ML19209A687
| ML19209A687 | |
| Person / Time | |
|---|---|
| Site: | 07109132 |
| Issue date: | 08/15/1979 |
| From: | NUCLEAR PACKAGING, INC. |
| To: | |
| References | |
| NUDOCS 7910050201 | |
| Download: ML19209A687 (90) | |
Text
rop]gt 7 /_ 9131 r
l uP pguRGRl81Wu SAFETY ANALYSIS REPORT FOR THE FFTF FUEL PIN SHIPPING CASK MODEL - T3 REVISIO11 2 AUGUST 15, 1979
~
791005020/
][
NUCLEAR s NuPpc PACKAGING,INC.
W 1
0.28TH STREET. TACOMA, WASHINGTON 98409.,'206)S72 7775 838-1243
.7~J NUCLEAR (NuPbc) PACKAGING,INC.
,.^
815 SO. 26TH STREET TACOM A, WASHINGTON 98409 (206) $ 72 7775 E'61243 -
September 12, 1979 Mr. Charles E.
MacDonald, Chief Transportation Certification Branch Division of Fuel Cycle and Material Safety, I; MSS United States Nuclear Regulatory Commission Washington, DC 20555
SUBJECT:
Docket No. 71-9132 Model T-3 Shipping Package
Dear Mr. MacDonald:
In response to your letter of July 25, 1979 we have enclosed Revision 2 amendments to our Safety Analysis Report for the T-3 Shipping Cask.
Eight (8) copies of the amended pages, plus instructions for their incorporation, are attached.
Your prompt attention will be greatly appreciated.
Sincerely yours, N CLEAR PACKAGI!G, INC.
1 ohn D.
Simchuk JDS/dmm Enclosures - T-3 SAR (8 copies)
Revision 2, 8-15-79 T110 150 1c.czs
INSTRUCTIONS FOR INCORPORATING REVISIGN 2 AMENDMENTS TO MODEL T-3 SHIPPING CASK APPLICATION DATED AUGUST 15, 1979 Insert new page 1-6a Remove old page 1-6a Insert new page 1-6b Remove old page 1-6b Insert new page 1-6c Penove old page 1-6c Insert new page 1-6d Remove old page 1-6d Insert new page 1-6f Remove old page 1-6f Add new page 1-6g Add new page 1-6h Add new page 1-6i Insert new page 1-60 Remove old page 1-60 Insert new page 1-60b Remove old page 1-60b Add new page 1-60b (1)
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Insert new page 1-60d Remove old page 1-60d Insert new page 1-60e Remove old page 1-60e Add new page 1-60e (l)
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Add new page 1-60e (5)
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Add new page 1-60e(14) 1110 151
Page 2 Instructions, Cont'd.
Insert new page 1-60f Remove old page 1-60f Add new page 1-60f (l)
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Insert new page 1-60g Remove old page 1-60g Insert new page 1-60h Remove old page 1-60h Add new page 1-60i Add new page 1-60j Add new page 1-60k Insert new page 1-77 Remove old page 1-77 Insert new page 1-77a Remove old page 1-77a Add new page 1-77b Add new page 1-77c Add new page 1-77d Add new page 1-77e Add new page 1-77f Add new page 1-77g Add new page 1-77g (l)
Add new page 1-77h Add new page 1-7 7i Add new page 1-77j Add new page 1-77k i110 152
Page 3 Instructions, Cont'd.
Add new page 1-771 Add new page 1-77n Add new page 1-77n Add new page 1-77o Insert new page 1-90 Remove old page 1-90 Adel new page 1-90a Ad.d new page 1-90b Add new page 1-90c Add new page 1-90d Insert new page 1-91 Remove old page 1-91 Add new page 1-91a Add new page 1-91b Add new page 1-91c Add new page 1-91d Add new page 1-91e Insert new page 1-92 Remove old page 1-92 Insert new page 1-93 Remove old page 1-93 Add new page 1-93a Insert new page 1-94 Remove old page 1-94 Insert new page 1-111 Remove old page 1-111 Add new page 1-llla Add new page 1-lllb Insert new page 112 Remove old page 112 Insert new page ll3e Remove old page ll3e Insert new Dwg. H4-61289, Rev. 2 RemcVe old Dwg. H4-61289, Rev. 1 1110 153
Revision 2 August 15, 19'/9 1.1.2.2.2 Cask and Overpack Structural e'Tluation of non-containment vessels items such as the external skins, closures, overpacks, lifting and tiedown fitting were evaluated against yield and ultimate material pro-perties as presented in the ASME Code,Section III, Class I.
For Normal Conditions of Transport, yield strength was used as a maximum stress for the cask.
The overpack is allowed to exceed yield stress for normal conditions; hence, ultinate stress or strain is used as the acceptance criteria.
In evaluating 3.ccident Conditions, ultinate stress or ultimate strains were used as the acceptance criteria.
1.1.2.3 Other Structural Failure Mcces 1.1.2.3.1 Brittle Fracture The two primary materials used in the cask are 304 stainless steel and A516 carben steel.
Both of these materials meet the 0
requirement of ASTM A20-77 (13 ft-lb, Charpy) of -40 7.
Therefore, per Cask Designers Guide, ORNL-MSIC-63, they are considered to have adequate toughness and are safe from brittle fracture.
1.1.2.3.2 Faticue 1i10 154 1.1.2.3.2.1 Containme.
Vessel For the containment vessel, fatigue will not be a problem on the basis that the allowable strest for normal conditions (3 S ) will not exceed the allowable fatigue stress limit for the expected nunber of operating cycles.
Frcm Table I-1.2 of ASME Section III Appendix I, the T.ani=un value of th' stress intensity (5,)
at the 1-6a
Revision 2 August 15, 1979 maximum normal operating temperature ( < 200 F) is 20,000 psi (A240, Grade 304).
The expected number of operating cyclec (defined as the process of going from an empty cask, to one with a maximum heat load, at the maximum normal operating temperature and back again) for the T-3 Cask is below 3000.
From the ASME Code,Section III, Appendix I, Figure I-9.2, the fatigue allowable stress amplitude, S f the alternating stress component (1/2 a,
of the alternating stress range) for 3000 cycles is 65,000 psi.
The nonfatigue allowable stress limit ASME Section III Division 5
1, Subject NB-3222.4, however, is 60,000 psi (3 Sg).
Since this is less than the fatigue allowable, then the nonfatigue allowable stress criteria will govern, and fatigue is not a concern for the containment vessel.
1.1.2.3.2.2 Bolts End Closure Bolts - For the end closure bolts the maxinum cyclic stress is due to the preload.
From " Machine Design", September 11, 1969, Page 20, Table 4, the preload is given by:
D Mhere:
P = bolt load, lb.
T = torque, in-lb K = torque coefficient D = nominal bolt diameter, in.
1110 155
Revision 2 August 15, 1979 Based on data derived from the reference, the recommended design torque is 400 + 20 ft-lb, or a naximum of 5040 in-lb.
The bolts are nominally 1 in. diameter, hen e D = 1 in.
The torque coeffi-cient (lubricated) is K = 0.15.
Therefore, maximum bolt load is given by:
5040 p,
(.15) (1) 33600 lb.
=
The stress area of the bolt is.606 in Stress in the bolts is:
33600 U "
.606 55446 psi
=
From Para. NB-3232.3(c) ASME Code, the fatigue strength reduction factor is assumed to be 4.0.
In addition, the modulus of elasti-6 city at < 200 F is 29. 5x10 psi (Table I-6.0, ASME Code).
Since 6
Figure I-9.4 (ASME Code) is based on 30x10 psi, the equivalent allowable stress range is given by:
30 S
(55446)(4)(29.5)
=
range 224,000 psi
=
The alternating component is 1/2'of the stress range, or 112000 psi.
From Figure I-9.4, using the 2.7 S, curve, the allowable number of operating cycles is greater than 800.
This is equi-valent to eight years of continuous package service.
Operational procadures will soecify replacement of these bolts every five years, thus assuring a fatigue failure margin of +0.60.
1i10 156
Revision 2 August 15, 1979 Conta.nment Closure Bolt _s - Repeating the same approach as above.
Based on the reference data, the recommended design torque is 40 I 10 ft-lb, or a maximun of 600 in-lb.
This torque level assures that the preload exceeds the maximum load for operating and accident conditions.
Since "O" ring seals are used, minimal sealing pressure is required.
The bolts are 1/2 in, diameter, hence D =.5 in.
The torque coefficient (lubricated) is K = 0.15.
Therefore, the bolt load is given by:
(600) p,
(.15 ) (. 5 )
8000 lb.
=
The stress area of the bolt is.1419 in'.
Stress in the bolt is:
8000 U *
.1419 56,378 psi.
=
The equivalent allowable stress range is given by:
S (56,373)(4)(29 5}
=
range
= 227,766 psi The alternating component is 1/2 of the stress range, or 113,883 psi.
From Figure I-9.4, using the 2.7 S curve, the allowable m
number of operating cycles is greater than 800.
Tnis is equi-I valent to eight years of continuous package service.
uperatienal procedures will specify replacement of tnese colts every five years, thus assuring a fatigue failure margin of +0.60.
1110 157 1-6d
Revision 2 August 15, 1979 6
number of operating cycles is greater than 10 Since this is greater than the anticipated usage of the push rods, they will not experience any fatigue failure.
1.1.2.3.2.3 Buckling Buckling per Regulatory Guide 7.6 is an unacceptable failure mode for the containment vessel.
For normal and accident conditions, this can be demonstrated by a brief examination of the contain-ment vessel buckling failure modes.
The stress corresponding to an axial load sufficient to collapse the 8 inch diameter containment vessel, as a long column, can be estimated with the Euler column formula:
2 Cn E C=1 (Pin-ends)
(pjg)long (L/r)2 6
=
E= 29x10 column L = 147 inches 114350 psi r = 2.938 in. (Sch 40 Pipe)
=
The axial stress required to locally cripple a cylindrical tube can be estimated from the conservative formula:
E (P/A) crippling = 0.12
- Roark, 5' Edition, P.
428 269884 psi
=
Under the provisions of NRC Regulatory Guide 7.6, paragraph C.6, combined stresses (P +Pb) for accident conditions are limited g
to 3.6 S
- S whichever is less.
For the A312 pipe material:
m u,
(3.6)(20,000) = 72,000 psi 3.6 S
=
m S
= 75,000 psi u
1110 158 1
=
- Revision 2 August 15, 1979 Thus, application of these provisions provides an automatic minimum Margin of Safety against containment vessel buckling of:
M.S. = 114350/72000 -1 = +0.59 Buckling cannot be induced during the fabrication process because the final containment vessel to end cap weld is not installed until after lead pour cooldown, reference flagnote 12, sheets 1 of 3 and 2 of 3 Dwg. H4-61299, T-3 Shipping Cask.
Mhile buckling of the containment vessel cannot be induced by the fabrication process, eccentricities are permitted by the tolerance requirenents which lower the buckling allowables below those calculated above for a " perfectly" straight column.
In particular, there are three tolerance specifications perti-nent to containment vessel column eccentricity:
cylindrical within 0.200 inches (overall) straight within 0.060 inches in 3 feet straight within 0.015 inches in 1 foot The nost severe of these three tolerance specifications is the cylindrical requirement which limits maxinun eccentricity to i
0.200 inches.
Using the secant formula, Roark, 5th Edition.
Page 422, the critical buckling stress is found as:
Sv Scr "
^
r h S"
t+"i"*
(ko j
4e 1110 159 l-6g
Revision 2 August 15, 1979 For:
e =.20 inches c = 4.3125 inches 8" Sch. 40 Pipe r = 2.938 inches.
2 = 147 inches 6
E = 28.3x10 psi ASTM A312 Material 30000 osi S
=
y S
= 26355 psi cr For normal conditions, primary stresses in the containment vessel are linited to S
= 20000 psi.
This provides an implicit n
Margin of Safety against buckling of:
M.S. = 26355/20000 -1 = +0.32 For
.cident conditions, primary stresses in the containment vessel are limited to 2.4 S or 48,000 psi.
Importantly, l
m l
however, all accident related loadings are body force loads i
(i.e.,
columns loaded via their own weight); not pin supported l
1 and loaded, columns investigated above.
For columns of this I
I nature, the critical buckling load is considerably higher (Roark Sth Edition, Table 34, Case 3a):
(p t) cr = Kr EI Self Load:
g, y,gg t-t 2
'fI l
End Load :
P
=
g 1110 i60 1-6h
Revision 2 August 15, 1979 Thus, the critical buckling stress for a pin-ended column loaded by its self weight is 189% of the same column loaded by end forces, P.
Thus, the equivalent buckling stress for acci-dent loadings, considering eccentricities, is:
(26355)(1.88) = 49547 psi S
=
cr Again, a small but positive Margin of Safety is implicitly provided for accident events by application of MRC Regulatory Guide 7.6 provisions:
M.S. = 49547/48000 -1 = +0.03 1110 161 1-6i
Revision 2 August 15, 1979 1.6.5 Water Spray Since the package exterior is constructed of steel, this test is not required.
1.6.6 Free Drop The package weight of 38000 pounds dictates that the T-3 must survive a one foot free fall without substantially reducing its effectiveness in reacting subsequent accident conditions.
The package has been designed to withstand 30 foot falls (Ref.
Section 1.7.1).
Energies generated during the 30 foot drop are 7
1.368x10 in-lbs.
Energies associated with the one foot drop are:
KE = (38000 lbs) (12 in) 456,000 in-lbs.
=
For impact energies of this magnitude, the computer generated data shown in Section 1.7.1 provides maximum impact accelerations.
These loads are summaries below.
Condition 1 Foot Drop (g's)
End 16.0 Corner 9.8 Side drop conditions, presented in Section 1.6.6.3, are evaluated by finite element analyses using the principles from the Cask Designers Guide.
!110 162 1-60
Revision 2 August 15, 1979 For the End Drop condition the axial compressive stress in the containment vessel is:
(95. 48) (16 g's) = -1527 psi f
=
y The corresponding axial ctresses in the lead and outer steel shell are evaluated as follows:
~
3
(. 41 lbs/in ) (16 g) (166.75 in) = -1094 psi f
=
y Outer Steel Shell 3
?
7 (16 g) (. 29 lbs/in )
n (13. 0 5 -12. 05~) (177 ) +n (13. 22 ) ( 5. 2) g Y
n(13.05 -12.052) 2 s
= -990 psi Due to these axial compressive stresses and the Poisson effect, the additional stresses are imposed upon the containment vessel.
The extent of these stresses was investigated by a small ANSYS (Rev. 3) axisynmetric finite analysis using the model illustrated in the following sketch.
Resultant stresses are presented immediately following this sketch versus locations denoted in this sketch.
bS
/
T 'W'5I WS j, LAC m$m d
/,g xNx fasah x
x ia.
s s
N I
Ns x
x N 'x x
s N
'x 'x
\\\\s
'N
\\
s N 'n '
newsa,imu av N
N~~
k yo n! itaa,
'N f
N fes atxr i:ssif
~
n
/
1110 163 1-60b
Revision 2 August 15, 1979
-/ QTY)ti kl l
~/099h tt
-792 P,
s l
i l
}
V Y Y f f f 1 f f f _ _L Y._T_f_ T T ? _ 1. X Y -- T.
6 43&&"_
'8-%
44 99i MM]
r I
/9
/8
/4 19 x.,
17
/A
/9 fo 2/
W h
<3 2 ?
- 2) 2 a 3 GD f
/e
/ /// 2 // 6 4
5 6
7 8
9 '" /o '" //
mo I
=
.q SW '*/evi puyg VEW4 f,jppV b :r $ 9,4 S C W lf /- W.ifor/
Stresses Radial Axial Shear Hoop 6
Location x)
If )
(T y)
(f )
v 7
1 0
- 622.42 0
- 648.11 2
- 87.46
-2365.00
-28.51
-1153.70 3
0
-4026.00 0
-1562.4 4
0
- 323.90 0
- 165.05 5
0
- 102.45 0
+ 224.17 6
0
-1948.9 0
+3161.7 7
-128.07
-1259.1
-46.48
+3156.1 8
0
- 456.95 0
+3268.8 1110 164 1-6 0b (1)
Revision 2 August 15, 1979
[
These stresses must be combined with the normal pressure and thermal stresses of Sections 1.6.1 and 1.C.3.
For the contain-ment vessel, these stresses are:
Stresses (psi)
Radial Axlal Shear Hoop 1
(f )
If )
Itxy)
If x
y z
Pressure (39 psi):
-39
+ 232 0
+483 Thermal Diff:
0
+8701 0
0 Combining gives direct stress components of:
Containment Vegsel Locagion LS LB f
= -
39.
- 126.46 39.
x f
+8310.58
+6569.00
+4907.00
=
y 0
28.51 0
T
=
xy f
- 165.11
- 670.70
-1079.40
=
3 The corresponding principal stresses and stress intensities are:
Containment Vessel Location N
h a
fy=
+8310.58 6568.12 4907.00 f2=
39.
- 126.58 39.00 f3=
- 165.11
- 670.70
-1079.40 S
9475.69 7238.82 5986.40
=
7 Thus:
S
= 8475.69 psi max Material Properties:
S
= 20,000 psi (Type 304, Seamless Pipe / ASTM-A312)
Margin of Safety (Containnent Vessel) :
M.S.
= 20,000/8475.69 -1 = +1.36 1110 165 1-60b ( 2 )
Revision 2 August 15, 1979 Therefore, it can be concluded that the End Drop condition for IIormal Transport would have no detrimental effect on containment.
1.6.6.2 Corner Drop Internal loads produced by the Corner Drop can be broken into axial and lateral components.
Although the magnitude of the Corner Drop is only 60% of the End Drop loads, both components of the corner drop loads are evaluated in subsequent paragraphs.
Laterally irduced loads resulting from a Corner Drop can be determined as follows:
Internal Loads for Corner Impact M*
UE j y 2
3 F
I
- ME ot Y
" pf U
"H g
$ _ -FEsina
-6Fsin, Op 2I 2-02 x
S " Y 8i" "+ I# 2) e r
a = tan ~ D/R nN e x hN P
1110 166 1-60b(3)
Revision 2 August 15, 1979 f
(273.5 psi) (9.8 g's) ;
=
(89. 23) (9. 8)
=
b fb=
2680 psi (outer shell)
=I 874. psi (containment vessel)
Combined Lateral and Longitudinal Loads To the lateral bending stresses evaluated above must be added those stresses due to longitudinal impact forces (evaluated in Section 1.6.6.1) plus pressure and thermal effects.
These stress components nay be summari::ed as follows:
f f
T f
Containment Vessel:
x J
xy z
Pressure:
-39
+ 232 0
+483 Thermal Differential:
0
+8701 0
0 Location d (r = 3.991")
Longitudinal 0
-381.23 0
-396.97 Lateral Bending 0
I309.16 0
0 Location d*(r=4.132")
Longitudinal
-53.57
-1448.56
-17.46
-706.64 I 841.80 0
0 Lateral Beneling 0
Location d (r = 4.313")
Longitudinal 0
-2465.93 0
-956.97 Lateral Bending 0
I 874.44 0
0 Principal Strerses & Stress Intensity S
1 2
3 I
k*
Location
+ Bending 9360.9
-39.0
+ 86.0 9399.9
- Bending 7742.6
-39.0
+ 86.0 7781.6 See Sketch on Page 1-60b(1)
Ill0 l67 1-60e
Revision 2 August ?.5, 1979 Principal Stresses & Stress Intesity, (cont' d. )
f f
f S
l 2
3 I
Location d
+ Bending 8326.3
-92.6
-223.6 8549.9
- Bending 6642.7
-92.6
-2?3.6 6866.3 Location d
+ Bending 7341.5
-39.
-474.0 7815.5
- Bending 5592.6
-39.
-474.0 6066.6 Thus, maxime.a stress intensity in the containment vessel is:
S
= 9399.9 psi max Outer Stiell h
h h
h Pressure:
0 0
0 0
Thermal Differential:
0
+9876 0
0 Location d (r=12.05)
Longitudinal 0
-1193.70 0
+1936.54 Lateral Bending 0
I2442.81 0
0 Location d (r=l?.55)
Longitudinal
-78.44
- 771.20
-28.47
+1933.11 I25a4.19 0
0 Lateral Bending 0
Location d (r=13.05)
Longitudinal 0
- 279.88 0
+2002.14 I2G45.54 0
0 Lateral Bending 0
\\\\\\D \\b8 1-60e (1)
Revision 2 August 15, 1979 I
Principal Stresses & Stress Intensity:
f E
8 l
2 3
I Location [b
+ Bending
+11125.1 0
+1936.5
+11125.1
- Bending
+ 6239.5 0.
1936.5
+d239.5 Location [h
+ Bending
+11649.0
-78.5
+1933.1
+11727.6
- Bending
+ 6560.7
-78.5
+1933.1
+ 6639.3 Location db
+ Bending
+12241.7 0.
+2002.1
+12241.7
- Bending 6950.6 0.
2002.1 6950.6 Thus, It..ximum stress intensity in the outer shell is:
12241.7 psi S
=
max The Margin of Safety for the containment vessel is:
S /S
-1 M.S.
=
g nax 20,000/9399.9-1 = +1.13
=
The Margin of Safety for the outer shell is:
S /S
~l M.S.
=
y nax 30,000/12241.7-1 = +1.45
=
Under corner impact, lateral forces are produced which tend to shear the overpack from the T-3 Package.
The magnitude of this shear force is:
(9.8 g) (38000 lbs) sin R.56 F
=
g 55430. Ibs.
=
1110 169 l-60e(2)
Revision 0
)
August 15, 1979
%@ %ka This shear is resisted by a nachined lip of 3/o inch depth and one inch width on the overpack base plate that fits in a conpanion groove in the T-3 and cap / plate.
The effective shear area of this lip is:
2 (20.69 -19.692) = 61.85 in A
=
s The shear stress in the lip is:
f
= 55,430 lbs/61. 85 = 896 psi s
The shear yield for the AST'a 516, Grade 70 overpack base-i plate is:
3y ej /, 3 = 38,0007 3 = 21939 psi F
=F Thus, the Margin of Safety for shearing the overpack from the T-3 body under corner impact is:
21939/896 -1 = + Large M.S.
=
1 The bearing area is-o Ab = rdt = n (19. 69) (3/S) = 23.20 in" The bearing stress is:
f
= 55430/23.20 = 2389 psi The bearing allowable of the A516 overpack end plate and T-3 plug end closure plate is:
Fby = Fy = 38000 psi 1110 i70 1-60e(3)
Revision 2 August 15, 1979 The bearing allowable of the pusher end plate, ASTM 240 is:
F
=F
= 30000 psi I
{
Thus, the minimum Margin of Safety in bearing is:
30000/2389 -1 = +11.56 M.S.
=
A more general investigation of forces imposed upcn the c.erpack at arbitrary impact orientations (cblique angles) is discuss 2d in subsequent paragraphs.
This investigation is of parametric forn, sweeping all orientations fron nearly vertical (9
= 900) g 0 ).
The investigation is cor. prised of t io to horizontal (O
=
g parts.
The first part determines impact fcrces ccniistan:.._ :h the rigid body dynamics of an inclined T-3 package.
The seccnd part of the paranetric analysis considers the maxinum forces that can be developed in an inclined overpack at de flec tic n.3 corresponding to a "bottoning-out" of that overpack-i.e.,
when the T-3 body corner contacts the unyieldin; surface.
- The lesser of these two predictions constitutes the maninur possible force imposed upon the cverpack at any.gi'can angla.
I The forces associated with the rigid bcdy dynamics cf the package are developed using the nathematical r.c'el illustratac' on the follcwing page.
1110 171 1-60e (4)
Revision 2 August 15, 1979 Y
/
/
z
./4 C'
>x M = p2
/
/
I=
l I
1 6 = Crush Depth A
4 l
F The equations of motion of the bcdy are:
y = h
-g 3 = 12F E
(7 cos A - R sin o) gz3 1110 172 1-6 0e ( 5)
Revision 2 August 15, 1979 Uhere F is nonlinear function of the deflection, 6,
representing the load deflection characteristics of the overpack presented on Page 1-93.
The deflection, 6,
is expressed in terns of problen variables as:
6 = 16 cos 0 - R3 sin 0
-Y 2
'3HERE :
S=
(9 - 9 )
O
= the initial value of 9 at tine t = 0.
g The initial conditions at the ncnent of impact, t= 0, are:
Y
=0 o
2gh h = 360" (accident) = 12" (normal)
Y
=
o o
o 6
= varies fron 0 to 55 o
e
=0 o
For each selected value of e, the equations of notica are g
integrated to find the ma::inun values of total force, shear and' thrust.
Those values are plotted in Figure 1.6.6.2-1.
The maximum forces associated with a "bottoned-out" cverpack are linited by geometric considerations only.
Specifically, the overpack can crush laterally antil tha ccrner of thc T-3 package directly contacts the unyieldin~ surface.
At this 1110 173 1-sna(6)
. ". ;a'C';? ~;,,
' ' C I' Figure 1.6.6.2-1 nvernack Forces for
^
Oblique Impacts, One Foot IJornal Drop C
O
- 425,805 Ibs.
O i
Total, Force, F "M
C 7s aon-
"+
i
-- 4 2 2,742 lbs.
PY e
S,
- Thrust, F'.
3qn_
t e
222,4 50 lbs.-
o H
5 c)
O h
c 200u 1----
k 231,427 lbs.
l Shear, F g s
CD n
i I
i i
i I
I I
)
l I
N 4
40 on 70' 60 ~~
50 40
~30
'70 10
Revision 2 August 15, 1979 point, further increases in total impact force are borne by the T-3 ends, not the overpack.
The geometry is illustrated below:
h
\\
r = 13.22 g,
i f
Overpack
\\
,/
Q T-3 Bodv h
id shdep]
_I
=
ru max e - hen Am Crush Footprint Area, A g,f F
A
/
//
b=r X
/
s/
f/l
~
m r
/;
Center of Pressure b=r
/
(Centroid) y
~
a a
From the above sketch, the geometric preperties of the elliptical crush footprint are:
6
= h sin 0 max a = r/ sin e c = h/cos 0 1110 175 1-6 0e (0) z _.
c
Revision 2 August 15, 1979 The area, A, and the centroidal offset, E, of the crush I
footprint are derived as:
when c < a:
h 2
2 A=2a y=-
a -x
/
ydx a
(a-c) 2 g
a -x'dx A=
a 2
k l
-1 ( {c 2
-]! - (a-c) (2ac-c )
A=
+a sin Ax -
fu x
a -x dx (a-c) 2b 2
x = y- (2ac-c )
/A Mhen c > a:
A = rab - A AX
_.=
X A
A and _x are as defined for A and x_,
e:: cept that c replaces c.
c
= 2a - c The forces inposed on the overpack are:
Total Force:
F=0 A
Shear F
= F cos e s
Thrust F
= F sin 9 Moment M=F e
}
i t
a i110 176 1-Ana(9)
Revision 2 August 15, 1979 Where:
1000 psi e = a - x - 2r sin 6 o
=
O A=
3.97678x10 ~
o
= a (1 + AeBc) cr o
B= 6.43812 The tern, e,
represents the nonent arn through.shich the total overpack force, F,
tends to pivot the overpack about the upper nost corner of the T-3 body.
This nonent is resisted by six overpack attachment bolts.
Mhen "e" takes on a negative value, the resultant force, F,
lies inside the upperg.ost corner and no nonent is imposed on the overpack attachment bolts.
The enpirical expression for fcan crush str':ss, c represents a good least squares fit of the stress-strain relation shown in Figure 1. 3. 5-1.
The strain, c, of the foan enployed in the above expression is conputed at the center of pressure as:
~l 2
< tan (h/2r)
Cylindrical undisturbed lower surface-cp/2.
e=5 intl Uhere:
6
=3
+ e tan 6 cp max intl = (2r + e/ sin 9)/cos 9 tan" (h/2r)
Circular plate end lower surface; o >
C "0cp!* intl 13he re :
6
=5
- f ctn e cp nax f = 2r sin e-h cos eA e z.
= h/ sin 9 intl 1110 177 1-Gae (10) i
Revision 2 August 15, 1979 The results of this analysis are presentod in Figure 1.6.6.?-?
for total force, F,
shear, P thrust, F and'no ent, M F -
e.
s, Figure 1.6.6.2-2 represents an overlay of results from Figures 1.6.6.2-1 and 1.7.1-3.
Piaxinum Total Force 425,805 A 9=
81.5
=
231,427 lbs 0
0=
29 tiaxinum shear
=
7.5" Naxinun ?!o ent 1.35671 x 10 in-lbs O G
=
=
The maxiruin shear lorl cc*crns the ecaluation e shea? ar1 r
bearing capabilitics for t'.e ove rp rA to T-1 119 She,r strec:
is found c
231,427/61.05 - 3742 psi f
=
s The tiarg:
of c a f r: t ; in
-hc'r fiir tho
<<p-4 bin 12' lig n
ASTM 516, Grade 70 n 21939/3742 -1 = +4.86 M.S.
=-
The corresporcling b-ring stress anM V-rc n of Safety 1s-c f
/
psi b
38000/9975 -1 = +2.81 ri. S.
=
This shear load in less t h ce. the closuce pl:tc shear 10 -1 associa ted vi tt side drol., c :m ale l in
~=,-tio3 1.6.6.3.
Thus, s he.i t loM t r.m. re in the T-3 cask clo:u're plate 1, < P not be checkel.
1110 1/8 1-Ana(11)
A ::
(]
f (=E ' 5 &TZT,.'M"7.2.', o. 'T' 46 0700
]
a
_ _ _ _. 7 i
i i
i i
l i
i, j
i l
f i
i "C3 l
r 4
i i
4 Q
[
i Figure _1.6.622d2_ Maximum.OverpackiForces;for_ _ _ _ _ _. _.. _ _.. _ _ _. _ _
i-Ob]igue Impacts, One Foot Normal Drop
,l Z
t r
r (425,805 lb.
g i
i-Total Force, F---
--I-
- - Q ---
- _.- 400 l
=
t
~p l
l I
d-(
\\
D 1
l
{
N g. N.
g 8
- -300 N-\\-
~
i t__/'
\\ N Thrust, F N \\
^
\\
i i
_ =_
4 1 00
- - - - b 2 31 ;-4 27 : lbs - - - -
i
' Shear, F~
l
. N i
s i
l
.\\..
\\
4
- - 100 --
-- s --- -
j l
l N
l m
i t
i I
L i
O l t
N N
N s
N !
O, W '
i i
i i
i 4
Initial' Angle with I Respect to ' IIorizon (0,. degrees) i I
f
._m.
'Do 80 70 (oO 50 40 30 20 IO
Revision 2 August 15, 1979 i
The overpack uoment produces a maximum attachnent shear lead, F,,
estir.ated as follows:
300R E BINAL
,/
/
r
-1,
r M
= 2Fa (1-cos 60')r+2Fa (1+cos 60 ) r
^r o
a '~
w N
M
=6F g
6 F.e 1.35671x10 y
1 014 lbs.
=
a (6 ) (13. 2 2 )
Shear stress in the 1-9 UNC bolts ( AS T'e A-3.3 0, L43) is:
l'Old f
' = 2A267 psi
=
s
.6051 I
Bending stresses induced by single shear lcading of the bolts by the 3/S" plate doublers is estinated as-
_ Mr _ 32M
'b I
nd3 But, M=F t/2 t=
3/9" F
= 17014 lbs.
a d=.8466 inch 16 Fat
" (16)(17013)(3/S) f 5382n,, psi b"
nd' n(.8466),
=
Combining bending and shear gives a r.w.i.~.ur 35ress in ': = l i ty c : -
1 2
k b
6
=2
+F~
= 78066 psi I
12 s.
l Thus, the :targin of Safety of the A - 3 ' 3, L*? b-lts is-
=
~ 35 i
105000/75c36
-1 M.S.
=
1110 180
.1-60e(I3)
Revision 2 August 15, 1979 The bearing stress in the 3/3" A414, Gr. A doublers is estimated as:
b
! }j
( }(
f E8 The resultant Margin of Safety is:
M.S. = 70000/45371 -1 = +0.54 Notably, the overpack and its components are allowed to yield and/or crush under normal events per Section 1.1. '. 2.'2 of the T-3 design criteria.
In this instance, bearing yield in the doublers is allowed at the attachment bolts in order to schieve an improved redistribution of attachment bolt loads.
The margins calculated above for overpack retention under oblique drops is conservative because two additional retention mechanisms have been totally ignored.
These include:
Moment resistance provided by the " pin-in-a-socket" interaction of the cask and its overpack; and Increased shear resistance provided by frictional forces proportional to the thrust component of impact force.
is concluded that the overpack remains attached t$o the T-3 It Package under corner and oblique impact conditions.
Ii10 181 1-6 0e (14 )
Revision 2 August 15, 1979 1.6.6.3 Side Drop Side impact loads are evaluated using the AIISYS finite element loads model depicted in the sketch shown below.
T-3 Side ImpactJ40de1, _ _ _
AY d
1
-_ A A
I 2T S
4 5'
G' 7'
_8' ci Yio ll e
i PUSHER PLUG m
l76,94" w
EN D END l
2 3
4 5
6 7
8 9
10 l_ I
~X
@$ @@$@@s $ @$ @@$ @ $
'3.o5 -
i 1 22
@d@r24@
G W G 4
@ @ d @2idy 23 24 32 33 Typ. Element Numbering Sc,horc-
,i l+1
&h, BEAM @
= 3 (i-1) + 3
('E TIF 23) w.i. span @ = sci-i)+ i (srir i )
.L + 22 GAP
= 3(l-l) + 2 (STIF 12) 1110 182 1-60f
Revision 2 August 15, 1979 The T-3 body has been subdivided into ten beam segments and eleven groups of non-linear elements representing the lateral load resistance of the cylindrical T-3 body.
The 38,000 lb.
mass of the T-3 is uniformly distributed to the el2ven nodes of the model via an appropriate density for the beam segments.
The non-linear elements representing the lateral load resistance consist of an axial force-only spar and a compression-only gap element in series.
The axial force spar possesses load-deflection characteristics based upon Shappert's Cask Designer's Guide, ORNL-NSIC-68, relations for side impact of cylindrical packages.
The analysis properties of the two critical elements, the beam and the non-linear spar,are summarized as follows:
Beams:
Element K; K= 3(i-1)+3; i= 1, 11:
(Leac Ignored) 2 2
A = {
26.1 -24.1 +8.625 -7.981 ]
= 87.253 in 4
4 4
4 I=g 26.1 -24.1 +8.625 -7.981 l
f I
4 6292.195 in
=
39000 pequiv, (87.253)(176.94)(386.4) i j,ygggb,
= 6.37x10-lb-sec /in
'7 987Zd.
, d?tG, /47 49. b. _
I d /./O Jr,d.
1i10 183 1-6 0 f (l)
Revision 2 August 15, 1979 Non-Linear Spars; Element L; L=3(i-1)+1; i=1, 11 (Outer steel shell neglectod)
The Resisting Crush Force is:
F6"# plast NHERE:
= Dynamic Flow Stress g
st S
S = 2R sin e gg I,[
/
fl h 4 T = Slice thickness R = 13.05" j
But:
6 = R (1-cos 0 )
-1 {
Thus:
0 = cos
-_s : - s sin 0 =
1-R 1-(
S = 2R Thus:
2-(
F Ta l~
=
6 plast From Shappert's Cask Designers Guide ORNL-NSIC-6R.,
n.
99-Aa, Mat'1 plast Steel 45000 Lead 10000.
The stress-strain relation describing the material characteristics of these spars is determined from the foregoing load deflection relation and:
c = F /A 6
e = 6/2 l
1110 184 1-60f(2)
Revision 2 August 15, 1979 For all spars, L = 13.05 inches T = 176.94/10 inches G
= 10000 psi plast For all spars except elements 1 and 31 (the ends) the area, A,
is assumed as unity.
The areas of elements 1 and 31 are compu-ted knowing the steel and lead thicknisses and the steel to lead dynamic flow stress ratio, 4.5:1.
Thus, the stress-strain relation is:
~1 p-6) 'b 2RToolast c=
i
\\R/
Where:
R= 13.05 T= 17.694 0000
=
plast A=1 6 = 13.05c Or:
~
o=
(4.6181x10 )
1-(1-c) '
Numerically evaluating:
e c (psi) 0.
O.
.0005 146.02x10 (E
= c/c = 292x106)
.001 206.48x10 3
.01 657.47x10 6
.05 1.442x10 6
.20 2.7709x10 1110 185 1-60f(3)
Revision 2 August 15, 1979 The effective areas of the end spars is found from:
4.5Tsteel + Tlead
^ effective "
17.694 For spars 1 and the 31 the effective analysis areas are:
T
^ ffective Spar Node steel lead e
1 1
2.000 6.847 0.896 31 11 8.200 0.647 2.122 Ini tial conditions for the analysis were chosen to establish a velocity at gap closure equivalent to a one foot drop.
=,[2gh=96.30in/sec.
Vg
~4 A time step increment of lx10 seconds was chosen based upon the criterion of at least 30 steps per cycle and a simplified hand-based prediction of apparent system natural frequency.
The results of the analysis are summarized in Figures 1. 6. 6. 3-1 1.6.6.3-2 and Table 1.6.6.3-1.
1110 186 1-60f(4)
300R OR;8 kill Figure 1.6.6.3-1:
Selected Time history Vertical Displacenents Revision 2 One-Foot Side Drop, T-3 Package August 15, 1979
- r_ i y evertican i
G I
lbf II
'" '# 3 I '
7~'2 3
4 5 6 7 8 9 f
PLUG
~' T-PUSifER END END b = Vertical (Y) displacement at ncde i l
~~
/
s 7-
+
A
/
~
_a l
s' i
d l
I
\\
-[/
d
- x.
\\
\\
i g
/
3:
I
'\\
\\
dA
\\
\\
j y
\\
t S
\\
ds
/
- 7
/
I
\\
/
x
'N Q c'-
,~~
w=
a_.__
,, ' ~ ~,.. _ _ _ _. _... _ _. _ _ _ _.. _,,.* ' ^_u_
_ ~ _
-is.
~--
~_ e [ ~
_ _. a T - 3 $ c?,
_c;-
3
.v.a
,i
+
o s
1-60f(51 1110 187
l Figure 1.6.6.3-2:
Selected Time History Lateral Compressive Forces Revit'on 2
-210L in Spar Elenents Forces, One-Foot Side Drop, T-3 Package August 15, 1979 g y < vert.c o I
WK.Q
--h 7p,7, *,
,3.,p x mm em s.,
s e
__.O
/
PUSHER UG s
s
[f i
END E_[{D, s
@ = Contact Force in Non-se
/,
Linear Element i 2.1
,f j
c3G e
/
l C'
,I
/
/
7
/
1
..3 I
i
--- S
]
r!
l
.1 d
l h
I l
wa-m}
~
--} - -. 7 - 77~-~~~_.-.
~
_. w
.m--
.~~
g
.; '* ::- e.r. _ +-
- p;n
. j
- 4 1-60f(6) 1110 188
Revision 2 August 15, 1973 Table 1.6.6.3-1 Maximun. Side Drop Responses Node /
Time Response Quantity Element (sec)
Magnitude Deformations (in):
Pusher End 1
.0017
.077972 in.
Plug End 11
.0011
.045373 Center 7
.0022
.11771 Forces (1bs, in-lb) :
Pusher End 1
.0017 398,288. lbs.
Plug End 31
.0011 669,493. lbs.
Center 19
.0022 591,295. lbs.
6 Beam Moment 24
.0017 8.4937x10 in-lb 1110 189 l-60f(7)
Revision 2 August 15, 1979 The load imposed on the plug closure plate is transferred to the cask body end cap by shear across a stepped lip.
No loads are imposed upon the closure plate bolts by this lateral shear load because the total diametrical clearance of the bearing surface is 0.060", whereas each bolt possesses a clearance of 0.080 inches.
The effective depth of this step is 1. 55", wi+ - an effective width of 20.68, Thus, the bearing stress is:
. psi f
=
brg " (1.55 20 68)
The Margin of Safety in bearing is:
000/20886.-l = +0.82 bry!fbrg-
=
M.S.
=F Mnere:
F
=F
= 38000 psi (ASTM A516, NB-3227.1, ASME bry Section III)
The effective shear area is conservatively approximated as one-half the total annular section of the closure plate or:
(20.68 _142) 2 91.0 in
( )
A
=
=
s Thus, the shear stress is:
= 7359.2 psi f
=
s The allowable shear stress in ASTM A516 is:
38000/ [ = 21939.
sy " f* /
P
=
f Thus, the Margin of Safety is:
sy/f -1 = 21939/7359-1 = +1.98 M.S.
=F s
The shear transferred by the plug end closure plate to the end cap produces a bearing stress in the end cap of 20886 psi.
The associated margin of safety is:
-1 = 30000/ 20886-1 = +0. 44 bry!fbrg M.S.
=F F
= F =30000 psi (ASTM A240) bf y
1-60f(8)
Revision 2 August 15, 1979 The shear stress in the end cap is:
669493 f
= 6281. psi
=
s 2
(26.44 -20.68 )
The associated Margin of Safety is:
30000/ h
-1 = +1.76 M.S.
=
5281 This load is next transferred to the outer shell of the T-3 package via a circumferential weld between the plug end cap plate and the outer shell.
The area of the weld is:
( 1 ) (n) (26.44) 2 58.73 in A
=
=
T The shear stress and Margin of Safety is:
f
= 669493/58.73 = 11400 psi 0000/Tf-1=+0.52 M S.
=
11400 At the pusher end, the maximt m impact force is 398,288 lbs.
This load is transferred to the T-3 outer shell by shear through a weld of identical size and proportion to that used at the plug end.
Thus, the shear stress and margin of safety is:
f
= 398288/58.73 = 6781.7 psi 30000/Tb
-1 = +1.55 M.S.
=
6782 The bending stresses induced in the outer shell and containment vessel are:
1110 191 1-60f(9)
Revision 2 August 15, 1979 6
f
= Mc/I M = 8.4937x10 in-lb (Table 1.6.6.3-1) b c = 13.05 in (outer shell)
= 4.313 in (containment vessel) 4 I = 6292.195 in Component Bending Stress (psi)
Outer Shell 17616.
Containment Vessel 5822.
For the outer shell, these bending stresses must be combined with thermal differential stresses as follows:
f f
T f
x v
y z
Thermal Diff.
O.
9876.
O.
O.
Bending 0
Il7616 0.
O.
The resultant maximum stress intensity is:
S
= 27492 psi The associated Margin of Safety for the outer shell is:
M.S. = F /S,g-1
= 30,000/27492-1 = +0.09 For the containment vessel, these stresses must be combined with pressure and thermal differential stresses as well as stresses induced by lead deformation associated with lateral impact of the cylindrical T-3 section.
To assess these stresses, a plane strain, ANSYS finite element model, as depicted in the following sketch, has been employed.
1110 192 1-60f(10)
Revision 2 July 15, 1979 M
300R ORGNA-p' x r;-
~
/
~
Q
+9 vs.
8x s*
@y i,
pq
. ~
- 4
@ 6 @-.'
-t:
t:
y' g
h I_
7S 49
.. _ + -
_ \\
~'/f Q } \\@fasjp_
(
m a
y, 5
'A7
'y 1@
'/
/
\\
d
~
Z f
4t nd'20-hr)
This side impact model consists of 144 elements and 120 nodes arranged along radial lines at 15.
Twenty-four shell elements, each, are used to represent the containment vessel and outer shell.
Ninety-six isoparametric quadrilaterals are used to 1110 193 1-60 f (11)
Revision 1 August 15, 1979 represent the lead shield between these circular shells.
The imposed loading consists of a nominal 100 g body force reacted by a knife-edge support at the idealized point of impact (node 19).
This knife-edge support conservatively represents the load distribution at tile point of impact.
Containment vessel stresses resulting from this 100 g nominal load are plotted in Figure 1.6.6.3-3.
Table 1.6.6.3-1 indicate.3 the maximum inpact force imposed upon a 17.694 inch segment (1/10 length) of the T-3 is 591,29 5 lbs..
This is equivalent to a lateral acceleration of:
= 155.6 g's S
=
g 18000 0
Thus, r, tresses tabulated in Figure 1,0 6.3-3 must be multiplied by the factor, F,
to predict containment vessel stresses under normal side impact.
Fu
= 1.556 0
For convenience, these containment vessel stresses are summarized, versus location in the following sketch.
Ot)TG12.%C-FACE (b 49)\\"\\
henducFACE @= SAD 3
4,5G l
!e E6 D / // // / /
5GkT DtJC vLc 2-
/// // ///
/
1i10 194 1-60f(12)
")l Revision 2 jg(
Ok August 15, 1979 L
u
-2
--r i
l s
s<._y
.o 4,L1 --7 5
Y is
!"" '~
w._W i
\\
\\
v L
'\\
T v
f
\\
1 1
+
A V
/
/
W r
f f
f W3 e
c
/
c/.
wea v
i n_
L t
^
pe-J s
j v
M s"
f r
/
\\./
T /l N/4 y'
Vg y
$L-3-u,
y Fe a-+,
c w_
x, 2
~
V y
n x(x o
,N
=
m m
a e
ai
,NN y
r t
i ee
/
/
9-A r
gjf
\\cN, x" y
/
FSf i4,m
.s s
.s
.e x
s
,s 1
x,_
pr_
&:t q
w e
??
y t
1-w s.ry3-E: 3-a l-s s-r 3
1 l
i cp*"
n't
,b
,I.
/
7
,T e
_x 1 -
e
~~-
/
i m
m s
u
.s =e q,;Cic Jps="m
/~
A 2
=
b 1.
"g*h.-o_
's 'x.
~
=
,e:.
+,
r_-
a 4
- N y
o cg
=
s s!?
5!a?G
. ',l 1
AY.
'/ %
i
.an -
3 g_p
.r__
y g
i-4i r__
_[_
_,3 f--
-lU
/ (-/ -A
-N
[s v'd A,x~~\\
) J M S f/
"'ra '
,g f
L_i 7
m.
%m.
m m
2 x.
2
/
4 x.
s 1
~
g_
-17 O-~
k-l 4
_m 3
_ x_,, _ __ !
u o
m __.l
_g-
.g_ p__ g
'I_us _d r_
L_
m.
2_,b--
t.
x-x e%,__mt=r!
,y__
_n x-A
.t r
\\m t
x v
n t
T r
m
_. l Q
g Q
- p. _ _ -, _ _ -. _
L&
qw u nmuy2aapnamsv9
_. i i
i 1110 195 1-m nu
Revision 2 August 15, 1979 Location z (Hoop Stress)
(See P. 1-60f(12)
(psi) 1
+ 1789 2
+ 4635 3
+ 7480 4
- 7584 5
-11928 6
-17029 7
+
613 8
+ 8267 9
+16817 The direct stress components for the containment vessel under normal side impact may be summarized as:
Stresses (psi) f f
T f
x y
xy z
Load Orig'.n Location (radial)
(axial)
(shear)
(hoop)
(P. 1-60f (12) m) (1)
-39
+ 232 0
+
483 Pressure (P 0
+8701 0
0 Thermal Diff. (Q)
Lateral Bending andgateralCompres-1 0
-5822 0
+ 1789 sion 2) (P )
2 0
-5605 0
+ 4635 3
0
-5387 0
+ 7480 4
0 0
0
- 7584 5
0 0
0
-11928 6
0 0
0
-17029 7
0
+5822 0
+
613 8
0
+5605 0
+ E267 9
0
+5387 0
+16817
( I Bending stress component = fy Lateral compression stress conponent = f (1) Symbols denote load classifications per hable NB-3217-1 ASME Boiler & Pressure Vessels Code,Section III, Division 1.
1110 196 1-6 0 f (14 )
Revision 2 August 15, 1979 The maximum stress intensities, versus location, are:
Stress Intensities (psi)
Location (P )
(P
+Pb)
(P
+Pb + 0) m P.1-6 0 f (12 )
1 522.
7862.
3150 2
10491.
5157 3
13118.
8002 4
7333.
16034 5
11677.
20378 6
16778 25479 l
6093 14794 7
8 8789 14577 9
v 17339 l'/339 The S valu f r the A 312 seamless pipe containment vessel is m
20 hsi.
Thus, the appropriate Margins of Safety for the containment vessel are:
P
< l. 0 S
- m M.S. = 20000/522-1 = + Large (P, + Pb) < l.5 S :
(1. 5) (20000)/17339-1 = +0. 73 M.S.
=
(P
+Pb + Q) < 3. 0 Sm m
(3. 0) (20000) /25479-1 = +1. 35 M.S.
=
1110 197 1-60f (15)
Revision 2 August 15, 1979 The local stresses induced in the containment vessel due to the 565,000 lb. trunnion force can be estimated by referral to the plane strain analysis discussed above.
The equivalent lateral acceleration and multiplying factor applied to the stresses shown in Figure 1.6.6.3-3 are:
= 148.68 g's A
=
g 0
1.4868.
F=
=
The direct stress components are therefore:
Stresses (psi) l f
f f
T x
y xy z
Load Origin Location (radial)
(axial)
(shear)
(hoop)
Pressure (P )
-39
+232 0
- 1483 Thermal Diff (Q) 0 8707 0
0 Direct Compression: (P 1
0 0
0
+ 1709 b
2
+ 4429 3
+ 7147 4
- 7247 5
-11398 6
+16272 7
+
586 8
+_7899 9
v v
V
+16069
- Defined on Page 1-60f(12) 1110 198 1-60h
Revision 2 August 15, 1979 The maximum stress intensities, vs. location, are:
Location (P )
(P
+Pb}
(n+
b+
1 522 2231.
8972 2
4951 8972 3
7186 8972 4
6996 15697 5
11147 19848 6
16021 24722 7
1108 8972 8
8421 8972 9
16591 16591
- Defined on Page 1-60f(12)
The appropriate !!argins of Safety for the containment vessel are:
P
< l. 0 S :
M.S.
= 20000/522-1 = +Large (P
+P)
< l.5 S :
b (1. 5) (20,000) /16 591-1 = +0. 81 M.S.
=
(P
+Pb + 0)
.0 S
- m m
(3. ) (20000) / 24722-1 =
+1. 43
.t.S.
=
Side impact on the trunnicas induces a deceleration of 14.87 g's.
565,000 lbs. = 14.87 g's 38,000 lbs.
Ii10 199 l-60i
Revision 2 August 15, 1979 This acceleration tends to shear the overpacks fron the T-3 Package. The magnitude of this shear force is:
(1050 lbs) (14. 87) = 15614 lbs.
F
=
s In Section 1.7.1.1, the shear area of overpack attachment is found to be 61.83 in of A516 steel.
The shear yield for A516 Grade 70 is:
ty/
=38000/[=21939 psi f
=F sy Thus, the Margin of Safety for overpack shearing resistance is:
(21939) (61. 85) /15614-1 = +Large M.S.
=
This acceleration also induces a bending noment which loads the overpack attachment bolts and doublers.
The noment is:
a = 140526 in-lb M=F s
Mhere:
15614 lbs.
F
=
3 a = 18/2 = 9" This moment is assumed to be reacted by five of the six overpack attachment bolts (1-8 UNC; ASTM A320, Grade L43) and the opposite corner of the package end.
The bolt shear force is:
Pb = 140526/ (6) (13. 22) = 1772 1ha.
Shear Stress in the knit is:
f
= P /A = 1772/.6051 = 2928 psi s
b 1-60j
Revision 2 August 15, 1979 Allowable shear strength of the bolt is 35 kai (ASTM A320, L43).
Thus, the Margin of Safety in the bolt is:
sy/f -1 = +10.95 M.S.
=P s
Bearing stress in the 3/8" doubler (A414) is:
fb" (1 3/8) 4725 psi
=
The yield allowable for A414 is 30 ksi, thus the Margin of Safety for the doubler is:
M.S.
= F /f -l " +s I5 y
b Therefore, it can be concluded that the T-3 can safely withstand a 12 in. side drop and meet the requirements of 10CFR71.35.
1.6.6.4 Summary of Results External Skin Containment Vessel Margin Margin Drop Stress of Stress of Orientation (psi)
Safety (psi)
Safety End 8476
+1.36 Corner 12242
+1.45 9400
+1.13 Side 27492 j
+0.09.
17339
+0.73 From the above it can be concluded that the package will experience some small amount of local deflection but total loads prcduce stresses well below yield.
Therefore, the T-3 can safely react the drop conditions associated with Normal Conditions of Transport.
Ii10 201 1-60k
Revision 2 August 15, 1979 Lateral loads are reacted by a thick stepped joint.
The lateral shear force is:
P = NG sin (arc Tan D/L)
Where:
W= 38000 lbs G= 102.1 g's D = 26.5 in L= 212 in P=
(38000)(102.1) sin Tan-1(26.5/212)
P= 481229 lbs Shear stress is:
f
= P /A s
Where:
P
= 481229 lbe a
A = 9 0. 5 in (Ref. Page 1-60f(8) )
9 f
= 4 81229/90. 5 in~
s f
= 5318 psi s
Material:
(cask body)
ASTM A240/304 F
= 75000 psi j
tu i
(. 6) (Ftu)
F
=
g i110 202 1-77
Revision 2 August 15, 1979 Margin of Safety (Shear Step)
(Ftu) (.6)/f ~1 M.S.
=
s
(.6)(75000)/5318-1 M.S.
=
M.S.
= +7.46 Therefore, the stepped lip is more than adequate for reacting lateral loads.
As noted, in Section 1.6.6.2, the laterally induced loads resulting from the corner drop produce bending moments that must be reacted by ';he external shell.
These loads were calculated as a function of "g" loade (Ref. Page 1-60d).
fb = 273.5 psi per "g" (outer shell)
= 89.23 psi per "g" (containment vessel)
From Table 1.7.1-1 the maximum corner drop acceleration is 101.1 g's.
(273. 5 psi per "g") (102.1 g 's) f
=
b f
= 27924 psi (outer shell) b
= 9110 psi (containment vessel)
To these lateral bending stresses must be added three other stress contributions - two associated with normal transport pressure and thermal differentials and the third associated with i110 203 1-77a
Revision 2 August 15, 1979 longitudinal thrust forces.
This latter longitudinal force considers the Poisson induced radial stresses upon both the outer shell and the inner containment vessel, as outlined in Section 1.6.6.1.
The factor applied to the analysis of Section 1.6.6.1 corresponds to the ratio of axial g's for accident corner drop to axial g's for normal end drop:
accident, corner 102.1 cos 8.5 6.311 F=
=
1*
^ normal, end The direct stress components are summarized in the following table:
Stresses (psi) f f
T f
x y
zy z
Location (Radial)
(Axial)
(Shear)
(Hoop)
Containment Vessel Pressure
- 39
+
232 0
+ 483 Th6. al Differential 0
+ 8701 0
0 Location (((r=3.991)
Longitudinal 0
- 3928.
0
,-4090.
Lateral Bending 0
I 8430 0
0 Location ds 'r=4.152)
Longitudinal
-552
-14926
-180
-7281.
Lateral Bending 0
I 8770 0
0 Location ghs (r=4. 313)
Longitudinal 0
-25408 0
-9860.
Lateral Bending 0
I 9110 0
0 I
i l
i
- See location sketch on 1-60b(1) 1110 204 1-77b
Revision 2 August 15, 1979 Stresses (psi) f T
x y
xy z
Location *
(Radial)
(Axial)
(Shear)
(Hoop)
Outer Shell Thermal Differential 0
+ 9876 0
0 Location [h (r,12.05)
Longitudinal 0
-12300 0
+19950 Lateral Bending 0
I25784 0
0 Locatior.[b(r=12.55)
Longitudinal
-808.
- 7946.
-293.
+19918.
Lateral Bending 0
I26854 0
0 Locatior._ dh (r=13. 05)
Longitudinal 0
- 2884 0
+20629 Lateral Bending 0
I27924 0
0 The principal stresses and stress intensities are:
l Bending Stresses (psi)
S Location
- Direction 1
2 3
I Containment Vessel
/h
+
13435 39.
- 3607 17042
,3
-39
-3425
- 3607 3568 CA
+
2787
- 601
- 6798 9585
-589
-6798
-14765 14177
[J
+
-39
-7365
- 9377 9338
-39
-9377
-25585 25546 Outer Sh jh
+
23360 19950 0
23360 19950 0.
-28208 48158
((
+
28787 19918 811 29598 19910
- 804
-24928 44846 db
+
34916 20629 0.
34916 206,29 0.
-20932.
41561.
- See location sketch cn 1-60b(1) i110 205 1-77c
Revision 2 August 15, 1979 The maxinum stress intensity in the containnent vessel is 25546 psi.
The Margin of Rafety versus faulted allowables is:
(2. 4) (20000)/25546 -1 = +0. 83 M.S.
=
The maximum stress intensity in the outer shell is 43159 psi.
The Margin of Safety versus ultimate is:
f t. S. - 75006/49158-1 = +0.56 Under corner impact, lateral forces are produced which tend to shear the overpack from the T-3 package.
The nagnitude of this shear force is:
(102.1 g) (33000 lbs) sin 8.56 F
=
g 577,489 lbs.
=
'nis shear is resisted by a nachined lip of 3/8 inch depth and one inch width on the overpack base plate that fits in a companion groove in the T-3 and cap / plate.
The effective shear area of this lip is:
(20.69 -19.692) = 61.85 in A
=
s The shear stress in the lip is:
l f
577,489 lbs/61.85 = 9337 psi
=
s The shear ultinate for the ASTM 516, Grade 70 overpack base-plate is:
tu/ -/ 3 = 70,000/ ( 3 = 40a15 psi F
F
=
g 1i10 206 1-77d
Revision 2 August 15, 1979 Thus, the Margin of Safety for shearing the overpack frem the T-3 body under corner impact is:
M.S. = 40415/9337 -1 = +3.33 The bearing area is:
2 A = ndt = v (19. 69) (3/8) = 23.20 in 3
The bearing stress is:
f
= 577489/23.20 = 24895 psi b
The ultimate bearing stress of the A-516 overpack end plate and T-3 plug end closure plate is:
F
=F
= 70,000 psi bu The ultimate bearing stress of the pusher end plate, ASTM 240 is:
= 75,000 psi F
bu u
Thus, the minimum Margin of Safety in bearing is:
M.S. = 70000/24895 -1 = +1.81 A more general investigation of forces imposed upon the overpack at arbitrary impact orientations (oblique angles) is discussed in subsequent paragraphs.
This investigation is of parametric forn, sweeping all orientations from nearly vertical (e 90 )
=
g to horizontal (0 0 ).
The investigation is comprised of two
=
g parts.
The first part determines impact forces consistent with the rigid body dynamics of an inclined T-3 package.
The second part of the parametr.'.c analysis considers the maximum forces that can be developed in an inclined overpack at deflections 1110 207 1-77e
Revision 2 August 15, 1979 corresponding to a "bottoning-out" of that overpack; i.e.,
when the T-3 body corner contacts the unyielding surface.
The lesser of these two predictions constitutes the maximum possible force imposed upon the overpack at any given angle.
The forces associated with the rigid body dynamics of the package are developed using the mathematical model illustrated below:
RN
/
Y A
/
/*l l
G C
x M = pl I
/
h
/ '"Wf 6 = Crush Depth A
I I
I I
i F
The equationc of motion of the body are:
7
-g
=
i 9=~ $(hcos0-Rsin9)
I ii10 208 1-77f
Revision 2 August 15, 1979 Uhere P is nonlinear function of the defler. tion, 6, representing the load deflection characteristics of the overpack presented on Page 1-83.
The deflection, 6, is expressed in terms of problen variables as:
cos 0 6=
- RS sin 0 -Y
'3HERE :
8= (0 - 9g)
O
= the initial value of 6 at time t = 0.
g The initial conditions at the moment of impact, t=
0, are:
Y
=0 g
k
=3[2gh
~
h = 360" (accident) = 12" (normal) g O
= varies from 0 to 95 g
9
=0 o
For each selected value of 9 the equationc of notion are g,
integrated to find the maximum values of total force, shear and thrust.
Those values are plotted in Figure 1.7.1-2.
The maximum forces associated with a " bottomed-out" overpack are limited by geometric considerations only.
Specifically, the overpack can crush laterally until the corner of the T-3 packaga directly contacts the unyieldinct surface.
At this 1110 209 l-77a
^
C
^
{
~.,*l? U:s' ?";;
7+
?Go702
)
. Figure.l'.7.1-2 Overpack Forces for
{
ObliquejImpacts, 30'. Accident Drop 3,329,765: lbk...
i 4
i 1
3.-
,.4 I
3,298,315 3.bs.
f
[
~
O i.. _.
g
~ _~
- /.
t.
.h
-- 4 2.
1
~ ~ Total' Force,i P
l
-._m
/- Ny s
m tc ;
N D
T *Ol_
D
.2
~1 f
y t.
D e
rH ;
g g E!
D
~
Thrust, F
,T e;
u t
ol
_C5"3 u
~
~
EP M.
r"'**
._i.
i l
Shear,.F %
1
..__ s_
g_
.620,230 lbs.
1,059,077 lbs.
o C
I Ol t
i i
t I
i i
t0 80 70 60 50 40 30 20 10 Initial Angle with Respect to IIorizon (6, degrees)
Revision 2 August 15, 1979 point, further increases in total impact force are borne by the T-3 ends, not the overpack.
The geometry is illustrated below:
h
\\
r = 13.22
(
Overpack r
,/
T-3 Body g
p'/ 9f/V S
cash dep
'L-Moment Arm max k
0 =
g,f Crush Footprint Area, A l
F
~
k
//
b=r 1
=*
I
/
Center of Pressure b=r I
(Centroid)
W l
l 4
a a
=
From the above sketch, the geometric properties of the elliptical crush footprint are:
S
= h sin 0 a = r/ sin 0 l
l c = h/cos e 1110 21; l-77h
Revision 2 August 15, 1979 The area, A, and the centroidal offset, x,
of the crush footprint are derived as:
Uhen c < a:
b 2
2 A=2a y=1 a -x
/
ydx a
(a-c)
Q a -x dx A=
a 2
k
-1("-)1 2
2
-j! - (a-c) (2ac-c )
,3 sin A=
h /*
x ka -x 2
dx Ax =
(a-c) 3/2 2b 2
-x = y- (2ac-c )
/A Mhen c > a:
A = nab - A
-=x A
A and _x are as defined for A and
_x, except that c replaces c.
c
= 2a - c The forces inposed on the overpack are:
total Force:
F=c A
Shear P
= F cos 0 s
Thrust F
= F sin 9 l
Moment M=F e
l i
1110 212 1-77i
Revision 2 August 15, 1979 Mhere:
e = a - x - 2r sin 0 0
= 1000 psi 0
-2
^
0
= c (1 + Ae
)
B = 6.43812 cr o
The term, e, represents the moment arm through which the total overpack force, F,
tends to pivot the overpack about the upper most corner of the T-3 body.
This nonent is resisted by six overpack attachment bolts.
When "e" takes on a negative value, the resultant force, F,
lies inside the uppermost corner and no moment is imposed on the overpack attachment bolts.
The empirical expression for foan crush stress, cr' represents a good least squares fit of the stress-strain relation shown in Figure 1. 3. 5-1.
The strain, c, of the foam employed in the above expression is computed at the center of pressure as:
Cylindrical undisturbed lower surface; 6 < tan ~
(h/2r) cp/~ intl c=6 Uhere:
6
=6
+ e tan 0 cp
- intl = (2r + e/ sin 0)/cos 0 Circular plate end lower surface-0 > tan ~
(h/2r)
C *Ocp!* intl Mhere:
S
=6
- f ctn 0 ep g
i f = 2r sin 0-h cos 0+e z
= h/ sin 0 l
int!
1110 213 1-77j
Revision 2 August 15, 1979 The results of this analysis are presented in Figure 1.7.1-3 for total force, F,
shear, P thrust, F and moment, M F
e.
s, t
Figure 1.7.1-4 represents an overlay of results fron Figures 1.7.1-2 and 1.7.1-3.
Maximum forces are found as:
Maximum Total Force
= 3.329765 x 10 G 0 = 81.5 6
Maximum Shear
= 1.059077 x 10 lbs
@ 0 = 66 6
Maximum Moment
= 1.35671 x 10 in-lbs 9 0 = 7.5 The maximum shear load governs the evaluation of shear and bearing capabilities for the overpack to T-3 lip.
Shear stress is found as:
6 f
= 1.059077x10 /61.85 : 17173 psi s
The Margin of Safety in shear for the overpack base plate lip ASTM 516, Grade 70 is:
M.S. = 40415/17173 -1 = +1.36 l
The corresponding bearing stress and Margin of Fafety is:
6 f
= 1.059077x10 /23.20 = d5650 psi b
I M.S. = 70000/45650 -1 = +0.53 This shear load is less than the closure plate shear load associated with side drop, examined in Section 1.7.1.2.2.
Thus, shear load transfer in the T-3 cask closure plates need not be checked.
l 1
1110 214 1-77k
-yo. "'s ' x) ' 'd d - b ' Lo*NH > """M H o
s y
e e
o w
y i
a 5
O gi 1
O 5
h h
~
=
+m J
N f b f
g o
g 9 f d
- M "e
- ,e +c 7
c u
! b
-I
,o mO o e
f I D A 1 d T r
2 nt i y
O I
W
~
r U
M o.
3
~~
d v
e h.
N,
~
('
~
i' 15
./
l 4
h I
k f
8 a'
z r
s h
.k M
OF e
a "5
i t
[
y l
M y) d u
8 L
h J
l I
s a
=
I i
N O!
d4M(4 M b 4Ik{ k
/
.a 1-771
{
' i b '.l.' W % 5 "1 46 070C
)
~
i 3,329,765 lbs.
j Figure 1.7.1-4 Maximum Overpack Forces for Oblique Impacts, 30' Accident Drop
,\\
l 3,298,315 lbs
'\\
i 3,
7
- \\
\\
\\
i i
.t
\\
\\
ma
' Total Force, F
~
s e
1 0
\\
a
\\ y-3 x
g x
C"3 g
Total Thrust, F u
o L
.\\
C""3
\\
M Ci 3 y
s j,
. Shear,.F _.
~~w--
["'""
g 1,059,077 lbs
~
CD 6
_. _O f
t I
I I
I JO 80 TO foO 50 AD 20 20 to Impact Orientation with Respect to IIorizon (0, degrees)
Revision 2 August 15, 1979 The overpack moment produces a maximum attachment shear load, F
estimated as follows:
a, o
%a s'
/
2 r
'a r
U M
= 2F3(1-cos 60 )r+2Fa ( +cos 60 ) r+Fa' g
M
=6F o
a 6
F 1.35671x10 Fa" ( 6 ) (13. 2 2 )
= 17014 lbs.
Shear stress in the 1-8 UNC bolts (ASTM A-320, L43) is:
f
= 29267 psi s
1 Bending stresses induced by single shear loading of the bolts by the 3/8" plate doublers is estinated as:
- Mr _ 32M
'b lF nd' But, M=F t/2 t=
3/9" 17014 lbs.
F
=
a d =.8466 inch at
" (16)(17014) (3/8) f 53836 psi b"
nd' n(.8466)'
=
Combining bending and shear gives a naximum stress intensity of:
f 6
=2
+F
= 78066 psi 7
s.
l Thus, the Margin of Safety of the A-320, La3 bolts is:
M.S. = 125000/78066 -1 = +0.60 1110 2I/
l-77n
Revision 2 August 15, 1979 The bearing stress in the 3/3" A414, Gr. A doublers is estimated as:
45371 psi f
= 17014/
(1) (3/8)
=
b The resultant Margin c f Safety is:
M.S. = 70000/45371 -1 = +0.54 It is concluded that the overpack remains attached to the T-3 Package under corner and oblique inpact conditions.
1110 218 1-77a
Revision 2 August 15, 1979 1.7.1.2 Free Drop Impact Analysis, Side Drop Side drop is assessed with the analytic model as described in Section 1.6.6.3.
The model was changed in two respects.
Beam material properties were supplemented with bi-linear stress-strain data allowing accurate prediction of inelastic strains.
These data consisted of a specified yield of 30 ksi and an ulti-mate of 75 ksi at a total strain of 40%.
In addition, initial conditions were adjusted to establish an initial contact velocity corresponding to a 30' drop.
= jf2gh = 527.45 in/sec.
Vg The results of the analysis are summarized in Table 1.7.1.2-1 and Figures 1.7.1.2-1,
-2,
-3.
Figure 1.7.1.2-1 presents selected vertical motions of the T-3 during the impact event.
Figure 1.7.1.2-2 presents selected side impact contact forces for the event and illustrates that the analysis duration was sufficiently long to allow the T-3 to rebound.
Figure 1.7.1.2-3 illustrates beam flexural stress response of the T-3 at selected locations.
I110 219 l-90
Revision 2 August 15, 1979 Table 1.7.1.2-1 Maximum Side Drop Responses, 30' Drop Node /
Time Response Quantity Element (sec)
Magnitude Deformations (in)
Pusher End 1
.0025
.61932 inch Plug End 11
.0015
.32857 Center 7
.0030
.86266 Forces (lb, in-lb)
Pusher End 1
.0025 1,238,300 lbs.
Plug End 31
.0015 1,985,400 Center 13
.0030 1,579,100 Beam Moment Stress 24
.0023 30423 psi 1110 220 1-90a
9 POOR ORIG!Bi 8tevision 2 August 15, 1979 rigure 1.7.1.2 1 Selected Displacements of Beam Nodes, T-3 30' Side Drop y i v., tic.o
- CC*
i l
l I
I
- ~)*~ ~ ' ~ - 04
<,p x iso,iront.i >
]-2 b* ~ 5 6
- ~
s 9 PUSHER
{
PLUG
- CCC' E!;D Et:D d= Vertical (Y) Displacement at node i i
it?
->a n
T i
ss-t l
u, n
(
V
,/
4
/
$7 I
- 4; g__
,/
l
/
d' /
zc.
/ /
/
,/ /
g
/,-
/,
r
'N
/
//
,/ /
s
/, /
i/,/
/
o
'l -/
.f
%g
/
\\ \\
/
\\\\s\\
i
\\\\
/
- *c0
\\
y..
i r3. 'C:;';.
CCCC is ' OC
.C+;
CCCCC CC'CC CC**'.
CCCGC JCe*J CC%C 200 32m
.ct % L - O r-yr
- ,st s 1-90b 1110 221 t
9 P00RORUM Revision 2 August 15, 1979 Figure 1.7.1.2-2 Selected Forces in Spat Elements T-3 30' Side Impact ITiCCCS I
f l
8 l
1 l
1 i
t i
i I
y (vertican 1
i l
8 i
i
- 33XC1 i
-- %~f ppy py-
<p x (Ho,.rontan i
/
a e
a a
A h
/
'\\
3 i
~
~~
j PUS!!ER PLUG i
. c,_
END END
\\
- @ = Contact Force in Non- -
,i Linear Element i t
l l
nrf f
N
, Y,
\\-
e;.
ss
\\
iI j
teo
.=,
K T' i !
ig '
\\
/
/
4' z
\\,
1 1
Kgg N
\\
I
\\
\\
1
\\
\\
ll i
me,
\\'
- '\\
\\,
s k
i o
K~C X1 1
i e
4
.\\{.
\\
\\
l'
.i
,' g
- \\
i
\\
.\\
i
.i i
5 _= =m I
cCn.s s_ _.m
. e
=;. :
_m.= :
m:. ;
.s:
=n. :
.=
..m ;
, ; c1 w :.r, - w w_ v y 5 - n re yne.
1-90c 1110 222 o
e 9
2]D1 ORE!AL l
Revis.in 2 August 15, 1979 i
Figure 1.7.1.2-3 Selected Bending Stresses in outer Shell T-3 30' Side Impact sn';:']-
t...
....e 4,
=
, +x. wrwreyfr- ~.-.~
h) tD tD 9 & O P Ll'G PUSliER
'2 ^ 7 2 END END
= Stress in Plastic Beam ~
Element i i
1
- < =
u
/
l
~
,e,e..
l 7"
f \\
'N
'Ti 1
c@
s 3
.y-
-,g n.
\\s
/
- \\
b k,
\\
/
-,' /
Cx,f
.,,/
x s
m
. JPJ,, llVp(& /p $
\\
\\
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Revision 2 July 15, 1979 1.7.1.2.1 "ask Shell & Containment Vessel The stress induced in the T-3 outer shell due to compression flattening of the shell can be estimated, given the maximum deformation predicted for the side, 6=.86266 inches, reference Table 1.7.1.2-1.
6 = R(1-cos 0)
-1 0 = cos (R-6)/R
-1
= cos (13.2 -.86266)/13.2
= 20.83 If we conservatively assume that the stainless steel shell maintains its original shape in the area adjacent to the crush zone, strains can be calculated.
l1 R
we I
i i
-\\
, [~ _~ _ _-,-
~~
l L
m c = change in shell length / original shell length c = S-1/S (RO-R sin 0)/R0 9 = 20.83 (180)
. 635 radians
=
=
(.3635-sin.3635)/.3635 =.0219
=
1110 224 1-91
Revision 2 August 15, 1979 To these circumferential strains must be added the longitudinal strains associated with nominal thermal differential and beam flexure.
Table 1.7.1.2-1 indicates the effective beam stress in the T-3 outer shell is 30423 psi, whereas Section 1.6.1.2 gives the thermal differential stress as 9876 psi.
This is equivalent te a longitudinal strain of:
S L
Where:
S
= 30000 psi S
~~~~~~---
9 y
u g
y l
S
= 75000 psi u
l 6
E = 28.3x10 psi E
I I
e
= 0.40 (per ASTM A240)
-e u
Cu The longitudinal strain is:
y/E + (S ~8v) (
-S /E) b = 30423+9876 = 40299 psi c
b u
y b
(S -8y) u 0.0924
=
The total strain intensity is thus:
.0924 +.0219 =.1143 c
=
7 On a strain basis, the margin of safety in the outer shell is:
M.S.
=.4/.1143-1 = +2.50 On a stress basis, the margin of safety in the outer shell is:
(c -S,/E)(S -Sg 7
S
=S
+
^ = 42773 psi o
y (c -8 /E) u y
M.S.
= S /8 -1 = +0.75 u
o 1110 225 1-91a
Revision 2 August 15, 1979 It should be observed that these margins of safety are very conservative predictions since the thermal differential stresses added to the bending stresses are secondary, self limiting stresses that would tend to disappear as the outer shell experiences inelastic strains.
The containment vessel under side impacts must be assessed for the following load or stress components:
Pressure (Pm)
Thermal Differential (y)
Lateral Bending (Pb}
Lateral Compression (P )
b The pressure and thermal differential components are as evaluated and discussed in Section 1.6.6.3.
The bending and compression stress components are evaluated as follows:
Lateral Bending The stress in the outer shell under side impact bending is 30423 psi, Table 1.7.1.2-1.
This is equivalent to a bending strain in the outer shell of:
(S -8y) IE -S /E) b u
y
-3 e
- S /E +
= 4.810lx10 b
y (g _gy) o u
Assuming plane sections remain plane, the strain in the outer fibre of the containment vessel is:
(4.8101x10-3) = 1.5897x10 -3 e
b 05 c
1110 226 1-91b
Revision 2 August 15, 1979 This is equivalent to a containment vessel bending stress of:
(c
~S//E) (S ~by) b u
c psi S
=S
+
=
b IC ~b /E) u y
Lateral Compression The lateral compression loads due to the lead surrounding the containment vessel was assessed in Section 1.6.6.3 with a plane strain model of the T-3 cross section loaded by acceleration induced body forces.
For the 30' drop event, the applicable acceleration is obtained from the peak lateral force exerted on the T-3 by crush upon an unyielding surface.
Table 1.7.1.2-1 gives this peak force as 1,579,100 lbs.
Thus, the lateral acceleration is:
1,5 9, 415.55 g's A
=
=
g 00 The normalizing coefficient applied to stresses given in Figure 1.6.6.3-3 is:
415.55 F=
= 4.1555.
The stresses in the containment vessel at the nine locations examined in Section 1.6.6.3-3 are:
f (psi) Location
- z(psi)
Location
- z 1
+ 4779 6
-45478 2
+12379 7
+ 1637 3
+19975 8
+22079 4
-20254 9
+44913 5
-31356 See Page 1.-60f(12) 1-91c
Revision 2 August 15, 1979 The direct stress components for the containment vessel under 30 foot side drop conditions may now be tabulated as:
f f
T f
x y
xy z
Load Or.igin
- Location, (radial)
(axial)
(shear)
(hoop)
Pressure (P )
-39
+
232 0
+
483 Thermal Differential (Q) 0
+ 8701 0
0 Lateral Bending &
Compression (Pb) 1 0
-30060 0
+ 4779 2
0
-28938 0
+12379 3
0
-27816 0
+19975 4
0 0
0
-20254 5
0 0
0
-31856 6
0 0
0
-45478 7
0
+30060 0
+ 1637 8
0
+28938 0
+22078 9
0
+27816 0
+44913 3
The maximum stress intensities, versus location, are:
Stress Intensities (psi)
P (P +Pb}
Location
- m l
522 35090 2
41568 3
48042 4
20003 5
31605 6
45227 7
j 30331 8
i I
29209 f
9 45435
- See Page 1-60f(12) 1110 228 1-91d
Revision 2 August 15, 1979 The S value f r the A 312 seamless pipe containment vessel is m
20 ksi.
Thus, the margins of safety for accident conditions, l
l per NRC Regulatory Guide 7.6, C.6 are:
P vs. 2.4 S or 0.7 S m
m u*
i l
(2.4) (20000)/522 -1 = + Large i
M.S.
=
(P
+ P ) vs. 3.6 S
- b
- 3 m
u (3. 6) (20000)/48042 -1 = +0. 50 M.S.
=
Therefore, it can be concluded that the external shell and containment vessel will maintain their integrity after the 30 ft. side drop.
1110 229 l-91e
Revision 2 August 15, 1979 1.7.1.2.2 Closure Plate and End Cap Shear loads across the plug closure plate and end cap generated as the result of the side drop conditions, can be calculated from the results presented in Table 1.7.1.2-1.
The total force exerted on the plug end is 1,985,400 lbs.
This force is distributed between the closure plate and end cap on the basis of steel width contact surface thicknesses.
closure " 8.
(,985,400) = 1,259,034 lbs.
F
"(8 )
(1,985,400) 726,366 lbs.
F
=
cap The load imposed on the plug closure plate is transferred to the cask body end cap by shear across a stepped lip.
No loads
/,
are imposed upon the closure plate bolts by this lateral shear load because the total diametrical clearance of the bearing surface is 0.060", whereas each bolt possesses a clearance of 0.080 inches.
The effuctive depth of this step is 1.55", with an effective width of 20.68.
Thus, the bearing stress is:
1,259,034 f
39279 psi
=
=
brg (1.55)(20.68)
The Margin of Safety in bearing is:
M.S. =Fbru!fbrg-1 = 70000/39279-1 = +0.7S Uhere:
0000 psi (ASTM A516, NB-3227.1, ASME F
=
bru u
Section III)
The effective shear area is conservatively approximated as one-half the total an: alar section of the closure plate or:
2 2
(20.68 _y42)
( ) = 91.0 in A
=
s 1110 230 1-92
Revision 2 August 15, 1979 Thus, the shear stress is:
, 1,259,034 = 13836. psi fs The allowable shear stress in ASTM A516 is:
fsu " f /
= 70000/ [ = 40415.
u Thus, the Margin of Safety is:
M.S. =Fsu/f -1 = 40415/13836 = +1.92 s
The shear transferred by the plug end closure plate to the end cap produces a bearing stress in the end cap of 39279 psi.
The associated margin of safety is:
M.S. =Fbru!fbrg -1 = 75000/39279 -1 = +0.91
= 75000 psi (ASTM A240)
Fbu "
u The shear stress in the end cap is:
1,259,034 f
11813 psi
=
=
(26.44 -20.682) s The associated Margin of Safety is:
750c0/
-1 = +2.67 M.S.
=
11813 This load is next transferred to the outer shell of the T-3 package via a circunferential weld between the plug end cap plate and the outer shell.
The area of the weld is:
1 2
( b5 ) (n) (26.44)
= 58.73 in A
=
g 1110 231 1-93
Revision 2 August 15, 1979 The shear stress and Margin of Safety is:
f
= 1,985,400/58.73 = 33806 psi s
000/T
-1 = +0.28 M.S.
=
33806 At the pusher end, the maximum impact force is 1,238,300 lbs, reference Table 1.7.1.2-1.
This load is transferred to the T-3 outer shell by shear through a weld of identical size and pro-portion to that used at the plug end.
Thus, the shear stress and margin of safety is:
f
= 1,238,300/58.73 = 21085 psi s
0/ k
-1 = +1.05 M.S.
=
21085 From the above it can be seen that the step in the closure plate will react the ehear loads.
No shear loads will be transmitted to the bolts, therefore, the plate will remain intact.
1110 232 1-93a
Revision 2 August 15, 1979 1.7.1.2.3 Impact on Trunnions Should the cask undergo a 30 ft. drop onto the trunnions, the load introduced into the cask shell will be limited to the crush or yielding capacity of the lug.
The capacity is defined as follows:
F=SA yT Where:
S
= 30000 psi (yield 304)
A
= 9.42 in-T 2
F=
(30000 psi) (9. 42 in )
282,600 lbs per lug
=
The strain energy required to compress the trunnions is only:
S.E.
(282,600 lbs) (2 lugs) (1. 625 in)
=
918,400 in-lbs
=
This represents Jess than 7% of the total kinetic energy available.
Therefore, it can be concluded that the trunnions fully yield under the side drop accident condition.
The loads induced in the outer shell and containment vessel by impact upon the trunnions are limited by the yield characteristics of the trunnions and are therefore identical to the evaluation in Section 1.6.6.3, Normal Side Drop.
I 1110 233
Revision 2 August 15, 1979 Using ORNL-NSIC-68 for the side wall evaluation, the required shell thickness for puncture integrity can be calculated as:
1 t=
(W/S)*
Where:
W = 38,000 lbs.
S
70,000 psi (Ref. 1.3.1) u (38000/70000).71 t
t=
.65 in From the drawing it can be seen that the external shell is fabricated from 1.00 in thick 304 stainless steel and covered or clad with.134 in str. nless steel.
The following Margin of Safety exists:
M.S.
= 1.134 in/.65 in-1 M.S.
= +.74 The presence of a large positive margin of safety provides assurance that the skin will not puncture even if we were to consider such things as the small rclaction in mechanical pro-perties of the lead at maximum steady state temperature of 140 F.
Should the puncture impact occur at the c.g. of the package, bending moment stresses would be induced in the outer shell and containment vessel.
The magnitude. of these stresses ii10 234
Revision 2 August 15, 1979 I
is evaluated as follows:
Where:
r = 13.22 (outer shell)
= 4.313 (containment vessel)
I = 7118 in4(Ref. 1.6.6.3)
Wa L 9
M=
8 W= 38,000 lbs.
E = 177 inches Or:
Wa ir o=
= 118.12 ra g
g 1561.49 psi per g (cuter shell)
=
509.43 psi per g (containment vessel)
=
The acceleration, a,
can be conservatively estimated from the g
area of the 6 inch diameter puncture pin and the dynamic flow stress of the steel shell.
This app 7ach ignors the deformation of the lead backing; hence, conservatively overpredicts the deceleration force.
"^
^g" plast n
(6)
}
= 33.5 g's a
=
g 8
1110 235 1-111a
Revision 2 August 15, 1979 Thus, the induced bending stresses, f '
b fb= (33. 5 g) (1561. 49) = 52283 psi (outer shell)
(33.5 g) (509.43)
= 17057 psi (containment vessel)
=
To these stresses must be added the pressure and thermal differential stresses associated with normal conditions:
E f
T x
y xy z
Outer Shell Pressure 0
0 0
0 Thermal Differential 0
+ 9876 0
0 Bending 0
I52283 0
0 Containment vessel Pressure
-39
+
232 0
+483 Thermal Differential
+ 8701 Bending 0
+17057 0
0 The maximum stress intensities are:
S
= 62159 psi (outer shell)
= 26029 psi (containment vessel)
The ultimate tensile strength is S
= 75 ksi (A240/A312), thus, u
the Margins of Safety are:
M.S. = S ! m~
u
= 75000/62159-1 = +0.21 (outer shell)
(2. 4) (20000) /26029 -1 = +0.84 (containment vessal.)
=
ii10 236 1-lllb
Revision 2 August 15, 1979 Therefore, it can be concluded that the cask body can safely react the 40 inch puncture condition.
For puncture conditions on the package in :he area of the over-pack, it should be noted that the overpack will absorb considerable amounts of energy.
To calculate the amount of energy that the foam is able to absorb the EYDROP program was run assuming that the package or overpack diameter was equal to the 6 inch diameter pin.
Therefore the following parameters were considered:
Package Weight
= 38,000 lbs Package Diameter = 6 in.
Overpack Depth
= 18 in.
Drop Height
= 3.33 ft.
From the attached printout (Table 1.7.2-1) it can be seen that the strain energy available in the foam is adequate to react the total kinetic energy of the package.
This produces a maximcm acceleration of 18.2 g's and 691,380 pounds of force.
It should be noted that these numbers are extremely conservative since they do not account for the energy required to shear the foam away from the pins edge as it penetrates the overpack.
Secondly, foam exhibits a coning effect, which tends to distribute tha load over a bigger foot print.
It wil..,
therefore, utilize a.'.arger volume foam for energy absorption.
1110 237 1-112
Revision 2 August 15, 1979 The analysis approach assumed inelastic behavior of the lid interface contacts and bolts.
The analysis was performed in three load steps.
The first load step, under zero external loads, consisted of three iterations, in order to establish realistic load flow under bolt preload conditions.
The second load step, comprised of seven iterations, incrementally applied the puncture load of 700,000 lbs.
The third load step, comprised of a maximum of six iterations, held this 700,000 lb load and allowed final convergence of the non-linear components.
The final results are briefly summarized in Figure 1.7.2-2.
The results indicate the lid remains totally elastic.
The applied force of 700,000 lbs. is reacted by compressive forces at the inner most contact points and a moment couple comprised of these contact forces and the bolt force.
The margin of safety of the lid, ASTM A516, Grade 70, is a minimum at element 20:
Margin of Safety:
(Closure Plate)
M.S.
-1 = +1.73 h
25625 The margin of safety of the bolts, ASTM A320-L7, is:
125,000 M.S.
=
It
-1 = +1.35 (44647. 7) (2x) / (8) (. 606)
Thus, the plug closure plate and bolts are cacable of safely with-s_anding puncture loads.
1i10 238 1-ll3e
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