ML20141H649
| ML20141H649 | |
| Person / Time | |
|---|---|
| Site: | Peach Bottom |
| Issue date: | 01/15/1986 |
| From: | Herrick R Calspan Corp, Franklin Research Ctr |
| To: | Soon Kim Office of Nuclear Reactor Regulation |
| Shared Package | |
| ML20141H654 | List: |
| References | |
| CON-NRC-03-81-130, TAC 59012, TAC 59013 TER-C5506-585, NUDOCS 8601170206 | |
| Download: ML20141H649 (36) | |
Text
APPENDIX A TECHNICAL EVALUATION REPORT NRC DOCKET NO. 50-277, 50-278 FRC PROJECT C5506 N RC TAC NO. 59012, 59013 FRC ASSIGNMENT 26 NRC CONTRACT NO. NRC-03-81-130 FRC TASK 585 EVALUATION OF SPENT FUEL RACKS STRUCTURAL ANALYSIS PHILADELPHIA ELECTRIC COMPANY PEACH BOTTOM UNITS 2 AND 3 TER-C5506-585 t
Prepared for Nuclear Regulatory Commission FRC Group Leader: R. C. Herrick Washington, D.C. 20555 NRC Lead Engineer: s. B. Kim January 15, 1986 This report was preparedas an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, or any of their employees, makes any whrranty, expressed or implied, or assumes any legal liability or responsibility for any third party's use, or the results of such use, of any information, appa.
ratus, product or process disclosed in this report, or represents that its use by such third party would not infringe privately owned rights.
I Prepared by:
Reviewed by:
Approved by:
A&d Vu- &n.
N k 1A Principal Author Departme/t Difctor J
Date: 3d's M N4 Date: b I8,!f 5 Date:
l~' Y N f
FRANKLIN RESEARCH CENTER
/
OtVISION OF ARVIN/ CAL 5 PAN toen a sacs sTowTs mteostma se issos
% (
>ie u
+
L TER-C5506-585 CNTENTS Section Title Pace 1
INTRODUCTION 1
1.1 Purpose of the Review.
1 1.2 Generic Background.
1 2
ACCEPTANCE CRITERIA.
3 I
(
2.1 Applicable Criteria 3
2.2 Principal Acceptance Criteria.
3 i
3-TECHNICAL REVIEW 6
3.1 Mathematical Modeling and Seismic Analysis of Spent Fuel Rack Modules 6
3.2 Evaluation of the Nonlinear Dynamic Displacement Analysis 11 r-3.2.1 Description of the Model 11 3.2.2 Frictional Force Between Rack Support Pads and the Pool Liner.
14 f~
3.2.3 Hydrodynamic Coupling Between Fluid b
and Rack Structure.
15 3.2.4 Seismic Loading 16 P
3.2.5 Integration Time Step 17 3.2.6 Rack Displacements 17 3.3 Evaluation of the Detailed Three-Dimensional Linear Model.
19 3.3.1 Description of the Model 19 3.3.2 Review of Stress Levels 20 3.4 Review of Spent Fuel Pool Structural Analysis.
20 3.4.1 Spent Fuel Pool Structural Analysis 20 3.4.2 Analysis Procedure.
23
~
3.4.3 Susanary of Results.
27 l
1 iii 15
H l
TER-C5506-585
[
CONTENTS
[
Section Title Page 1
INTRODUCTION 1
1.1 Purpose of the Review.
I 1.2 Generic Background.
1 2
ACC1'PTANCE CRITERIA.
3 1...
2.1 Applicable Criteria 3
2.2 Principal Acceptance Criteria.
3 3
TECHNICAL REVIEW 6
3.1 Mathematical Modeling and Seismic Analysis of Spent Fuel Rack Modules 6
3.2 Evaluation of the Nonlinear Dynamic Displacement Analysis 11 3.2.1 Description of the Model 11 3.2.2 Frictional Force Between Rack Support Pads and the Pool Liner.
14 3.2.3 Hydrodynamic Coupling Between Fluid and Rack Structure.
15 3.2.4 Seismic Loading 16 3.2.5 Integration Time Step 17 3.2.6 Rack Displacements 17 3.3 Evaluation of the Detailed Three-Dimensional Linear Model.
19 3.3.1 Description of the Model 19
[
3.3.2 Review of Stress Levels 20 3.4 Review of Spent Fuel Pool Structural Analysis.
20 3.4.1 Spent Fuel Pool Structural Analysis 20 3.4.2 Analysis Procedure.
23 3.4.3 Sunmary of Results.
27 r*
P' w
[
iii
[
TER-C5506-585 a
CONTENTS (Cont.)
o Section Title Page
~e.
3.5 Fuel Handling Accident Analysis 27 3.5.1 Fuel Handling Crane Uplift.
27 3.5.2 Accidental Fuel Assembly Drop 30 4
CONCLUSIONS.
31 32 5
REFERENCES.
I f.
[
[
E L
[
[
[
[
.IV
TER-C5506-585 FOREWORD This Technical Evaluation Report was prepared by Franklin Research Center under a contract with the U.S. Nuclear Regulatory Comunission (Office of Nuclear Reactor Regulation, Division of Operating Reactors) for technical assistance in support of NRC operating reactor licensing actions. The T
technical evaluation was conducted in accordance with criteria established by the NRC.
I
'p-b r
F>
I
[
]
l I
t V
[
.-x_,
_-____.__y..7
,..____rm__...
y
v TER-C5jiO6-585 1.
INIRODUCTION 1.1 PURPOSE OF THE REVIEW This technical evaluation report (TER) covers an independent review of the Philadelphia Electric C m y's licensing report (1) on high-density spent b
fuel racks for Peach Botton Units 2 and 3 with respect to the evaluation of the spent fuel racks' structural analyses, the fuel racks' design, and the F
pool's structural analysis. The objective of this review was to determine the r
structural adequacy of the Licensee's high-density spent fuel racks and spent 5
fuel pool.
9 1.2 GENERIC BACKGROUND Many licensees have entered into a program of introducing modified fuel g
L racks to their spent fuel pools that will accept higher denrity loadings of spent fuel in order to provide additional storage capacity. However, before f
4 the higher density racks may be usad, the licensees are required to submit rigorous analysis or experimental data verifying that the structural design of the fuel rack is adequate and that the spent fuel pool structure can accommodate the increased loads.
e-The analysis is complicated by the fact that the fuel racks are fully immersed in the spent fuel pool. During a seismic event, the water in the pool, as well as the rack structure, will be set in motion resulting in fluid-structure interaction. The hydrodynamic coupling between the fuel assemblies and the rack cells, as well as between adjacent racks, plays a significant role in affecting the dynamic behavior of the racks.
In addition, the racks are free-standing. Since the racks are not anchored to the pool floor or the pool walls, the motion of the racks during a seismic event is governed by the static / dynamic friction between the rack's mounting feet and the pool floor, l
and by the hydrodynamic coupling to adjacent racks and the pool walls.
Accordingly, this report covers the review and evaluation of analyses submitted for Peach Botton Units 2 and 3 by the Licensee, wherein the structural analysis of the spent fuel racks under seismic loadings is of primary concern due to the nonlinearity of gap elements and static / dynamic S -
TER-C5506-585 friction, as well as fluid-structure interaction.
In addition to the evaluation of the dynamic structural analysis for seismic loadings, the design
[
of the spent fuel racks and the analysis of the spent fuel pool structure under the increased fuel load are reviewed.
s L,
m, L,.
e L.
1h l
\\
i l
l l
i I
i i l
- ~. -
5 TER-C5506-585
(
r 2.
ACCEPTANCE CRITERIA
(
I 2.1 APPLICABLE CRITERIA The criteria and guidelines used to determine the adequacy of the high-density spent fuel racks and pool structures are provided in the following
~
documents:
o OT Position for Review and Acceptance of Spent Fuel Storage and Handling Applications, U.S. Nuclear Regulatory Commission, January 18, 1979 [2]
o Standard Review Plan, NUREG-0800, U.S. Nuclear Regulatory Commission Section 3.7, Seismic Design Section 3.8.4, Other Category I Structures Appendix D to Section 3.8.4, Technical Position on Spent Fuel Pool Racks Section 9.1, Puel Storage and Handling o ASME Boiler and Pressure Vessel Code, American Society of Mechanical Engineers,Section III, Division 1 Regulatory Guides, U.S. Nuclear Regulatory Commission o
1,29 - Seismic Design Classification 1.60 - Design Response Spectra for Seismic Design of Nuclear Power
~
Plants
[a 1.61 - Damping Values for Seismic Design of Nuclear Power Plants 1.92 - Combining Modal Responses and Spatial Components in Seismic
[
Response Analysis 1.124 - Design Limits and Loading Combinations for Class 1 Linear-Type
[
Component Types o Other Industry Codes and Standards American National Standards Institute, N210-76.
2.2 PRINCIPAL ACCEPIANCE CRITERIA The principal acceptance criteria for the evaluation of the spent fuel racks' structural analysis for Peach Bottom Units 2 and 3 are set forth by the
[
+
TER-C5506-585 NRC's OT Position for Review and Acceptance of Spent Fuel Storage and Handling Applications (OT Position Paper) [2].Section IV of the document describes the mechanical, material, and structural considerations for the fuel racks and their analysis.
[
The main safety function of the spent fuel pool and the fuel racks, as stated in that document, is "to maintain the spent fuel assemblies in a safe
[
configuration through all environmental and abnormal loadings, such as earth-quake, and impact due to spent fuel cask drop, drop of a spent fuel assembly, or drop of any other heavy object during routine spent fuel handling."
Specific applicable codes and standards are defined as follows:
" Construction materials should conform to Section III, Sub'ection NF of s
the ASME* Code. All materials should be selected to be compatible with the fuel pool environment to minimize corrosion and galvanic effects.
Design, Lorication, and installation of spent fuel racks of stainless steel materials may be performed based upon the AISC** specification or r
Subsection NF requirements of Section III of the ASME B&PV Code for Class
(
3 component supports. Once a code is chosen its provisions must be followed in entirety. When the AISC specification procedures are g
adopted, the yield stress values for stainless steel base metal may be obtained from the Section III of the ASME B&PV Code, and the design 5'
stresses defined in the AISC specifications as percentages of the yield stress may be used.
Permissible stresses for stainless steel welds used P
in accordance with the AISC Code may be obtained from Table NF-3292.1-1 6
of ASME Section III Code.
4 Other materials, design procedures, and fabrication techniques will be reviewed on a case-by-case basis."
i Criteria for seismic and impact loads are provided by Section IV-3 of the OT Position Paper, which requires the following:
o Seismic excitation along three orthogonal directions should be y
imposed simultaneously.
The peak response from each direction should be combined by the
,_3 o
square root of the sum of the squares.
If response spectra are available for vertical and horizontal directions only, the same horizontal response spectra may be applied along the other horizontal direction.
I
- American Society of Mechanical Engineers Boiler and Pressure Vessel Codes, Latest Edition.
- American Institute of Steel Construction, Latest Edition.
L
~
I TER-C5506-589 1
o Increased damping of fuel racks due to submergence in the spent fuel pool is not acceptable without applicable test data and/or detailed analytical results.
o Local impact of a fuel assembly within a spent fuel rack cell should 1,
be considered.
Temperature gradients and mechanical load combinations are to be considered in accordance with Section IV-4 of the OT Position Paper.
The structural accejtance criteria are provided by Section IV-6 of the OT Position Paper.
For sliding, tilting, and rack impact during seismic events, Section IV-6 of the OT Position Paper provides the following:
"For impact loading tha ductility ratios utilized to absorb kinetic energy in the tensile, florural, compressive, and shearing modes should be quantified. When considering the effects of seismic loads, factors of safety against gross sliding and overturning of racks and rack modules under all probable service conditions shall be in accordance with the Section 3.8.5.II-5 of the Standard Review Plan. This position on factors
~
of safety against sliding and tilting need not be met provided any one of the following conditions is met:
(a) it can be shown by detailed nonlinear dynamic analyses that the amplitudes of sliding motion are minimal, and impact between adjacent rack modules or between a rack module and the pool walls is prevented provided that the factors of safety against tilting are within the values permitted by Section 3.8.5.II.5 of the Standard Review Plan
]
(b) it can be shown that any slid 4ng and tilting motion will be J
contained within suitable geometric constraints such as therral clearances, and that any impact due to the clearances is incorporated."
r u
b o
b P
m I
I m
P 6
s TER-C5506-585 s
I 3.
TECHNICAL REVIEW
[
l 3.1 MATHEMATICAL MODELING AND SEISMIC ANALYSIS OF SPENT FUEL RACK MODULES f
Submerged spent fuel rack modules exhibit highly nonlinear structural dynamic behavior under seismic excitation. The sources of nonlinearity can generally be categorized by the following:
a.
The impact between fuel cell and fuel assembly: The fuel assembly standing inside a fuel cell will impact its four inside walls repeatedly under earthquake loadings. These impacts are nonlinear in nature and when compounded with the hydredynamic coupling effect will significantly affect the dynamic responses of the modules in seismic events.
b.
Friction between module base and pool liner: The modules are free-standing on the pool liner, i.e., they are neither anchored to the pool liner nor attached to the pool wall. Consequently, the modules are held in place by virtue of the frictional forces between the module base and pool liner. These frictional forces act together with the hydrodynamic coupling forces to both excite and restrain the module during seismic events.
peach Bottom Units 2 and 3 plan to utilize high density fuel racks comprising nine variations in storage capacity that are arranged in the spent g
fuel pools as shown in Figures 1 and 2 (1). Data pertaining to the rack module designs are provided in Table 1.
Note that the clearance space between the rack modules and the pool structure is shown in Figures 1 and 2 by the boxed dimensions. The minimum rack module to rack module clearance is 1.68 r
inches, as reported by the Licensee (3).
The rack modules for each unit ranged in capacity (and size) from 9 x 14 cells to 19 x 20 cells. These largest and smallest racks were chosen by the Licensee for structural dynamics analysis. Since experience indicates that, for a given rack height, the rack module with the smallest horizontal dimensions will usually yield the highest rack displacements (tipping), the Licensee's choice of modules for analysis is acceptable.
The seismic analysis was performed by the Licensee in two parts. The e
first part was a three-dimensional, nonlinear, time-history analysis of dynamic rack displacements employing a mathematical model of a spent fuel rack module, P
modeled as shown in Figure 3, to include the fuel assemblies and hydrodynamic w
P=,
4 TER-C5506-585 r
l+
N (r
=.-
1-
=
l10.15l7
~*
a 4,,,
<ii, 9
- .81 CASK AR E A
==
==
.==
l.96 '4 10.15' i
+-
a
+m
++
f
'F SuP 99 i
s r.
l12.28]
as 4+
,e e,
oe d
.=
==
=
==
g as an de t
g, ge l
~
.E"."
.=
131.6 4 116.43 H at
>+-
h
+s f
h**"
1 33%)$]9/f$;&ill(W9fffA g
+
~
~
- t. i6.52i 1
i
=
r-T Figure 1.
Spent Fuel Storage Rack Arrangement Unit 2 e
6..
m.
TER-C9506-589 f
1 I
1 N
7 7 110.151
~=
-=
mr y,
I
+. 81
+
CASK AR E A em
-+
e 110.151 4.96 1
++
a.
e.
99 9e T
M y
9.m l12.28 6
~
J e
4.
+
l-3 l'
7 g,
9, 7
"E" CRB 131.641
. L h 6.431 ~f W
~
~
=
4, i
- I'856
-l-j$!$$&$%%%%9% LrI6.s2 -
+
i
~
o l6.521 L
F m
Figure 2.
Spent Fuel Storage Rack Arrangement Unit 3 L -._
~
I TER-C5506-585 f
Table 1.
Rack Module Data (Per Unit)
I
~
Storage Rack Assembly Dry Weight (1b)
Qty Array Locations Dimensions (inches)
Per Rack Assembly 1
9 x 14 126 54 x 89 x 180 10,000 2
10 x 14 280 64 x 89 x 180 11,200 1
11 x 14 Mod.
119 70 x 89 x 180 9,500 1
12 x 15 180 76 x 95 x 180 14,400 1
12 x 17 204 76 x 107 x 180 16,300 2
12 x 20 480 76 x 126 x 180 19,200 2
15 x 19 570 95 x 120 x 180 22,800 1
17 x 20 340 107 x 126 x 180 27,200 w.
_4 19 x 20 1,520 120 x 126 x 180 30,400 15 racks 3,819 Storage locations center-to-center spacing (inches) 6.28 Storage cell inner dimension (inches) 6.07 d
Intermediate storage location inner dimensions (inches) 6.12 Type of fuel BWR 8 x 8 BWR 8 x 8 (R)
BWR 7 x 7 f
L.
P 6
F w
T w
P g
TIR-C5506-585 N
h N
b w
,/*
x
'et
+
h c
b.
/gl
/
N t
A-U
\\
g s,p ys w
/
[-
l
+N N/
L 1
1 3
1-1
+
Figure 3.
Three-Dinensional Nonlinear Seismic Model lf TER-C5506-585 coupling to other rack rodales and/or the pool vall. The secor.d part of the seismic analysis used a linear, three-dimensional, finite element model of the fuel rack, as shown in Figure 4, for the dual purposes of coeputing rack F
stresses and determining the rack module structural properties for usa in the ocnlinear dynamic displacement analysis.
Licensee's seinmic and stress analysis of the spent fuel rack modules considarsd full, partially filled,.and empty rack modules.
f The descrzption and evaluatien of the two models are addressed in detail in Sections 3.2 and 3.3.
The displac'eeent and stress results are discussed An appropriate subsections.
3.2 EVALUATION CF THE NCNLINEAR DYN?.MIC DISPLAN.'T ANALYSIS 3.2.1 Description of the Model The Licenses performed seismic displacement analyses of the free-standing
~
fuel rack modules with the use of the Westinghouse Electric Computer Analysis (WTAN) Code [1]. The analysis was performed as a time-history analysis using the thrse-dimensional r.athematical codel shown in Figures 3 and 5, with simultaneous application of three orthogonal, independent, acceleration time-histories (two horizontal and one vertical).
The effective structural preperties of the single cell nodel shown in 3
Figure 3 were modeled by thrse-dimensional beam elements and were derived frem F
linear three-dimensional analysis of the fuel rack to which the hydrod/namic mass of the water wa.s added. The fuel assembly, modeled by beam elements and represented in Figure 3 by the heavy vertical line, was cov.ected to the cell walls through springs, dampers, gap elements, and hydredyr.anic mass of the water in the cell. This model enabled the simulation of fuel assembly motien in the clearance space between the fuel assembly and the rack cell walls, as well as impact with the cell walls.
F Hydrodynamic mass coupling of the rack module to adjacent rack modules g
and to the_ spent fuel pool walls is shown in Figures 3 and 5, and is discussed in Section 3.2.3.
L The Licensee provided the following description of the modeling of support pads (1):
i
- g l
k r
1 Y
TER-C5506-585 I-sw n
s W
s,s v~
i n.
1 xx s
s m
, s..: s, s -
.s s
s, s
s s
s - ~- '
4 s
a g
a e
u F4 L'
- s--
e.._. ---_s---
s,.
s....:
j,.
'M 4D
- ~
1 pq g
g is
~ %:
v.
N
.s
!i %
q g
1:.: s L.,u..
..-<2 m.
_w%
i *i r,w.
y-.
is r: ~ :
-a s, my :
- ..,,---i=-
srt.
i t_
,e-
,-- w
'd
'a
'a t-y u
e 6
r L
e Figure 4.
Structural Model (Quarter Rack) m 6
s TER-C5506-585 HYOR00VNault W A$$
#C" CELL A55EW8LY FUEL ASSEMBLY I
@N lf 3:
/
,//
NYORODYNAMIC g,
[u.,,
MASS. FUEL a
L Dh
[
7,5
},
/
a
/
-u2
/
FUEL-TO-CELL GAP ELEMENT
/M.
/
-s X
~
J v2 y
w SUPPORT PAD
/*[4-h l/
\\
/
ELEMENT
/ o
,\\
,4 EvJ
/
1
/
XV
- " : xf J
j m
y-D
/
/
muu/uuuu///////
y
,1.. 5.
... 1_.,,,.... 1 _., _ 1._11 _. s.,
- i. ~.1
~
t l
i I
l TER-C5506-5 85 I
"The support pads are modeled by a combinatien of three-dia.ecsional dynamic friction elements connected by a " rigid" base beat arrangement which produces the spacing of support pads. The cell and fuel assemblies are located in the center of the base beam assembly and for:n a model which represents the rocking and sliding characteristics of a rack module f
in both directions on a plane. Vertical grounded springs at the st.pport i
pad locations are used to model and account for the interaction betveen ths racks and the spent fuel poc1 structure. The friction elements are capable of reversing the direction of the restraining force whan sliding changes direction."
Structural damping used in the analysis, with the exception of da:rping unique to fuel assembly impact, was 2% for the CBE event and 5% for SSE.
Added damping due to submergence in the pool water was not consadered.
Camping of the impact between the lirnher fuel assembliss and the walls of f
the storage cells requires consideration beyond that of usual structural damping.
In response to a request for additional information, the Licensee provided the following (3):
" Impact damping between the fuel assenbly and the rack cell war incin;!sd in the analysis. A riamping ratio of 0.04 was used for both the top and
~
botton fittings of the fuel assembly and is a conservative value for iepact damping of rigid structures since higher damping ratios are used in the seismic analysis for the reactor vessel and piping supports.
for the intectediate fuel grid assemolies a damping ratio cf 0.25 was used. The grid assembly is a flexible structure with frictional connections at the fuel rods which prodccen large impact damping values.
o J
A review of GE fuel inf ormation by the Westir.ghouse Nuclear Puol Division has deter:nined that a grid assembly damping ratio of 0.25 is appropriate.
[
This damping value is consistent with the g::id danping ratio that has L
been determined for WestinghouJe fuel DY tastS perforT.ed by the Westing-house Nuclear Fuel Division usir.g di fuel assenbly in air intacting on a rigid surface."
The Licensee's codeling of the rack codu.les trd use of fuel asseztly ze.pa::t damping is acceptable.
3.2.2 Frictional Force Between Rack Supp rt_P.sde_and the Pool Liner The Licensee used a maxirrum valua of 0.8 and a.sinimun value of 0.2 for the range of static friction coefficient batween the rack suppcrt pads and the pool liner (1]. Rsbinowicz, in a report to the General Electric Company (4),
focused attention on the mean and the lowest craffacient of friction to be i
(
TER-C5506-585 s
w used in these circumstances. While Rabinowicz supported the range of static n.
coefficient used by the C.icensee, he also indicated that the dynamic, or
~
sliding, coefficient of friction is inversely proportional to velocity.
The Licensee did not indicate whether the acalysis used an initial static coefficient of friction and a lower dyramic coefficient of friction once
-~
sliding motion began, While the use of a lower dynamic coefficient of
^*
friction may have yielded somewhat larger sliding displacements, the Licensee's computed sliding displacement was sufficiently small to dismiss further consideration of dynamic coefficients of friction. Thus, the j
Licer.see's use of friction coefficient between the suppert pads and the pool liner is acceptable.
3.2.3 Hydrodynamic Coupling Between Fluid and Cell Structure Hydrodynamic coupling acts between adjacent rack modules, between a rack module and the pool walls, and between fuel assemblies and the cells in which they are inserted.
Hydrodynamic coupling can have a significant effect upon the dynamic response of a rack module during seismic events.
In response to a request for additional information, the Licensee indi-
~
cated that the motion of adjacent racks may be out of phase or unrelated [3],
This assumption led to consideration of the motion of an individual cell surrounded on all four sides by rigid boundaries which are separated f rom the cell by equivalent gaps. The hydrodynamic coupling mass between the rack snodule and the pool wall, as shown in Figure 3, was calculated by evaluating the effects of the gap between the modules and the pool wall using the method outlined in the paper by Fritz (51 Fritz's (5) method for hydrodynamic, coupling is widely used and provides an estimate of the mass of fluid participating in the vibration of innersed mass-elastic systems.
Fritz's method has been validated by excellent agree-ment with esperimental results (5] when employed within the conditions upon which it was based, that of vibratory displacements which are very small com-pared to the dimensions of the fluid cavity. Application of Fritz's method for the evaluation of hydrodynamic coupling effects between rack modules and a pool wall has been considered by this review to serve as an approximation of 15*.
i
l TER-C5506-5t9 f,
the sctual hydrodynamic coupling forces. This is because the geometry of a fuel rack module in its clearance space is considerably different than that upon which Fritz's method was developed and expermentally verafied.
e Thus, the limitations of Fritz's [5] modeling techn;que for hydrodynamic coupling of rack modules adjacent to other rack modules or a pool wall indi-cate that the Licensee's fuel rack dynamic modal should be considered conser-vative only for dyna.nic displacements that are small relative to the available displacement clearance.
3.2.4 Seisnic Loading The Licensee indicated that the earthquake loading was predicated upon an operating basis earthquake (CBE) at the site having a horizontal ground accel-eration of 0.05 g, and that a safe uhutdown earthquaxe (SSE) with a horizontal ground acceleration of 0.12 g was used to che::k the design to assure no loss f.
of function [1]. The Licensee indicated further that these CBE and SSE desig-nations correspond to FSAR designations of design earthquake (DE) and maximum credible earthquake (MCE), respectively [1].
l l
In response to a request for additional infornation, the Licensee described the procedure used to determine the two orthogonal horizental and one vertical simulated earthquake acceleration time-histories as fo11cus (3):
" Simulated earthquake acenleration time histories in two orthogonal l
horizontal directions were generated f rom the Reactor Building seismic response spectra at the spent fuel pool floor evaluation using tha SIMQKE* computer program. The results were evaluated to ensure that statistical independence was achieved and that the resulting respcose spectra adequately enveloped the origar.41 Reactor Buildtng floor responce
[
spectra.
The two horizontal acceleration time histories are ger. orated from a' single seismic floor response spectra which represented the worst case for the structure. Therefore, seismic analyses of the fuel racks are conservatively based on the worst case horizontal seismic loading applied l
in both horizontal directions simultaneously."
l
- SIMQKE, A program for Artificial Motion Generation, User's Manual and Documentation, Department of Civil Engineering, Massachusetts Institute of Technology, November 1976.
(
{
TER-C506-58 5 I
The Licensee has stated further that one of the two orthogonal, hori-zontal, acceleration time-histories was directed across the short dimension of the rack module in the analynic of the 9 x 14 cell rack module (61 F
Evaluation indicated that the Licensee's develcgtent and application of simulated acceleration time-histories is ac.csptable.
I I
3.2.3 Intecration Time Step The Licar.see perforned a time step study in an effort to find the correct integration time stap to yield a converged solution (3].
Solutions using d4fferent time steps shcwed that the recults were the same for time increments j'
of 0.0025 see and 0.00125 sec. The Licanses then performed the final analysis j
using a time step of 0.QO25 sec.
3.2.6 Raek Displacements Tha Licensee's anslysis irdicated that the maxirrum sliding displacement l
1 occurred with the mininum friction coefficient of 0.2, whereas the casieue rock displacement at the top of the rack due to berding and tipping occurred l
with the mezimum friction coefficient of 0.8 (3].
7 The Licensee also noted that the maximua rack module displace:.ents occurred for full racks and that the displacement of the 9 x 14 cell rack p'
L module in the 9-cell directicn was the largest (3]. These largest displacements are presented in Table 2.
Maximum liftoff of a support pad from the pool liner was reported by the Licensee to be 0.0129 inch under the SSE event, and to occur on ene 9 x 14 cell rack in the 9-cell direction (3].
The mazinum computed displacements due to sliding, elastic defor1 ration, and tipping are shown in Table 2, which provides the data supplied with the Licensee's response (3) to a request for additional infornstion.
It is noted in Table 2 that each occurrence of sliding is relatively small with the sum of five CBE occurrences amounting to 0.049 inch.
[
l l
v TER-C5506-985 f
Table 2.
Rack Displacertents:
SSE Seismic + Maxirrum Normal Thermal r.
SSE Seismic
+ Normal Thermal f.
Displacements Rack Rack Symbol Units Top Base a
in 0.049 0.049 Max. Sliding Distance. 4 = 0.2 s
Os = (0.0098)S*
Max. Structural Defl., M s 0.8 6
in 0.647 0.0 Total Displacement One Rack f
a aOs+6 4
in 0.696 0.049 SRSS Combined Displacement 2 Racks I.
with Only 1 Sliding mx*
O I
a2. 62 O
in 0.950 0.049 ux Max. Normal Thermal Displacernent ST in 0.0P7 0.087 Max. Combined Thermal & Seismic Dis a
in 1.037 0.136 a. placements
[
6,. amax 0
in 1.68 1.03 Nominal Rack to Rack Cap
- 7his accounts for five ODE events.
f
[
[
[
[
TER-C5506-585 y
Maximum structural deflection at the top of the rack was reported to be 0.647 inch which, when combined with accumulated sliding, yielded 0.696 inch
~
(3]. For the case of adjacent dissimilar rack modules whose responses may be
[
out of phase, the Licensee combined the displacement of the two rack modules
~
by the square root of the sum of the squares to yield a combined displacement T
of 0.950 inch. After including the nazimum normal thermal growth, the Licensee compared the maximum combined' displacement of 1.037 inches to the installed clearance of 1.68 inches between racks (shown in Table 2).
With the combined 7
displacement of the two adjacent rack modules less than the available clearance space, the Licensee indicated that impact of the racks would not occur and that impact analysis of the rack modules is not necessary.
While the use of the square root of the sum of the squares is a reasonable approach to combining out-of-phase displacements of adjacent rack modules for k
comparison to the available clearance space, the worst possinle case is that of direct summation of the rack's displacement. This worst case would represent the point in time when the responses are 180 degrees out'of phase.
Thus, using the Licensee's displacement data as shown in Table 2, it can be P
seen that even the direct sum of two total displacements is less than the b
clearance space of 1.68 inches.
Note that the clearance space between the rack modules and pool structure, as shown by the boxed dimensions in Figures 1 and 2, is much larger.
The evaluation of the Licensee's computed maximum displacements and their comparison with the installed clearance space indicated that they are acceptable, and that rack module impacts with other rack modules and the pool structure is unlikely.
3.3 EVALUATION OF THE DETAILED THREE-DIMENSIONAL LINEAR MODEL 3.3.1 Description of the Model l
The Licensee used a finite element model of the rack module to determine the stresses in the module. The Licensee's description of the procedure follows [1]:
"The structural model, shown in (Figure 4), is a quarter section repre-sentation of the rack assembly consisting of be'am elements interconnected at a finite number of nodal points and general mass matrix elements.
The
. t
l
{
TER-C5506-585 f
beam elements model the beam action of the cell, the stiffening effect of the cell to cell welds, and the supporting effect of the support pads.
l The general mass matrix elements represent the hydrodynamic mass of the rack module. The beams which represent the cells are loaded with equiva-lent seismic loads and the model produces the structural displacements and internal load distributions necessary to calculate the effective structural properties of an average cell within the rack module.
In addition to the stiffness properties, the internal load and stress
[
distributions of this model are used to calculate stress peaking factors L
to account for the load gradients within the rack module."
The results of the seismic displacement analyses were searched throughout the full analysis time to obtain the maximum response forces. These maximum f
values were then adjusted by peaking factors from the structural model to account for stress grad 2ents through the rack module [1].
I.-
Load combinations and acceptance stress limits used in the Licensee's l
stress analysis were in accordance with the NRC's OT Position Paper (2] and are shown in Table 3.
The Licensee's computed stresses, allowable stresses,
~
and safety margins are shown in Table 4 (1). Note that the safety margins,
~
computed in accordance with the folicwing formula, are all greater than zero, thereby indicating acceptable conditions:
Safety Margin = ^ Design Stress
- -1 ft 3.3.2 Review of Stress Levels Evaluation of the rack module stresses indicated that the analysis, level of stresses, and acceptability criteria are satisfactory.
3.4 REVIEW OF SPENT FUEL POOL STRUCTURAL ANALYSIS P
3.4.1 Spent Fuel Pool Structural Analysis a
The spent fuel pool (SFP) structure was analyzed using linear and P
nonlinear finite element models to determine the maximum allowable fuel rack loads that could be imposed on the pool slab.
r w
T L
P' g
m TER-C5506-585 f
Table 3.
Storage Rack Loads and Load Combinations l
Load Combination Acceptance Limit D+L Nortnal limits of NF 3231.la D+L+Pg Normal limits of NF 3231.la r
D+L+E Normal limits of NF 3231.la D+L+T Lesser of 2Sy or S o
u stress range D + L + To + E Lesser of 2S or S stress range y
u D + L + Ta + E Lesser of 2Sy or Su stress range D+L+To + Pg Lesser of 2S or Su stress range y
D + L + Ta + E' Faulted condition limits of NF 3231.lc (See Note 3)
The functional capability of the fuel D+L+Fd racks shall be demonstrated Notes:
1.
The abbreviations in the table above are those used in Standard Review Plan (SRP) Section 3.8.4 where each term is defined except for T
- a which is defined here as the highest temperature associated with the postulated abnormal design conditions.
Fd is the force caused by the accidental drop of the heaviest load from the maximum possible height, and Pg is the upward force on the racks caused by a postulated stuck fuel assembly.
2.
The provisions of NP-3231.1 of ASME Section III, Division I, shall be amended by the requirements of Paragraphs c.2, 3, and 4 of Regulatory a
Guido 1.124, entitled " Design Limits and Load Combinations For Class A r.
Linear-Type Component Supports."
3.
For the faulted load ceabination, thermal loads were neglected when they are secondary and self-limiting in nature and the material is ductile.
f L
9 E
re i
L TER-C5506-585 1
Table 4. Sumary of Design Stresses and Minimum Margins of Safety Normal and Upset Conditions
\\
Design Allowable Margin Stress Stress of (psi)
(ps0 Safety 1.
Support Pad Assembly 1.1 Support Pad 7
Shear 1595 11000 5.90 Axial and Bending 10479 16500
.57 r'
Bearing 13645 27500*
1.02 1.2 Support Pad Screw 3
Shear 7958 11000
.38 1.3 Support Structure Axial and Bending 17626 27500*
.56
?
Shear Ic.13 11000 7.92 Weld Shear 19072 275000*
44 2.0 Cell Assembly r-2.1 Cell m
Axial and Bending
.816 1.0**
.23 2.2 Cell to Base Plate Weld F
Weld Shear 19082 24000
.26 4
2.3 Cell to Cell Weld o
Weld Shear 16286 21000
.29 Pin Shear 7384 9260
.25
)
l 2.4 Cell to Wrapper Weld Weld Shear 8300 11000
.33 2.5 Cell Seam Weld i
Weld Shear 3501 4516***
.29 2.6 Cell to Cover Plate Welds Weld Shear 11854 24000 1.03 l
Thermal Plus OBE Stress is Limiting Allowable per Appendix XVII -2215 Eq (24)
Design Load and Allowable Loa 3 in Lbs is sho-n 0 -_.
TER-C5506-5BS f
i Loading combinations required by USNRC Regulatory Guide 1.142, USNRC Standard Review Plan 3.8.4, the American Concrete Institute, and the American I
Institute of Steel Construction were satisfied. These were consolidated into n
the set of load combination requirements shown in Table 5, and were satisfied I
using strength design methods for the concrete structures and plastic design methods for structural steel (1).
Thermal loads were based on pool water temperatures of 150*F resulting
+
from a full core discharge under normal operating conditions, and saturation
[
temperatures for accident' conditions varying from 250*F at the bottom of the pool to 212*F at the free water surface. A conservative ambient air tempera-ture of 68'F was used. A stress free-temperature of 70*F was assumed.
p b
3.4.2 Analysis Procedures
?
3.4.2.1 Method of Analysis f
The Licensee employed the MSC/NASTRAN general purpose finite element program to investigate the spent fuel pool structure, using a three-dimensional finite model that included the entire spent fuel pool structure as l
well as adjacent key structural members. The model is shown in Figure 6.
The Licensee provided the following additional features of the model (1):
l
" Floor slabs and walls immediately adjacent to the SFP are modeled to simulate the proper lateral restraint on the pool structure. Complete fixity against translation and rotation is assumed at the base of the drywell shield wall. Cut-off boundaries of adjoining walls and slabs were restrained with translational springs. These springs permit the model to simulate the cantilever mode deflected shape of the Reactor Building under horizontal seismic loading. Tra alational springs simu-late lateral stiffness of the remainder of the Jeactor Building walls which were not included in the model.
In-plane r tations of all interior grid points on slabs and walls are restrained."
The overall model was estimated to contain 11,000 independent degrees of freedom (1).
While this was a linear mathematical model, the Licensee applied the external loads in increments to perform a piecewise linear solution to the I
nonlinear problem of cracking in the concrete under tensile stresses.
Checking of the computed stresses aq11nst the concrete cracking criterion and
- I
TER-C5506-585 Table 5.
Spent Fuel Pool Governing Design Load Combinations I,
Reinforced Concrete 1.
U = 1.40 + 1.4F + 1.7To 2.
U = 1.4D + 1.4F 3.
U = 1.40 + 1.4F + 1.7L + 1.9E 4.
U = D + F + L + E' + Ta
'5.
U = 0 + F + L + E' U = 1.05D + 1.05F + 1.3L + 1.43E + 1.3To 6.
Structural Steel 7.
Y = 1.7D + 1.7F + 1.7L + 1.7E 8.
Y = 1.30 + 1.3F + 1.3L + 1.3E + 1.3To 9.
Y = 1.1 (D + F + L + E' + Ta)
Notation:
D = dead load
~
E = OBE (design earthquake)
E'= SSE (maximum credible earthquake)
L = live load J
Ta= thermal load produced by accident condition To= thermal load during normal operation U = section strength required to design loads based on the Strength Design e
method for reinforced concrete Y = section strength required to resist design loads based on Plastic Design method for structural steel u
?
L P
L e
k e
L _-
TER-C3506-585 i
i i
i 4
i i
i L
1
! ll
~
i g,
l!l!:;t!!m! sit
%p!!!!
'ij.liin ill
!If
[
iii19 S!t e
{
l;!
11
=
P 5
l-
[.
C=
C T
Nr.A A A A A A J.t.t..~./
E
[
5
\\\\\\\\ M'//-
E
\\ \\ \\ \\ \\ \\ \\ /.'
E
///!//
I/,
y
\\
=
e
//// /if f
/\\ \\ \\ \\ \\ \\ y, C
E
.\\\\\\\\
C
\\ \\ \\ \\ \\'\\-
e O
.t n
\\\\\\\\\\\\
r jy
'\\-\\ \\ \\X \\ \\
.j s
[
////
- t
s
/\\ \\' \\ \\
e
////
/
[
3
/// /.
777y j :\\-\\ \\ \\
~
\\
/
\\ s4.\\
3 xsxin
'l
\\ \\ \\ \\ N' '. / - l. /
r,,'-
~
.f.f !f y
f
- j. p y
['
r
/ /
, /./
17 y-
\\ \\
\\.
t\\/ / / / /
o l l / 'N O
~
'/, l-
\\
\\
.. \\/ //
i-7 y
5 3
g
. c h d, I. ~,7.4-h i
[-
r
[
W\\, ff - d
/
i
~
- - ~ ~
\\
"\\
-(.-
syy j
o
~\\\\ '\\
s\\\\\\\\
/
A.I'stit
/t
\\/\\/1 *.
enum l
S l
1
=
t l
l
[
j
s TER-C9506-585 the adjustment of material properties to reflect crack development was 6
f reported to have been performed manually at the end of each iteration. Thus, f
each new iteration was begun using the accumulated load that included the new load increment as well as stiffness properties reflecting crack development to that point.
f Cracking criteria were applied primarily to the elements comprising the p
pool slab and lower portions of the pool walls. Application of the cracking p
criteria was carried out by comparing the local orthogonal tensile stresses against the modulus of rupture and adjusting the respective elastic modulus to reflect crack development.
F The critical section for slab shear and bending was taken at the face of j
b the walls in accordance with ACI Code provisions. The critical section in the l
tall was taken on the horizontal plane at the top of the slab elevation [1].
l r
6 Shear capacities of the steel beams and connections were determined in accordance with Part 2 of the AISC specifications for plastic design, y,
t N
With respect to thermal moment relaxation of local areas away from the pool slab, the approach used for the investigation was, in accordance with ACI f
349 Appendix A, to assume the structure is uncracked for siechanical loads and g
cracked for thermal loads.
F 3.4.2.1 Supporting Analysis I
In addition to the piecewise linear analysis described above, the Licensee performed a nonlinear finite element analysis of 2 simplified pool i
slab structure to provide an estimate of the pool slabs' ultimate load 5
carrying capacity. The pool slab was modeled using the ADINA finito element d
program by which it was possible to compute the collapse load of the slab considering the beneficial effects of arching (1].
The Licensee reported that the nonlinear analysis indicated no reinforcement yielding and very little concrete cracking at the design load.
The Licensee halted the nonlinear analysis when the applied load aporoached three times the factored design load. At this point, the analysis indicated that sees cracking at supports and at midspan would occur, that the top bar at supports would yield, but that collapse was not imuninent (1).
TER-C5506-58 5 f
3.4.3 Results of the Analvsis The Licensee reported the following (1]:
l I
o
" Reduced transverse shear capacity was used in the pool slab to reflect the small amount of membrane tension generated by the lateral fluid pressure on the pool walls. This shear capacity was compared against peak transverse shear forces from the MSC/NASTRAN finite element analysis results and is adequate."
o "The load transfer capacity of the wall / slab joints on the East and West sides of the pool were evaluated and found to be adequate."
o
" Additional shear stresses due to increased spent fuel storage 2
2
~
capacity are calculated to be 0.0020 kip /in and 0.0032 kip /in at EL. 180'-0" for OBE and SSE respectively. These shear stress increments are based on the MSC/NASTRAN finite element analysis results. These increments represent increases in total shear P
~
stresses from 89 percent to 92 percent of the allowable for OBE and from 69 percent to 70 percent.for SSE.
The resulting total concrete shear stresses are less than the allowable shear stresses."
r o
" Local areas of the North exterior wall of the Reactor Building were also evaluated due to the increased loads.
The areas checked are the support points of the East and West walls of SFP. These areas are adequate for combined axial load and bending.
Shear forces are also less than the shear capacity."
n The Licensee's maximum allowable fuel rack / pool floor interface loads and stresses are reproduced in Table 6.
The Licensee's comparison of the pool floor interface loads and stresses with allowable values is shown it. Table 7.
I Evaluation of the spent fuel pool analysis indicated that the analysis is satisfactory and that the spent fuel pool structure is adequate for the increased density,of fuel storage.
r a
3.5 FUEL HANDLING ACCIDDJT ANALYSIS 3.5.1 Fuel Handing Crane Uplift The Licensee provided the following with respect to crane uplift of a fuel assembly [1):
"The objective of this analysis is to ensure that the rack can withstand the maximum uplift load of 4,000 pounds and a horizontal force of 1,000 pounds of the fuel handling crane without violating the critically acceptance criterion.
The maximum uplift load is approximately two times a
W L l l
s TER-C5506-585 Table 6.
Maximum Allowable Fuel Rack / Pool Floor Interface Loads TOTAL L0t.DS VERTICAL HORIZONIAL LOCAL BEARING LOAD COMEINATION (XIP)
(KIP)
(KST) 1.
D+L 3,900.01 N/A 2.4
(
2.
D+L+To 3,900.01 N/A 2.4 3.
D + L + To + E 5,700.0 1,900.0 2.4 4.
D + L + Ta + E 5,700.0 1,900.0 2.4 5.
D + L + To + Pf 5,700.0 -
N/A 3.2 6.
D + L + Ta + E' 8,000.0 3,000.0 3.2 7.
D+L+Fd 8,000.0 N/A 4.76 Alternatel 8.
1.4 (D + L + To)
+ 1.9E 8,900.0 3,600.0 See Note 2 9.
1.4 (D + L + Ta)
+ 1.9E 8,900.0 3,600.0 See Note 2 10.
1.7 (D + L + To
+ E) 9,700.0 3.200.0 See Note 2 11.
1.7 (D + L + Ta
+ E) 9,700.0 3.200.0 See Note 2 i
Notes:
1.
Additional structural limits specified in load Combination No. 8, 9, 10, and 11 shall be satisfied if total vertical loads calculated for Load Combination No. I and 2 are less than 3,700.0 kip. Otherwise, Load Combination No. 8, 9, 10, and 11 may be used in lieu of Load Combination No. 1, 2, 3, 4, and 5.
2.
When total loads are evaluated using load Combination No. 8, 9,10, and 11, local bearing pressures shall satisfy Load Combination No. 1, 2, 3 4, and 5.
3.
Notations used in this table are the same as defined in SRP 3.8.4, Appendix D. - - -
v TER-C5506-585 w
Table 7.
Pool Floor Loads f
Design Allowable Ma gin Stress Stress of Lead Combination Condition
- or Load or Load Sa'ety 1.
D+L Local Bearing 1.76 2.4
.36 2.
D + L + To Local Bearing 1.76 2.4
.36 3.
D + L + To + E Local Bearing 1.94 2.4
.24 4.
D + L + Ta + E Local Bearing 1.94 2.4
.24 5.
D + L + To + Pf Local Bearing 1.76 3.2
.82 6.
D + L + Ta + E' Vertical 6180 8000
.29 Horizontal 1670 3000
.80 Local Bearing 2.63 3.2
.22 7.
D + L + Fd Vertical 4130 8000
.94
[,
Local Bearing 4.39 4.76
.05 8.
1.4(D + L + To) + 1.9E Vertical 7730 8900
.15 Horizontal 1590 3600 1.25 9.
1.4(D + L + Ta) + 1.9E Vertical 7730 8900
.15 r
Horizontal 1590 3600 1.25
- 10. 1.7(D + L + To + E)
Vertical 8760 9700
.11 Horizontal 1420 3200 1.25
- 11. 1.7(D + L + Ta + E)
Vertical 8760 9700
.11 w
Horizontal 1420 3200 1.25 b
r
- Vertical refers to total pool floor vertical load in kips.
Horizontal refers to total pcol floor horizontal load in kips.
Local bearing refe-s to pool floor bearing stress under the highest loaded support pad in ksi.
r L
w
TER-C5506-585 the capacity of the fuel handling crane.
In this analysis the loads are assumed to be applied to a fuel cell. Resulting stresses are within acceptable stress limits, and there is no change in rack geometry of a
[
magnitude which causes the criticality acceptance criterion to be I
violated."
3.5.2 Accidental Fuel Assembly Drop The Licenses provided the following {1]:
"Three accident conditions are postulated. The first accident condition assumes that the weight of a ft.el assembly and handling tool impacts the top and fitting of a stored fuel assembly or the top of a storage cell from a conservative drop height of 2 feet in a straight attitude. The second accident condition is similar to the first except the impacting mass is at an inclined attitude. The impact energy is absorbed by the dropped fuel assembly, the stored fuel assembly, the cells and the rack base plate assembly. UnJ these faulted conditions the criticality acceptance criterion is i"; violated and the pool liner is not perforated. The third acc.ient condition a.2sumes that the dropped assembly falls straight through any empty cell and impacts the rack base plate from a conservative drop height of 2 feet above the top of the rack. The results of this analysis show that the impact eTergy is abaorbed by the fuel assembly and the rack base pla *.e.
.ae spent fuel
~
pool liner is not perforated. Criticality calculat; w show the k,ff <0.95 and the criticality acceptance criterion is not violated.
In each of these accident conditions, the criticality acceptance criterion is not violated and the spent fuel pool liner is not perforated."
d 0
0 I
e we r
a P'
L F
w w
P i
e s
TER-C5506-585 4.
CONCLUSIONS I
Based upon the review and evaluation, the following conclusions were reached:
o The Licensee used three-dimensional, nonlinear dynamic displacement analyses with three simultaneous, independent, orthogonal, earthquake acceleration time histories to provide greater resolution of the rack module displacements than is possible with two-dimensional analyses combined by the square root of the sum of the squares method.
o The limitations of the modeling technique employed for hydrodynamic coupling of fuel assemblies within a fuel rack cell and of fuel rack modules to other rack modules and the pool walls indicate that the modeling technique contributes experimentally verified results only for displacements which are small compared with the available
~
clearance space. While the Licensee's reported rack module displacements are not small relative to the clearance space, the techniques used are acceptable in association with the conservative assumptions employed.
o The spent fuel pool structure has design margin to sustain the higher density floor 16adings.
P'4 ms W
4 2
I s
pm P
bh a
no hum T
L 1
' g
t TER-C5506-585 5.
REFERENCES Philadelphia Electric Company Safsty Analysis Report for Design and Installation of New High Density 1.
Spent Fuel Racks, July 1985 Or Position for Review and Acceptance of Spent Fuel Storage and Handling 2.
Applications, U.S. Nuclear Regulatory Commission January 18, 1979 Philadelphia Electric Company Response to a Request for Additional Information, October 9, 1985 3.
o E. Rabinowicz
" Friction Coefficient Value for a High-Density Fuel Storage System" 4.
Report to General Electric Nuclear Energy Programs Division November 23, 1978 R. J. Fritz "The Effect of Liquids on the Dynamic Motions of Imersed Solids" 5.
Journal of Engineering for Industry pp. 167-173, February 1972 Philadelphia Electric Company (Shields L. Daltroff), Letter to U.S.
Nuclear Regulatory Cornission (Daniel R. Muller), Dated Decerter 26, 6.
1985, Submitting Added Response to a Request for Additional Information e
VE w
t
.l 1
E I;
.. n}
j
.