ML20071B346
| ML20071B346 | |
| Person / Time | |
|---|---|
| Site: | Midland |
| Issue date: | 11/30/1982 |
| From: | Kennedy R, Short S, Tong W STRUCTURAL MECHANICS ASSOCIATES |
| To: | |
| Shared Package | |
| ML20071B337 | List: |
| References | |
| ISSUANCES-OL, ISSUANCES-OM, SMA-13701.05R, SMA-13701.05R00, SMA-13701.05R003-V06, SMA-13701.05R3-V6, NUDOCS 8302280176 | |
| Download: ML20071B346 (83) | |
Text
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. SMA 13701.05R003 (V0LUME VI) ,
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N MIDLAND SEISMIC MARGIN EARTHQUAKE STRUCTURAL EVALUATION -
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B0 RATED WATER STORAGE TANK'AND FOUNDATION f
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CONS'JMERS POWER COMPANY Ey
- - Jackson, Michigan g p-November, 1982 -
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- STRUCTURAL g
mECHR0lCS L
""""""* RSSOCIRTES A Calif. Cor p.
5160 Birch Street, Newport Beach, Calif. 92660 (714) 833 7552 -
8302280176 830216 -
ADOCK 05000329 -- _ _ _ _ .. _
SMA 13701.05R003(VOLUME VI)
MIDLAND SEISMIC MARGIN EARTHOUAKE STRUCTURAL EVALUATION VOLUME VI BORATED WATER STORAGE TANK AND FOUNDATION by Robert P. Kennedy Stephen A. Short Wen-How Tong l
Approved: N Approved: bd>
R. P. Kennedy g/ T. R. Kipp President Manager of Quality Assurance prepared for l CONSUMERS POWER COMPANY i
Jackson, Michigan Novembei, 1982 1
1 i
g g STRUCTURAL mECHRnlCS T
ASSOCIATES a Caht. Coro.
5
- 00 0:.
T h Street, Newport Beach, Calif. 92660 (714) 833-7552
REVISIONS Document Number SMA 13701.05R003(Volume VI)
Title Midland Seismic Marain Earthouake Structural Evaluation Volume VI, Bora ted Water Storage Tank and Foundation Rev. Description QA Project Manager 4-30-82 Draft for Review ,
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SEISMIC MARGIN REVIEW MIDLAND ENERGY CENTER PROJECT TABLE OF CONTENTS VOLUME N0. TITLE I METHODOLOGY AND CRITERIA II REACTOR CONTAINMENT BUILDING III AUXILIARY BUILDING IV SERVICE WATER PUMP STRUCTURE V DIESEL GENERATOR BUILDING VI B0 RATED WATER STORAGE TANK VII ELECTRICAL, CONTROL, INSTRUMENTATION AND MECHANICAL EQUIPMENT VIII NSSS EQUIPMENT AND PIPING IX BALANCE-0F-PLANT CLASS 1, 2 AND 3 PIPING, PIPE SUPPORTS AND VALVES X MISCELLANEOUS SUBSYSTEMS AND COMPCNENTS
TABLE OF CONTENTS Section Title Page L IST O F TABL ES . . . . . . . . . . . . . . . . . . iii LIST OF FIGURES ................. iv ..
LIST OF SYMBOLS ................. v \
)
1 INTRODUCTION . . . . . . . . . . . . . . . . . . . VI-1-1
1.1 Purpose and Scope
of Work . . . . . . . . . . VI-1-1 1.2 Description of the Tanks and Foundations .. VI-1-2 -
1.3 Seismic Ground Motion . . . . . . . . . . . . VI-1-3 2 SEISMIC ANALYSIS METHOD ............. VI-2-1 2.1 General . . . . . . . . . . . . . . . . . . . VI-2-1 2.2 Seismic Model . . . . . . . ........ VI-2-2 2.2.1 Impulsive Mode . . . . . . . . . . . . VI-2-2 2.2.2 Sloshing Mode ............ VI-2-5 2.2.3 Vertical Mode ............ VI-2-6 2.3 Soil-Structure Interaction ......... VI 2-8 2.3.1 Soil Properties .,......... VI-2-8 2.3.2 Soil-Structure Interaction Impedance Functions . . . . . . . . . . . . . . VI-2-11 2.4 Damp i n g . . . . . . . . . . . . . . . . . . . V I 16 2.4.1 Material Damping . . . . . . . . . . . VI-2-16 2.4.2 Equivalent Modal Damping . . . . . . . VI-2-16 3 SEISMIC BEHAVIOR OF THE MIDLAND BWST . . . . . . . VI 1 3.1 Modal Responses . . . . . . . . . . . . . . . VI 1 3.2 Base Shear, Overturning Moment, and Vertical l
Seismic Loads at Tank Basc ......... VI-3-1 3.3 Fluid Pressures on Tank Shell . . . . . . . . VI-3-3 4 CODE MARGIN FOR SEISMIC MARGIN EARTHQUAKE .... VI-4-1 4.1 General . . . . . . . . . . . . . . . . . . . VI-4-1 4.2 Foundation Code Margin ........... VI-4-1 i
l i
TABLE OF CONTENTS (Continued)
Section Title Page 4.2.1 Basic Code and Seismic Margin . . . . VI-4-1 4.2.2 Additional Foundation Capacity Checks ............... VI-4-3 4.2.2.1 Soil Bearing Capacity ... VI-4-3 4.2.2.2 Tank Sliding . . . . . . . . VI-4-5 4.2.2.3 Foundatica Uplift Capacity . VI-4-5 4.2.2.4 Concrete Foundation Capacity Checks without Differential Settlement .. V 7 7 4.3 Anchor Bolt Code Margin .......... VI-4-8 4.4 Tank Code Margin . . . . . . . . . . . . . . VI 10 4.4.1 Goverr.ing Codes and Standards . . . . VI 10 4.4.2 Tank Shell Hoop Stress ....... VI 12 4.4.3 Longitudinal Buckling of Tank Shell . VI-4-13 4.4.4 Local Membrane Stress in Shell at the Bolt Chairs . . . . . . . . . . . VI 15 4.5 solt Chair Bending . . . . . . . . . . . . . VI 16 5
SUMMARY
OF SME CODE MARGINS . . . . . . . . . . . VI 5-1 l
6 REFERENCES ................... VI 1 l
l ii
d LIST OF TABLES Table Ti tle Page VI 1 BWST Dynamic Characteristics . . . . . . . . . . . VI- 3-4 VI- 3-2 Summary of BWST Seismic-Induced Foundation Loads . VI 5 VI-4-1 Seismic Margin Stresses ............. VI 4-20 VI-5-1 SME Code Margins . . . . . . . . . . . . . . . . . VI-5-3 e.
t I
I
'ii
s LIST OF FIGURES F
b Figure Title Page VI-1-1 Borated Water Storage Tank Configuration . . . . . VI-1-4 VI-1-2 BWST Anchor Bolt and Bolt Chair Detail . . . . . . VI-1-5 VI 3 BWST Concrete Ring Foundation Detail . . . . . . . VI-1-6 i
VI-1-4 Midland - Top of Fill Site Specific Spectrum and I Housner Spectrum . . . . . . . . . . . . . . . . . VI-1-7 _
VI-1-5 Midland - Seismic Margin Earthquake (SME) Top of Fill Envelope Response Spectra . . . . . . . . . . VI-1-8 VI-2-1 BWST Horizontal Impulsive Mode Model . . . . . . . VI-2-18 [
VI-2-2 Horizontal Impulsive Seismic Model . . . . . . . . VI-2-19 y
VI-2-3 Assumed Soil Profile Beneath Midland BWST . . . . VI-2-20 VI-2-4 Strain Degradation Relationships . . . . . . . . . VI-2-21 VI- 2-5 Equivalent Soil-Spring Model . . . . . . . . . . VI-2-22 ;
VI- 2-6 Stiffness Coefficients for a Surface Footing over -
and Elastic Hal f-Space . . . . . . . . . . . . . . VI-2-23 VI- 3-1 Modal Properties of BWST Tank - Impulsive Water - -
Soil-Spring Model (Best Estimate Soil) . . . . . . VI-3-6 &
VI- 3-2 BWST Hydrostatic and Hydrodynamic Pressure I Distribution . . . . . . . . . . . . . . . . . . . VI- 3-7 VI- 4-1 Soil Bearing Pressure Distribution . . . . . . . . VI-4-21 ;
VI- 4-2 Foundation Uplift . . . . . . . . . . . . . . . . VI-4-22 VI- 4-3 Ring Wall Loading Conditions . . . . . . . . . . . VI-4-23 VI- 4-4 BWST Anchor 9olt Pullout Capacity . . . . . . . . VI-4-24 VI- 4-5 Calculation of Maximum Anchor Bolt Force . . . . . VI-4-25 VI- 4-6 Analysis Model for Local Membrane Stresses in Shell Due to Anchor Bolt Loading . . . . . . . . . VI-4-26 ;
VI- 4-7 Beam Model for Bolt Chair Design . . . . . . . . . VI-4-27 VI- 4-8 Yield Line for Bolt Chair . . . . . . . . . . . . VI-4-28 ,
F o
W iv .
_m ____ _ _ . _ . _ . _ . _ _
LIST OF SYMBOLS A = section shear area a,b,c,f,g,h,R H
= bolt chair dimensions a
g
= dimensionless frequency for soil-structure response B = elastic buckling factor C
H
= horizontal soil-structure interaction impedance function damping constant C
L
= collapse load capacity CM = code margin
= rocking soil-structure interaction impedance function C* dashpot constant C
V
= vertical soil-structure interaction impedance function dashpot constant D = tank diameter d = maximum fluid sl'osh height dg(ag) = horizontal frequency-dependent coefficient for soil damping DL = dead load d,(ag) = rocking frequency-dependent coefficient for soil damping dy(ag ) = vertical frequency-dependent coefficient for soil damping E = modulus of elasticity e = eccentricity of bolt chair load F = hydrostatic pressure from ground water loading f = frequency of the soil-structure mode F
B
= maximum anchor bolt force ff = concrete unconfined compression strength F.S. = factor of safety F
= seismic margin F
v
= vertical seismic-induced forces on ring foundation f
y
= cyclic vertical natural frequency v
I LIST OF SYMBOLS (Continued) g = gravity acceleration G = effective shear modulus at seismic shear strains e -
d = median effective shear modulus e
G,
= free-field small strain shear modulus 5, = median free-field small strain shear modulus -
= small strain shear modulus including. tank G"s surcharge effect H = lateral earth pressure loading h =- height of fluid in the tank I = section moment of inertia I, = mass moment of inertia of the tank about its base Kg = horizontal soil-structure interaction impedance function stiffness
= rocking soil-structure interaction impedance K* function stiffness Ky = vertical soil-structure interaction impedance function stiffness
[Ke ] = element stiffness matrix _
[K] = structure stiffness matrix 3
L = live load t,a,8,R = bolt chair yield line dimensions ,_
eff t
= portion of tank circum'ference tributary to t
each anchor bolt M = seismic-induced overturning moment MgMgM Mgg = hinge plastic moment capacities M = seismic-induced overturning moment due to sloshing 2
M
- = seismic-induced overturning moment on tank bottom B
r My = mass of tank and impulsive water M
tw
= total mass of tank and water vi
LIST OF SYMBOLS (Continued)
OBE = Operating Basis Earthquake P = anchor bolt load p = pressure P
y
= hydrodynamic pressure on tank shell from the horizontal .mpulsive fluid mode P
2
= hydrodynamic pressure on tank shell from the horizontal sloshing fluid mode P
= bolt chair code capacity P
static
= hydrostatic pressure on the tank shell P
vertical
= hydrodynamic pressure on the tank shell due to vertical seismic response R = tank radius S = allowable stress intensity Sa l
= spectral acceleration of the predominant horizontal impulsive mode Sa 2
= spectral acceleration of the sloshing mode Sa y = spectral acceleration for the vertical response mode sH(ag ) = horizontal frequency-dependent coefficient for soil stiffness SME = S'eismic Margin Earthquake s,(ag) = rocking frequency-dependent coefficient for soil stiffness sy(ag ) = vertical frequency-dependent coefficient for soil stiffness S
y
= minimum specified yield strength T = differential settlement loading t = shell thickness T
a
= anchor bolt tension J code ultimate respcnse from combination of all loads
=
vii
ime hs
-w '
LIST OF SYMBOLS (Continued) -m-a
~~
V = seismic-induced base shear from tank and impulsive fluid response _
soil shear wave velocity V = -
s V
2
= seismic-ir.duced base shear due to sloshing .
~
W = total fluid weight _
W = fluid effective sloshing weight 2 '__
Wg = impulsive fluid weights wy (y) = impulsive weight per unit height !
W R
= roof weight W = shell wall weights C-3 _
W T
= tributary weight of water directly above ring [
foundation y tank shell and fluid weight Wy =
~
X 2
= height above tank base of W 2
[
y = depth of fluid measured from fluid surface s
e
= logarithmic standard deviation of G e E S
m
= logarithmic standard deviation for G m S
r
= logarithmic standard deviation of (Gg/G m )
y = weight density _
a = displacement -.
I A
e
= element damping value E A = fraction of critical damping for horizontal H
impulsive response _
A m
= fraction of critical damping for mth mode A,
= fraction of critical damping for rocking response m
[
viii
LIST OF SYMBOLS (Continued)
A s
= soil material damping A
y
= fraction of critical damping for vertical response
[Ars ] = modified structure stiffness fonned by multiplying element stiffness matrix by element damping v = Poisson's ratio g = seismic shear strain o = bolt chair top plate stress or tank shell hoop stress cr
= allowable buckling stress o
DL
= compressive stress in tank shell due to dead '7ad a
tm
= 1 cal membrane hoop stress o
ms
=
tensile stress in tank shell due to seismic overturning moment o
g
=
free-field mean effective soil stress og =
mean effective soil stress with surcharge eT
=
tensile stress in the tank shell oy =
tensile stress in tank shell due to vertical earthquake
=
concrete capacity reduction factor or soil angle of internal friction
{4}m
= mth mode eigenvector w2
sloshing natural frequency ey
vertical natural frequency ix
- 1. INTRODUCTION 1.1 PURPOSE AND SCOPE OF WORK An evaluation of the borated water storage tanks (BWST) and their foundations for the Midland Nuclear Power Plant subjected to a Seismic Margin Earthquake (SME) and other loadings has been performed and is described herein. In this evaluation, site specific response spectra (SSRS) representative of the seismicity and soil conditions at the tank site have been used for the earthquake excitation. An envelope of the SSRS and the broad frequency content Housner response spectrum constitute the SME.
The Midland BWST's and their foundations have been evaluated based upon response spectrum seismic analysis. The tank has been represented by a lumped mass-beam element mathematical model with concentrated springs and dashpots for incorporating soil-structure interaction impedance functions. From the resulting seismic loads, the expected behavior of the tank shell, roof, ring wall and ring beam foundation and the underlying supporting soil has been e',aluated.
The purpose of this evaluation is to demonstrate that an accept-able margin against failure or damage to the Midland BWST's when subjected to SME ground motion exists in the as-designed configuration. From the tank SME response combined with response from other loadings, the margin of safety relative to code allowable structural capacities has been assessed. This value is defined as the " code margin", CM. In addition, the f actor by which the SME would have to increase (with oths:r loadings held constant) in order to reach code allowable structural capacities has been evaluated. This value is defined as the " seismic margin", F SME-For the evaluation of CM and FSME, allowable code capacities are taken from the governing codes used for the design of the tanks and their foundations (see Chap ~cer 4).
VI-1-1
-_ _~ ? _
1.2 DESCRIPTION
OF THE TANKS AND FOUNDATIONS There are two BWST's in the Midland Nuclear Power Plant complex, one each for Units 1 and 2. Each BWST is a right vertical, circular cylindrical, flat-bottom tank with a diameter of 52 feet and a cylindrical wall height of 32 feet and an umbrella-shaped roof as shown in Figure VI-l-l. The tank wall is 3/8 inch thick for the bottom 8 feet and 1/4 inch thick for the remainder of the cylindrical shell height. The bottom plate is 1/4 inch thick. The tank roof is 0.3 inch thick with a 52 foot radius and a height of 6 feet, 9-3/8 inches. Tank material is Type 304L stainless steel. Borated water is stored in the tank up to a height of 32 feet.
The BWST's are located outdoors in the tank f arm area, north of the Auxiliary Building. The Unit 1 tank,1T-60, is located on the west side of the tank f arm and the Unit 2 tank, 2T ", is located on the east side of the tank farm. Tank details are shown on Graver drawings NL12046, Rev. 3, NL-12047, Rev. 2, and NL-12051, Rev. 2.
The tank shell, roof, and part of the water in the tank (above the foundation ring wall) are supported by a reinforced concrete ring foundation. Compacted granular fill lies inside the ring wall and a 6-inch layer of oiled sand is between the tank bottom and the granular fill. Approximately 25 feet of compacted plant fill lies under the foundation structure and granular fill. The tank shell is anchored to the reinforced concrete ring foundation by forty 1-1/2-inch diameter, 3 feet 6 inches long A36 anchor bolts. These anchor bolts, which are evenly spaced and embedded around the circumference of the ring wall, provide anchorage to the tank to resist overturning caused by seismic induced lateral load. Details of the anchor bolt and its connection (anchor bolt chair) to the tank shell are illustrated in Figure VI-1-2.
The eccentricity of the anchor bolts relative to the outside of the tank wall have a nominal value of 3-inches. However, this dimension is not tightly controlled. Based upon field measurements of several bolt chairs, this dimension is considered to vary by + 1/4-inch. Thus, the maximum eccentricity used in all calculations was 3.25 inches.
V I-1-2
. s . . _,~_ . ._ ; ; ..' M
,s 9..; . x _v. . py g: tw. 3 y:p - M 7 . , 3.W. _ y 'l ;;
Ring walls for the two tanks are identical except in the valve pit area. Unit 1 has a larger valve pit than Unit 2. The reinforced concrete ring foundation which supports the tank shell and some of the stored water, consists of an originally constructed ring wall (1 foot 6 inches wide by 4 feet 6 inches high) and its footing (4 feet wide by 1 foot 6 inches high) and a ring beam (2 feet wide by 4 feet 6 inches high) integrally tied to the original ring wall. The ring beain was added as a result of the remedial soils program for this plant. Shear con-nectors which are installed to the original ring wall by drilling and grouting at one end and cast in the ring beam at the other end, are used to integrally tie the ring wall and the ring beam together. Figure VI-1-3 gives the cross-section detail of the ring foundation. The minimum specified concrete compressive strength (f' c
) is 4000 psi.
Grade 60 reinforcement is assumed to be used in the foundation construction . The outer radius of this ring foundation is 28.75 feet.
The inner radius is 24 feet. These values are utilized in the calculation of soil-spring and dashpot constants.
1.3 SEISMIC GROUND MOTION The earthquake excitation for the Midland Seismic Margin Evaluation program is specified in terms of ground response spectra.
This response spectra is the envelope of the SSRS developed by Weston Geophysical Corporation (Reference 1) for structures founded at the top-of-fill and the Housner response spectra (Reference 2) which is anchored to a 0.12g zero period (peak) ground acceleration. The individual SSRS and Housner spectra are illustrated in Figure VI-1-4 for 20 percent of critical damping. The envelope spectrum for horizontal ground motion is illustrated in Figure VI-1-5 for various damping levels. The vertical i ground motion component is defined as 2/3 of the enveloped horizontal motion illustrated in Figure VI-1-5. Peak (zero period) horizontal ground acceleration at plant grade elevation is about 0.15g.
VI-1-3
Axis of symetry n
6'-9-3/8" l o q a , :--
1 32' D = 52' I
v.
4 V *4, *[
, WINWW// OV/hW///%Y WV// %Y// %
Y/[W/ \W\W/fW *o *, \
6' y 4 ** 8 0 'd ? ~-
y #Idj e .'..
h*
\sy# in' fl"["k rugv FIGURE VI-1-1. BORATED WATER STORAGE TANK CONFIGURATION VI ,1-4
8" 1-1/2" l-1/2"
~ y 5/8 " TOP PLATE i * '
]
3/8" N
,/ 3/8"V
__1/2" GUSSET R, ,
TANK BOITOM 3" 1 Ig" PLATE %
3 ., VIEW A-A BOLT CHAIR 1-1/2" $ A.B. 3'-6" +--=
LONG, ASTM A-36 . ; TANK RADIUS = 26'-O" ,
-== A .
. hL -
= vl c
,8 12-1/2" a s .
.A ( ,
M.: .* .,:.:.',
. - ' ~r*W. ry.,- *::::;::*2::: ';.' :S'::..,'
' ~ HW/RHRe i -
D RING BEAM
! - q, 1-1/4" x 6" x 6" ,
Y g' RING WALL (1
') V 24" - 6" 12" 9
FIGURE VI-1-2. BWST ANCHOR BOLT AND BOLT CHAIR DETAIL VI-1-5
OUTSIDE RADIUS = 28'-9"
~-
a e J J 2'-0" _ l'-6" _
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- 9 f (TYP.) .
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- a w/ NUTS (TYP.)
/-5 5*
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., . 4' . . . . ,a INSIDE RADIUS 4'-0" = 24'-0" LEAN CONCRETE FILL -_
3, FIGURE VI-1-3. BWST CONCRETE RING FOUNDATION DETAIL VI-1-6 l
l
b . . . . . . . I , . , , ..I . . . .,,,,
m m- _
- 0.200 e- DRMP]NG _
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t- "' s' a $: ,
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,L Site Specific Spectrum -
tu oo-t-
3a - - --- Housner Spectrum
._, 'a a -u _
m m-m R: :
T w-O *~ ~
a .r-D -
tu m-m a ,y-
'a 10~' E 5 0 $ 5 i E 5 '10 E 5 0 $ 5 i E 5 '10' } 5 0 $ 0 i 5 5110 '
FREQUENCY (HERT2)
MIDLAND -
HOUSNER SPECTRUM VI 1-4. MIDLAND - TOP 0F FILL SITE SPECIFIC SPECTRUM AND HOUSNER SPECTRUM (20 Percent of Critical Damping) l l
'0
- ~ - - - - - - - Z - - - - - 1 i 6 i s e 4 i
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- 2. SEISMIC ANALYSIS METHOD 2.1 GENERAL The general analytical approach used to evaluate the BWST is outlined in the following paragraphs and detailed descriptions of the seismic model and treatment of soil-structure interaction and damping are addressed in subsequent sections.
T1e tank shell weight is supported on the concrete foundation which must also withstand the seismic-induced forces in the tank shell.
The seismic forces in the tank shell are nearly totally due to the water in the tank he tank shell weight is negligible compared to the weight of ti.. .ater. Thus, the primary seismic modeling concern is to conservatively model the seismic forces induced by this water on the tank shell and thus, on the foundation. The seismic-induced effects of the water on the BWST can be considered in three parts; 1) the impulsive mode; 2) the sloshing mode; and 3) the vertical mode of fluid-structure interaction. Each of these modes of response is best modeled with its own individual model. The seismic forces imposed upon the tank shell and foundation from each of these three models are combined by the square-root-sum-of-squares (SRSS) method.
Soil-structure interaction has been incorporated into the analysis by use of frequency-dependent impedance functions. The soil beneath the tank was treated as an elastic half-space corrected to account for minor layering effects of the soil beneath the BWST. Best estimated soil properties have been evaluated from test data on the underlying fill and till material to establish impedance function " spring stiffnesses" and " dashpot constant" values. Strain degradation of the soil stiffness properties (approximate nonlinear behavior of the soil) was accounted for in establishing the impedance functions. To account for uncertainties in soil properties and in the mathematical modeling of VI-2-1
L'
. soil-structure interaction, the soil-structure interaction stiffnesses
-l L - are _ varied within the range from 0.6 to 1.67 times the "best estimato" soil-structure interaction stiffnesses. The seismic-induced loads are
- basA on the envelope of seismic responses obtained for soil-structure interaction:stiffnesses which vary throughout this range of possible stiff nesses.
4 Energy dissipation within the tank; fluid and soil system is approximated in the dynamic models as ' viscous (velocity proportional) ;
i damping. Damping consists of material (hysteretic) damping and radiation I damping or the radiation of energy fror.i the structure back into the p supporting soil . In' order to conservatively account for effects of soil j layering or variation of properties with depth, the soil radiation.
I damping used in the seismic evaluation have been taken as 75 percent of the theoretical elastic half-space values. F l
2.2 SEISMIC MODEL ,
2.2.1 IffULSIVE MODE The dynamic model of the BWST used.for determining-the seismic
. forces on the ring foundation from the horizontal impulsive fluid mode is i illustrated schematically in Figure VI-2-1. The' tank shell stiffness is 1
modeled by vertical beam elements between mass points distributed up the tank shell . The beam elements represent the shear and flexural' stiffness of the tank.- The ovalling stiffness of this tank is judged to be insigni-
~
ficant to the seismic response as the tank is held in round by its base 4
at the bottom and by the roof at the top. The roof weight, WR ' IS lumped at the roof level . The shell wali weights, W 3, are lumped at discrete points on the tank shell. Impulsive fluid effective weights,
, Wy , are added to the tank shell weights at each of these node points at and below the top surf ace of the fluid. For. computations of tank seismic response, a rigid link between impulsive fluid weights and shell wall weights as is schematically shown on Figure VI-2-1 is not required. The actual model used for evaluating horizontal impulsive _ seismic response is illustrated in Figure VI-2-2. Numerical values for-the weights, tank stiffmss and geometry are presented on this figure.
! ~
VI-2-2'
_ ~ - . .. ~?.._._._ . _ _._._ _.__._ _ _ - . . .
For a rigid mode of horizontal tank vibrdtion, it has been shown by Housrer (Reference 2) that the total effective horizontal impulsive -
weight of the fluid, W I is given by:
y , W tanh(0.866 D/h) (2, j,)
I 0.866 D/h where 'W = total fluid weight
~
0 = tank diameter .
h = fluid height This total effective impulsive weight is distributed parabolically over the fluid height as shown in Figure VI-2-1. The impulsive weight per unit height, wi(y), over the fluid height is given by:
wy (y) = 0.866 n Dh tanh(0.866 D/h)
{-f{ (2-2) where i = fluid density y = is the depth of fluid measured from the fluid surface With a flexible tank, the impulsive fluid effects should more precisely be considered as an impulsive pressure rather than effective impulsive weights. However, it has been shown by Veletsos (Reference 6) that the effective impulsive weight distribution developed by Housner for rigid tanks can be used to conservatively predict impulsive mode base shears and overturning moments at the bottom of flexible tanks (i.e., the forces on the ring foundation). For tanks similar to the BWST, this approximation leads to base shears which are between a f actor of 1.1 and 1.2 times greater than would be obtained using flexible tank impulsive press ures . The overturning moments obtained assuming a Housner effective weight distribution are within 2 percent of those obtained using a flexible tank impulsive pressure distribution. This slight improvement in accuracy does not warrant the substantial added effort of treating the tank shell as flexible when determining the impulsive fluid effects. The VI-2-3
l l
effective impulsive fluid weight distribution given by Equation 2-2 and shown in Figure VI-2-1, is adequate for computing seismic-induced base shear and overturning moment for the impulsive mode.
Note that for evaluating hoop streses in the shell wall of flexible tanks, a more accurate reprecentation of hydrodynamic pressures over the tanic height is needed as the pressure distribution derived for a rigid wall tank (Equation 2-2) is unconservative for the upper portion of the tank and overly conservative near the base of the tank. For computation of tank wall stresses, the hydrodynamic pressure., P1 , on the tank shell resulting from the horizontal impulsive fluid mode at depths y from the top of the fluid greater than 0.15h have been obtained from:
, for y/h 2 0.15 V
P y= 1.453 Dh (2-3) where V = the seismic-induced base shear as determined from the response spectrum seismic analysis.
The pressure increases linearly from the top of the fluid (y = 0) to the value from Equation 2-3 at y = 0.15h and greater. Equation 2-3 provides an adequate description of the pressure distribution with respect to height on the tank shell for a flexible tank which is in reasonable agreement with the results presented in References 6 and 7 for flexible tanks.
The seismic model shown in Figure VI-2-2 is suitable for computing seismic-induced loads on the concrete foundation for the horizontal impulsive mode. There are also seismic-induced loads on the tank bottom. These loads may be expressed as an additional overturning moment applied over the area of the tank bottom. The additional overturning moment, MB ran be conservatively evaluated by the following expression taken from Reference 2:
V I-2-4
(
Mg = 0.1045 DWSai (2-4) where Sal = is the spectral acceleration of the predominant horizontal impulsive mode For the BWST, this moment is applied primarily to the soil' inside the ring wall foundation and not to the concrete foundation directly. However, this moment does result in some additional forces on the foundation due to the effect of the water directly above the concrete foundation.
2.2.2 SLOSHING MODE The horizontal fluid sloshing mode is a long period (low-frequency) mode of vibration. Because of its low frequency, this mode of vibration does not interact with the effects of tank flexibility or soil-structure interaction. A dynamic model is not required in order to evaluate the forces imposed on the tank shell and ring foundation by this mode. The natural frequency of vibration, m2, of this mode, the fluid effective slashing weight, W2 , and height of application, X2 '
above the tank base are given by relations from References 2 and 7 as presented below.
3.67g 3.67h gg . tanh (2-5) 3.67h W2 = 0.230 h tanh (2-6) i i
3.67h h cosh -h X2 "h- (2-7) 3_.67h sinh [3.67h)
D \ D /
where g = gravity acceleration (32.17 ft/second2 ), ,
VI-2-5
The base and overturning moment at the tank shell base due to this sloshing mode are given by:
V2
- N 2Sa2 (2-8)
M2 " N 22 X Sa2 (2-9) where Sa2 = the spectral acceleration at frequency m2-To evaluate tank shell stresses, the hydrodynamic pressure, P2 '
on the tank shell resulting from the horizontal sloshing fluid mode at depth y from the top of the fluid has been evaluated by:
h-y 0.533 WSa 2 cosh (3.68 P2" Dh (2-10) cosh (3.68h/D)
To evaluate the potential effects of sloshing on the tank roof, the fluid slosh height, d has been estimated from:
d = 0.42 DSa 2 (2-11)
~~
2.2.3 VERTICAL MODE In the vertical mode, the water in the tank is supported directly on the soil and the tank itself is very stiff. Therefore, both the tank and the fluid can be modeled as rigid in this mode. The only source of flexibility comes about because of soil-structure interaction effects. A dynamic model is not required for such a simple problem. The natural frequency of vibration is given by: .
my = (2-12) v VI-2-6
^
l l
where W y is the sun of the tank shell weight, W s
, and the total fluid weight, W, and yK is the vertical soil-structure interaction impedance function stiffness. This is a rigid structure mode of vibration for which the fraction of critical damping, Ay , is given by:
0.75 C*
A y
=
+A s (2-13) 2 / K yy W /g where yC is the vertical dashpot coefficient from the soil-structure interaction impedance function for the foundation, g is gravity acceleration (32.17 feet /second2 ), and A s is the appropriate soil material damping (5 percent of critical 'as discussed in Section 2.4.1).
The 0.75 factor is included to account for soil layering effects as discussed.in Section 2.1 The ring wall foundation primarily supports the vertical seismic forces from the shell. The vertical fluid forces are supported directly on the soil. However, it should be noted that the tributary weight of water locaced directly above the ring wall, W T
, does result in additional vertical seismic loads on the foundation. Thus, the vertical seismic forces on the ring foundation are given by:
Fy= Sa (W y s+WT ) (2-14) where Sa y represents the design seismic vertical spectral acceleration at damping level, A y , and cyclic natural frequency, fy , where fy =
wy /2n.
VI-2-7
2.3 S0IL-STRUCTURE INTERACTION 2.3.1 Soil Properties The soil profile beneath the BWST has been estimated based upon several sources. The fill properties extend from elevation 610 to 634.
The originai glacial till extends down from elevation 610 to elevation 410. A very ense, gra.. alar soil er,tends from elevation 410 to bedrock at elevation 50. The fill properties were based.upon estimates made by Dr. Woods (Reteence 8) and Wc, ton Geophysical (Reference 1). The original till properties were based upon estimates from Weston Geophysical (Reference 1) and Dames & Moore (Reference 10). Based upon these refer-ences, the soil profile presented in Figure VI-2-3 was developed. This figure shows the most probable range for density, y, Poisson's ratio, v ,
shear wave velocity, Vs , and free-field small strain shear modulus, Gm , for each layer beneath the BWST down to elevation 463. Properties beneath elevation 520 could not possibly influence the soil-structure interaction properties for the BWST. Thus, this profile was not extended below elevation 463. Figure VI-2-3 shows that shear wave velocity and free-field small strain shear modulus increase with depth. Although Figure VI-2-3 divides the soil-profile into several layers, the actual increase in stiffness is considered to be gradual rather than in abrupt layers down to elevation 553 where an. abrupt layer change is likely to exist. The soil profile between elevation 628 (bottom of ring foundation) and elevation 571 primarily influences the soil-structure interaction properties for the BWST. Based upon a weighted averaging of the soil properties between elevation 571 and 628, it was estimated that the average free-field small strain shear modulus value has the following median and logarithmic standard deviation values:
Gm m 2.4 x 103 ksf (2-15)
Sm = 0.19 which corresponds to a plus and minus one standard deviation range of Gm = 2.0 to 2.9 x 10 3 ksf VI-2-8 m.
Several corrections must be applied to the average free-field small strain shear modulus before it can be used to ' estimate soil-structure interaction effects. First, the tank and fluid weight apply a surcharge to the upper layers of soil in the inmediate vicinity of the tank and this surcharge effectively increases the small strain shear moduli for these upper layers. Secondly, for the SFL, the scismic strains associated with these soft upper layers are not small and the effective shear moduli of these upper layers must be. reduced below the small strain shear moduli to account for tin high seismic strain levels.
Based upon the Hardin and Drnevich approach (Reference 10), the tank surcharge effect on the small strain shear modulus can be estimated from' 4 Gm os/Co (2-16) where G, is the small strain shear modulus corrected for surcharge, o s is the mean effective stress with surcharge andn o is the free-field mean effective stress. The following estimates of Gm /6b s have been made:
Elevation 625: G/
m 1.3 to 1.6 s ~
(2-17)
Elevation 595: G /4 = 1.0 to 1.2 Estimates of intemediate elevations can be obtained by interpolation.
Figure VI-2-4 (from Reference 10) presents the relationship between the effective shear modulus at higher seismic shear strains, Ge , and t ie small strain shear modulus, G m. The following ranges of s
seismic '. hear strains, g , have been estimated for the seismic margin eart5qu.tke level:
V I-2-9
Elevation 625: g = 0.08 to 0.04%
(2-18)
Elevation 595: . ( = 0.04 to 0.02%
Based upon these estimates, the corresponding range of Ge/Gn from s
Figure VI-2-4 are:
Elevation 625: Ge / 4s = 0.25 to 0.45 (2-19)
Elevation 595: Ge /b s= 0.30 to 0.60 Combining the results of Equation 2-17 and 2-19, it is estimated that throughout the profile fmm Elevation 628 to ! 11, the ratio of effective shear modulus to free-field small strain shear modulus has the following median and logarithmic standard deviation values:
v (Ge/Gm ) = 0.48 (2-20)
BR = 0.46 which corresponds to a plus and minus one standard deviation. range of:
(Ge /4) = 0.30 to 0.75 Combining Equations 2-15 and 2-20, the effective shear modulus has the following median and logarithmic standard deviation values:
v 3
Ge = 1.15 x 10 ksf (2-21)
Se = 0.50 Thus, the corresponding plus and minus one standard deviation range is:
~
G3 = 0.69 to 1.90 x 103 ksf VI-2-10
In determining soil-structure interaction parameters, the following three values for effective shear modulus were used:
Low Intermediate High 3
Ge (ksf) = 0.69x10 1.15x103 1. 90x103 (2-22)
As will be subsequently shown, the low value of effective shear modulus (0.69 x 103 ksf) leads to the largest 8WST seismic responses for the seismic margin earthquake. ,
The following effective values for Poisson's ratio, and soil density were used in evaluating soil-structure interaction properties; Poisson's Ratio: u = 0.45 (2-23)
Density: y = 115 pcf The lower bound density of 115 pcf was used in order to conservatively underestimate radiation damping effects of the soil.
2.3.2 Soil-Structure Interaction Impedance Functions, Soil-structure interaction impedances have been modeled by the usage of the lumped parameter stiffness approach. Thus, the resisting f orces which are developed when the structure moves relative to the surrounding soil mass are incorporated into the analytical model by means of impedance functions represented as equivalent springs and dashpots connecting the structure to the ground.
The resisting forces developed when the structure moves relative to the underlying soil, which are applied at the soil-structure interf ace, am illustrated in Figure VI-2-Sa. In Figure VI-2-Sb, the equivalent soil springs by which the resisting forces at the soil-structure interf ace are included in the structural model are illustrated. Note that there are horizontal and vertical translational springs and a rotational VI-2-11
spring to include forces at the interf ace of the soil and the bottom of the foundation. The forces and moments at the soil-structure interf ace are developed during seismic response of the structure.
In addition to the soil springs shown in Figure VI-2-5b, corres-ponding soil dashpots .are included to incorporate the damping of the soil in the soil-structum model. Soil damping is composed of two types of dampi ng: one ir.troduced by the loss of energy through propagation of elastic waves from tH imediate vicinity of the foundation (i.e.,
fee.iback of energy from the structure to the surrounding soil), and the other being material or internal damping associated with energy losses within the soil due to hysteretic or viscous effects. Material damping for the soil underlying the Midland SWST is assumed to be 5 percent of critical damping (see Section 2.4.1). The calculation of dashpot constants to mpresent energy feedback is described below. Energy feedback is eften called geometrical or radiatie damping.
Values for soil springs and dashpots have been calcula:.ed based on formulas from References 4 and 5. These formulas are approximate analytical solutions for the condition of a rigid structure resting on an elastic half-space. Sal spring (K ' HE and v K,p) and dashpot (CH, C yand C,) constants for horizontal and vertical translational motion and for rocking motion are determined fmm the following relations:
Horizontal Trans1atien_
K e (2-24)
H = sH (ag) (2-v) 8G R2 Cg = dH(ag ) (2 v)~ #e9
~
0.75 CH A = +A (2-26) 2yK"I H
VI- 2-12
Rocking 8G R3 K, = 5,(ag ) 3(1 v) (2-27) 8G R4 C, = d,(ag ) 3(1 v) Y/G g (2-28) a 0.75 C* + As A, = (2-29) 2 /K,I Vertical Translation 4GgR Ky =_s y (a g ) (2-30) 1-v 4G R2 e
Cy = dy(ag ) 3, Y/Ge9 (2-31) 0.75 C V A
V
= +A (2-32) 2/KMy tw where R = the tank radius M
tw = the total mass of tank and water fi g = the mass of tank and impulsive water I,p = the mass moment of inertia of the tank about its base AH'A9 and A v = radiation damping plus soil material damping in the horizontal, rocking and vertical directions expressed as fractions of critical damoing
, dg(ao ), s (a o), d.p(ao ), sy(ao ), dy(ao) = coefficients SH ("o)hich w are dependent on the dimensionless frequency parameter ao as shown in Figure VI-2-6.
VI- 2-13
ag = 2xfR /y/G eg f = the' frequency of the' seismic response for the soil-structure mode.
- _g = gravity acceleration For horizontal and vertical translation, seismic-induced forces -
are transmitted to the underlying soil over the entire tank-and ring wall-area. Thus, the tank radius used in Equations 2-24, 2-25, 2-30 and 2-31 f or norizontal and vertical translation is 28.75 feet to the outside of -
the ring wall. However, in rocking, seismic-induced forces are trans-mitted to the underlying soil primarily through the ring wall foundation.
Thu's for the rocking stiffness and damping, the spring and dashpot constants were evaluated by utilizing Equations 2-27 and 2-28 with the outer foundation. radius of 28.75 feet and then subtracting from the i resulting values the stiffness and danping corresponding to these equations for the inner foundation radius of 24 feet.
The frequency-dependent coefficients (s H , dg, etc.) were determined from Figure VI-2-6 using a coupled horizontal translational and rocking natural frequency of 4.6 bz and a vertical mode natural frequency of 5.6 bz which will be subsequently shown to be the best estimate fundamental horizontal impulsive and vertical mode natural j f equencies. The resultant f requency-dependent coefficients are:
F requency-Depend ent F requency-Depend ent Coeffi ci ent Coefficient for Stiffness for Damping Horizontal Translation 0. 96 0.59 (R = 28.75 ft.)
R = 28.75 ft. 0.72 0.19 Rocking R = 24 ft. 0.77 0.16 Vertical Translation 0.69 0.86 (R = 28.75 ft.)
V I-2-14
To account for minor layering effects, the radiation damping portion of the values (AH A $, and A y) given by Equations 2-25, 2-29 and 2-32 are taken as 75% of the theoretical elastic half-space values.
Soil material damping of 5% of critical is added to the radiation damping.
3 The best estimate (G, = 1.15 x 10 ksf) soil st.?fness and radiation damping values are as follows:
Horizontal Vertical Translation Rocking Translation Stiffness, 5 7 ft- p 5 K' $, or Ky 1.629x10 kip /ft 3.598x10 1.650x10 kip /ft H
Radiation Damping k-sec 5 kip-$
CH , C,, or C y 5125 f
7.536x10 k-sec-ft 10470 ft Radiation Damping plus soil material damping 0.88 0.56 0.39 AH'A$ ' #A v To account for uncertainty in the effective soil modulus, the soil shear modulus was varied over the range of about 0.6 to 1.67 times the best estimate value as discussed previously. Variation in soil shear modulus linearly affects the soil st1ffness and does not change the radiation damping expressed as fraction of critical damping. Note that frequency dependent effects are assumed to be covered by varying shear modulus and frequency dependent parameters are not recomputed for lower and upper bound soil cases.
VI-2-15 -
2.4 DAMPING 2.4.1 Material Damping Fluid Sloshing 0.5 percent of critical damping Tank Shell and Impulsive Fluid 4.0 percent of critical damping Soil Material 5.0 percent of critical damping The tank shell and impulsive fluid value is consistent with damping values specified for the SSE in USNRC Reg. Guide 1.61 (Reference 3). Reference 19 demonstrates that 5 percent. damping is conservative for either sand or clay soil conditions at shear strains of 0.01 percent or greater. In Reference 20, 0.5 percent of critical damping is recomended for the hcrizontal sloshing mode unless a higher value can be substantiated by experimental results.
2.4.2 Equivalent Modal Damping The damping approach used for the evaluation of the Midland BWST is to compute equivalent modal damping by assuming that the element damping is proportional to the element stiffness for each element. Thus, for the mth mode, the equivalent modal damping value im is given by:
($},[lK s3I*}*
A*= (2-33)
{&} [Ks 3f*I m where {4}m is the mth mode eigenvector, s[K ] is the overall structural stiffness matrix, and [AKs ] is a modified structural stiffness matrix formed by multiplying each element stiffness matrix [Ke] by the element damping value A, prior to adding the modified element stiffness matrix into the structural stiffness matrix.
T VI- 2-15
For horizontal impulsive modes, which are a combination of.
structural response and soil-structure interaction, modal damping values are not permitted to exceed 20% of critical. This upper limit was estab-lished to provide conservative composite modal damping values. This limit was validated by comparing (best estimate soil conditions) the base shear and overturning moment from modal time history analyses in which a 20% damping cutoff is used with those from direct integration time history analyses in which concentrated dashpots with properties given in the preceding section are used to represent soil radiation damping. The modal analysis with a composite modal damping cutoff of 20% led to base shears and overturning moments equal to 1.14 and 1.05 times those obtained from time history anlaysis with concentrated soil dashpots. Thus, the
- use of a 20 percent cutoff for modal damping produces reasonable and conservative tank seismic response from analyses of the horizontal
- impulsive tank-fluid mode.
The horizontal fluid-sloshing mode was 0.5% damped. The vertical response mode consisted entirely of soil response with a rigid structure.
The full vertical soil-structure interaction damping was assigned to this mode with no upper bound limit on modal damping because no questions exist on the accuracy of composite modal damping for this pure soil mode of response.
VI- 2-17
Roof W R4 5 Rigid Lir.k (Typ.)
Top of Fluid
- g Parabolic Distribution q q of Effective Impulsive Fluid Mass W g
- \
>--e 1 \
~
\
,f W3 (typical), Wg (typical) y =
~
\
d
~
a l 4 - y a 4
.f* *jj g Base 'I "
Soil-Structure - l g interaction h
impedance functions FIGURE VI-2-1. . BWST 110RIZONTAL IMPULSIVE MODE MODEL
O T_ANK SilELL PROPERTIES 6
E = 4.176x10 ksf; v = 0.3 94 > 35.4' t X I Rigid Linkg 1.70 ft 2 1150 ft 4 84 9 32.0' 1/4" '
Node No. Weight (kips) 2 4 3/8" .55 ft 1726 ft 1 277.9 X = Shear Area II
- 2 503.6 I = Moment of Inertia - 3 523.8 T 4 512.1 5 6( ) 22.4' a 5 426.0 S0Il IMPEDANCE FUNCTION 6 312.7
< PROPERTIES T 7 172.3 q 5( ) 17.6
[ STIFFNESS 8 25.9 H d' 9 28.6 (k/ft) (k-ft/ rad) 5 7 4I I M Lower Bound 0.977x10 2.159x10 5 7 . gq Best Estimate 1.629x10 3.598x10 S I 0 7 Upper Bound 2.72x10- 6.009x10 8' 3(
i sn j 2( p 4' DAMPING ,F , ,
m gII Ag = 56% k 1 4 0' A, = 39% (3 g nn FIGURE VI-2-2. HORIZONTAL IMPULSIVE SEISMIC MODEL
57.5' _
[ - Midland BWST Elevation 634' Q $ $6' p,jj y = 115 to 125 pcf Vs = 500 to 575 fps v = 0.4 to 0.45 Gm = 0.9 to 1.2x103 ksf 615' Fill y = 115 to 125 pcf V = 750 to 850 fps s
v = 0.4 to 0.45 G,= 2.0 to 2.7x103 ksf 610' Original Till y = 115 to 135 pcf Vs = 850 to 1290 fps v = 0.42 to 0.47 .
Gm = 2.7 to 7.0x103 ksf 553' y = 135 pcf Vs = 1690 to 2300 fps v = 0.42 to 0.47 Gm = 12 to 22x103 ksf Original Till 463' Stiffness increases below 463' FIGURE VI-2-3. ASSUMED S0IL PROFILE BENEATH MIDLAND BWST VI- 2-20
CURVE EXTRAPOLATED a
w' okk'b j%
&nsf.Nd 83 y
! \[{ono1
- J Ni a e a 0 GREENWOOD PS AR 3
(0 70 FEET) .
g j 3
\
N' '
M .s g l o a 0" *
\
k \ 4^ A 3 (SEED & !DRISS) kO \ \g CLA 1 (SEED & IDRISS) \
l 0
! \
- C 5 '
g ,
MIDLAND -
s \, . h DYNAMIC % g g'
TRIAX1AL $ %,4 % 'g 0.2 ' '- ' '\
.4 2 4 6 8 3 2 4 6 8 2 2 4 68 1 2 mg 4 6 8 SHE AR -STR AIN, */.
E XP L AN ATION:
O LOW PLASTICITY SILTS AND CLAYS ( ARANGO et al)
A HIGH PLASTICITY SILTS AND CLAYS ( ARANGO et ol)
RECDMMENDED BAND
- FIGURE VI-2-4. STRAIN DEGRADATION RELATIONSHIPS (From Reference 10)
VI-2-21
Structure Model Foundation
'H tttti V A
V M
- a. Soil Resistance Forces Soil- cture gH- horizontal translation spring K -vertical K,p-rocking spring translaEionsprings
- b. Equivalent Soil Springs FIGURE VI-2-5. EQUIVALENT S0IL SPRING MODEL r
VI-2-22
SWAYING STIFFNESS COEFFICIENTS a sg d 1.0 1.0.g i
.5
-_ ag /2n . . . . . ag/2n
.2 .4 .6 .8 1.0 .2 .4 .6 .8 1.0 ROCKING STIFFNESS COEFFICIENTS s, 3 dp 1.0 ,
l.C .
.5 . .5 .
t, e e
.i .i "6/2. ,; ,; ,; .
ag 2,
.6
.'d go ,, ,,,
VERTICAL STIFFNESS COEFFICIENTS isy ad 1.0 ' l.0.y
.85.M. _ _ _ _ _ _ _ _2
.5 . .5 .
. > . . . . . ag/2x
.2 .4 .6 .8 1.0 a g/2n .2 .4 .6 .8 1.0
--- Approximatio of Frequency-Dependent Stiffness Coefficients (apolicable to v = 0.45)
FIGURE VI-2-6.
STIFFNESS COEFFICIENTS FOR A SURFACE FOOTING OVER AN ELASTIC HALF-SPA (REFERENCE 5)
VI-2-23
- 3. SEISMIC BEHAVIOR OF THE MIDLAND BWST 3.1 MODAL RESP 0NSES The natural frequency, modal damping and corresponding spectral acceleration for the sloshing, impulsive and vertical response modes are summarized in Table VI-3-1. The horizontal sloshing mode is at a very low frequency such that the spectral acceleration is governed by the Housner response spectrum rather than the sit 6 specific spectrum. For horizontal impulsive response, there are two modes at frequencies below 33 hz with the first mode including participation of nearly all of the system mass and accounting for nearly all of the impulsive seismic response. The mode shapes for the impulsive response modes with the best estimate soil properties are illustrated in Figure VI-3-1. As mentioned in Chapter 2, the predominant response mode is at a frequency of 4.6 hz for the best estimate soil properties and includes coupled soil translation and rocking as well as structure response. From Table VI-3-1, it may be seen that the lower bound soil case leads to the largest spectral accelerations and thus, would produce the greatest seismic response. The evaluation of the tank seismic margin as discussed in the following chapter, is therefore based on seismic-induced loads as determined from analyses with lower bound soil properties. The tank itself is rigid in the vertical direction (i.e., vibration frequency greater than 33 bz). The lower frequencies shown in Table VI-3-1 are totally due to soil response in the vertical direction. The frequencies shown am in the amplified region of he response spectrum. However, at the very large damping appropriate f or the vertical direction, there would be no amplification of the ground motion which, in the vertical directico, is 2/3 of the zero period horizontal ground acceleration of 0.15g.
3.2 BASE SHEAR, OVERTLRNING M0 MENT, AND VERTICAL SEISMIC LOADS AT TANK BASE Seismic-induced base shear, overturning moment and vertical load at the top of the ring foundation are sumarized ir> Table VI-3-2.
V I-3-1
Individual response modes have been combined by the square-root-sum-of-squares (SRSS) method. As indicated by the spectral accelerations presented in Table VI-3-1, it is confimed that the lower bound soil properties lead to the largest seismic-induced loads on the tank and its foundation. The maximum base shear is 539 kips, or about 20 percent of the tank and impulsive fluid weight. The maximum overturning moment at the base of the tank is 8154 foot-kips. The maximum vertical load on the foundation is 74 kips which is 10 percent of the weight of the tank (110 kips) plus the weight of a two foot wide ring of water, 32 feet high, directly above the ring wall footing (627 kips). These seismic induced loads have been used as the basis for the evaluation of the safety margin f or the Midland BWST.
Other seismic response quantities of interest are the slosh height as determined from Equation 2-11 and the moment due to hydrodynamic pressures acting on the tank bottom as determined from Equation 2-4. The fluid slosh height has been computed to be approximately 1.0 feet. The dome roof of the BWST permits this level of sloshing without significan't reduction of the free surf ace of the fluid. It is concluded that fluid sloshing during seismic response will not produce any damage to the tank roof.
The seismic-induced moment acting on the tank bottom computed in accordance with Equation 2-4 for the lower bound soil properties is 4930 foot-kips. A portion of the bottom pressure acts directly on the underlying soil and a portion of the bottom pressure is transmitted through the ring foundation and then into the soil. The amount of the bottom pressum moment acting on the two foot wide strip of tank bottom around the circumference of the tank directly above the foundation is 1350 foot kips. When evaluating the overturning moment on the ring wall, this 1350 foot-kips should be added to the overturning moment of 8154 foot-kips mported in Table VI-3-2 for the base at the tank shell. Thus, the total overturning moment on the ring wall is 9404 foot-kips. The remaining bottom pressure moment of 3580 foot-kips acts directly on the ,
soil in the central region of the tank.
VI-2-2
m 3.3 FLUID PRESSURES ON TANK SHELL The hydrostatic and. hydrodynamic pressures from the vertical earthquake canponent on the tank shell are triangular distributions given by:
P static = YY (3-1)
Pvertical "YYS*v (3-2) where y = the fluid density y = depth of fluid measured from the top of the fluid Sa y
= the vertical spectral acceleration The hydrodynamic pressures in the impulsive, 1P , and sloshing, P2 '
modes over the height of the tank may be determined from Equations 2-3 (V .= 534k) and 2-10 -(Sa 2 = .0469 ), respectively. The resulting pressure distributions are illustrated in Figure VI-3-2. The hydrodynamic pressures are combined SRSS and then added absolutely to the hydrostatic pressure to obtain the total pressure on the tank shell. One may note that the seismic margin earthquake hydrodynamic pressures are small compared to the hydrostatic pressure.
t V I-3 -3
, ~ . .. . . .
TABLE VI-3-1 BWST DYNAMIC CHARACTERISTICS Response Frequency (Hz) Modal Damping (%) Spectral Acceleration (g)
Sloshino 0.24 0.5 0.046 Impulsive Low:r Bound Mode 1 3.7 20.0 0.214 Mode 2 11.5 20.0 0.188 B;st Estimate Mode 1 4.6 20.0 0.211 Mode 2 14.0 20.0 0.175 Upper Bound Mode 1 5?. 20.0 0.210 Mode 2 16.6 20.0 0.166 Vertical Low 2r Bound 4.3 88.0 0.100 Best Estimate 5.6 88.0 0.100 Upper Bound 7.2 88.0 0.100 VI-3-4
TABLE VI-3-2
SUMMARY
OF BWST SEISMIC-INDUCED FOUNDATION LOADS SME Seismic Response Sloshing Base Shear 72k Overturning Moment 1479 ft-k Impuls'ive
'0"*"
Base Shear 534k Overturning Moment 8019 ft-k Best Base Shear 520k Overturning Moment 7886 ft-k Upper Base Shear 507k Overturning Moment 7811 ft-k Vertical Vertical Load 74k Combined Sloshing-Impulsive L **"
Base Shear 539K Overturning Moment '
8154 ft-k Best Base Shear 525k Overturning Moment 8023 ft-k Upper Base Shear 512K Cverturning Moment 7950 ft-k Maximum Response Base Shear 539k Overturning Moment 8154 ft-k Vertical Load 74k VI-3-5
Undeformed Shape
-.-Shape due to soil translation
-x -Shape due to soil rocking
- -. Mode shape
- a = 0.227 ----
- a = 0.192 -
. \\ \, x
/ /
l
\\' -
/
/
\\ \' ~
e = 0.00306 l/
\ *t /
e = - 0.00719- 4/
\
t \\-
l
/
h _. _
l '
a = 0.044 a' = 0.150 First Mode Second Mode f) = 4.6 Hz f2 = 14.0 Hz Participation Factor = 8.7?' Participation Factor = 3.177 FIGURE VI-3-1. MODAL PROPERTIES OF BWST TANK - IMPULSIVE WATER -
SOIL-SPRING MODEL (BEST ESTIMATE S0IL)
VI- 3-6
[
l l
_ 0.063 ksf 0.063 ksf i
0.30 ksf 0.03 ksf 0.22 ksf 0.045 ksf 0.53 ksf l
l 0
Y t
=
b b 7 ; _1.44 ksf _ 0.14 ksf _ 0.22 ksf 0.016 ksf 1.70 ksf b T) 1 ft.
2.22 ksf
/ d) 1.93 ksf l 0.013 ksf r 1 - 0.19 ksf -
0.22 ksf y
)_ l 2.0 ksf 0.2 ksf 2.30 ksf
!!ydrostatic_ Vertical Impulsive Sloshing otal
=, w w /
s
" Hydrodynamic I FIGURE VI-3-2. BWST HYDR 0 STATIC AND HYDRODYNAMIC PRESSURE DISTRIBUTION
- 4. CODE MARGIN FOR SEISMIC MARGIN EARTHQUAKE 4.1 GENERAL The mar: ins against the applicable code criteria are reported for the seismic margin earthquake in this chapter. These margins are determined for the concrete foundation, the tank, and its anchorage to the ring wall. .
To determine the code margin, the seismic margin earthquake (SME) is substituted for the Safe Shutdown Earthquake (SSE) in the applicable code equations.
4.2 FOUNDATION CODE MARGIN 4.2.1 Basic Code and Seismic Margin For the concrete foundation, the applicable code for the seismic margin review is taken to be ACI-349-76 as supplemented by US NRC Regulatory Guide 1.142. For the SME, the governing load combination equation is:
U = DL + T + F + L + H + SME (4-1) where DL = dead load T = differential settlement F = hydrostatic pressure from ground water L = live load H = lateral earth pressure SME = Seismic Margin Earthquake However, Bechtel Corporation has already design-checked the concrete foundation for the OBE and a foundation SSE level of 1.5 times the FSAR SSE level to this same design code (Reference 12). This design check of VI-4-1
the foundation was performed by applying inertial loads at the foundation level obtained from a tank seismic analysis to a finite elment model of the concrete foundation including the ring wall, footing, ring beam, the dowels between the ring beam and ring wall, and the valve pit. The most critical load combination equation for this design check was:
U = 1.4DL + 1.4T + 1.4F + 1.7L + 1.7H + 1.9 OBE (4-2)
For this load combination, Table 2 of Addendum No. 1 of Reference 12 shows a minimum code margin (code capacity divided by applied load) of 1.02. - As -
a result, the minimum code margin for Equation 4-1 is:
CM = 1.4(1.02) = 1.43 The OBE overturning moment applied to the ring wall was 11,061 ft-kips minus 3359 ft-kips or 7702 ft-kips (Table 4 of Reference 12),
Section 3.2 defines an SME overturning moment of 9504 ft-kips. Comoaring Equations 4-1 and 4-2 indicates a conservative minimum seismic margin for Equation 4-1 of:
F SME = (1.9)(1.02) = 1.57 Note that the seismic margin F SME is the factor by which the SME could be increased.with other loads held constant before response at the code capacity in accordance with Equation 4-1 is reached. Thus, since the concrete foundation has already been design-checked for Equation 4-2 with a conservative OBE overturning moment, it is unnecessary to check this foundation for the SME. Simply by comparing the SME overturning moment to 1.9 times the conservative OBE overturning moment, one shows a minimum seilmic margin of 1.57. The actual seismic margin for the foundation is much larger than 1.57 as the code margin of 1.02 for Equation *-2 is primarily due to differential settlement. A very large seismic marqin will be demonstrated by calculations of the concrete foundation seismic ,
behavior as described later in this chapter.
VI_4-2
. _ . _ _ ~. .._. _ - . _. _ _. ,-
4.2.2 Additional Foundation Capacity Checks Even though extrapolation of the design-check load combinations indicate a minimum seismic margin for the SfE combined with dead load, settlement, hydrostatic pressure, live load, and lateral earth pressures of at least 1.57, some additional seismic margin checks have been perfomed on the concrete foundation and supporting soil. These checks have been on:
a) Soil bearing capacity under the footing b) Taak sliding c) Upl1/t d) Concrete foundation capacity checks without differential settlement These checks were performed to provide independent verification of the seismic capability of the foundation to withstand the SME. These checks considered dead load and SIE only. Note that in addition to the above items, bending and torsion of the ring beam during seismic response have been considered. However, for these behavior modes, it is judged that foundation loads will be transmitted directly into the surrounding soil and the seismic margin will be very large without capacity calculations.
4.2.2.1 Soil Bearing Capacity Compressive forces due to the weight of the tank, contained fluid and foundation and due to seismic-induced loadings can potentially lead to a bearing f ailure of the underlying soil. Based upon conservatively considering the weight of the tank shell and roof, the weight of the water directly above the foundation, the weight of the concrete foundation (ring wall and new ring beam), the weight of soil above footing as well as the seismic-induced load on the tank bottom plate, seismic-induced load due to vertical earthquake motion, and the seismic-induced load on the tank shell due to the cverturning moment, the soil bearing pressure distribution (at the most critical section) shown in Figure VI-4-1 was obtained . The average bearing pressure is 3.26 ksf on the footing VI 3
cross-section with a maximum value of 3.96 ksf. The average bearing pressure of 3.26 ksf is comprised of 2.12 ksf due to static loading and 1.14 ksf due to the SME.
For soil beneath the ring wall subjected to combined static and earthquake loadings, the net bearing capacity is reported to be 8.05 ksf in Reference 17 Note that the value given above, is net bearing capacity defined as the pressure that can be supported at the base of the footing in excess of the pressure at the same level due to the surrounding surcharge. Considering a footing depth of six feet and a soil density of 115 pcf. the bearing factor of safety for the SME would be:
8.05 ksf = 3.13 3.26 ksf - 6 ft(D.115 kcf)
For design, FSAR Subsection 2.5.4.10.1 (Reference 9) specifies a minimum factor of safety of 2.0 for operating loads plus SSE. Thus, the
" code" margin is:
3 CM = 3;9 = 1. 57 The f actor F3pg by which the SME ground motion would have to be multi-plied to reach code allowable stress is:
F (8.05/2.0)-2.12 + 6(0.115) = 2.28 SME = 1.14 VI- 4-4
M 4.2.2.2 Tank Sliding The seismic-induced base shear from Table VI-3-2 is 539 kios.
This horizontal force will be transferred into the underlying soil by friction. The weight of the tank and contents is approximately 4,350 kips. Considering vertical earthquake effects, the effective weight' could be reduced to about 4,180 kips at the time of maximum base shear.
Therefore, the required friction coefficient to resist sliding is 539/4,180 a 0.13.
- . The tank bottom is not flat or particularly smooth. The tank bottom consists of 1/4 inch plates joined together by welds at lap joints.
In addition, the tank bottom is designed to be higher. in the center than at t,he tank walls to. f acilitate draf nage. As a result, the friction coef-ficient is governed by the cohesion and angle of internal friction of. the soil. The soil directly beneath the tank bottom is a granular fill
. material for which a r.ohesion value of zero and an angle of internal friction,4, of 30 degrees are conservative. These properties correspond to a friction factor of about 0.3'6'(conservatively estimated as tan 2/3 & )
which would provide a f actor of safety against tank sliding of 2.8.
Based upon a recuired f actor of safety against sliding of 1.1 (appropriate for SE level), the " code" margin is:
CM = h = 2.5 The f actor, FSFE, is also 2.5 since seismic is the only loading causing sliding.
4.2.2.3 Foundation Uplif t Capacity l
The weight of the steel tank, the concrete foundation, and the fluid and soil above this foundation are all available to resist uplift
-due to seismic-induced overturning moment. Considering the weight of the original ring wall and footing, the new ring beam, the tank shell and roof, and the water and soil directly above, the resulting static pressure VI 5
on the soil beneath the 4-foot-wide footing is 2.12 ksf computed as shown in Figure VI-4-2. Considering vertical earthquake and negative hydro-dynamic pressures which reduce the hydrostatic pressures on the tank bottom plate above the footing, this pressure can be reduced to 1.87 ksf during the. SE as shown in Figure VI-4-2. For this calculation, it is assumed that 40% of the peak negative vertical earthquake effects act concurrently with the maximum overturning moment. This assisnption is consistent with the SRSS of earthquake components.
The overturning moment that would overcome the minimum compres-sive pressure of 1.87 ksf such that uplift of the ring foundation is initi ated is 15,885 f t-kips as comput.ed in Figure VI-4-2. Compared to the SE seismic-induced overturning moment of 8,154 f t-kips (Table VI-3-2),. the foundation uplif t f actor of safety is:
F. S. = 15,885 = 1.95 8,1 54 Foundation uplif t does not constitute a f ailure mode for the tank.
Thus, a minimum f actor of safety of 1.0 should be acceptable for the SE. In this case, the code margin is:
CM = 1.95 The f actor F 3g by which the SE earthquake would have to be multiplied to lead to an uplift f actor of safety of 1.0 is:
F 15885( h "M SME "
8154 + 15885 /2.12-1.87)
\ 1.87 /
The seismic margin factor, F3g, is less than the code margin, CM,
- because the vertical earthquake component increases as the horizontal ground motion increases. Thus, the vertical earthquake component reduces the capacity to withstand horizontal overturning moments without uplift.
V I-4-6
4.2.2.4 Concrete Foundation Capacity Checks without Differential Settlement The basic code and seismic margin for the concrete foundation has been presented in Section 4.2.1. This foundation' design check is extremely conservative as it is predomirantly affected by differential settlenent and not by seismic loadings. It is unlikely that the conserva-tive 40-year predicted differential settlements occur at the same time as the SME. Furthennore, settlement stresses are displacement controlled (i.e., self-limiting), and are not expected to contribute to failure-during an earthquake. Therefore, the following analysis which neglects stresses.due to differential settlement is considered to give more realistic values for the failure capacity of the concrete foundation.
The reinforced concrete tank foundation consists of the original ring wall and footing and the new ring beam as illustrated in Figure V I-1-3. The foundation was checked for the two seismic-loading conditions illustrated in Figure VI-4-3: 1) bending of the footing; and 2) hoop tension of the ring beam due to outward pressure of .the entrapped soil within the foundation ring resulting from vertical loads on this soil.
As mentioned previously, bending and torsion of the ring beam during seismic excitation were also considered but it was judged that for these behavior modes the seismic loads would be transmitted directly into the surrounding soil such that the seismic response of the ring beam in bending and torsion would be very small. The concrete foundation, including both the original ring wall and footing and the ring beam added during foundation remedial work, are made of concrete with minimum unconfined compression strength, f'c of 4000 psi and reinforcing bars with minimum yield strength of 60,000 psi.
V I-4 -7
The loading shown in Figure VI-4-3a imposes a bending moment onto the 1.25-foot-long footing extension of 2.42 f t-kips /ft. The ACI 349-76 ultimate moment capacity of this footing extension is 28.3 -
f t-kips /ft. Thus, the code margin of this footing extension is:
CM = h = 11.7 The soil entrapped within the ring foundation is subjected to vertical loads due to the water weight as well as due to the maximum hydrodynamic pressure from vertical seismic and overturning moment bottom pressures acting on the tank bottom. This loading, act'ing on the entrapped soil, results in the ring beam being in hoop tension due to lateral pressure resulting from this vertical surcharge (Figure VI-4-3b).
(Only the teasile steel within the new ring beam was considered effective in withstanding this loading). It has been conservatively assumed that the lateral pressure resulting from the vertical load is one-half of the vertical loading. In evaluating -the foundation for this loading, the constraint from the soil outside the ring beam has been conservatively ignored. By this extremely conservative approach, there is a f actor of safety of 11.3 against yielding of the foundation circumferential reinf orcement. Thus ,
CM = 11.3 4.3 ANCHOR BOLT CODE MARGIN Anchor bolt capacity is governed by the lesser of:
- 1. Bolt pullout from the concrete
- 2. Tensile cepacity of the bolt
- 3. Tensile capacity of ring wall to footing connection Anchor bolts are spaced at about equal 49 inch intervals around the tank circumference. The 1.5 inch disneter A36 anchor bolts extend into the concrete ring wall foundation 24 inches as is shown in Figure VI-1-3.
Each bolt has a 2.5 inch thick, 6 inch square anchor head plate at its end about 22 inches below the top of the ring wall.
VI 8
The pullout capacity of the bolt and embedment plate has been evaluated in accordance with ACI-349 provisions. By this approach, the capacity is evaluated based on a uniform tensile stress of 4 4 / f'c acting on an effective stress area which is defined by the projected area of a stress cone radiating toward the surface of the footing from the ,
bearing edges of the anchor head (see Figure VI-4-4). The effective area is. limited by overlapping stress cones, by the intersections of cones with concrete surf aces, by the bearing area of the anchor head and by the 4 embedment depth of the anchor hud. The inclination angle for calculating projected areas is taken to be 45 degrees. For this evaluation, the f actor has been taken to be 0.65 which corresponds to the case in which the embedded anchor head does not extend beyond the far f ace reinforce-ment of the footing. It should be noted that the ring beam to be added around the outside of the original ring wall foundation will provide confinement to the original ring wall to prevent f ailure due to lateral
' bursting forces at an anchor head which is the concern of Paragraph B.5.1.1 of the code. However, this ring beam does not increash the effective stress area as the original rng wall and ring beam are not tied together until a depth of 18 inches which is almost equal to the anchor bolt einbedment length (see figure 1-3).
The allowable load for the bolt itself is based on AISC Manual of Steel Construction, Part 2 criteria. Section 1.5.2.1 of the AISC Code states that for tension on the nominal bolt area, the allowable stress is 1/3 of the ultimate tensile stress. Further, Part 2 of the AISC Code allows an increase f actor of 1.7 for ultimate capacity. Thus, for 1-1/2 inch diameter A36 bolts with an ultimate tensile strength of 58 ksi, the allowable ultimate load capacity is 57.4 kips.
The construction joint between the original ring wall and under-lying footing is crossed by #7 bar reinforcing steel spaced at 12 inches on each f ace. Thus, a total of 4.9 square inches of 60 ksi yield strength reinforcing steel crosses this joint for each anchor bolt. The ultimate tensile capacity of this construction joint is 294 kips per arichor bolt.
V I-4 -9
i Thus, the anchor bolt capacity is governed by the tensile capacity cf the bolts and is 57.4 kips.
The maximum uplift force on the bolts is computed from the seismic-induced overturning moment of 8154-f t-kips. Since the tank shell is in compression due to dead weight, a portion of this moment relieves the compressive stresses and the remaining moment goes into the bolt f orces. In Figure VI-4-5, it is illustrated that the maximtzn bolt force is 13.2 kips. This force is made up of 15.7 kips SE overturning _ moment tensile force minus 2.5 kips of dead load compression which must be over-come before anchor bolt tensions develop.
Reference 15 reports a maximum anchor oolt tension of 6.0 kips due to ccabined settlement and dead load. Thus, the total anchor bolt tension due to dead load, settlement, and the SE is:
T3 = 15.7 kips + 6.0 kips = 21.7 kips This anchor bolt load is compared to the code allowable capacity in Table V I-4 -1. .
The minimum anchor bolt code margin is:
CM = 57.4 kips = 2.65 21.7 kips The f actor, F3g, by which the SE ground motion would have to be multi-plied to reach code allowable stress is:
p 57.4-6.0 = 3.27 SE , 15.7 4.4 TANK CODE MARGIN 4.4.1 Governing Codes and Standards The BWSTs are designed and code stamped to the ASE code,Section III, Nuclear Power Plant Components, Subsection NC, Class 2 Components, Paragraph NC3300, Design of Vessels. The 1974 code, with no V I-4-10
addenda, are applicable and Code Case 1607-1 is applicable for upset, cmergency and faulted condition stress allowables. The API 650 code (Reference 13) is also specified for design. In cases of conflict, the ASME Code governs.
The basic design _is conducted using API-650 criteria since NC3300 of the-ASME code does not specifically address flat-bottom storage tank designs. NC3800 does provide criteria for flat-bottom storage tanks and is essentially identical to API-650. The ASME code stress acceptance criteria from Code Case 1607-1 is used for evaluation of the OBE and SSE events.
Under the governing criteria, the following stress inten?ities are allowed.
Loading Primary Local Membrane plus Condition Primary Membrane Primary Bending Design and Normal S 1.5S Upset 1.lS 1.65S Emergency 1.5S 1.8S Faulted 2.0S 2.4S Testing 1.25S* 1.87S**
- Not to exceed 0.9 S
- Not to exceed 1.35 sy The allowable stress intensity, S, is 15.7 ksi for 304 L stain-less steel. Secondary stresses do not require evaluation for Class 2 components designed by rule (NC3300 criteria). Minimum specified yield strength, Sy , is 25 ksi.
For the code margin check, SME response is added to that from ,
dead load, fluid hydrostatic pressure, and settlement with the resultant stresses compared to faulted condition allowables. These allowables are VI- 4-11
d l
-31.4 ksi for primary membrane and 37.7 ksi for primary local membrane plus primary bending. Whenever dead weight reduces the effect of seismic loads, ~only 90 percent of the dead weight stress is included.
Settlenent stresses added to stresses resulting from the SME are obtained from the Addenda to Reference 15.
4.4.2 Tank Shell Hoop Stress Hoop tensile stresses in the tank shell occur due to internal pressure on the tank wall from the contained fluid. Internal pressures are due to the static head of fluid plus hydrodynamic pressures resulting from seismic response in the sloshing, impulsive and vertical modes. Hoop stresses are evaluated for both the 3/8-inch-thick shell and for the 1/4-inch thick shell. The Code (Reference 13) requires hoop stress to be evaluated at an elevation which is one foot above the bottom of the shell course under consideration. For hydrostatic and hydrodynamic pressures, the hoop stress is- given by a = pR/t where p is' pressure, R is tank radius -
and t is tank wall thickness. The hydrostatic and SME pressures were pre-sented in Figure VI-3-2. Based upon these pressures, the SME seismic and hydrostatic hoop stresses are presented in Table VI-4-1. These stresses are compared to a primary membrane stress of 31,400 psi.
The minimum hoop stress code margin is: ,
31400 psi CM =
14733 psi = 2.13 The f actor, FSME, by which the SME ground motion would have to be multi-plied to reach code allowable stress is (see Table VI-4-1 for individual response values):
SbE -, 314002253
- 12430 = 8.40 p
V I-4 -12
4.4.3 Longitudinal Buckling of Tank Shell The maximum SE overturning moments at the base of the tank and eight feet above the base of the tank (i.e., at the bottom of the 1/4-inch section) are 8154 and 4358 f t-kips,- respectively. Assuming a linear variation .of stress over the tank diameter, the corresponding SE longi-tudinal compression stresses in the 3/8-inch and 1/4-inch shell sections are 853 and 684 psi, respectively. Respective dead load compression stresses are 15 and 18 psi which are negligible when combined SRSS.with the horizontal overturning moment stresses. Reference'15 reports the suiimation of dead load -and maximum settlement compressive stresses to be 1066 and 1164 psi for the 3/8-inch ahd 1/4-inch shell sections, respect-ively. These stresses are tabulated in Table VI-4-1.
For the large diameter, thin-wall storage tank, buckling will occur in the elastic range. The ASE Code buckling criterion for axially loaded cylinders nominally contains a safety f actor of 3 for sustained design loads. The ASE Code specifies in Article NC-3000 that the maxi-mum allowable compressive stress to be used in the design of cylindrical shells shall be the lesser of:
a) The allowable S value given in Tables I-7.0 of the Code b) The value of B determined from the applicable chart in Appendix VII of the Code.
For the case under consideration, the latter criterion governs.
The value of B for elastic buckling in Appendix VII can be obtained with a higher degree of accuracy by using the design formula shown below, taken from the 1977 ASE Code.
B= 0.0625 Et (4-3)
VI 13 t-
where E = modulus of elasticity t = shell thickness R = inside radius of shell This fonnula applies to the linear portion of the buckling curves in Appendix VII and is applicable for the BWST analysis. The buckling allow-ables, B, for the design and normal loading conditions are therefore:
B = 1417 psi (for 1/4" shell)
B:= 2126 psi (f or 3/8" shell)
Based on Code Case 1607-1, the Faulted Condition allowables can be increased by a f actor of 2.0 for primary membrane stresses. Thus, the buckling allowables for faulted conditions,~ o. cr = 2B, are:
o cr = 2834 psi (1/4" shell) a cr = 4252 psi (3/8" shell)
These allowable capacities ana compared with the SME, dead load and settlement applied stresses in Table VI-4-1.
The buckling code margin is controlled by the 1/4 inch.shell section for which the buckling allowable is 2834 psi and the combined seismic, dead load and settlement stress is 1848 psi (see Table VI-4-1).
Thus, the minimum code margin for buckling is:
2834 CM = Ts4T = 1.53 V I-4 -14
The factor,.Fsm, by which the SE ground motion would have:to be multi--
plied to reach code allowable stress is:
p 2834-1164 ,
SE , 684 where 1164 psi is the tank shell compression stress due to settlement and dead load and 684 psi is the SE tank shell compressive stress (see Table V I-4-1) . .
4.4.4 Local Membrane Stress in Shell at the Bolt Chairs Bolt chairs attach to the tank shell at approximately one foot above the tank bottom as shown in Figure VI-4-6. Anchor bolt tension acting on these bolt chairs produce local membrane hoop stresses in the tank shell due to the eccentric lever arm of the anchor bolt relative to the tank shell centerline. Section 5.3 of Reference 15 computes local membrane hoop stresses of 13,200 psi due to a 31.31 kip anchor bolt tension based upon the methods of Reference.16. Thus, local membrane hoop stresses, o , are given by:
tm " 1 s Ta = 422 . T, (4-4) where Ta is the anchor bolt tension. These local membrane hoop stresses which are a function of the anchor bolt tension add to the overall hoop tensile stresses reported in Table VI-4-1 for the 3/8-inch shell at this same location.
The total local membrane hooo tension due to the SE is: ,
o = 1676 psi + 422 psi / kip (15.7 kips) = 8301 psi Due to dead load, hydrostatic pressure, and settlenent, this stress is:
e,m = 11177 psi + 422 psi / kip (6.0 kips) = 13709 psi
~ DW+S' VI-4-15
These stresses are combined in Table VI-4-1 and compared to the primary local membrane plus primary bending allowable stress of 37,700 psi.
The local membrane stress code margin is:
CM = 37700 psi = 1.71 22010 psi and the f actor, FSg , is-37700 -13709 F = 2.89 SE = 8301 4.5 BOLT CHAIR BENDING The top plate of the bolt chair is subjected to bending due to anchor bolt tension. Original bolt chair bending design-analysis was conducted by the conservative design method contained in Reference 14.
The method assumes that a beam of width, f, equal to the edge distance from the hole to the plate outside edge carries one-third of the total bolt load. Figure VI-4-7 shows the analytical model. In this figure, it is shown that the beam span is g, the top plate thickness is c and the loading occurs over a width equal to the bolt diameter, d. For a total bof t load, P, the maximun top plate stress,o , is given Oy:
o= (0.375g-0.22d) (4-5) fc2 The computed stress was to be held to the f aulted condition primary l
bending allowable stress of 37,700 psi (Section 4.4.1). Based upon this approach, the total f aulted condition bolt capacity would be:
(Conservative Design Method): Pgp = 23.6 kips The above represents a very conservative capacity estimite bas.ed upon a conservative procedure used in design.
VI 16
The capacity can be more accurately evaluated using the AS?E ;
Code,Section III, Nuclear Power Plant Components, Subsection NF, j Component Supports, Paragraph NF 3200, Design of Class 1 Component Supports,1980. It is acceptable. to use Class 1 design criteria to evaluate the supports on a Class 2 tank because Class 1 criteria are more stringent than Class 2. Paragraph NF 3220, Design of Plate and Shell-Type Supports by Analysis, allows the Level C Service Linits (comparable with the 1974 Emergency Loading Condition) to be establisned for primary membrane plus bending by the limit analysis method. The maximum allowable value of the combined stresses by this method is 0.8 Ct where CL des-ignates the collapse load calculated on the basis of the lower bound theorem of limit analysis using the yield strength value for Type 304 L stainless steel of 25 ksi. In our judgment, component supports should not be allowed to exceed 0.8 Ct, for Level D Service Limits (Faulted Loading Condi tion) . Therefore, this Level C limit will also be applied to Level D.
The collapse load is determined by a yield-line analysis of the bolt chair top plate. The applicable yield-line (collapse mechanism) is shown in Figure VI-4-8. The bolt load bears on the two least deformed points of the top plate in its yield mechanism under the bolt nut. These points are shown in Figure VI-4-7 at a distance R eff f rom the bol t center. Lines
@, @, @ and @ repesent yiel'd hinges. The clastic moment caoacitv of hinge @ is governed by two (2) times the clastic moment caoacity of -
the tank wall which is less than the clastic manent capacity of the too
- pl ate . The plastic moment caoacitv of hinoe @ is coverned by the vertical gusset plate plastic monent capacity, Thus, (25 ksi)(2) 0.375 in)2 = 1.76 in-kips /in Mg =
M . (25 ksi) 0.5 in)2 = 1.56 in-kips /in 3 ,g , (25 ksi) 0.625 in)2 = 2.44 in-kips /in VI-4-17
The collapse load capacity is given by:
CL* (g/2 R,ff) h
+ Mg(b) + Mg(tsina + f)+Mg(1 cosacota)l where (g/2) -R H cos 8 cot a =
a -Rh sin 8 a -RH sin 8 E "
~ sina The angle 8 is varied until the minimun value of Ct is obtained from Equati on 4-6. The capacity C is insensitive to the angle S between 0 t
and 55 degrees but is a minimum at an angle 8 of about 25 degrees.
'f gnoring any benefit from the bolt nut in spreading the load, R gf is conservatively underestimated to be 0.834 inches or less than the hole radi us. With this value of Rdf and a 8 angle of 25 degrees, the collapse load capacity is:
Cg = 40. 6 ki ps The code capacity, PCAP, based upon the collapse load is 0.8(40.6 kips) or 32.5 kips. Thus:
(Collapse Load Approach): PCAP = 32.5 kips VI 4-18 1
The anchor bolt loads were presented .in Section 4.3' and'are sunnarized in Table VI-4-1. Comparing capacity to load leads to a mininum code margin for the bolt chair of:
32.5 kips
- CM =
21.7 kips = 1.50 and a multiplication f actor on the SPE of:
p _ 32.5 -6.0 = 1.69 SME - 15.7 The 3/8-inch fillet weld between the bolt chair gusset plates and the tank shell was also checked and found to be not governing the bolt chair capacity.
V I-4 -19
TABLE VI-4-1 STRESS COMBINATIONS - SME + DW + SETTLEMENT Total Allowable Seismic Response.from SME DW + Settlement Response Response Response Parameter (Faulted Condition) 12,853 psi 31,400 psi 1676 psi 11,177 psi Tensile Hoop Stress in 3/8" Shell 14,733 psi 31,400 psi 2253 psi 12,480 psi Tensile Hoop Stress in 1/4" Shell 1,919 psi 4,252 psi 853 psi 1,066 psi Compression Stress in 3/8" Shell 1,848 psi 2,834 psi 684 psi 1,164 psi 22,010 psi 37,700 psi Compression Stress in 1/4" Shell 13,709 psi 8301 psi 7 Local Menbrane Stress in Shell 21.7 kips 32.5 kips t at Bolt Chair 15.7 kips 6 kips Bolt Chair Top Plate Bending Load 21.7 kips 57.4 kips o
15.7 kips 6 kips Anchor Bolt Load SME = Seismic Margin Earthquake DW
= Deadweight + Hydrostatic Pressure Loads
w 1
l
!g BWST 2'-0" --
1 ,
1_ _ -
J'
. . ; , . } '[-: .' .'-' ' -
_ s New Ring =
Ring Wall e Beam ,,--
e f
l a
- 1. 25 ' _ -
Ring Wall M
- e
[ Foundation -
y 4'-0" _
=
'k_'
j, j j ,
Ii j b dI Il 2.55 ksf 3.96 ksf FIGURE VI-4-1. S0IL BEARIrlG PRESSURE DISTRIBUTI0il VI-4-21
Tank Shell (Weight = 110.3 kips)
New Ring Beam "
1
( t = 235.4 Fluid Annulus abcve Footing (Weight = 627.3 kips)
! 1 i .
Entrapped Soil (Weight = 100.1 kips) w Original Ring Wall and Footing (Weight = 312.4 kips)
TOTAL WEIGHT = 1386 kips n i neona
- Soil Pressure Due to Dead Load 1386
= 2.12 ks f n(282-242)
- - - - -=
~ Reduction in Soil Pressure Due to Vertical Earthquake = 2.12 (0.10g x 0.4) = 0.08 ksf a a e Reduction in Soil Pressure Due to Bottom Pressure Moment (see Sections 2.2.1 and 3.2)
= 1 4930(25) = 0.17 ksf 2
w(26)"/4 Total Soil Pressure = 2.12 - 0.08 - 0.17 = 1.87 ksf Uplift Moment = (1.87)(4)n(26)2 = 15885 k-ft Factor of Safety Against Uplift of 15885
=
8154
= 1.95 the Foundation FIGURE VI-4-2. FOUNDATION UPLIFT VI- 4-22
n y BWST
< . . //M/hY//
J.
.. J .
Ring Wall New Ring Beam qj' " ,
$(1.2S'
- * - / *
'g oilSLoads, and Fluid 0.70 ksf Surcharge 1441, o*- .* *r a
(
,u 1
s 4
s o4 4 ft. wide footing 4 il ll .ii al il 2.55 ksf L ~
I rSoil Bearing Pressure L ' '
3.52 ksf '3.96 ksf a) Soil Bearing on Footing 9
Vertical Load Due to Bottom Pressure Moment ,
(see Sections 2.2.1 and 3.2)
"V, + Vertical Load Due to
[ Fluid Weight i !liAIL li1 lAAA *
- - ?. = -- ,. .
, ,. : ~ . ,
I.' .
'.el ; . ~1 ' 7 j f
Lateral Soil Pressure frcm Vertical Loads Causing Hoop Tension on the Ring Beam b) Hoop Tension on the Foundation FIGURE VI-4-3. RING WALL LOADING CONDITIONS VI-4-23
6" ] g " ig A+
49" a 1-1/2" 4 A.B. I:
- 1
1-1/2"4A.B. I g
- n s .
o [
's ,N'
, 's i
New Rina s/f Ring Wall . StressN 's '
's .
E, Beam AA--. -
3g.
T W Cone [/ , 2 6" x 6" x 1-1/4" l Q r-SECTION A-A ELEVATION A-i 49"
,, Stress Cone
/d 18" O h6"x6" R ?
s __ (Area Eff ective Stress
= 827 in' PLAN Concrete Strength = 4e f'c Pullout Capacity = Concrete Strength
- Effective Stress Area
, 4x(0.65) / 4000 x 827 1000
= 136 kips FIGURE VI 4-4. BWST ANCH0P, BOLT PULLOUT CAPACITY VI- 4-24
g N Maximum Bolt Force, FB " "t ttt ..
where a t
= tensile strees in the tank shell due to seismic-induced over-Tank Shell kips* turning moment, M . .
Weight = 110.3 t = shell thickness = 3/8 inch M = 8154 foot-kips t t = Portion of to tank circumference tributary each anchor bolt "DL l { { { [ { { { l = n(52)/40 = 4.08' a" +
t ms v ~"DL o i 1 4 4 4 4 6 6 i o = tensile stress due to M V where ms o
V
= tensile stress due to vertical earthquake g .
O = compressive stress due to dead load
- 7 2 DL 5 Il -
2 1 Area of 3/8 inch shell = 5.l f8154 2, (99.3) (.10) _ 99.3 A, ,t (66.4j 5.1 5.1 = 103.3 ksf.
Section modulus of 3/8 inch 3
ft Shell = 66.4 F = 103.3(.375/12)(4.08) = 13.2 kips B
- NOTE: Use 90 percent of the tank weight in accord-ance with ACI 349-80 since dead load is beneficial to bolt force W = 0.9(110.3)=99.3 kips 3
FIGURE VI-4-5. CALCULATION OF MAXIMUM ANCHOR BOLT FORCE :
r
. +
P e = 3-1/4" 7 k
y 1 I 2 ye 3
h 0.625" .
- 0.375" .
312"R 1
"m -
3
'm b _
P = ANCHOR BOLT LOAD
.c
=
U --
_P_e _, s h .
FIGURE VI-4-6. ANALYSIS MODEL FOR LOCAL MEMBRANE STRESSES F IN SHELL DUE TO ANCHOR BOLT LOADING -
E E
E VI 4-26 E-
g -_-
I
=r f
r r 4 T -i
'. j_
'If : _
5 sm e
\ TANK WALL -
. =
h l 3 1 r: .
m b-I \
BOLT HOLE d l +
\ L
%2
~
-h n
=
~
f = l.875" r ASSUMED TOP PLATE BEAM i V -
? q PLAN VIEW
- d L f(boltdiameter)=1.5"
~
=
1/3 ANCHOR BOLT LOAD
_f BOLT CHAIR
_; TOP PLATE q #
g y y ,,,,-,, i--
4 ,
~
c = 0.625"l j k)l ~
h Ak Ak l
\ PARTIALLY FIXED u
l
, igI 14 ,
g = 4.0"
=
ELEVATION VIEW 5 j
FIGURE VI-4-7. BEAM MODEL FOR BOLT CHAIR DESIGN (Reference 14) >
VI-4-27 _.
E
h -
[
9 YIELD LINES Tank Wall N O L g = 4.0" _
i j~ y t < l
\ 0 a h
??
( T-t
- 1 -
e h
] + 4 7
n A
N m / g
/ ~
/ \
\
/ l4 l
R
- I
=
l M eff _ e l
'I P
$ + S' ' I _
h iw i .
e
_ h Ll'% N N /
/
')
,'~'.;.
2 s / ,,, : r.. . .
% / .y % .
~
L_
_ ..w , .
, w J -
A e c = 0.625" ' ~ ' ~i ;
e _.....
H .
Y % ,' '.
3 . q....
'I y dh/f
_ P T
P [h:[
, 2
+ Ref .
pe' ,f.
+ -6 Q ;. .
,I 27 m* s E ~ Gusset -
- ll I l 9 3r N(
6 Load 3 N
[
1r i
q r 0.5" Plate
-[.[.
s y ; y
+ ?4 . .. -
- ;.y. .t, a a
_ ;. p. ,
FIGURE V I 8. YIELD LINE MODEL FOR BOLT CHAIR hnsA . ;,j VI 4-28
_ _ _ _ _ _ _. 1.
N 1
- 5.
SUMMARY
OF SME CODE MARGINS jE b
9 The SME Code Margin (CM) and the multiplication factor (FSME) ,
by which the SFE would have to be multiplied to raise stresses to code __
alloaable levels are sLmnariZed in Table VI-5-1 for various elements.
The icwest CM and FSME reported in Table VI-5-1 are for the concrete e foundation as discussed in Section 4.2.1. The FSME value of 1.57 for -
the foundation was evaluated in an extranely conservative manner by -
scaling the margin from the goveraing foundation design check load ?L combination which iacluded 1.9 times the OBE by the ratio of 1.9 times the OBE overturning moment and the SME overturning moment. This proces.s -
is extremely conservative because the foundation dn agn check margin was _
predominantly aff ected by differential settlement and not by 1.9 OBE. It Ei is denonstrated in Section 4.2.2.4, that the seismic margin f actor, _
FSNE, of about 11 is mere accurate for the concrete foundation.
f5 However, the CM and FSME values in Table VI-5-1 are significantly over ;J 1.0 and are based upon the detailed foundation design check analyses of the finite element representation of the ring wall, footing, ring beam and valve pit. (( -
Other than for the concrete foundation, the lowest code margin reported in Table VI-5-1 is 1.50 associated with bolt chair uplif t -2 capacity. In this case, the SME would have to be multiplied by a f actor 3 of 1.69 to reach code capacity. Considering that the SME is a 0.15g $=
earthquae, the earthquake that would be required to reach code allowable [$
stresses in the BWST would have to be (0.15g)(1.69) or 0.25g. !
w The code margin capacity does not represent a f ailure capacity 'jj for the following reasons: ;
i
=
5 '
V I-5 -1
- E
I
- 1. The Code Margins (CM) and SfE multiplication f actors (F reported in Table VI-5-1 are based upon the combination of the SE and conservative end-of-life settlement stresses.
The full end-of-life settlement stresses are unlikely to exist during the SME. Furthermore, settlement stresses are displacement controlled stresses and are not expected to contribute to a f ailure during an earthquake. Even so, these stresses have been added to SE induced stresses.
- 2. The code capacities have built-in f actors of safety. Thus, the actual failure capacities are substantially greater than the code capacities.
- 3. The stress and/or load parameters with the lowest code margins or Fsm do not directly contribute to f ailure of the tank. When the uplift capacity of the bolt chairs, or the uplif t capacity of the foundation are exceeded, the tank will lift slightly. This lif ting is not detrimental.
In f act, many tanks are designed with no hold-down bolts because of the 1ack of consequences of uplift. All that uplif t of one side of the tank does is to increase the compressive stresses on the opposite side.
- 4. The stress condition which most directly leads to tank failure is compressive buckling of the shell or which Fsm equals 2.44. In addition, considering that the shell compression is due to an overturning moment rather than uniform axial compression, the code capacity for compressive buckling contains a built-in f actor of safety of 1.68 even under faulted condition allowables when compared with the buckling formula for bending based upon extensive static test data given in Reference 11. Even more relevant test data was recently published (Reference
- 18) for seismic shake table tests of cylindrical storage tanks. Buckling behavior during these tests would indicate that the code capacity for buckling with f aulted condition allowables has a f actor of safety of 2.98.
Considering these f actors, the failure capacity earthquake for the BWST and its foundation is more than twice the 0.259 level at which code capacity is reached.
The BWST and its foundation easily pass the seismic margin earthquake check in all aspects.
V I-5 -2 L - - - - . - - -
TABLE VI-5-1 SME CODE MARGINS (SME + DW + SETTLEMENT)
F Stress or Load Parameter CM SME Concrete Foundation 1.43 1.57*
Soil Bearing Capacity 1.57 2.28 Tank Sliding Capacity 2.5 2.5 Uplift Capacity of Foundation 1.95 1.75 Anchor Bolt Uplift Capacity 2.65 3.27 Bolt Chair Uplift Capacity 1.50 1.69 3/8" Shell 2.44 12.1 Tensile Hoop Stress 1/4" Shell 2.13 8.40 3/8" Shell 2.22 3.74 Compressive Buck-ling Stress 1/4" Shell 1.53 2.44 Local Membrane Stresses of Bolt Chair 1.71 2.89
- Very conservatively evaluated l
l VI-5-3
- 6. REFERENCES
- 1. " Site Specific Response Spectra Midland Plant - Units 1 and 2, Part II - Response Spectra Applicable for the Top of Fill Material at the Plant Site", Weston Geoohysical Corporation, Westboro, i
Massachusetts, May 1, 1981.
l
- 2. " Nuclear Reactors and Earthquakes", TID-7024, Prepared by Lockheed Aircraft Corporation and Holmes & Narver, Inc., for the Division of Reactor Development, U.S. Atomic Energy Commission, Washington, D.C.,
August, 1963.
- 3. USNRC Regulatory Guide 1.60, " Damping Values for Seismic Design of Nuclear Power Plants", October, 1973.
- 4. Veletsos, A. S., and Y. T. Wei, " Lateral and Rocking Vibration of Footings", ASCE Soil Mechanics Journal, SM9, September,1971, pp. 1227-1248.
- 5. Kausel, E., and R. Ushijima, " Vertical and Torsional Stiffnesses of Cylindrical Footing", Massachusetts Institute of Technology, Department of Civil Engineering, Research Report R79-6, February, 1979.
- 6. Veletsos, A. S., " Seismic Effects in Flexible Liquid Storage Tanks",
Proceedings of the International Association for Earthquake Engineering Fifth World Conference, Rome, Italy, 1974, Vol. 1, pp. 630-639.
- 7. Veletsos, A. S., and Yang, J. Y., " Dynamics of Fixed-Based Liquid-Storage Tanks", Presented at U.S.-Japan Seminar for Earthquake Engineering Research with Emphasis on Lifeline Systems, Tokyo, Japan, November, 1976.
8.
Letter,50.54(f),
10 CFR Vol. 6, TAB 120.Dr. D. P. Woods to Dr. S. S. Afifi, February 22, 1980,
- 9. " Final Safety Analysis Report, Midland Plant - Units 1 and 2",
Consumers Power Company, 1981.
- 10. " Soil Dynamic Modulus Study, Midland Units 1 and 2, Consumers Power Company", Dames & Moore Job No. 05697-039-07, Dames & Moore, Park Ridge, Illinois, February, 1982.
- 11. NASA SP-8007, " Buckling of Thin-Walled Circular Cylinders", National Aeronautics and Space Administration, September,1965.
VI-6-1
REFERENCES (Continued)
- 12. " Design Report for the Borated Water Storage Tank Foundations -
Consumers Power Company Midland Plant Units 1 and 9" transmitted to J. G. Keppler, U.S. Nuclear Regulatory Commission, Glen Ellyn, Illinois, from J. W. Cook, Consumers Power Company, Jackson, Michigan, November 13, 1981 and Addendum No. 1, November 24, 1981.
- 13. API 650, " Welded Steel Tanks for Oil Storage", Fifth edition and Supplement 1, October, 1973, American Petroleum Institute.
- 14. AISI Steel Plate Engineering Data - Vol. 2, "Useful Information on the Design of Plate Structures", Part VII, Anchor 3 cit Chairs, February, 1979, American Iron and Steel Institute, Washington, D.C.
- 15. Campbell, R. D., et al, " Evaluation of Midland Nuclear Power Plant Borated Water Storage Tank for Non-Uniform Support Loading Resulting from Ring Wall Settlement", SMA 13704.01-R001 including Addenda,
" Borated Water Storage Tank Analysis for End-of-Life Soil Settle-ment and Seismic Marlin Earthquake Loading Conditions", Structural l Mechanics Associates, Inc., Newport Beach, California, March, 1982.
- 16. Welding Research Council Bulletin 107, " Local Stresses in Spherical and Cylindrical Shells due to External Loadings", Welding Research Council, New York.
- 17. Hendron, A. J., Testimony to the Atomic Safety and Licensing Board, U.S. Nuclear Regulatory Commission, Consumers Power Company (Midland Plant, Units 1 and 2), Docket Nos. 50-329 OM, 50-330 OM, 50-329 OL, 50-330 OL, February, 1982.
- 18. Niwa, A. and R. W. Clough, " Buckling of Cylindrical liquid Storage Tanks under Earthquake Loading", Earthquake Engineering and Structural Dynamics, Vol, 10, No. 1, pp. 107-122, John Wiley and Sons, January-February, 1982.
- 19. Structural Analysis and Design of Nuclear Plant Facilities, ASCE -
Manuals and Reports on Engineering Practice - No. 58, American Society of Civil Engineers, op 396- 397, New York, New York, 1980.
- 20. "Recocmended Revisions to Nuclear Regulatory Commission Seismic Design Criteria", NUREG/CR-1161, Lawrence Livermore Laboratory, Livermore, California, December,1979 (Draf t) page 38.
VI 2
. . . _ _ .