final borated water storagp tanic seismic anat,ysir …
TRANSCRIPT
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3 SMA 13701.01-R001* '
Novemb:;r,1981
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FINAL BORATED WATER STORAGP TANIC SEISMIC ANAT,YSIR
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1. TAE DESCRIPTION
The borated water storage tank (8WST) is a vertical cylindricaltank with a diameter of 52 feet and a cylindrical wall height of 32 feetand a domed head as shown in Figure 1. The tank wall is 3/8 inch thickfor the bottom 8 feet and 1/4 inch thick for the remainder of thecylindrical height. The tank roof is a 0.3 inch thick dome segment witha 52 foot radius and a height of 6 feet, 9-3/8 inches. Tank material isstainless steel. Borated water is stored in the tank up to a height of32 feet.
The tank shell is supported on a ring foundation. The outerradius of this ring foundation is taken to be 28.75 feet, the valuecorresponding to the foundation after remedial work is performed. The
inner radius is 24 feet. These values are utilized in the calculation ofsoil-spring and dashpot constants. Soil beneath the tank is fill materialoverlying ' original till material. There is a large valve pit beneath the ,
tank which is judged to not have any significant influence on tank seismicresponse.
2. ANALYTICAL APPROACH
The purpose of this seismic analysis is to determine the seismic-induced forces acting on the ring wall foundation. These forces havebeen computed for three levels of earthquake excitation. These are:
a. FSAR (Reference 1) SSE horizontal site design rsponsespectrum as given in Figure 3.7-2 with the 50 percentincrease described in Subsection 3.7.1.1 of the FSAR.
b. One and one-half times the FSAR response spectrum describedin a) above.
c. The 84th percentile, top of fill, site specific responsespectrum developed by Weston Geophysical Corporation(Reference 2). Note that for this case, the larger of thesite specific spectrum and the spectrum given in FSARFigure 3.7-2 (without 50 percent increase) is utilized.
hokkOO O 000 1
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_. - _ - . . _ _ _ _ , . _ _ _ _ . _ , . _ _ , . _ . _ _ _ . _ _ - - _ . _ _ , - _ _ _ _ _ __.
.; ,
The tank shell is supported on the foundation which must,
withstand the seismic-induced forces in the tank shell. These forces arenearly totally due to the water in the tank since the tank shell weightis negligible compared to the weight of this water. Thus, the primaryseismic modeling concern is to properly or conservatively model theseismic forces induced by this water on the tank shell and thus, on thefoundation. One must model the impulsive mode, the sloshing mode, and
the vertical mode of fluid-structure interaction. Each of these modes ofresponse is best modeled with its own individual model. The seismicforces imposed upon the tank shell and ring foundation from each of thesethree models are added by the square-root-sum-of-squares (SRSS) method.
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Soil-structure interaction has been evaluated using frequencyindependent impedance functions based on the soil beneath the tank beingtreated as an elastic half-space. Best estimated soil properties havebeen evaluated from test data on the underlying fill and till material.These value are then utiized to establish impedance function " springstiffnesses" and " dashpot constant" values. Strain degradation of thesoil stiffness properties (approximate nonlinear behavior of the soil)was included in establishing these properties. To account foruncertainties in soil properties and in the mathematical m'odeling ofsoil-structure interaction, the soil-structure interaction stiffnesses,
are varied within the range from 0.5 to 1.5 times the "best estimate"
soil-structure interaction stiffnesses. The seismic-induced foundationloads are based on the envelope of seismic responses obtained for
| soil-structure interaction stiffnesses which vary throughout this range! of possible stiffnesses.
Energy dissipation within the tank, fluid and soil system isapproximated in the dynamic models as viscous (velocity proportional)damping. Damping consists of material (hysteretic) damping and radiationdamping or the radiation of energy from the structure back into thesupporting soil.
2|
-- .. ._ - . _ . ._ _ _ __ -
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., .,
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Material damping values conservatively assumed for seismicanalysis of the BWST are:
Fluid Sloshing - 0.5 percent of critical dampingTank Shell and Impulsive Fluid - 1.0 percent of critical dampingSoil Response - 3.0 percent of critical damping
Soil radiation damping is computed in accordance with relations given inBC-TOP-4-A (Reference 3). Material damping and radiation damping forsoil elements are sumed together absolutely.
The assumption that the soil beneath the foundation is an elastic
half-space can lead to an overprediction of the radiation damping (i.e.,the radiation of energy from the structure into the ground). Thissituation occurs because an elastic half-space assumption does not accountfor the variation of soil properties with depth. Underprediction of theradiation damping results in too much energy dissipation being incorpor-ated into the overall dynamic model which can lead to overprediction ofthe structural responses from this model. For the seismic evaluation of
the BWST, this potential problem,is compensated for in the followingconservative fashion:
1. For modes of structural vibrations which are a combinationof soil-structure interaction and flexible structuralresponse (e.g., the tank fluid impulsive mode), thecomposite modal damping is computed. If this composite
- modal damping (made up of structural damping, soil materialdamping, and radiation damping) exceeds 10% of critical,then the composite modal damping is arbitrarily andconservatively limited to 10% of critical.
2. For modes of structural vibrations which are nearlyexclusively soil-structure interaction modes (i.e., rigidbody structural response modes such as the BWST verticalresponse mode), the radiation damping used will be limitedto 75% of the theoretical radiation damping levels.
3. For modes of structural vibration which are nearlyexclusively structural modes (e.g., fluid sloshing mode),the composite modal damping value is not influenced byradiation damping into the soil and this discussion isirrelevant.
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The layering effects beneath the BWST are relatively minor asthe top 50 feet of the original till material and the approximately 30feet of fill material have similar shear wave velocities such that theradiation damping levels will be at least 75 percent of the theoreticalelastic half-space values. Furthermore, the limitation of compositemodal damping levels to 10% of critical for combined vibration modes has
' been shown by many studies to be an extremely conservative criteria whichleads to overprediction of structural responses. Imposing this criteriamore than compensates for any unconservatism which might result from the
use of elastic half-space theory to estimate the radiation damping levels.
3. SEISMIC MODEL
3.1 IMPULSIVE MODE
The dynamic model of the BWST used for determining the seismicforces on the ring foundation from the horizontal impulsive fluid mode isillustrated schematically in Figure 2. The tank shell stiffness ismodeled by vertical beam elements between mass points distributed up thetank shell. The beam elements represent the shear and flexural stiffnessof the tank. The ovalling stiffness of this tank is judged to be insig-nificant to the seismic response as the tank is held in round by its baseat the bottom and by the roof at the top. The roof weight, W , isg
lumped at the roof level. The shell wall weights, WS are lumped atdiscrete points on the tank shell. Impulsive fluid effective weights,W I, are added to the tank shell weights at each of these node points atand below the top of the fluid.
For a rigid mode of horizontal tank vibration, it has been shownby Housner (Reference 4) that the total effective horizontal impulsiveweight of the fluid, W , is given by:I
W tanh(0.866 D/h)NI* 0.866 D/h (1)
4
.. _, , .. - _. . _ _ -- -
* t,
'
where W is the total fluid weightD is the tank diameterh is tne fluid height
This total effective impulsive weight is distributed parabolically overthe fluid height as shown in Figure 2. The impulsive weight per unitheight over the fluid height. V, is given by:
W (y) = 0.866YD h(tanh 0.866 0/h)I
[h-y(g h-y 1(2),
\ /..
.
where y is the fluid densityy is the distance above the base of the tank
With a flexible tank, the impulsive fluid effects should moreprecisely be considered as an impulsive pressure rather than effectiveimpulsive weights. However, it has been shown by Veletsos (Reference 5)
'
that the effective impulsive weight distribution developed by Housner forrigid tanks can be used to conservatively predict impulsive mode baseshears and overturning moments at the bottom.of flexible tanks (i.e., the
forces on the ring foundation). For tanks similar to the BWST, this approximationleadto base shears which are between a factor of 1.1 and 1.2 times greater
than would be obtained using flexible tank impulsive pressures. Theoverturning moments obtained assuming a Housner effective weight distri-bution are within 2% of those obtained using a flexible tank impulsivepressure distribution. This slight improvement in accuracy does notwarrant the substantial added effort of treating the tank shell asflexible when determining the impulsive fluid effects. The effectiveimpulsive fluid weight distribution given by Equation 2 and shown inFigure 2 is adequate.
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The horizontal impulsive mode tank model is attached to theground at its base by soil-structure interaction impedance functions(defined in tenns of a translational and rocking stiffnesses and dashpots)derived as per Section 4 of this report. The ground motion is fed intothis tank model through these impedance functions. The resultant over-turning moment and base shear at the base of this model represent theforces imposed on the ring foundation by the horizontal impulsive mode.
The actual model used for evaluating horizontal impulsive seismicresponse is illustrated in Figure 3. Numerical values for the weights,tank stiffness and geometry are presented on this figure.
The seismic model shown in Figure 3 is suitable for computingseismic-induced loads on the ring wall foundation for the horizontalimpulsive mode. During seismic response of the BWST, there are alsoseismic-induced loads on the tank bottom. These loads may be expressedas an additional overturning moment applied over the area of the tank
bottom. The additional overturning moment, M , can be conservativelyB
evaluated by the following expression taken from Reference 5:
MB = .1045 0 W Sa (3)l
where Sal is' the spectral acceleration of the predominanthorizontal impulsive mode
For the BWST, this moment is applied to the soil inside the ring wallfoundation and not to the ring wall directly.
3.2 SLOSHING MODE
The horizontal fluid slashing mode is a long period (low-frequency) mode of vibration. Because of its low frequency, this mode ofvibration does not interact with the effects of tank flexibility or soil-structure interaction. A dynamic model is not required in order toevaluate the forces imposed on the tank shell and ring foundation by this
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-- _ ._- -
W
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mode. The natural fmquency of vibration,"2, of this mode, the fluideffective sloshing weight, W , and height of application, X , above2 2the tank base art given by relations from Reference 4 as presented below.
2 3.67g l3.67htanh iw .
I.67h\W 3W 0.230 tanh=(5)2 h \ /
hcosh(3.67h -hX h-
2 (6)=
3.67hsinh (3.67h
2where g is gravity acceleration (32.17 ft/second )
The base shear and overturning moment on the ring foundation due to thissloshing mode are given by:
V2 * W Sa2 (7)2
W2 * W X Sa2 (8)22
where Sa2 is the spectral acceleration at frequency w2-
Note that the fluid slosh height, d, can be estimated from:
d = 0.420 Sa2 (9)
3.3 VERTICAL MODE
In the vertical mode, the water in the tank is supporteddirectly on the soil and the tank itself is very stiff. Therefore, boththe tank and the fluid can be modeled as rigid in this mode. The only
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. ..
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source of flexibility comes about because of soil-structure interactioneffects. A dynamic model is not required for such a simple problem. Thenatural frequency of vibration is given by:
b9Y" W (10)"
v
where Wy is the sum of the tank shell weight, W , and the total fluid3
weight, W , and Ky is the vertical soil-structure interactionw
impedance function stiffness. This is a rigid structure mode of vibration
for which the fraction of critical damping, Sy, is given by:
Cy.
By = + 8 (11)32/K W /gyy
where Cy is the vertical dashpot coefficient from the soil-structureinteraction impedance function for the foundation, g is gravity accelera-
2tion (32.17 feet /second ), and 83 is the appropriate soil materialdamping (3% of critical). The 0.75 factor is included to account forsoil layering effects as discussed in Section 2.
The ring foundation only supports the vertical seismic forcesfrom the shell. The vertical fluid forces are supported directly on thesoil. Thus, the vertical seismic forces on the ring foundation are givenby:
Fy = W *Say (12)3
where Sa represents the design seismic vertical spectral accelerationy
at damping level Sy and cyclic natural frequency fy where fy =wy/2 w. Thus, the vertical seismic forces on the ring foundation can bedetermined without developing a mathematical model.
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4. SOIL-STRUCTURE INTERACTION
Soil properties used in the evaluation of impedance functionproperties beneath the BWST were established by using a weighted averageof the shear modulus values of the material below the tank to a depthequal to the diameter of the foundation. Soil properties were based onshear wave velocity tests for the fill (Reference 6) and properties ofthe natural material as given in Subsection 2.5.4.7.2 of the FSAR(Reference 1). The low soil strain shear modulus as determined by test,was degraded to 70 percent of its value to account for nonlinear. soilbehavior associated with larger shear strains occurring during seismicevents. The resulting composite soil properties used in the evaluationof soil-spring stiffnesses and dashpot constants for the BWST seismicanalyses are the following:
Shear Modulus, G 1510 ksf (best estimate)=
Poisson's Ratio,v 0.45=
2 4Soil Density, p .00357 k-sec /ft=
As mentioned previously, uncertainties in soil properties and soil-structure interaction modeling were accounted for by considering soilshear modulus variation over the range of 0.5 to 1.5 times the bestestimate value (i.e., G varies from 755 ksf to 2265 ksf).-
Soil-spring and dashpot constants were evaluated based onrelationships given in BC-TOP-4-A (Reference 3) as follows.
i Horizontal Translation
32(1-v)GRK (13)y= 7-8v
| CX= 0.576 k R / p/G (14)x
CX
s*= (15)2JK My7
9
- - -. . . . . . _ _
. ..
.
Rocking
K 8GR
$ 3(1-v) (16)"
0.30 K,R /p/G(17)C, 1+3
=
$
3( v)B, (18)=
5
C*S* (19)=
2 /K,I,
Vertical Translation
4GRK ,y (1-v) (20)
.
C 0.85 K R / p /G (21)=y y
CyB y (22)=
2/KMy
where R is the tank radius
M is the total mass of tank and water
M is the mass of tank and impulsive waterI
I, is the mass moment of inertia of the tank about its base
10
., ,
Note that for the rocking stiffness and damping, the spring and dashpot,
constants were evaluated by utilizing Equations 16 through 19 with theouter foundation radius of 28,75 feet and then subtracting from theresulting values the stiffness and damping corresponding to theseequations for the inner foundation radius of 24 feet. In this manner, the
impedance function for the ring foundation is detemined from relationsfor a circular disk foundation. In rocking, seismic-induced forces aretransmitted to the underlying soil primarily through the ring foundation.However, for horizontal and vertical translation, seismic-induced forcesare transmitted to the underlying soil over the entire tank area. Theresulting soil stiffnesses and radiation damping percentager are summarizedbelow for the lower bound, best estimate and upper bound values for soilshear modulus:
Lower Best UpperBound Estimate Bound
G(ksf) 755 1510 2265
5k (k/ft) 1.124x10 2.247x105 3.371x105x
7k, ( rad an) 3.639x107 7.277x107 10.916x10
5 5k (k/ft) 1.579x10 3.157x10 4.736x105y
8x (% of Critical) 64.9 64.9 64.9
8, (% of Critical) 51.3 51.3 51.3
B (% of Critical) 90.8 90.8 90.8y
Again, note that for the coupled impulsive fluid-soil mode, compositemodal damping ratios are computed and limited to 10 percent of criticaldamping. For the vertical rigid body response mode, 75 percent of theradiation damping shown above is utilized.
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5. TANK DYNAMIC CHARACTERISTICS AND FOUNDATION SEISMIC LOADS.
The natural frequency, modal damping, and corresponding spectralacceleration for the slashing, impulsive and vertical response modes andthe three input response spectra considered (i.e., FSAR,1.5*FSAR andsite specific, top of fill) are summarized below.
Spectral Acceleration (g)
Modal SiteResponse Frequency Damping FSAR (SSE) 1.5 FSAR Specific
Sloshing 0.24 Hz 0.5 .046 .069 .046Impulsive
Mode 1 4.2 10.0 .210 .315 .276Lower Bound ?!ade 2 12.9 10.0 .12 .18 .200
M de 1 5.5 10.0 .122 .183 .271Best EstimateMode 2 16.2 10.0 .12 .18 .180
"
Mode 1 6.3 10.0 .12 .18 .265Upper BoundMode 2 18.1 10.0 .12 .18 .170
Vertical
Lower Bound 5.4 Hz 71.1 .12 .18 .15
Best Estimate 7.7 Hz 71.1 .12 .18 .15
Upper Bound 9.4 Hz 71.1 .12 .18 .15
12
.. 1
- . . .
.. .
For horizontal impulsive response, there are two modes at< *
frequencies below 33 Hz with the first mode including participation ofnearly all of the system mass and accounting for nearly all of'theimpulsive seismic response. The mode shapes for the impulsive responsemodes and the best estimate soil properties are illustrated in Figure 4
Seismic-induced base shear, overturning moment and vertical loadat the top of the ring foundation are sumarized in Table 1. For allthree spectra considered, the lower bound soil properties give thelargest seismic-induced foundation loads. For the FSAR spectra, thelower bound soil properties result in the predominant horizontal inpulsivemode falling 'n the 50 percent increased region of the input spectra whilethe other soil properties considered result in this mode being out ofthis region. Note that the foundation loads from the 1.5 times FSAR
spectrum are greater than the loads from the 84th percentile, top of fillsite specific response spectrum.
It should be noted that the fluid slosh height has been computedin accordance with Equation 9 and is 1.0 feet for the FSAR and site
specific risponse spectra and 1.5 feet for the FSAR spectra scaled by 1.5.,
I The dome roof of the BWST permits these levels of sloshing withoutsignificant reduction of free surface area. As a result, it is concludedthat the fluid in this tank is free to slosh, such that the calculation
i of seismic-induced foundation loads as discussed above, is applicable.
The seismic-induced moments acting on the tank bottom computedin accordance with Equation 3 are summarized below:
Moment on Tank Base
Input Response Spectra
Soil Case FSAR (SSE) 1.5*FSAR Site Specific
Lower Bound 4839 ft-k 7259 ft-k 6359 ft-kBest Estimate '2812 ft-k 4217 ft-k 6245 ft-kUpper Bound 2766 ft-k 4148 ft-k 6107 ft-k
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._. . . - _ , - - - - . . - _ - - - _
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6. REFERENCES
1. " Final Safety Analysis Report, Midland Plant - Units 1 and 2",Consumers Power Company,1981.
2. " Site Specific Response Spectra Midland Plant - Units 1 and 2,Part II - Response Spectra Applicable for the Top of Fill Materialat the Plant Site", Weston Geophysical Corporation, Westtoro,Massachusetts, May 1,1981.
3. Bechtel Power Corporation, Seismic Analyses of Structures andEquipment for Nuclear Power Plants, Revision 3, November,1974(BC-TOP-4-A).
4. " Nuclear Reactors and Earthquakes", TID-7024, Prepared by LockheedAircraft Corporation and Holmes & tiarver, Inc., for the Division ofReactor Development, U.S. Atomic Energy Commission, Washington, D.C.,August, 1963.
_
5. Veletsos, A. S., and Yang, J. Y., " Dynamics of Fixed-Based Liquid-Storage Tanks", Presented at U.S.-Japan Seminar for EarthquakeEngineering Research with Emphasis on Lifeline Systems,- Tokyo,Japan, November, 1976.-
,
6. Letter, Dr. D. P. Woods to Dr. S. S. Afifi, February 22, 1980,10 CFR 50.54(f), Vol. 6, TAB 120. '
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TABLE 1*
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' 'N'/ SUMMARY OF BWST SEISMIC-INDUCED FOUNDATION LOADS
|*.
Input Response Spectrum|
Response FSAR(SSE) 1.5 * FSAR Site Specific
SloshingBase' Shear 72k 108k 72kOverturning Moment 1479 ft-k 2219 ft-k 1479 ft-k
Impulsive .-
Ba~se Shear 537k 806k 706kLower Overturning Moment 7861 ft-k 11792 ft-k 10340 ft-k
Base Shear 305k 458k 675k-
Best Overturning Moment 4571 ft-k 6857 ft-k 10130 ft-kBase Shear 294k 441k 646k
Upper Overturning Moment 4477 ft-k 6715 ft-k 9866 ft-k
VerticalVertical Load 13k 20k 17k
Combined Sloshing ' e-
Base' Shear 542k 813k 710k'
l **" Overturning Moment 7999 ft-k 11999 ft-k 10445 ft-ks.
Bas ~e Shear 313k 471k 679k'
-Best OveFturnirig Moment 4804 ft-k 7207 ft-k 10237 ft-k
,
Ease Shear 303k 454k 650kUpper Overturning Moment 4715 ft-k 7073 ft-k 9976 ft-k
Maximum Responsey
Base Shear 542k 813k 710k- '
Overturning Moment 7999 ft-k 11999 ft-k 10445 ft-kVertical Load 13k 20k 17k
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._ _ _ _ _ _ _ _ _ _ . - _ _ _ _ _ __ - _ _ _ _ _ _ _ __
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Roof WR4D Rigid Link
Ni Top of Fluid S
4i Wa g
y g Parabolic DistributionSq QWg of Effective Implusive
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Fluid Mass, W.
I--,
\S Wq g
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SidIW
hsff, S *WBase V' "; I _;,/ -
Soll-Structure hinteractionimpedancefunctions
1
FIGURE 2. BWST HORIZONTAL IMPULSIVE MODE MODEL
_ _ __
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ -_ __
..
. .
.
.'T_ANK SilELL PROPERTIES
6E = 4.176x10 ksf; v = 0.3 94 > 35.4'
t X I Rigid Link2 41/4" 1.70 ft 1150 ft 84 > 32.0'
4 Node No. Weight (kips)3/8" 2.55 ft 1726 ft
'
7() 27.2'2 503.6
3 523,8-
"e 4 512.1d 6() 22,45 426.0
S0ll IMPEDANCE FUNCTION t
f 6 312.7Properties
b 'O *
STIFFNESS 8 25.9k kg x
9 28.6(k/ft) (k-ft/ rad),
5 7 12.8'Lower Bound 1.124x10 3.639x10
5 7Best Estimate 2.247x10 7.277x105 7Upper Bound 3.371x10 10.916x10 3g 8',_.
".
$q 2()
DAMPlHG f K "x
g = 65% 1( O'
6,= 51% () K4
nn
FIGURE 3. Il0RIZONTAL IMPULSIVE SEISHIC MODEL
.
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Undeformed Shape.
Shape due to soil translatior-.
Shape due to soil rocking-x-
- - -- Mode shape
\ 'f 'l ig" /.
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\ *I/
/g e'
/\ *t e = 0.00219 /
~
\ /
g e = -0.00514 /
\t-\' .
.. _-
- :
a = 0.047 a = 0.136
First Mode Second Mode
fy = 5.5 Hz f2 = 16.2 HzParticipation Factor = 8.785 Participation Factor = 2.959
FIGURE 4. MODAL PROPERTIES OF BWST TANK - IMPULSIVE WATER -S0IL-SPRING MODEL (BEST ESTIMATE SOIL)
19
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FIGURE 1. 80 RATED WATER STORAGE TANK CONFIGURATION
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CONSUMERS POWER COMPANYGRID LOCATION MIDLAND PLANT UNITS 1 & 2
BWST FOUNDATIONMAXIMUM DESIGN LOADS AND
CAPACITIES OF INTERFACE SHEARCONNECTORS (MIDLAND CRITERIA)~
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CONSUMERS POWER COMPANY ,
MIDLAND PLANT UNITS 1 & 2GRID LOCATION
BORATED WATER STORAGE TANKMAXIMUM DESIGN LOADS AND
CAPACITIES OF INTERFACE SHEAR- CONNECTORS (ACI 349 CRITERIA)
FIGURE 21.
O
Midltnd ricnt Units 1 and 2Design Raports Borsts'd WaterStoraga Tcnk Foundations
TABt.E I
SUMMARY OF CALCUIATED LOADS AND CAPACITIES OF Ti!E NEW RING BEAM
(MIDIAND CRITERI A)
' Antal and Flexural Antal, Shear, and TornionInteractionInteractionCalculated
Load 883 Calculated loadlU
Load Grid Antal Moment Load Grid Axial Shear
Category Combination'l Number Tension Moment Capacityt t,3 8 Combination 8'l Number Tension Shear Torsionssp Capacityt t,4 33 t
Region A 10 34 28 3 2,492 3,573 10 14 290 31 237 185
10 36 282 142 345 249Region B 10 6 290 3,153 3,575
,
Region C 10 5 285 3,547 6,492 10 37 278 135 394 553
Region D 10 4 293 3,822 8,225 10 38 288 123 679 333
Region E 10 3 280 4,041 7,464 10 39 274 120 932 619
Refer to Section 5.0 of the design Report for the Borated Water Storage Tank roundations for load combinationsl'8
Axial and shear are measured in kips! moment and torsion are measured in ft-kipstal
88' Interaction capacities at calculated axial load
881 nteraction capacities at calculated axial load and torsionI
l'' Including torsion due to eccentricity of the interface shear force
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Mad!Knd Flint Unsts 1 arus dDesign Raport: Dorctsd WaterStorage Tcnk Foundttions
TABLE 2
SUMMARY OF CAlfULATED IDADS AND CAPACITIES OF THE NEW RING DEAM
(ACI 349-76 LOAD COMBINATIONS AS SUPPLEMENTED BY REGULATORY GUIDE 1.142)
Axial and FlexuralInteraction Axial, Shear, and Torsion
Calculated InteractionLoadl81 Calculated loadIU
Load Grid Axial Moment Ioad Grid Axial ShearCategory Combinationt'l Number Tension Moment Capacityl8.81 Combina t iont 'l Number Tension Shear Torsicnt8l Capacitytt.el
Region A A 8 239 2,731 3,638 A 28 259 3 310 123
Region B A 6 226 3,494 3,660 A 36 309 153 439 156
Region C A 5 215 3,919 6,640 A 37 308 147 510 460
Region D A 4 211 4,316 8,458 A 38 323 130 855 193
Region E A 3 187 4,653 7,701 A 39 312 124 1,154 502
C. 13 1
hl'icontrolling ACI 349-76 load combination is:
---
A. U = 1.4D + 1.4T + 1.4F + 1.7L + 1.711 + 1.9E_ g
-
where - .no s ' ' q g
D = dead load |:L
" " * ' 'L = live loadF = hydrostatic pressure from groundwaterT = differential settlement . -
H = lateral earth pressure :
E = operating basis earthquake , , , , , , ,
188 Axial and shear are in kips: moment and torsion are measured in ft-kips
188 Interaction capacities at calculated axial load , , , , ,
l*lInteraction capacities at calculated axial load and torsion ,
188 Including torsion due to eccentricity of the interface shear forcemesa _
. . . .
.
.
8
Mid1cnd Plent Units I cnd 2Design Report: Borsted waterStoraga Tcnk Foundations
TABLE 1,
SUMMARY OF CALCULATED LOADS AND CAPACITIES OF Tile VALVE PIT MEMBERS
(MIDLAND CRITERIA) .
Axial and F1texuralInteractionq2s |
Shear Calculated i,
Load in-Plane Transverse Axial flomentCategory Combinationst'' Calculated Capacity Calculated CapacTty Tension Moinent Capacityl88
,
Exterior walls 10 198 331 - - 180 903 1,570
Interior wall 10 51 204 - - 172 2,734 3,700
(ring wall)
Roof slabl*l,
N-S direction *I NA 18.6 41.1 16.4 19.4 7.3 8.7 50.5I ts:
E-W directionist pgt s 18.6 60.3 4.9 19.9 0.1 3.7 33.0'
Floor slab'''N-S direction *I NAtsi 28.6 45.8 15.7 23.4 16.7 20.6 27.5I
E-W directionte 10 28.6 42.8 11.4 22.9 33.3 5.3 8.5
|
8'' Refer to Section 5.0 of the Design Report for the Borated Water Storage Tank Foundations for load combinations j
sa' Units are in kips and feet.
188 Interaction capacity at calculated axial load 15-PLUS sEEAR
*
talrorces shown are per linear foot of slab.
ssBased on maximum of all load combinat' ions
88' Direction of the axial forceM3eert
s'>< upmmes s==An
/ h NN -
AIIAL TEN 8105
'% ARIAL TERSIDWg
- _ a.
.
e
S
.4e
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ - _ _ _ _ - _ _ _ _ _ _ _ _ - _ _ _ _ _ - _ _ _ _
Mid1rnd Pltnt Units I cnd 2De0ign Riport: Borcted W';tsrStartge T:nk Found tion]
TABLE 4
SUMMARY OF CALCULATED I4 ADS AND CAPACITIES OF THE VALVE PIT MEMBERS
(ACI 349-76 LOAD COMBINATIONS AS SUPPLEMENTED BY REGULATORY CUIDE 1.142).
Axial and FlexuralInteractionia- '
Shearl'8 calculated. *
Load In-Plane Transverse Axial Moment
Category Combinations 'l Calculated Capacity Calculated Capacity Tension Moment Capacityf38t*.
- - 192 1,411 1,570Exterior walls A 200 331
Interior wall A 71 206 - - 156 3,381 3,700
(ring wall). s
Roof slabl*3N-S direction '' NA' ' ' 24.5 42.2 15.2 10.0 1.5 11.9 53.8. I
E-W directiont'l NAq s a 24.5 60.3 5.3 19.9 0 3.6 33.0-
Floor slabt*IN-S direction''' A 34.4 45.8 15.2 23.0 16.6 26.2 27.8
E-W directiont'l NA s 34.4 42.9 13.7 23.0 32.7 7.6 9.4t,
l'icontrolling ACI 349-76 load combination is:,
A. U = 1.4D + 1.4T + 1.4F + 1.7L + 1.7H + 1.9E as-russ smaan
.
where (%D = dead load
L = live load.
F = hydrostatic pressure from groundwaterT = differential settlement meest
H = lateral earth pressure ,/',
E = operating basis earthquake ) ,,, ,4
/ \\883 Units are in kips api feet.utaL tenstou '
888 Interaction capacity at calculated axial load.
' *s utaL tunsica8*' Forces shown are per linear foot. N in-russ oma'
ta' Based on maximum of all load combinations: unas sua
''' Direction of the axial force
.
.
'.
-
Midland Plcnt Uni *c 1 cnd 2** * DeDign R: port s t' s Md W3 tor
Storage Tank Foundaticns-
.
TABLE 5
SUMMARY OF CALCULATED LOADS AND CAPACITIES OF THE
FOUNDATION FOOTING (MIDLAND CRITERIA)
LoadType of Load CombinationU I Calculated Load (2) Capacity (2 3
Moment 7 3.0 37.5
Axial Tension 7 19.5 30.3
Shear 7 3.7 15.6
( I Refer to Section 5.0 of the Design Report for the BoratedWater Storage Tank Foundations
(2 Units are in kips and feet per linear foot of footing
,-^N,A'
,- - I
N ', ;
8 'T.
! | 8,
| i , il 1
| |. ,
,
t ik /
/AxIAz. m stow
norgyr SHEAR
.. . . . , ,. . ..
. . . _ . . _ . . _ _ _ . . __ -. . - . _ - . - _ .
r
Midland Plcnt Unito 1 cnd 2Decign R; port: BoratOd WatGr* * *
Chorage Tank Foundations.
.
'
TABLE 6i
SUMMARY OF CALCULATED LOADS AND CAPACITIES OF THE
FOUNDATION FOOTING
(ACI 349-76 LOAD COMBINATIONS AS SUPPLEMENTED BY
REGULATORY GUIDE 1.142)
-LoadType of Load CombinationU8 Calculated Load (2) Capacity (2)
Moment A 3.3 37.5
Axial Tension A 24.5 30.3
Shear A 4.1 14.8
UI Controlling ACI 349-76 load combination is:
A. U = 1.4D + 1.4T + 1.4F + 1.7L + 1.7H + 1.9E
where
D = dead loadL = live loadF = hydrostatic pressure from groundwaterT = differential settlementH = lateral earth pressureE = operating basis earthquake
(2) Units are in kips and feet per linear foot of footing.
,%-
$ ,'', A,''i
|'t i
| || |
'!i
'I
h /*
/p// um ms.
- ==
- - . . . . , . . . .. ..-- -. -..
.
---. - _ _ _ _ _
.
. ..
-.
|
.
i mm~
, - CAPACITY ENVELOPE_-I r--- I
----
i.
70,0 $ i | - ene eg
i l I y .
7 I i i i -
i 80.0 i ; , , , , ,
1 I IIa I I i
So o |$ i i | .
'g L______J L_______E
'40.0
ji e .
Ufl DESIGN FORCE ENVELOPE I
30 0o MIDLAND LOAD COMBINATIONS 1
,
7 ..
W / ^.20 0 I / \w
! - N' A #10.0 y7,
' ' ' ' ' ' ' '[ 0.0
S 10 15 20 25 30 35 40.
CONSUMERS POWER COMPANYGRID LOCATION MIDLAND PLANT UNITS 1 & 2
BWST FOUNDATIONMAXIMUM DESIGN LOADS AND
* CAPACITIES OF INTERFACE SHEARCONNECTORS (MIDLAND CRITERIA) ,
'
FIGURE 20
._
__ ---_ .____ .___-- . - _ - .
. . .
.
i
.
REY PLAN
pCAPACITY ENVELOPE__q p___, ___.
70.0 | !-
meig3
I I i;I ! Ii
60.0 j i- **"
. | I ' g
! si | i l |i
|$ 50.0'*
g y
[ L_______I I _____aE 40.0e'
.
8$ 30.0 DESIGN FORCE ENVELOPE' FOR ACI 349 COMBINATIONS
! %' m
E 20.0
^10.0 - y'
~
' ' ' ' ' ' ' '
! o.oI s to is 20 2s ao as 4
CONSUMERS POWER COMPANYi MIDLAND PLANT UNITS 1 & 2
GRID LOCATION
80 RATED WATER STORAGE TANKMAXIMUM DESIGN LOADS AND
CAPACITIES OF INTERFACE SHEAR'
CONNECTORS (ACI 349 CRITERIA)
| FIGURE 21-
,
i
. - --- - - - - -
_ _ _ _ _ _ _ _ _ - _ _ - _ _ _ _ _ _ _ - . _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ - - - - _ _ _ _ _
, ..,
Mid1rnd Plcnt Units 1 cnd 2*Design R2 ports Borctid W2t r
Storag2 Tcnk Foundations
.
TABLE 1
SUMMARY OF CALCULATED LOADS AND CAPACITIES OF Ti!E NEW RING BEAM
(MIDLAND CRITERIA)
Axial and Flexural'
Interaction Axial, Shear, 'and TorsionInteractionCalculated
Loadtas Calculated LoadN3
C,oad Grid Axial Moment Load Grid Axial Shear
category Combination'l Number Tension Moment Capacityt 2,3 3 Combinationt'l Number Tension Shear Torsion (s) C apac ity(2,4 6at
1, Region A 10 34 28 3 2,492 3,573 10 14 290 31 237 185
Reg ion B 10 6 290 3,153 3,575 10 36 282 142 345 249
Region C 10 5 285 3,547 6,492 10 37 278 135 394 553
Region D 10 4 293 3,822 8,225 10 38 288 123 679 333
Region E 10 3 280 4,041 7,464 10 39 274 120 932 619-
Refer to Section 5.0 of the Design Report for the Borated Water Storage Tank Foundations for load combinationsl'I
(88 Axial and shear are measured in kips: moment and torsion are measured in ft-kips
188 Interaction capacities at calculated axial load'
l*l nteraction capacities at calculated axial load and torsionI
ishneluding torsion due to eccentricity of the interf ace shear force
i bb Da
C -- :( 2 '$__-_-.O
1f x -p sf x_.- -
..
- . . > n-- -
\_ _V_
.
. _ _ . . _ _ . . x
_ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ - _ - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
m
Madidna a*1rnt us: A tas a assu a*Design R; ports Borct d W3t:;r '
Stt ug2 T nk Foundstiena e
TABLE 2 ,
SUMMARY OF CALCULATED IDADS AND CAPACITIES OF THE NEW RING BEAM
(ACI 349-76 LOAD COMBINATIONS AS SUPPLEMENTED BY REGULATORY GUIDE 1.142)
Axial and FlexuralInteraction Axial, Shear, and Torsion
InteractionCalculatedLoadl88 Calculated load m
Load Grid Axial Moment Load Grid Axial Sheari
'
Category Combinationt'l Number Tension Moment Capacityl8.38 Combinationt'l Number Tension Shear Torsiontal Capacitytt.el
Region A A 8 239 2,731 3,638 A 28 259 3 310 123
Region B A 6 226 3,494 3,660 A 36 309 153 439 156,
Region C A 5 215 3,919 6,640 A 37 308 147 510 460
Region D A 4 211 4,316 8,458 A 38 323 130 855 193
Region E A 3 187 4,653 7,701 A 39 312 24 1,154 502
,
i .f. '--til ontrolling ACI 349-76 load combination is: #e .----yC
2
A. U = 1.4D + 1.4T + 1.4F + 1.7L + 1.7H + 1.9E L er_
{'- :t 3 i q' <'
' ass F N /where q
D = dead load "''*8'L = live loadr = hydrostatic pressure f rom groundwater .
T = differential settlementH = lateral earth pressureE = operating basis earthquake am a e a e m em m
188 Axial and shear are in kips moment and torsion are measured in ft-kips
88' Interaction capacities at calculated axial load' ,_,,
8*lInteraction capacities at calculated axial load and torsion ,
talIncluding torsion due to eccentricity of the interface shear force '* m1
O'- - . .
:t
,
* ' *Midicnd Plcnt Unito 1 cnd 2Design RIports BorctGd Wat3r *
Storag2 T:nk round;tiens.
.
TABLE 3
SUMMARY OF CALCULATED LOADS AND CAPACITIES OF THE VALVE PIT MEMBERS
(MIDIAND CRITERIA)
Axial and FlexuralInteractionl88
- ' Shear Calculated
Load In-Plane Transverse Axial Moment
Category Combinationstil Calculated Capacity Calculated Capacity Tension Moment Capacityl88
180 903 1,570Exterior walls 10 198 332 - -
172 2,734 3,700Interior wall 10 51 204 - -
(ring wall)
Roof slab *llNA 'I 18.6 41.1 16.4 19.4 7.3 8.7 50.5lN-S direction''Ii
| E-W directiontel NA el 18.6 60.3 4.9 19.9 0.1 3.7 33.0t
Floor slab'*ltei ygts8 28.6 45.8 15.7 23.4 16.7 20.6 27.5
7 N-S direction! E-W directionte 10 28.6 42.8 11.4 22.9 33.3 5.3 8.5
7
)' l'3 Refer to Section 5.0 of the Design Report for the Borated Water Storage Tank Foundations for load combinations 1
1
; tr' Units are in kips and feet.
883 nteraction capacity at calculated axial load in-rsm s susanI
'
l*3 Forces shown are per linear foot of slab.
sol ased on maximum of all load combinat' ionsB
telDirection of the axial force .MtMNT*
y>( n=sanse saman
/ h N. INA1tAL 79810E
'
N A11AL TD$tod
- _
.
|
' ' *Midicnd Plcnt Unita 1 and 2' *Design Report: Borcted W; tarStorage Tank Foundations
.
s
TABLE 4
SUIMARY OF CALCULATED IDADS AND CAPACITIES OF THE VALVE PIT MEMBERSi .
. ' ' ( ACI 349-7614AD COMBINATIONS AS SUPPLEMENTED BY REGULATORY CUIDE 1.142),
| '
Axial and Flemural,
Interactiont a s.;'
Shearl88 Calculatedi.:
') Load In-Plane Transverse Axial Moment
Category combinations 'l calculated capacity calculated capacity Tension Moment Capacityf 388*
;3
192 1,411 1,570'eExterior walls A 200 331 - -
156 3,381 3,700Interior wall A 71 206 - -
.
i 2 (ring wall)
Roof slabtilN-S direction''' NA'88 24.5 42.2 15.2 20.0 1.5 11.9 53.8.
E-W directioni'l NA''l 24.5 60.3 5.3 19.9 0 3.6 33.0-
i 's Floor slabl8l ,
N-S direction'l A 34.4 45.8 15.2 23.0 16.6 26.2 27.8I
E-W direction'l NA'*l 34.4 42.9 13.7 23.0 32.7 7.6 9.4t. . .
.
tilControlling ACI 349-76 load combination is:-i.
A. U = 1.4D + 1.4T + 1.4F + 1.7L + 1.7H + 1.9E to-russ susaa
* . where
. * D = dead load' - L = live load
F = hydrostatic pressure from groundwaterT = differential settlement neemt
i V,t H = lateral earth pressure ,/,
'
(.E = operating basis earthquake .
\'\ta Units are in kips and feet.
uta teste
ta Interaction capacity at calculated axial load*
. 's una Tsetoml'IForces shown are per linear foot. N to eums smaa
.'. 888 Based on maximum of all load combinationsma:J. saas
'*1 Direction of the axial force
,
9
, .-
Midland Plcnt Unita 1 cnd 2De31gn R port: Borotsd WatOr. * a *
Storage Tank Foundations |y
I'.
TABLE 5
SUMMARY OF CALCULATED LOADS AND CAPACITIES OF THE
FOUNDATION FOOTING (MIDIAND CRITERIA)
LoadType of Load Combinatio n(1) Calculated Loadt2) Capacityt2p
Moment 7 3.0 37.5
Axial Tension ? 19.5 30.3
Shear 7 3. 7 15.6
('l
Water Storage Tank Foundations 'gn Report for the BoratedRefer to Section 5.0 of the Desi
(2) Units are in kips and feet per linear foot of footing
,-^sD,/ ,/
- - IN |
',
|* 'Y |
', Ii , i
il i'
I/E ik
//AIIAL TDSION
PO ENT SEAll
!
|
|
.. , . , . . . . . - , e . .
e
Mid10nd Plant Unito 1 cnd 2DeDign R2 ports BoratCd Watsr
, . .. , GtcrCgs Tank FCundations,.
* TABLE 6
SUMMARY OF CALCULATED LOADS AND CAPACITIES OF THE
FOUNDATION FOOTING
(ACI 349-76 LOAD COMBINATIONS AS SUPPLEMENTED BY
REGULATORY GUIDE 1.142)
LoadType of Load Combination '8 Calculated Load (2) Capacityt2)I
Moment A 3.3 37.5
Axial Tension A 24.5 30.3
Shear A 4.1 14.8
(11 Controlling ACI 349-76 load combination is:
A. U = 1.4D + 1.4T + 1.4F + 1.7L + 1.7H + 1.9E
where
D = dead loadL = live loadF = hydrostatic pressure from groundwaterT = differential settlementH = lateral earth pressureE = operating basis earthquake
(2) Units are in kips and feet per linear foot of footing.
^~,,,
,'1'- .
s's ,- |'
-
!ri
I
j lI i 1
e
i I'
,1 , -o
/ Axur. mstou
sumam su m
. . .. -.. . .
.
_ _ _ _ _ __