrent with the impact.
A summary for the three defined targets is:
- 1. '
CORE BARREL At4ALYSIS
'The missile energy is assumed to be absorbed by the core barrel in elastic strain energy.
The value used in the analysis was for the conservative assumption of minimum target mass and a coefficient of restitution (e) equal to 0.8.
The stresses were calculated for both the overall response of the core barrei, and the local shell stresses at the point of impact.
The impact stresses when combined with the normal operating stresses are within ai Lwable values.
2.
24 strut /EilT TUBE AffALYSIS The penetrations are evaluated for two postulated hits.
The first case.is for maximum impact height above the reactor vessel.
This is referred to as the "berding strike".
The second case is for minimurn height above the reactor vessel, and is referred to as the " shear strike".
The instrument tube is able to withstand either of the postulated impact strikes.
0583E:1 3-29
/
s, s.___._-__..___.--
3.
TilERMAL SHIELD FLEXURE ANALYSIS The therraal shield flexure was analyzed for impacting loose parts at two postulated locations - at the center of the flexure and near the flexure support.
The flexure was shown to be structurally acequate for both of :ne postulated impact strikes.
9 0583E:1 3-30
~ %
/
w.--a
.. a..a :. _,,,,z _, __
f P 4 - ?_ o U. N c N N ~'. h s
M AcaiNE S cas.W
( $ EE 3 v a y_.. 3 m r f } -
N'
')
WASHER.
o.D = Ic "
TH I CXIJESS : 4, l
G y :20 unc i
4 Nur l
Id ACRoSS FLATS p..
7.
PottdT - To-PotNT i
TRIC.14 NESS
- k "
4 i
! AL.L PAPTS STAJ N LESS STEEL
- 4 INCH
!oVERALL lei 4GTH 1
w ElGHT OF ASSEMBLY =
0.3 otJwcE.-
L 1
C i
f!T
- _]
l y7(
3".
V
.v l
l 5
~,.
, a-37.
1+
l 3cLr
- 35. TAIL FIGURE 3-la LOOSE BOLT ASSD! SLY i
3-31
/
k;"
--,II wa; h Sl H,i" Q
D<
4~
4,-
' 4 >=r s\\ @ ;-
g v__
4 Tsicut4tss = o.or o ira.
o m
i l's i
i r~
i-t 4
{
L L.
r n
r, "
e~
- 1Le FIGURE 3-lb hit!GE FRAGME{TS 3-32
g i
A M
i.!
gC.ma:.-
i
_u s
E55 P
G L.G e 9 4
j
"' " '!' W 0 [9 r[.:355fik; l
j t.
o.i,
i 3=
l i
2.
d
.wlk =l i
d'i 1
'l
?%-
J >L l
il l: ilt @ i '!!
E k,I l
[.
i[ [$
i I E, pd) (. ! ); 'lj j d-.
[1 l
+-
ki. 'y N k @ di.d6Md E/
'#iE===mMUSHPNI $
2 mgg. 9 3 l
lifffd.
1j#
hb.YN IDE E E
y e
2 gg g
u0 MIINNO((
[MTThiaals'k.
I
)
\\
i ii
}
1 i
e
,yF M,.q,p
/
U, DETAIL AT NOZZLE t
11 k
b !p} C IMPACT
=
REACTOR VESSEL GENERAL ASSEMBLY Figure 3-2a. Actual Core Barrel Configuration 3-33
9 I
1
?
o i
r
~
t sh P
t P
L k
s D
I
+
w t.
w-t.
k h
t t
L
- 5h F
i iI l
Figure 3-2b. Idealized Core Barrel (Local Model) y lI e
p 3-34 I
' -THERMAL U
- I SHIELD j
i i
1.
1 m
,n
~.,J.
'y N'//}~
'-d
'.f4 N
N N N N N N N
'NN x / / A-
\\.a.
3t.:= m. _. %-
( FLEXUriE x
^
7 ;;A
/
/,-
/
i CORE BARREL
//
..t.
4 i-Figure 3-3. Actual Thermal Shield Flexure i
3-35 I
t m-
..g--.__,,-~,__,,_,,,m.,
,_,,-w_.~
,. _,, - _ _, ~
gmet-e tp n.
-im'. --e+
-9r.* # # #' ?
g*md' L-. r~,,
_a s.
,.s
' h*
, /, '1 '.'!I! e.,
,N y
.}
m L-. -
-g s
fi m
~. ' ' '
. ;.1
.d 1F
.i'
,e.
ful il.,
..'s,
- j M,#q s
i i'
.F
!h
\\'
/
-l' '; ; l! ;"'!
~
- }
(!, ; 5 j f,'
\\
,\\
/
I,l hl' l
i
,/
c-,,,-...
64 s
7.-,.7 ', 7
\\,
i:
g g'
\\'
. "t,,
/
j ll.
f
- i;t.
N i
'+t i
f Q
'[
,;i*I 3a,
\\
m e.
m._'
j s
.s
, a f;,
- 0. i t.
t.,
Y)'d em ii,. g '- 4 l
,/
y
\\
/
- l,'
h
-: k lh
- l.,
~
i e:
s
- f
,l' q.
- ' '! h
\\
pj; i -
t a
j
- 3. y.. ' C- -..
___..m.__.._,,_
P,
,1, a
'.. r,---
3,
- ,w.
s...- - ~. -
.m._,-
ej..-
in s
w;.:.
~
2 c
- a,r.
. u =. :.
w d a... m :.. 1 W. -, a w : u -! '.. = c..
...w....,,
u:
. _ ~_.d,
, g-W/ " W/
W/ $"
7,.
-/
- / W) M x
r c
, C. /.
u.-
n a.
e w -~
Ly or 8
/
ih w?
I' e
d
,.1 jp
>i I
a Wj
}
6 r
.i I.
N.'
l P
I
[
1 fy p
u,'
f (
E,
'j ;a,
/y/M
/
F r
//,
! V
/ f' 4
+
t-49 m,-
/
=
N W
(
Al[f f.-]!
,J
'/
E
}
N*
d A
i 3
' '; p r
A r
t ej; (j
4 s.
h l
ed~' O A rN
- n n(ih x.K
>a
't (
ipf r
r a-0 i
4 l m} NAjd1
-/1.Y
[
x 4
N
\\..
[
\\
,Lw p
m. u..-
m \\.?./
I,
. /
e MN
/K N
LJ e"J. '
e 1i
\\
A<<h',.
N Tj
\\
m s
n m
t i
o 4
i g
N n'
3>
F A
- h. H.
l I,. :] ~l'.~-
v, /\\
t s
i 7%g+. i, \\
h
$r%
W CN'>I t
/
\\
~S x-%[j:2.. m
.;_ %w ;i N
u%
4 N
ap-k
\\
N.- :- w.___ a =c m/ )
N 3 gj y s
/r N
~
IMPACT ON A.;
WEDGED BOLT AREA- '
TUBEISPCL.
BOTTOM MOUNTED INSTRUMENTATION Figure 3-4a. Actual BMI Penetration Configuration 3-36 l
l
_,,,__,....m.
.. ~.
m
= * - ' * ~~- ~ s
=~ *****"' ~ '
~~ - ~ ~ ' - -
~
' ' * ' ~
or 2 + -
e v,
l 19,178-17 I
~
an IDEAll2ED BMI PENETRATION (BENDING STRIKE)
I
,y
=
(
IDEAll2ED BMI PENETR ATION (SHEAR STRIKE)
Figure 3-4b. Idealized BMI Penetration Configuration 3-37
{ll l<ll I
0 h
=
=
x x '
x o
y V
=
YT IC O
L EV T
T C
E A
G P
R E
A v
2 L
M L
S T
E
(
I S
D i.
T S
f O
A I
M S
M N
t O
=,
R r
A I
T E
O H
1 M
S fkit E
G L
N I
I I
S H
S C
s I
M N
e U
I P
e l
il f t4 ni ob l
l1I\\fll 1[$h i
Ir1'6ll 1l!i
,l i qi 6
l l
1
l l
$~ ~-r~ s g
,-3
's,%,
s' S
~~
, s (A) ELASTIC
?
?
s
[., ' s
/3 n
s~~
~%w__ps#
(B) ELASTO-PLASTIC 9,
,' ' e - -
x
=
~.
. s
's's s-
s,
/,s (C) PLASTIC Figure 3-6 Atsumed Static Deformed Shcocs for Determination of Efke:ive,n=
3-39
/
/
../
2.0 Co 1.5 HO<
u.
O<o 1.0 a
9
- 3<::
0.5
/
O db.b.---
l-I !_! ! I I
I-l ! l llI 5
10-1 2
5 100 2
5 101 CT = td/T Figure 3-7. Dynsmic Lead Facter for Linear Ebstic System Rectangular Impulso Load (From Rei 12) 3-40
~~" %. m. _,c, c _ _ _ _.s _._ ___.
O bb OO UUV UU PERIOD OF PERIOD OF DEFORMATION RESTITUTION PERFECTLY ELASTIC COLLISION e=1 UU UV UV PERIOD OF PERIOD OF DEFORMATION
- RESTITUTION INELASTIC COLLISION 0<e<1 h
PERIOD OF PERIOD OF DEFORMATION RESTITUTION PERFECTLY PLASTIC COLL 1010N o=0 Figure 3-8.
Deformation During Collisien e
3-41
~-
4 GEOVETTitCAL i
DAWihG LAW g2 2
e t
. o o ffx 3
RAYLEIGH WAVC
- )
t HQ R tI,.
'f r=03
[
~
[
CC..
'^
x u
r i s y
i
?
~ 1.
SHEAR Ag/K *
\\g yg
- W}
AMP L17U;,2 (a
N, t
e.. %w..n
\\f e', l
\\
qf Gr. CME'TRICAL CAP #tNG LAtt Nj%.N/.
/
...Y 1,
j%_
~
,.1 [% -
$ HEAR
%' CC!.;:)Rf.TJ;!GN WAVE ~
2' W1NDOW
=2<11-umurs
~
1 (s) v s.
4 4
t (b)
P2n C:;tT CF WAVE TYP3 TOTAL f.NERGY RAYLE!CH E7 iMr1.n 23 CoMPfiEI:?f0M 7
s THE EASIC FEATUTIES OF THIS WAVE FIELD AT A RELATIVELY LARGE DISTANCE
- FROM TH'I SOUTiCE ARE SHOWM IN FIG. :-12a. THE DISTANCE JSOM THE SOURCE OF V! AVES TO EACH WAVE FRONT IN FIG. 3-12a IS
~
ORAWi! IM PROPORTION TO TMd VELCCITY OF EACH WAVE FOR A MEDIU.*.* WITH r = 1/4. TliE LODY WAVEG PROPAGATE RADIALLY OUT-WARD FHO.'.1 THE ECURCE ALC JG A H !E:)MERICAL WAVE FRONT (HEAVY CARY. Llt'~S IN FIC' C-12a) AT'"; THE RAYLE;GH WAVE PROPAGATO.
RADIALLY OUTV.'ARD ALOij3 A CYLINuRICAL WAVh FRONT.
'ACCORDING TO LYSTMER (RU?.14), A DLUANCE OF 2.5 WAVE LENGTHG FROM THE SOUfiCE IS A LAEGE DISTANCE.
Figure 3-9. Distribution of Di:abCement Waves From a Circular Fcoting on a Homogeneous.1:c:repic, E!c :ic Half-SpaC:. (From Ref.13) t L
i s
O
y T
N N
X A
E
\\N p
Y.
M ND
=
B E
3 C
ERN u
D A
xU DN E
X Y
S L
y S N P
n T
N U-A S
x YO I
I O
L n
c D
Y GLN I
I R
E T
T G
xE R
C C
RD I
in CN E
U EA a
x EAN NT I
L D
NO n
i F
S E
E EL T
xINS e
D L
NC AAN B
l
! I b
L W
RC xRTYN i
E A
AL l
B TY a
O N SB v
A SC A
L W
L N
1 O
A g
NNN n
L i
L
=
w A
p o
hS
/.
n e
3 Nx f
p v
X r
1.~
C R
t D
n A
e O
n r
L
-e S
Y i
S G
p P
E!
i s
A L
D E [/
L O
L N
A E O
L ec C
N i
I l n
A; ta VA s
AR s
T e
F r
S N
\\
0 1
'NNx r
/
3
/
u L
1 f
/ //
j f
iL t
/
/
f3t F
X 4x
./ / /
0' Yf h
' j
\\
g R
R' g oE J"
~
Y
DESCRIPTION RESISTANCE ST1 F F'!E C (1) CANTILEVER R
M
/
Y Rg=
K = 3E1
/
u 3
L
/n w
L (2) SIMPLY SUPPORTED R
I
[
Rg K=
a U2 U2 (3) FIXED SUPPORTS R
g 4(M+ + M')
Ru=
K = 192E!
u u
(_
Y f
3 I
[
L
/
/
Igx e/
U2 U2 4(M+ + M')
(4) MULTI-SPAN nu--~
K = 97*d I u
u.
R L3 y
trhi.
Oh Ah Ahr h
- wh 2>!-:U2-M :
d L
L/
L WHERE M ' = ULTIMATE POSITIVE MOMENT CAPACIT
u M
= ULTIMATE NEGATIVE MOMENT CAPAC;T u
I
= MOMENT OF INERTIA (in.4)
Figune 311 Stiffnca and Recistance Values for Beams
_ - = - - -.
DESCRIPTION RESISTANCE STIFFNESS (1) SIMPLY SU.' PORTED ON ALL 4 SIDES WITH LOAD AT CENTER I
a R
<Ru = 2rM K=
u
_2 aa gi_p2)
_L h
b b/a 1.0 1.1 l
1.2 1.4-l 1.6 1.0 2.0 '
3.0
=
a
.1390
.1510
.1624
.1701
.1084
.1944
.1981
.2029
.2031 N
4 v
= POISSON'S RATIO 0;
t
= TillCKNESS (in.)
E
= MODULUS OF ELASTICITY (iblin.2) e t
= MOLtENT OF INERTIA PER UNIT WIDTil lin.I/in.)
(2) FIXED SUPPORTS ON ALL 4 SIDES WITil g"+ = ULTIMATE POSITIVE MOMENT CAPACITY (in./lb/in.)-
LOAD AT CENTER Mf =. ULTIMATE NEGATIVE MOMENT CAPACITY (in./lblin.)
T a
-R Rg = 2 r (M,+ + M -I K=
u 2(j_g,2) aa
_1 p w{
b/a 1.0 1.2 1.4 1.6
~1.0 2.0 m
n
.0G71
.0776
.0830
.0854
.0864
.03G6
.0871-1:iyne 3 12 Satinen anil ikshtuu! Vahics ha l'l;ite> anet St.ibithules Concenst;ite!!'l umis '
t
TYPE OF LOAD SUSTAINED LOAD CYCL!C. LCA D P
O F
U F
l m
k
/
P f
'l N
V
[\\\\\\\\NS
/ -P s
(a)
I 1
3 5
X X
m m
R 7
R m
w P'
p>
t Y
Y t
M'\\,'\\N N W
wL P..
2 R
L f.1
/\\' y m
3 p
NONE DEFLECTION a 4
d 0
3 2
3 (c) 8 (ht - t,*,3 )
PL3 y
3 P3=-L a,.
102 El 32 f*I 7 (P2-P)L 1
1 P -P3= 0 2
2 1
5 L
763 E !
(Rm -P;) L3 k6 03-02" gg,
.h, I
NONE NONE (d)
LOADS Tif AT 00 NOT CAUS~ CCT' DING If1 Tile PLANE OF THE EEAM CO NOT EFFLCT Tl:E ENEriGY,CICRPTION: BUT SHOULD SE CONSIDERED WHEN TOTAL STR AINS AP.E EVALUATSD.
}\\\\ \\3 = LCIT E?JEriGY (1) TifE EFFECTIVE FORCE P FOR SEPARATE CYCL!C EXCITATION CONDITIONS SHOULD7~
CCf.*B!NED BY THE SRSS METHOD.
~~ - ~
_ n-_
IMPACT AT CENTER FIXEO - FIXED BEAM Figure 3-13 a.
Energy Redue: ion for Concurrent Loads
TYPE OF LOAO SUSTAINED LOAD CYCLIC ' t OA D p
Rm
/
N F
F I
1)
)
l
/<
'D
/ \\.N N N N N N P'
~
1 3
g j
(al X
5 X
3 m
m P' = 1.SSOP j
W h
l l l l-l l l l
F Rm
/
t v i t V y 7 "y
\\
F R*
9
.s'-
p.
p.
XNNNNN:NN 2 2
(b) 6 P ' = 1.540 E 2
.2 U
L m
y M
P 3
2
--f NONE 1
a M 4 o
4 3
A s
,1 --
y y
/
/
DEFLECTION a i
A 0
g, GEla 1
2 h
L#
P, = 7'lll L
(Mp-M) a; =
(M
-M )
3 3
L 64El p
(d 5
P2=*L (13 Mp - M,)
42=
(0.C332 M + 0.0255 M El p
R M
m p
d2=
(0.C937 M + 0.14c 5 M.
(
p 5
- e s
e A/
^
LOADS THAT CO NOT CAUSE BENO!NG IN THE PLANG OF THE SEA'M CC NOT AFFECT THE ENORGY ASSORPTION BUT SHCULD BE CO.';31CdiiE:
(d)
WHEN TOTAL STRAING ARE EVALUATED.
[
= LO.'.T ENERGY IMPACT AT POINT L/4 FRCM SUPPORT FIXED KiXEO SEAM Figure 3-13b. Energy accuc: ion for concurrent Leads 4
- ? <17. - - - - - - - - - - - - - - - - -
.e S
! Id 1 I e
G MCO mDoC C
A
~
Ce E
mD MC CO oCm 1
Co Eo O
_4 e
O le U
C to
=
MCE V
e c
w U
..O.
1 L
_I
'N a.se"
-THERMAL SHIELD 4
_.// 7
~
'x ' x N /.:' /,
=< -.-.
c3 Q
m
\\
['
1 2
C
- --C 4
,7 NN M
y v
N N N N N N N f
_if--'~ ~_~ T
(!
h.=e - ~rd
~T~)
FLEXURE
\\
CORE BARREL sh 1 - CENTER STRIV,E 2 - END STRIKE Figure 3-15 Actual Thermal Shield Flexure 6A
~ - - - "
\\
I
..m
'k i
4 I
t.
Figure 316. Flexure Normal Loads (Concurrent Loact) wars
p a
se ruxe l
F d
l ie hS la m
re h
T no itcnu F
tne m
e c
a lp s
iD
-ecna t
is se R
7 1-3 e
ru ig F
= = _ _ _ _
!'+
v
-.tA j i
i i
t
?
t E
t i
r l
r l
l v
l t
f l
=
I r
!w
- i
- N m
t l
J r
1 1
1 l
I I
1 i
i I
1 i
1 1
Figure 3-18 Resistance-Displacement Function for Thermal Shield Flexures i
I i.
f
4.0 REFERENCES
' ~ " ~ ~ ~ ~ ~
1.
Singleton, ti.
R., Davidson, A. C., and Hluhan, R. A.. " Phase I Analytical Assessment for Effect of Loose Parts InWian Point Plant Unit No. ?",
WCAP-9924, 1981 (Westinghcuse % crietary).
2.
Roark, R.
J., and Young, W. C., " Formulas for Stress and Strain" McGraw-Hill, 5th Ecition 1975.
3.
." Reactor Ccolant System Operating Limitations",
Zion Plant, Unit No.1, Telecopy Ccmunication, May 4,1982.
4.
"WECAN - Westinghouse Electrical Computer Analysis User's Manual",
Westinghouse Electrical Co.
5.
Davidson, A. C., " Calculation Brief on IPP Unit No. 2, Section 2.0 Phase I Report", Unpublished report, 1981.
6.
Richart, F. E. etal, " Vibrations of Soil and Foundations", Prentice-Hall, 1970.
7.
Manjoine, M.
J., " Influence of Rate of Strain and Temperature on Yield Stresses of Mild Steel", Trans. Amar. Soc. letch. Enors.
J. App. Mech. Pages 211-218, 1944.
8.
Williamson, R. A. and Ralvy, N. R., " Impact effects of Fragments Striking Structural Elements", Holmes and Nauer, 1973.
9.
Linderman, R. B., et al, " Design of Structures for Missile Impact",
BC-TOP-9-A, (Rev. 2), Bechtel Pcwer Company 1974 10.
ANS-58.1 (AfiSI-N177), Draft, " Plant Design Against Missiles",
American Nuclear Society, August 1975.
11.
Biggs, J. M., " Introduction to Structural Dynamics", McGraw-Hill, New York, 1964.
12.
" Manual of Steel Construction", 7th Edition, American Institute of Steel Construction", 1973.
4-1
_