ML20038C172
| ML20038C172 | |
| Person / Time | |
|---|---|
| Site: | Midland |
| Issue date: | 11/30/1981 |
| From: | CONSUMERS ENERGY CO. (FORMERLY CONSUMERS POWER CO.) |
| To: | |
| Shared Package | |
| ML20038C170 | List: |
| References | |
| SMA-13701.01-R, SMA-13701.01-R0, SMA-13701.01-R001, SMA-13701.01-R1, NUDOCS 8112100209 | |
| Download: ML20038C172 (35) | |
Text
-
3 SMA 13701.01-R001 Novemb:;r,1981 4
FINAL BORATED WATER STORAGP TANIC SEISMIC ANAT,YSIR 1.
TAE DESCRIPTION The borated water storage tank (8WST) is a vertical cylindrical tank with a diameter of 52 feet and a cylindrical wall height of 32 feet and a domed head as shown in Figure 1.
The tank wall is 3/8 inch thick for the bottom 8 feet and 1/4 inch thick for the remainder of the cylindrical height. The tank roof is a 0.3 inch thick dome segment with a 52 foot radius and a height of 6 feet, 9-3/8 inches. Tank material is stainless steel. Borated water is stored in the tank up to a height of 32 feet.
The tank shell is supported on a ring foundation. The outer radius of this ring foundation is taken to be 28.75 feet, the value corresponding to the foundation after remedial work is performed. The inner radius is 24 feet. These values are utilized in the calculation of soil-spring and dashpot constants. Soil beneath the tank is fill material overlying ' original till material. There is a large valve pit beneath the tank which is judged to not have any significant influence on tank seismic response.
2.
ANALYTICAL APPROACH The purpose of this seismic analysis is to determine the seismic-induced forces acting on the ring wall foundation. These forces have been computed for three levels of earthquake excitation. These are:
a.
FSAR (Reference 1) SSE horizontal site design rsponse spectrum as given in Figure 3.7-2 with the 50 percent increase described in Subsection 3.7.1.1 of the FSAR.
b.
One and one-half times the FSAR response spectrum described in a) above.
c.
The 84th percentile, top of fill, site specific response spectrum developed by Weston Geophysical Corporation (Reference 2). Note that for this case, the larger of the site specific spectrum and the spectrum given in FSAR Figure 3.7-2 (without 50 percent increase) is utilized.
hokkOO O 000 1
S
The tank shell is supported on the foundation which must withstand the seismic-induced forces in the tank shell. These forces are nearly totally due to the water in the tank since the tank shell weight is negligible compared to the weight of this water. Thus, the primary seismic modeling concern is to properly or conservatively model the seismic forces induced by this water on the tank shell and thus, on the foundation. One must model the impulsive mode, the sloshing mode, and 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 ring foundation from each of these three models are added by the square-root-sum-of-squares (SRSS) method.
Soil-structure interaction has been evaluated using frequency independent impedance functions based on the soil beneath the tank being treated as an elastic half-space. Best estimated soil properties have been evaluated from test data on the underlying fill and till material.
These value are then utiized to establish impedance function " spring stiffnesses" and " dashpot constant" values. Strain degradation of the soil stiffness properties (approximate nonlinear behavior of the soil) was included in establishing these properties. To account for uncertainties in soil properties and in the mathematical m'odeling of soil-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 foundation loads are based on the envelope of seismic responses obtained for l
soil-structure interaction stiffnesses which vary throughout this range of possible stiffnesses.
Energy dissipation within the tank, fluid and soil system is approximated in the dynamic models as viscous (velocity proportional) damping. Damping consists of material (hysteretic) damping and radiation damping or the radiation of energy from the structure back into the supporting soil.
2 l
Material damping values conservatively assumed for seismic analysis of the BWST are:
Fluid Sloshing -
0.5 percent of critical damping Tank Shell and Impulsive Fluid -
1.0 percent of critical damping Soil Response -
3.0 percent of critical damping Soil radiation damping is computed in accordance with relations given in BC-TOP-4-A (Reference 3). Material damping and radiation damping for soil 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). This situation occurs because an elastic half-space assumption does not account for the variation of soil properties with depth. Underprediction of the radiation damping results in too much energy dissipation being incorpor-ated into the overall dynamic model which can lead to overprediction of the structural responses from this model. For the seismic evaluation of the BWST, this potential problem,is compensated for in the following conservative fashion:
1.
For modes of structural vibrations which are a combination of soil-structure interaction and flexible structural response (e.g., the tank fluid impulsive mode), the composite modal damping is computed.
If this composite modal damping (made up of structural damping, soil material damping, and radiation damping) exceeds 10% of critical, then the composite modal damping is arbitrarily and conservatively limited to 10% of critical.
2.
For modes of structural vibrations which are nearly exclusively soil-structure interaction modes (i.e., rigid body structural response modes such as the BWST vertical response mode), the radiation damping used will be limited to 75% of the theoretical radiation damping levels.
3.
For modes of structural vibration which are nearly exclusively structural modes (e.g., fluid sloshing mode),
the composite modal damping value is not influenced by radiation damping into the soil and this discussion is irrelevant.
3 l
The layering effects beneath the BWST are relatively minor as the top 50 feet of the original till material and the approximately 30 feet of fill material have similar shear wave velocities such that the radiation damping levels will be at least 75 percent of the theoretical elastic half-space values. Furthermore, the limitation of composite modal damping levels to 10% of critical for combined vibration modes has been shown by many studies to be an extremely conservative criteria which leads to overprediction of structural responses.
Imposing this criteria more 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 seismic forces on the ring foundation from the horizontal impulsive fluid mode is illustrated schematically in Figure 2.
The tank shell stiffness is 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 insig-nificant to the seismic response as the tank is held in round by its base at the bottom and by the roof at the top. The roof weight, W, is g
lumped at the roof level. The shell wall weights, WS are lumped at discrete points on the tank shell.
Impulsive fluid effective weights, WI, are added to the tank shell weights at each of these node points at and below the top of the fluid.
For a rigid mode of horizontal tank vibration, it has been shown by Housner (Reference 4) that the total effective horizontal impulsive weight 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 weight D
is the tank diameter h
is tne fluid height This total effective impulsive weight is distributed parabolically over the fluid height as shown in Figure 2.
The impulsive weight per unit height 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 density y
is the distance above the base of the tank 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 5) 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 leadto base shears which are between a factor of 1.1 and 1.2 times greater than would be obtained using flexible tank impulsive pressures. The overturning moments obtained assuming a Housner effective weight distri-bution are within 2% 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 effective impulsive fluid weight distribution given by Equation 2 and shown in Figure 2 is adequate.
5
l The horizontal impulsive mode tank model is attached to the ground 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 into this tank model through these impedance functions. The resultant over-turning moment and base shear at the base of this model represent the forces imposed on the ring foundation by the horizontal impulsive mode.
The actual model used for evaluating horizontal impulsive seismic response 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 computing seismic-induced loads on the ring wall foundation for the horizontal impulsive mode. During seismic response of the BWST, 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, M, can be conservatively B
evaluated by the following expression taken from Reference 5:
MB =.1045 0 W Sa (3) l where Sal is' the spectral acceleration of the predominant horizontal impulsive mode For the BWST, this moment is applied to the soil inside the ring wall foundation 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 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 6
W mode. The natural fmquency of vibration,"2, of this mode, the fluid effective sloshing weight, W, and height of application, X, above 2
2 the tank base art given by relations from Reference 4 as presented below.
2 3.67g l3.67h tanh i w
I.67h\\
W 3
W 0.230 tanh
=
(5) 2 h
\\
/
hcosh(3.67h
-h X
h-2 (6)
=
3.67h sinh (3.67h 2
where g is gravity acceleration (32.17 ft/second )
The base shear and overturning moment on the ring foundation due to this sloshing 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 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 7
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:
b9 Y"
W (10) v where Wy is the sum of the tank shell weight, W, and the total fluid 3
weight, W, and Ky is the vertical soil-structure interaction w
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) 3 2/K W /g yy where Cy is the vertical dashpot coefficient from the soil-structure interaction impedance function for the foundation, g is gravity accelera-2 tion (32.17 feet /second ), and 83 is the appropriate soil material damping (3% of critical). The 0.75 factor is included to account for soil layering effects as discussed in Section 2.
The ring foundation only supports the vertical seismic forces from the shell. The vertical fluid forces are supported directly on the soil. Thus, the vertical seismic forces on the ring foundation are given by:
Fy = W *Say (12) 3 where Sa represents the design seismic vertical spectral acceleration y
at damping level Sy and cyclic natural frequency fy where fy =
wy/2 w.
Thus, the vertical seismic forces on the ring foundation can be determined without developing a mathematical model.
8 4
-.--v
4.
SOIL-STRUCTURE INTERACTION Soil properties used in the evaluation of impedance function properties beneath the BWST were established by using a weighted average of the shear modulus values of the material below the tank to a depth equal to the diameter of the foundation. Soil properties were based on shear wave velocity tests for the fill (Reference 6) and properties of the 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. soil behavior associated with larger shear strains occurring during seismic events. The resulting composite soil properties used in the evaluation of soil-spring stiffnesses and dashpot constants for the BWST seismic analyses are the following:
Shear Modulus, G 1510 ksf (best estimate)
=
Poisson's Ratio,v 0.45
=
2 4
Soil Density, p
.00357 k-sec /ft
=
As mentioned previously, uncertainties in soil properties and soil-structure interaction modeling were accounted for by considering soil shear modulus variation over the range of 0.5 to 1.5 times the best estimate value (i.e., G varies from 755 ksf to 2265 ksf).
Soil-spring and dashpot constants were evaluated based on relationships given in BC-TOP-4-A (Reference 3) as follows.
i Horizontal Translation 32(1-v)GR K
(13) y=
7-8v l
CX=
0.576 k R
/ p/G (14) x C
X s*=
(15) 2JK M y7 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 4GR K
y (1-v)
(20)
C 0.85 K R / p /G (21)
=
y y
Cy B y (22)
=
2/KM y
where R
is the tank radius M
is the total mass of tank and water M
is the mass of tank and impulsive water I
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 the outer foundation radius of 28,75 feet and then subtracting from the resulting values the stiffness and damping corresponding to these equations for the inner foundation radius of 24 feet.
In this manner, the impedance function for the ring foundation is detemined from relations for a circular disk foundation.
In rocking, seismic-induced forces are transmitted to the underlying soil primarily through the ring foundation.
However, for horizontal and vertical translation, seismic-induced forces are transmitted to the underlying soil over the entire tank area. The resulting soil stiffnesses and radiation damping percentager are summarized below for the lower bound, best estimate and upper bound values for soil shear modulus:
Lower Best Upper Bound Estimate Bound G(ksf) 755 1510 2265 5
k (k/ft) 1.124x10 2.247x105 3.371x105 x
7 k, ( rad an) 3.639x107 7.277x107 10.916x10 5
5 k (k/ft) 1.579x10 3.157x10 4.736x105 y
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 90.8 y
Again, note that for the coupled impulsive fluid-soil mode, composite modal damping ratios are computed and limited to 10 percent of critical damping. For the vertical rigid body response mode, 75 percent of the radiation damping shown above is utilized.
11
5.
TANK DYNAMIC CHARACTERISTICS AND FOUNDATION SEISMIC LOADS The natural frequency, modal damping, and corresponding spectral acceleration for the slashing, impulsive and vertical response modes and the three input response spectra considered (i.e., FSAR,1.5*FSAR and site specific, top of fill) are summarized below.
Spectral Acceleration (g)
Modal Site
Response
Frequency Damping FSAR (SSE) 1.5 FSAR Specific Sloshing 0.24 Hz 0.5
.046
.069
.046 Impulsive Mode 1 4.2 10.0
.210
.315
.276 Lower Bound
?!ade 2 12.9 10.0
.12
.18
.200 M de 1 5.5 10.0
.122
.183
.271 Best Estimate Mode 2 16.2 10.0
.12
.18
.180 Mode 1 6.3 10.0
.12
.18
.265 Upper Bound Mode 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 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 and the best estimate soil properties are illustrated in Figure 4 Seismic-induced base shear, overturning moment and vertical load at the top of the ring foundation are sumarized in Table 1.
For all three spectra considered, the lower bound soil properties give the largest seismic-induced foundation loads. For the FSAR spectra, the lower bound soil properties result in the predominant horizontal inpulsive mode falling 'n the 50 percent increased region of the input spectra while the other soil properties considered result in this mode being out of this region. Note that the foundation loads from the 1.5 times FSAR spectrum are greater than the loads from the 84th percentile, top of fill site specific response spectrum.
It should be noted that the fluid slosh height has been computed in 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 without significant reduction of free surface area. As a result, it is concluded that 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 computed in 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-k Best Estimate
'2812 ft-k 4217 ft-k 6245 ft-k Upper Bound 2766 ft-k 4148 ft-k 6107 ft-k 33
s s
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 Material at the Plant Site", Weston Geophysical Corporation, Westtoro, Massachusetts, May 1,1981.
3.
Bechtel Power Corporation, Seismic Analyses of Structures and Equipment for Nuclear Power Plants, Revision 3, November,1974 (BC-TOP-4-A).
4.
" Nuclear Reactors and Earthquakes", TID-7024, Prepared by Lockheed Aircraft Corporation and Holmes & tiarver, Inc., for the Division of Reactor 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 Earthquake Engineering 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.
f 14 s.
x
- ~ >.
y 3
\\ t L e 7
vy q,. ' i i.
TABLE 1
,'N'n J.
Y N'/
SUMMARY
OF BWST SEISMIC-INDUCED FOUNDATION LOADS l
Input Response Spectrum l
Response
- FSAR Site Specific Sloshing Base' Shear 72k 108k 72k Overturning Moment 1479 ft-k 2219 ft-k 1479 ft-k Impulsive.
Ba~se Shear 537k 806k 706k Lower 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-k Base Shear 294k 441k 646k Upper Overturning Moment 4477 ft-k 6715 ft-k 9866 ft-k Vertical Vertical Load 13k 20k 17k Combined Sloshing '
e Base' Shear 542k 813k 710k l **"
Overturning Moment 7999 ft-k 11999 ft-k 10445 ft-k s.
Bas ~e Shear 313k 471k 679k Best OveFturnirig Moment 4804 ft-k 7207 ft-k 10237 ft-k Ease Shear 303k 454k 650k Upper Overturning Moment 4715 ft-k 7073 ft-k 9976 ft-k Maximum Response y
Base Shear 542k 813k 710k Overturning Moment 7999 ft-k 11999 ft-k 10445 ft-k Vertical Load 13k 20k 17k h
4 h
\\
15
?
s
_?
s s.
i Roof WR4D Rigid Link N
i Top of Fluid S
4 i
W a
g y
g Parabolic Distribution Sq QWg of Effective Implusive Fluid Mass, W I
\\
S W
q g
\\
=
Y N A I
\\
S
~
}
WSidWI
~
l SidI W
hsff, S
- W Base V
I
/
Soll-Structure h
interaction impedance functions 1
FIGURE 2.
BWST HORIZONTAL IMPULSIVE MODE MODEL
T_ANK SilELL PROPERTIES 6
E = 4.176x10 ksf; v = 0.3 94 >
35.4' t
X I
Rigid Link 2
4 1/4" 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
4 512.1 d
6()
22,4 5
426.0 S0ll IMPEDANCE FUNCTION tf 6
312.7 Properties b
'O STIFFNESS 8
25.9 k
k g
x 9
28.6 (k/ft)
(k-ft/ rad) 5 7
12.8' Lower Bound 1.124x10 3.639x10 5
7 Best Estimate 2.247x10 7.277x10 5
7 Upper 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
~
~
Undeformed Shape Shape due to soil translatior Shape due to soil rocking
-x-
- - -- Mode shape
\\ 'f
'l i
g"
/
i
/
\\
/
\\;
/
\\
- 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 Hz Participation Factor = 8.785 Participation Factor = 2.959 FIGURE 4.
MODAL PROPERTIES OF BWST TANK - IMPULSIVE WATER -
S0IL-SPRING MODEL (BEST ESTIMATE SOIL) 19
lL 6'-9 3/8" I
s I
32' D = 52'
=
l 4
',f,, - N/VWWV// uwANY/A%V L\\Y// W/r*V/ANw/ tv+%w/p/Ag'*,.y g?
i L t\\\\
6'
,Q ?, 4 Entrapped Soil O f n i
4 htl * * *. $
ff*;0.[%
g$/4 LL%
/NgsV I
FIGURE 1.
80 RATED WATER STORAGE TANK CONFIGURATION l
l 16
sty rLAss
_ _/_, CAPACITY ENVELOPEp____,
ae t 70,0 s
I e
g I
I I
i l,.
1 1
I i
60.0 j
j j
I I
I I
I E
I I
L________-l 5-I 1
I 8
L______J E
40.0 U
fl DESIGN FORCE ENVELOPE l
h 30 0 MIDLAND LOAD COMBINATIONS 1
/
f
!E
/
^
.1 nu 5
/
\\
A 10.0 yv
.r 0.0 5
10 15 20 25 30 35 40 CONSUMERS POWER COMPANY GRID LOCATION MIDLAND PLANT UNITS 1 & 2 BWST FOUNDATION MAXIMUM DESIGN LOADS AND CAPACITIES OF INTERFACE SHEAR CONNECTORS (MIDLAND CRITERIA)
~
^
FIGURE 20 9
R EY PL Aff 80.0 pCAPACITY ENVELOPE
__q
"'o '
70.0 j
g s
I I
l 1
i
/
60.0 j
i l
I I
I i
s l
l I
i g
j Eg s0.0 g
L_______I I
_____a E
40.0 E
i 8
[
30.0 DESIGN FORCE ENVELOPE j
f y
FOR ACI 349 COMBINATIONS 6
l l
[3 20.0
\\
A 10.0 y
w t
0.0 s
s 20 2s 30 as 4
CONSUMERS POWER COMPANY MIDLAND PLANT UNITS 1 & 2 GRID LOCATION BORATED WATER STORAGE TANK MAXIMUM DESIGN LOADS AND CAPACITIES OF INTERFACE SHEAR CONNECTORS (ACI 349 CRITERIA)
FIGURE 21 O
Midltnd ricnt Units 1 and 2 Design Raports Borsts'd Water Storaga 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 Tornion Interaction Interaction Calculated 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 3 3
t Region A 10 34 28 3 2,492 3,573 10 14 290 31 237 185 10 36 282 142 345 249 Region 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 combinations l'8 Axial and shear are measured in kips! moment and torsion are measured in ft-kips tal 88' Interaction capacities at calculated axial load 881 nteraction capacities at calculated axial load and torsion I
l Including torsion due to eccentricity of the interface shear force e e s
.0 Carr. e, tam s
N
[
h<
o ussA N
/
9 N'
/
==
\\
_ _J_x
.._____.o.
9 8
Mad!Knd Flint Unsts 1 arus d Design Raport: Dorctsd Water Storage 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 Flexural Interaction Axial, Shear, and Torsion Calculated Interaction Loadl81 Calculated loadIU Load Grid Axial Moment Ioad Grid Axial Shear Category 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. 1 3 1 h
l'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 L = live load F = hydrostatic pressure from groundwater T = 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 force mesa 8
Mid1cnd Plent Units I cnd 2 Design Report: Borsted water Storaga Tcnk Foundations TABLE 1,
SUMMARY
OF CALCULATED LOADS AND CAPACITIES OF Tile VALVE PIT MEMBERS (MIDLAND CRITERIA)
Axial and F1texural Interactionq2s l
Shear Calculated i
Load in-Plane Transverse Axial floment Category 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 50.5 I
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 27.5 I
E-W directionte 10 28.6 42.8 11.4 22.9 33.3 5.3 8.5 l
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 force M3eert s'
upmmes s==An
/
h N
N AIIAL TEN 8105 ARIAL TERSIDW g
a.
e S
4 e
Mid1rnd Pltnt Units I cnd 2 De0ign Riport: Borcted W';tsr Startge 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 Flexural Interactionia Shearl'8 calculated Load In-Plane Transverse Axial Moment Category Combinations 'l Calculated Capacity Calculated Capacity Tension Moment Capacityf38 t
192 1,411 1,570 Exterior walls A
200 331 Interior wall A
71 206 156 3,381 3,700 (ring wall)
. s Roof slabl*3 N-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*I N-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 9.4 t
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 groundwater T = 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 tunsica 8*' 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)
Load Type 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 Borated Water Storage Tank Foundations (2 Units are in kips and feet per linear foot of footing
,-^N
,A I
N 8 'T l
8 l
i i
l 1
l l
t ik
/
/
AxIAz. m stow norgyr SHEAR
r Midland Plcnt Unito 1 cnd 2 Decign R; port:
BoratOd WatGr Chorage Tank Foundations TABLE 6 i
SUMMARY
OF CALCULATED LOADS AND CAPACITIES OF THE FOUNDATION FOOTING (ACI 349-76 LOAD COMBINATIONS AS SUPPLEMENTED BY REGULATORY GUIDE 1.142)
-Load Type 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 load L = live load F = hydrostatic pressure from groundwater T = differential settlement H = lateral earth pressure E = operating basis earthquake (2) Units are in kips and feet per linear foot of footing.
$,, A i
l't i
l l
l l
i I
h
/
- /p
//
um ms.
==
l i
mm
~
, - CAPACITY ENVELOPE
_-I r---
I i
70,0 i
l ene e g
i l
I y
7 I
i i
i i
80.0 i
1 I
I I
a I
I i
So o l
i i
l g
L______J L_______
E 40.0 j i
e U
fl DESIGN FORCE ENVELOPE I
30 0 o
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 COMPANY GRID LOCATION MIDLAND PLANT UNITS 1 & 2 BWST FOUNDATION MAXIMUM DESIGN LOADS AND CAPACITIES OF INTERFACE SHEAR CONNECTORS (MIDLAND CRITERIA)
FIGURE 20
i REY PLAN pCAPACITY ENVELOPE
__q
- p___,
70.0 l
mei g
3 I
I i
I I
i 60.0 j
i l
I g
si l
i l
l i
l 50.0 g
y
[
L_______I I
_____a E
40.0 e
8 30.0 DESIGN FORCE ENVELOPE FOR ACI 349 COMBINATIONS m
E 20.0
^
10.0 y
~
o.o I
s to is 20 2s ao as 4
CONSUMERS POWER COMPANY i
MIDLAND PLANT UNITS 1 & 2 GRID LOCATION 80 RATED WATER STORAGE TANK MAXIMUM DESIGN LOADS AND CAPACITIES OF INTERFACE SHEAR CONNECTORS (ACI 349 CRITERIA) l 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 Torsion Interaction Calculated 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 6 a
t 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 combinations l'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 torsion I
ishneluding torsion due to eccentricity of the interf ace shear force i
bb D
aC
- (
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 Flexural Interaction Axial, Shear, and Torsion Interaction Calculated Loadl88 Calculated load m Load Grid Axial Moment Load Grid Axial Shear i
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.----
y C
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 load r = hydrostatic pressure f rom groundwater T = differential settlement H = lateral earth pressure E = 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 m
1 O
t
Midicnd Plcnt Unito 1 cnd 2 Design 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 Flexural Interactionl88 Shear Calculated Load In-Plane Transverse Axial Moment Category Combinationstil Calculated Capacity Calculated Capacity Tension Moment Capacityl88 180 903 1,570 Exterior walls 10 198 332 172 2,734 3,700 Interior wall 10 51 204 (ring wall)
Roof slab *l l
NA 'I 18.6 41.1 16.4 19.4 7.3 8.7 50.5 l
N-S directionI i
l E-W directiontel NA el 18.6 60.3 4.9 19.9 0.1 3.7 33.0 t
Floor slab'*l tei 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 susan I
l*3 Forces shown are per linear foot of slab.
sol ased on maximum of all load combinat' ions B
telDirection of the axial force MtMNT y
>(
n=sanse saman
/
h N.
I N
A1tAL 79810E N
A11AL TD$tod l
Midicnd Plcnt Unita 1 and 2 Design Report: Borcted W; tar Storage Tank Foundations s
TABLE 4 SUIMARY OF CALCULATED IDADS AND CAPACITIES OF THE VALVE PIT MEMBERS i
( ACI 349-7614AD COMBINATIONS AS SUPPLEMENTED BY REGULATORY CUIDE 1.142) l Axial and Flemural Interactiont a s Shearl88 Calculated i.:')
Load In-Plane Transverse Axial Moment Category combinations 'l calculated capacity calculated capacity Tension Moment Capacityf 38 8
- 3 192 1,411 1,570
'e Exterior walls A
200 331 156 3,381 3,700 Interior wall A
71 206 i 2 (ring wall)
Roof slabtil N-S direction
NA'88 24.5 42.2 15.2 20.0 1.5 11.9 53.8 E-W directioni'l NAl 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 27.8 I
E-W direction'l NA'*l 34.4 42.9 13.7 23.0 32.7 7.6 9.4 t
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 groundwater T = 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 Tsetom l'IForces shown are per linear foot.
N to eums smaa 888 Based on maximum of all load combinations ma:J.
saas
'*1 Direction of the axial force 9
Midland Plcnt Unita 1 cnd 2 De31gn R port:
Borotsd WatOr a
- Storage Tank Foundations y
TABLE 5
SUMMARY
OF CALCULATED LOADS AND CAPACITIES OF THE FOUNDATION FOOTING (MIDIAND CRITERIA)
Load Type 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 Borated Refer to Section 5.0 of the Desi (2) Units are in kips and feet per linear foot of footing
,-^s D
,/
,/
I N
l l
'Y l
I i
i i
l i
I
/
E ik
//
AIIAL TDSION PO ENT SEAll l
l e
e Mid10nd Plant Unito 1 cnd 2 DeDign 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)
Load Type 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 load L = live load F = hydrostatic pressure from groundwater T = differential settlement H = lateral earth pressure E = operating basis earthquake (2) Units are in kips and feet per linear foot of footing.
^~,
,'1 s's l
!r i
I j
l I
i 1
e i
I
,1 o
/
Axur. mstou sumam su m
.