ML20005B818
| ML20005B818 | |
| Person / Time | |
|---|---|
| Site: | Fermi  |
| Issue date: | 08/31/1981 |
| From: | Soler A JOSEPH OAT CORP. |
| To: | |
| Shared Package | |
| ML20005B796 | List: |
| References | |
| TM-614, NUDOCS 8109020305 | |
| Download: ML20005B818 (48) | |
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.e ES T ABLGit 01780 JOSEPH OAT CORPOR ATION CHEMIC AL ENGINEERS & F ABRIC ATORS EVALUATION OF FERMI-2 IIIGli DENSITY RACKS for
.TIIE GITE SPECIFIC EARTIfQUAKE by Dr. Alan I. Soler JOSEPII OAT CORPORATION OAT J67025/J#2437' REPORT #TM-614 8109020305 810831 PDR ADOCK 05000341 A PDR 2500 Broadway / Drawer 1 O / Carnden. Nova Jersey 08104 / 1G001 G41 2000
A
- Introduction The Fermi high density racks, designed and fabricated by Joseph Oat Corporation, were initially analyzed for three coincident pool floor accelerations.
These statistically indeponedent time histories were generated by Stone and Webster Corporation and were intended to be used as the input motion corres-1 J ponding to plant faulted condition. IIeretofore, we will refer to them as the I
Design Basis Earthquake (DBE). A large number of seismic analysis runs were
,made for the DBE condition. Sensitivity studies on percentage structural damping, fluid damping, etc. , were performed. It was found that the stresses and displacements in the rack (all size modules) for the most conservative set of parameters (zero structural damping, no fluid damping, etc.) satisfy the stipulated limits with wide margin of safety. These results are reported in detail in Oat's Seismic Analysis report (Report #.M bIk Joseph Oat ,
Corporation, 1981).
j Recently, Detroit Edison Company asked Oat to assess the effect of a new set of seismic time history accelerations which are referred to as " Site
. Specific Earthquake." The time history data for this case was prepared by Sargent and Lundy, Engineers. The scismic analysis was performed by Oat using the same structural model used for analyzing DBE conditions mentioned above.
The value of structural damping is fixed at 5% of critical. In what follows, a brief description of the modules is given for the sake of continuity of presentation. Only abstracted results are presented here. A moro detailed output for all cases analyzed is given in the appendix.
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DOCUMENT TITLE:
EVA LU ATIOtd oF FE RmT- 2 M& H TsE N itTY R Mks FOR
~Bi E s t T F. SPEC I FI C EARTHQOOkC d-701 REPORT NO. T tG ti GI 4- _; DOCUMENT CLASS:[2] B THIS DOCUMENT CONFORMS 10 THE REQUIFO!ENT OF T!!E DESIGN SPECIFICATION AND Ti!E APPLICABLE SECTIONS OF *11fE COVERNING CODES.
. SEAL oonnro, f .** f'*,,
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PROFESSIONAL ENGINEER l'$i tuc;Nttn $55
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. APPROVALS (Signatures & Dates) 1 ORIGINAL '
ISSUE REV. 1 REV. 2 REV. 3 REV. 4 REV. 5 DATE 7-lf-SI.
AUT110R bw A L. A ra gg g3L REVIEWER (Method of jW( -
Review) [4] I~
CERTIFIER M t.d Tk REI. EASED BY -
, PROJECT ENG.
] NOTES:
[1] For all Class A documents customer has to respund in writing that all requirements of his design specification pertaining to the intent of this report has been satisfied.
[2] C3nss A: For review and written approval by customer. B: For submittal to
, customer, Information only, C: Internal document; not to be submitted to customer.
l [3] This document is proprietary to Oat. Its confidentiality must be observed i
by the designated recipient.
[4] Code as follows:
- 1. Reviewed method of analysis only *
- 2. Reviewed met hod of analysis and numerical computations .
- 3. Verified by alternate calculation method.
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- 2. General Arrangement
- he high density spent fuel storage for Fermi II station provides for a
. total of 2305 storage locations arranged in 14 modoles. Thirteen of these modules each contain 169 storage- cells. The fourteenth module (labeled B-1 in Figure 2.1) has 108 cells. All the modules (also hereafter reforred to as storage racks) are free standing; i.e. they are not enchored to the pool floor or connected to the pool' wall through snubbers or lateral restraints. The gap between adjacent racks is at least 3.625" at all locations. Sufficient gap
. is also maintained between the mcidules and the pool walls. The minimum' gap
.between the fuel pool wall and rack modules is l' 11-3/4" (ref. Fig. 2.1) .
Adequate clearance from other pool resident hardware is also provided. In this manner, the possibility " inter-rack impact, or rack collision with other pool hardware during the postulated ground motion events is precluded.
In addition to the spent fuel storage locations, a rack for storing defective fuel storage containers, control rods, control rod guides is also provided. It containc 31 storage ?rcations for defective fuel storage containers / control rods, and 4 locations for control rod guide tubes. It is labeled as C-1 in Figu';e 2.1.
The reaxs are constructed from SA 240, Type 304, austenitic steel sheet
- materia?. JA 240, Type 104 austenitic steel plate material and SA 182, Type F 304 austenitic steel forging material.
j A typical module contains storage cells which have 6" minimum (+0.1~' *,
-0") internal cross-sectional openings. These cells are straight to within i
10.125". These dimensions ensure that fuel assemblies with maximum per.* ole
-out-of-straightness can be inserted into the storage cells wi:~out i "
ence.
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13 F I G. 2.1 RACK MODULES ARR ANGEMEN T @
- 3. Design Analysis and Results Summary
- a. There are three different rack geometries, labelled as rack types A,B,C. There are 13 modules of rack type A, and one each of types B and C.
Dimensional details are shown in Figures 3.1 - 3.4.
Each rack class was medelled as a thirty-two degree of freedom lumped mass, linear and non-linear spring model. The model permits three dimen-sional motions and is subjected to a time history analysis with load input being the simultaneous application of three directions of seismic .1ovement of the pool floor. Each directional input seismic motion used is statistically independent from the other two directions of motion. The 3-D model has been analyzed using two different sets of seismic inputs for the SSE seismic event.
- 1. Design Basic Earthquake (DBE) provided by Stone and Webster (4% structural damping)
- 2. _ Site Spccific Earthquake (5% structural damping)
Analyses for both sets of seismic inputs have been carried out for each rack type, assuming a variety of fuel load configurations within a rack module.
Coefficients of friction between rack base support and pool floor liner are taken as either .2 or .S. The results indicate that the higher ceefficient of friction value yielded tAe highest stresses in the rack and the largest rack displacements. Thir, is due to the increased potential for sticking of a single support leg whic h in turn causes coupling between both horizontal rack responses and initiation of twisting of the rack.
The rack design analyses have been carried out neglecting some parameters whose inclusion would significantly reduce both rack total displacement and stress levels. Hence, the results for stress and displacement quoted herein are conservative; significant parameters neglected in the analyses are
- listed below
i a. The structural ficxibility of the floor slate has been disregarded.
In our experience, inclusion of this flexibility would reduce thi stress levels by as much as 30%.
, b. The energy dissipation due to relative mction between fuel assemblies cnd the surrounding storage elements is er.tirely neglected. We have found that stress levels decrease by as much as 25% if only 10% of the fluid drag reported in the literature for comparable configurations is used.
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- c. Resalts Summary Consistent with ASME Section NF and the applicable USNRC Regulatory Guide 1.124, the following stress ratios are computed in critical parts of the rack and support structure.
R1 = average cross section tensile or compressive stress / S AD R2 = average cross section shear stress /S Ag R3=(maximumcrosssectionbendingstress R4 J in x or y direction)'SAB R5 = R1 + f R3 + f R4 x y R6 =(maximum cross section stress due to direct load and bending intwoplanesfSAC where Sg, S g, S g, SAC are code allowable stresses and f , f, are geometry parameters.
For structural integrity during a plant faulted condition, all of the stress ratios Rg (i = 1,2, . . 6) must remain below 2.0. Results are presented here for the following simulations:
Full Rack; COF = .2, .8; rack types A, B, or C Empty Rack;COF = .2, .8; rack types A, B, or C The following summary table lists the maximum value of a stress ratio governing the structural integrity of a particular component. The numerous simulations examined indicate that for each rack type, the critical stress (o'dition occurs for a full rack with coefficient of friction = 0.8.
Table 3.1 - Summary of Maximum Stress Patios Q.OM focioFS)
(Site Specific Earthquake, Safe Shutdown -
5% Structural Damping) l RACK TYPE ROOT OF RACK
- A .21 s
r B .177 C .982 TOP OF SUPPORT LEG A .933 B .713 C. 1.442*
- Allowable load factor = 2.0 1 i safe shutdown Table 3.1 (continued)
RACK TYPE BOTTOM OF SUPPORT LEG A .801 B .572 C 1.46*
- Allowable load fr.ctor = 2.0 for safe shutdown The maximum rack displacements obtained for the full or empty rack during a safe shutdown event using the site specific earthquake are summarized in Table 3.2 below:
Tabic 3.2 - Maximum Rack Displacemnt*
RACK TYPE CONDITION MAXIMUM DISPLACEMEITh (in.)
A Full .488 A Empty .508 B Full .536 B Empty ,
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l C Empty -
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- Allowable displacement = 1.875" for A a nd C racks;. B is isolated (maximum allowable displacement = 4.75")
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Additional simulations hav' been carried out using various rack fuel load geometries and in all cases, the stress ratios were lower than those reported here, and the displacements of the rack were such as to permit us to conclude that impact of adjacent racks will not occur, and that the racks will not tip even if the seismic input is increased by 50% above the safe shutdown cond. tion.
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I FI G. 3.4 H O R I Z O'N TA L. C R O S S SECTION
- f. DEFECTIVE FUEL STORAGE R ACK
APPENDIX A A. Details of Seismic Analysis APPENDIX A A. SEISMIC ANALYSIS A.1 Analysis Outline The spent fuel storage racks are seismic category I equipment. Thus in accordance with ref. (1) they are required to remain functional during and after an SSE (Safe Shutdown Earthquake). As noted previously, these racks are neither anchored to the poor floor,
<s-nor are they attached to the side walls. The individual rack modules are not interconnected. Furthermore, a particular rack may be completely loaded with fuel assemblies (which corresponds to greatest rack inertia), or it may be partially loaded so as to produce maximum geometric eccentricity in the structure. The coefficient of frictiun between the supports and pool floor is another indeterminate factor. According to Rabinos~cz (2),
the results of 199 tests performed show a mean value of p to be
.503 with a standard deviation of 0.125. The upper and lower bounds (p + 26) are thus 0.753 and .253, respectively. In this report, analyses are performed for each rack type with values of p equal to 0.2 (lower limit) , and 0.8, respectively. The following four separate analyses are performed for each rack type using the latest seismic acceleration data for the specified site.
- 1. Fully loaded rack (all storage locations occupied); p = 0.8
- 2. Fully loaded rack, p = 0.2
- 3. 10% loaded rack with no geometric asymmetry, p = 0.8
- 4. 10% loaded rack with no geometric asymmetry, p = 0.2 The method of analysis employed is the well known Time History I method. The ground acceleration in the vertical direction is the design basis SSE earthquake specified by Stone & Webster Engineering corporation. For use in this study, a magnification factor of 2 is applied to the Stone and Webster data. The ground acceleration data in the two horizontal directions are the site specific SSE data supplied by Sargent and Lundy (See Appendix C) .
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j The object of the time history seismic analysis is to determine i the structural response (stresses, deformation, rigid body motion, etc.) due to simultaneous application of the three orthogonal excitations. Thus, recourse to approximate statistical summation techniques such as SRSS method (Ref. 3) is avoided and the dependability of computed results is ensured. Because of the possibility of sliding racks, accuracy of results is assured only by employing the time history method of analysis.
i The seismic analysis is performed in four steps; namely, (i) Develop the non-linear dynamic model consisting of beam, gaps, spring, damper and inertia coupling elements.
(ii) Derive and compute element stiffnesses using a sophisticated clastostatic model.
(iii) Layout the equations of motion, decouple these equa-tions and solve them using the " component element time integration" procedure (Ref. 4). Determine nodal forces.
(iv) Compute the detailed stress field in rack structure using a detailed elastostatic model and applying the nodal forces calculated in Step iii above. Determine if the stress and displacement limits (given in Section A.5) ar'e satisfied.
In the iollowing sections, we present a brief description of the dynamic model.
i 1
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A.2 Fuel Rack - Fuel As*amnly Model .
A.2.1 Assumptions
- a. The fuel rack metal structure is represented by five lumped masses connected by appropriate clastic springs. (Refer to Fig. A'.l.) The spring rates simulate the elastic behavior of the fuel rack as a beam like structure.
- b. The fuel assemblies are represented by five lumped masses located, relative to the rack, in a manner which simulates either full or partially filled conditions.
- c. The fuel rack base is considered as a rigid body supported at four points.
- d. The rack base supports may slide or lift off the pool floor.
- e. The pool floor is assumed to have known time history ground acceleration in three orthogonal directions.
- f. Fluid ccupling between rack and assemblies, and between rack and adjacent racks is simulated by introducing appropriate inertial coupling into the system kinetic energy.
- g. Potential impacts between rack and assemblies are accounted for by appropriate spring gap connectors between masses involved.
- h. Fluid damping between rack and assemblies, and between rack and adjacent rack is sumulated by inclusion of appropriate equivalent linear damping *.
- i. The supports are modeled as rigid beams for dynamic analysis. The bottom of a support leg is attached
, to a frictional spring as described in Section A.2.2.
The elastic properties of the support beams are derived and used in the final computations to determine support leg stresses.
- j. The effect of sloshing is shown to be negligible and is hence neglected. It is to be noted that the tcp of the rack is over 20' below the free water surface.
- For conservative results, all fluid damping constants have been set equal to zero in the simulations described in 'his c report.
A . 2. 2 Model Description The absolute degrees of freedom associated with ca;h of the mass locations i, i* are as follows (Fig. A.1).
LOCATION DISPLACEMENT ROTATION U uz 0x Oy O.
(NOTE x uy z 1 P1 P2 P3 94 95 96 1* Point is assured fixed to base at XD,YB, Z=0 2 P7 Pg q11 q12 2* P P 8 10 3 P P 917 918 13 15 3* P y4
'16 4 P yg P 924 21 923 4* P 20 P
22 5 P E P 930 9 31 25 27 32 929 5* P P
, 26 28 Thus, there are 32 degrees of freedom in the system.
Note that clastic motion of the rack in extension is represented only by generalized coordinates p3 and p32 This is due to the relatively
. high axial rigidity of the rack. Torsional motion of the rack rela-tive to its base is governed by q31*
The members joining nodes 1 to 2, 2 to 3, etc., are beam elements with deflection due to bending and shear capabi}ity (Ref. 4, pp 156-161). The elements of the sti.finess matrix of these beam elements are readily computed if the effective flexure modulus, torsion mod-ulus, etc. for the rack structure are known. These coefficients follow from the elastostatic model as described later. The node points i* (i* = 1,2 .. 5) denote the cumulative mass for all the fuel assemblies distributed at 5 elevations. Referring to G.E.
specification (Ref. 5), the bending and torsional stiffnesses of the fuel assenEly (channeled or unchanneled) are several orders of mag-nitude smaller than the stiffeners of the rack beam elements. Hence, it is reasonable to neglect the spring elements joining these lumped
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masses. The nodes i* are located 7.t X = X3, Y = YB in the global coordinate system shown in Figure 4.1. The coordinates (XB' YB}
are determined by the center-of-mass of the set of fuel assemblies.
For a symmetrically loaded rack XB"YB = 0.
A .2. 3 Fluid Coupling .
An effect of some significance requiring careful modeling is the so-called " fluid coupling effect." If one body of mass my vibrates adjacent to another body (mass m3), and both bodies are submerged in a frictionless fluid medium, tiren the Newton's equation of motion for the two aobodies h.a.ve the form y) Xi-M12 X.2 = applied forces on mass my (my +,,My
-M 21 X1+ (m2 + M22) X2 = applied forces on mass M2 M11, M12' M21 and M22 are fluid coupling coefficients which depend on the shapes of the two bodies, their relative disposition; etc.
Fritz (6) gives data for M ij for various body shape and arrangements.
It is to be noted that the above equation indicates that effect of the fluid is to add certain amount of mass to the body (M yy to body 1),
and an external force which is proportional to the acceleration of the adjacent body (mass m2). Thus, the acceleration of one body affects the force field on another. This force is a strong function of the inter-body gap, reaching large values for very small gaps.
This inertial coupling is called fluid coupling. It has an importent effect in rack dynamics. The lateral motion of a fuel assembly inside the storage location will encounter this effect. So will the motion of a rack adjacent to another rack. These effects are in-cluded in the equations of laotion. The fluid coupling is between nodes i and i* (i = 2, 3 ... 5) in Figure A.l. Furthermore, nodal masses i contain coupling terms which model the effect of fluid in the gaps between adjacent racks.
Finally, fluid virtual mass is included in vertical direction vi-bration equations of the rack; virtual inertia is added to the governing equations corresponding to rotational degrees of freedom, m __ _ _
such as q4, 95 ' 911'
- A .2.4 Damping In reality, damping of the rack motion arises from material hysteresis (material damping) , relative inter-component motion in structures (structural damping), and fluid drag effects (fluid damping). The fluid damping acts on the i* nodal masses, as well as on i nodal masses in the analysis, a maximum of 5% structural damping is imposed on elements of the rack structure during SSE seismic simulation. This is in accordance with the NRC specifications for this site specific level of ground excitation.
A.2.5 Impact The fuel asscmbly nodes i* may impact the corresponding structural mass node i. To simulate this impact, 4 impact springs around each fuel assembly node are provided (Figure A . 2) . The fluid dampers are also provided in parallel with the springs. The spring constant of the springs is equal to the local stiffness of the vertical panel computed by evaluating the deficction of a 6" diameter circular plate
(.075") uniformly loaded and built in around the edge. The spring constant calculated in this manner should provide an upper bound on the local stiffness of the structure.
A'. 2. 6 Assembly of the Dynamic Model 1he dynamic model of the rack, rack base plus supports, and internal fuel assemblics is modelled for the general 3-D' motion simulation, by five lumped mass and inertia nodes for the rack, base and supports, and by five lumped masses for the assemblage of fuel assemblics. To simulate the connectivity and the elasticity of the configuration, a total of 37 linear spring dampers, 20 non-linear gap elements, and 18 non-linear friction elements is used. A summary of spring, gap and friction elements, with their connectivity and purpose given, is presented in Table A .l.
If we restrict the simulation model to two dimensions (one horizontal motion plus vertical motion, for example) for the purposes of model clarification only, then a descriptive model of the simulated structure which includes all necessary spring, gap and friction elements is
shown in Figure A .3. The beam springs K , K at each level, 6 B
- - '. which represent a rack segment treated as a structural beam (4) are located in Table A .1 as linear springs 2, 3, 6, 7, 10, 11, 14 and 15. The extensional spring Ke which simulates the lowest clastic motion of the re;k in extension relative to the rack base, is given by' linear spring 37 in Table A .1. The re-maining springs either have zero coefficients (if fluid damping is neglected), or do not enter into the 2-D motion described in Figure A . 3. The rack mass and inertia, active in rack bending, is apportioned to the five levels of rack mass; the rack mass active for vertical motion is apportioned to locations 1 and 5 in the ratio 2/1. The mass and inertia of the rack base and the support legs is concentrated at node 1.
The potential for impacts between fuel assemblies and rack are modelled oy t.e gap elements, having local stiffness Ky, in Figure A . 3. In Table A.1, these elements are gap clements 3, 4, 7, 8, 15, 16, 19 and 20. The support leg spring rates Ks "#8 modelled by elements 9, 30 in Table A.1 for the 2-D case. Note that the local elasticity of the concrete floor is included in K
- s To simulate sliding pote.'Liul, friction elements 2 plus 8 and 4 plus 6 (Table A .1) are shown in Figure A.3. The local spring rates K f reflect the lateral elasticity of the support legs.
Finally, the support rotational friction springs KR, eflect the rotational elasticity of the foundation. The nonlinearity of these springs (friction elements 9 p'us 15 and 11 plus i_
in Table A.1) reflects the edging' limitation imposed on the base of the rack support legs.
The 2-D model described above is solely for understanding of the various modelling elements. For the 3-D simulation carried out in detail by Joseph Oat, additional springs and support _
elements (listed in Table A.1), are included in the model.
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Coupling between the two horizonta1 seismic motions may be induced by sliding of the rack base and support leg liftoff which can cause rotation of the entire rack. The potential exists for the assemblage to be supported on 1 to 4 fikt during any instant of a complex 3-D seismic event. It is even possible for the entire rack to leave the pool floor under certain load combinations.
All of these potential events may be encountered during a 3-D motion and have been observed in the results.
A brief description of the clastostatic model follows. This detailed model is used to obtain overall beam stiffness formula for-the rack dynamic model, and to determine detailed stress distributions in the rack from a knowledge of the results of the time history analysis.
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' 1 I. Spring Dampers (37 total) -
. j diumber flode Loc'ation Description l
1 1-2 ,
X-Z rack shear spring ,
2 , .
1-2 Y-Z rack shear 3 1-2 Y-Z rack bending spring .
4 -
,1-2 X-Z rack bending 5 . 2-3 X-Z
. rack shear 6 2-3 Y-2 .)
7 2-3 Y-Z l h rac'k bending
. 8 2-3 X-I. J 9 3-4 X-Z 1 P rack shear 10 3-4 Y-Z )
11 3-4 Y-Z %
e rack bending 12 3-4 X-Z i .
13 4-5 X-Z ?
rack shear
. 14 4-5 Y-Z )(
15 4-5 Y-Z i h
O 16 , 4-5 ..
X-Z J rack bending 17 ,
'l - 5 :*- Rack torsion spring 18*
1 _
Fluid damping of rack in torsion 19* ,
1 Fluid d,amping of rack in X directic-
,20* .1 Rack fluid damper in Y direction 21* -
2 ,
X direction rack fluid damper 22* 2 Y direction rack fluid damper 23* 3 -
X direction rack fluid damper 24* 3 Y direction rack fluid damper 25* 4 X direction rack fluid damper 26* 4- ,
Y direction rack fluid damper 27* 5 . X direction rack fluid damper
~28* '5 Y' direction rack fluid damper
~29* .
,2,2* X rack / fuel assembly damper
'30*
2,2* .Y rack / fuel assembly damper
- ~
- Note: Dampers 18-36 assumed inactive .
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L. --
Table A,1 (continued) .
Description
. Number . Node Location 31* 3,3* X rack / fuel assembly damper 32* 3,3* Y rack / fuel assembly damper
- 33* 4,4* 'X rack / fuel assembly damper 34* 4,4* Y rack / fuel assembly damper 35* 5,5* X rack / fuel assembly damper 36* 5,5* Y rack / fuel assembly damper 37 1-5 Z rack,extensional spring
- Hote: Dampers 18-36 assumed inactive for zero fluid dampening runs -
^
II. .flonlinear Sorings (Gap Elements) (20 total) flumber Node Location Description
. 1 2,2* X rack / fuel assembly in. pact spring 2 2.2* X rack / fuel assembly impact 3 2,2* Y rack / fuel assembly impact
~
4 2,2'* Y rack / fuel assembly impact 5 ,
3,3* X rack / fuel assembly impact Q6 -7 3,3*
3,3*
X rack / fuel assembly impact
,.Y rack / fuel assembly impact 3,3* Y rack / fuel assembly impact 8 ,
9 Support S1 -
Z compression spring 10 Support S2 I compression spring 11 Support S3 Z compression spring
~12 Support S4 Z compression spring 13 4,4* X rack / fuel assembly impact s,pring
. 14 - 4,4* X rack / fuel assembly impact spring 15 4,4* 'Y rack / fuel assembly impact spring 16 4,4* ,
Y rack / fuel assembly impact spring 17 5,5* X rack / fuel assembly impact spring
- 18. E,5* X rack / fuel assembly impact spring 19 '5,5* Y rack / fuel assembly impact spring
'5,5*
20 .
Y rack / fuel assembly impact spring O
1 11_
i .
- - - - . - - . -- - _ ~ -
i
Table A.1 (continued) ,
111. Friction Elements (16 t'o tal) l' umber Node Location Description 1 Support S1 X direction support friction 2 Support S1 -
Y direction friction
. 3 Support S2 .X direction friction 4 Support S2 Y direction friction 5 Support S3
- X direction friction 6 Support S3 -
Y d.irection friction 7
~
Support S4 X direction friction 8 Support S4 Y direction friction 9 S1 .. X Floor Moment
. 10 S1 .
Y Floor Moment
. 11 .
'S2 X Floor Moment 12 S2 Y Floor Moment 13 S3 X Floor Moment 14 S3 Y.F1oor Moment (G J '
l o- .S4 .:
X Floor Moment 16 S4 -
Y Floor Moment
~
l .
1 .
O .
y-
[ .- e
- . _ _ _- . .- . . = - - -
A .3 stress Analysis -
A .3.1. The fuel rack is a multi-cell folded-plate structure which has what is colloquially called an " egg-crate" configuration.
! This type of construction is very similar to the so-called
" stress-skin" construction of ribs spars and cover plates which i are widely used in aircraft constructicn. Techniques developed in the field of aircraft structural analysis are utilized herein to find the stresses and deformations in such structures. These
-methods have been thorough]y tested and their reliability has been I documentd in a number of well-known publications (e.g. ref. 8 thru 12).
Figure A.4 shows two cross-sections of the fuel rack which is modeled as a rectangular network of plates interconnected along
) nodal lines shown as points in Fig. A. l . An arbitrary load with components iFx , Fy i , Fzi acts at an arbitrary elevation on one
-of the nodal lines. We find the displacements and stresses due to such a. typical load according to the stressed skin model as.
follows:
4 .
The torsional deformations are solved for by using the classical
- theory of torsion for multi-celled thin walled cross-sections (ref. 13 ) ~.
I The bending-deformation is found by using the theory of shear flow (ref. 12) wherein all axial stresses are carried by the effective flanges (or stringers) formed by the intersections of the plates and all transverse shears are carried by the plates modeled as shear panels.
From a knowledge of the shear flows, the bending and torsional deformations, it is possible to provide a set of. influence functions or the following section properties for the fuel rack as a whole:
-(EI) eg. = Bending rigidity (in two places)
-(GJ) eq = Torsional rigidity (AE) eq = Extensional rigidity
'~
ks == Shear deformation coefficient
. ~
'. '. Such propertiee are used for the dynamic analysia of
, ., scismic loads.
A 3.2 Combined Stresses and Corner Displacements The cross-sectional properties and the Timoshenko shear cor-rection factor calculated in the previous section are fed into a dynamic analysis of the system shown in Figure A .5, (which is re laceu by, e lumped mass-sprin modql of .A ), loading .
wl h a spec 1 led ground motion slgiulating cart qua ,
-From the dynamic analysis, the stress resultants (Fx, Fy, Fz, M,x My, Mz) acting as shown in Figure A6 are computed for a large number of times t = a t, 2at ... etc., at a selected number of cross sections. The displacements (Ux, U'y,U) z at selected nodal points on the z axis are also provided by the dynamic analysis as well as rotations (8x, Oy ,6z) of the cross-sections at the nodes.
Figure A7 shows a typical sub-division of the structure into elements, nodes and sections. The stresses are calculated at all sections and the displacements at all four corners of the rack are calculated at these elevations.
Since the displac'ement is linear o'n tho cross-section and achieves its extreme values at one of the Jour corners of the rack. The shear stresses due to torsional loads (.M) 3 achieve their extreme values near the middle of each side. The shear stresses due to lateral forces (F x, F) will achieve their extreme values at y
the center of the cross section or at the middle of each side.
Thus, candidates for the most critical point on any section will be the points labelled 1, 2 ... 9 in Figure A . 8. The expression for the combined stress and kinematic displacement for each of these points is written out. Similarly the stresses in the support legs are evaluated.
An Oat proprietary computer program "EGELAST" computes the stresses at the candidate points in each level. It sorts out the most stressed location in space as well as time. The highest stress, and maximum kinematic displacement are thus readily found.
4 .
A. 4 Time Integration of the Equations of Motion Having assembled the structural model, the dynamic equations of motion correspondin~ to each degree of freedom can be written by using Newton's second law of motion; or using Lagrange's equation. For example, the motion of node 2 in Y-direction (governed by the generalized coordinate p )g is written as follows:
The inertial mass is "22 + ^222 + B211 where m 22 is the mass of node 2 for y-directional motion.
A 222 .is the fluid coupling mass due to interaction with node 2*,
and B 211 is the fluid coupling mass due to interaction of node 2 with the reference frame (interaction between adjacent racks).
Hence, Newton's law gives
(*22
- A222 + B211) Pg+A212 510 + B212 =0 9 where og represents all the beam spring and damper forces on node 2. A
~
212 is the cross term fluid coupling effect of node 2*, and B 212 is the cross term fluid coupling effect of the adjacent racks. A represents the ground acceleration.
Let 9 9 =P 9 - u; gl0 =P10 -"
i.e. g g - is the relative displacement of node 2 in y-direction -
with respect to the ground. Substituting in the above equation, and rearranging, we have I"22 + A222 + U211) 9+A212 10 =0 9 -
(m 22 + ^222 + B211
+A #
212 212) i Simipar equations for each of the 32 degrees of freedom can be written out. The system of equations can be represented in matix notation as: -
a f O
- P w
l l
. \
IM] {Q) = 10] + (G) l where the vector [0] is a function of nodal displacement and velocities, and G depends on the coupling inertias and the ground acceleration.
~
Pre-multiplying above equation by [.M ] renders the resulting equations uncoupled in mass.
We have:
{k } = [M] ~ [Q] + [M] ~ {G}
This equation set is mass uncoupled, displacement coupled; and L
is idealy suited for numerical solution using the central dif-ference scheme. The computer program developed by G.E. and described in ref. (4) performs this task in an efficient manner.
This computer program, named "DYNAliIS" in Oat's computer program library is documented in ref. (4), and also internally at Oat.
The genrealized force O g, which contains the effects of all spr.ing elements acting on rode 2 in the " direction" of coordinate
,gg (the relative displacement of node 2 in the y-direction),
can easily be obtained from a free body analysis of node 2. For example, in the 2-D model shown in Fig. A.3, contributions to O g are obtained from the two shear springs of the rack structure, and the two impact springs which couple node 2* and node 2. Since each of these four spring elements contain couplings with other component deformations through the spring force-deformation re-lations, considerable static coupling of the complete set of equations results. The level of static coupling of the equations further increases when 3-D motions are considered due to the -
inclusion of rack torsion and general fuel assembly group centroid offset. ,
~
For example, referring to Fig. A.3, a 2-D simulation introduces static coupling between coordinates 2, 9 and 15 in the expression for 0 ; this coupling comes from the shear springs simulating 9
~
the rack clasSicity which have constitutive relations of the form IFl = K lg g -q 2 '
6915 ~99 ,*
Further, the impact springs introduce two additional forces having constitutive equations of the form l F ( = K7 jg g -g yg(.
Of course, at any instant, these forces may be zero if the local gap is open. The local gap depends on the current value gg- q10*
It should be noted that in the numerical simulations run by Joseph Oat to verify structural integrity during a seismic event, all elements of the fuel assemblies are assumed to move in phase.
This will provide maximum impact force level and hence induce additional conservatism in the time history analysis.
Having determined the internal forces as a function of time, the computer program "EGELAST" computes the detailed stress and displacement field for the rack structure as described in the preceeding section.
A.5 Structural Acceptance Criteria There are two sets of criteria to be satisfied by the rack modules:
(a) Kinematic Criterion: This criterion seeks to ensure that adjacent racks will not impact during SSE (condition E' in Ref.
14), assuming the lower bound value of the pool surface friction coefficient. It is further required that tht factors of safety against tilting specified in Ref. (15) are net (1.5 for'OBE, 1.1 for SSE).
(b) Stress Limits: The stress limits of the ASME Code.
(1) Criteria: Section III, Sub-Sec. ion NF, 1980 Edition were
-chosen to be met, since this Code provides the most consistent set of limits for various stress types, and various loading con-ditions. The following loading cases (taken out of the set specified in Ref. (14) are meaningful.
4
O SRP Designation ASME Designation (i) D+L Level A (normal Condition)
(ii) D+L+E Level B (upset Condition)
(iii) D+L+T o No ASME Designation. Primary membrane plus bending stress required to be limited to lesser of 2 Sy* and S
- u (iv) D+L+T g +E No ASME Designation. Stress limit same as (iii) above.
(v) D+L+T +E No ASME Designation. Stress limit same as above.
(vi) D+T+T a + E' Level D (faulted condition) where D: Deat weight induced stresses L: Live load induced stresses, in this case stresses developed during lifting E: OBE (Time history loading)
E': SSE Tg: Stresses due to assymmetric heat emission from the fuel assemblics T Thermal stresses due to accidentr.
a:
The conditions T and Tg cause local thermal stresses to be a
produced. The worst situation will be obtained when an isolated storage location has a fuel assembly which is generating heat at the maximum postulated rate. The surrounding storago locations are assumed to contain no fuel. Futhermore, the loaded storage locations are assumed to have unchanneled fuel. Thus, the heated water makes unobstructed contact with the inside of the storage walls thereby producing maximum possible temperature difference between the adjacent cells. The secondary stresses thus produced are limited to the body of the rack, i.e., the support legs do not experience the secondary (thermal) stresses, e
(2) Basic Data: The following data on the physical proper-ties of the rack material are obtained from the ASME Code,Section III, appendices.
- S Yield stress of the material, S ultimate stress y u e m .~e
TABLE A2 PITYSICAL PROPERTY DATA Property Young's , Yield Ultimate Allowable Modules Strength Strength Stress E S 'S S y u :
4 6
Value 23.3 x 10 25 KSI 71 KSI 17.8 Psi .
KSI, Reference- Table Table Table Table I-6.0 I-2.2 I-3.2 I-7.2 (3) Stress limits for normal and upset, and faulted conditions:
The following limits are obtained from NF-3230 inconjunction
.with Appendix XVII as modified by the USNRP Regulatory Guide 1.124.
(3.1) Normal and upset conditions (level A or level B) .
(i) Allowable stress in tension on a net section = F t"
.- .6Sy or F t = (.6) (25000) = 15000 Psi F t is equivalent to primary membrane stresses (ii) On the gross section, allowable stress in shear is Fy = 0.4 Sy
= (0.4) (25000) = 10,000 Psi (iii) Allowable stress in compression, F a p' , )l - @)Q/ S
[g) . Op)yscc -(@y'ec;;
Evaluated at 200 F. This temperature is higher than the pool water bulk temperature under any of the loading conditions under consideration. .
ehrzrw 1 (g[f_)Y 2.
Ce=
~
= 147.81 Sy Substituting numbers, we obtain, for both support leg and
" egg-crate" region:
Fa = 15000 Psi (iv) Maximum bendi:ig stress at the outermost fiber due to flexure about one plane of symmetry:
Fb = .60Sy = 15000 Psi (v) Combined flexure and compression:
F
+ _mx MbX +Cmyk e where* DxFx b pFy Yb 1 fa: Direct compressive stress in the section f bx: Maximum flexural stress x-axis Fby: Maximum flexurel stress y-axis Cmx = Cmy = 0.85 Dx = 1 a f_a Fe#x ,
p Y
=\- h 7e.Y Where iE M E Fe 'x = g3(ag't .
to (vi) Combined flexure and compressien (or tension)
, kY 6 1.0
- bX by The above requirement should be met for both direct tension or compression case.
20-t i
y
gemsy m
, ., F-1370 (Section- III, Appendix F), states that the limits for the faulted condition are
- 1. 2 ( F times the corresponding t
limits for normal condition. Thus the multiplication factor is Factor = (l.2,X25ga) Coo
= 2.0 (3.3) Thermal Stresses:
There are no stress limits for thermal (self-limiting) stresses in Clais 3-NF Structures for linear type sup-
. ports.
However, the range of primary and secondary stress intensity is required to be limited to 3 Sm in the man-ner of class 1 components, Sm is the allowable stress intensity of the rack material at the maximum operating temperature.
A.6 nosults a) Critical cross sections of the rack and the support legs are monitored to check satisfaction of the structural accep-tance criterial outlined in part A.5 of this document. The following stress ratios are computed for each cross section:
R1 = SD/15000 R2 = T/10000 R3 = SBX/15000 .
R4 = SBY/15000
- R5 = R1 + .85 ( , )
x y RG = (SD + SBX + SBY)/15000 '
i a where SD = average direct tension >r compression stress T = average shear stress o' n cross section SBX = bending stress due to bending in Y-Z plane SBY = bending stress due to bending in X-Z planc
~
For structural integrity during SSE, all of these factors must be less than 2.0.
- - . - - -- . - - - - - n-,
- For an OBE simulation, all of these factors must be less than 1.0.
The ratios are calculated including any additional static or thermal stresses which occur at the cross sections. Each of the stress ratios Rl-R6 is calculated individually for every section at every sampled time point to find the maximum. Thirteen sections of the structure have been examined (five sections in the rack, 4 sections for the top of each support leg, and four sections at the bottom of each support 19) . The " time" point at which each maximum occurs is also printed out in the structural acceptance summery.
Results of the stress comparisons are shown in Appendix B for the 12 simulations carried out for this report. Appendix C contains a listing of the horizontal components of the site specific OBE seismic loading.
The following summary table containing the maximum ratio valdes for the twelve runs performed is shown below. This table A.3 can be compared with the similar table in the original licensing
. document.
Table A 3 Results Summary for SSE Case Using Site Specific SSE Earthquake and 5% Structural Damping RACK TYPE RATIO A B C ROOT OF RACK R1 .004 .004 .022 R2 .025 .021 .216 R3 .135 .102 .580 R4 .09 '
.1 .681 R5 -
.179 .151 .835 R6 .21 .177 .982 TOP OF SUPPORT LEC R1 .317 .208 .519 R2 .326 .176 .209
. R3 .498 .293 .246 R4 .545 381 .866 R5 .816 .623 1.303 R6 .933 .713 1.442 9
. - _ _ _ _ _ . , . .__ __ . - . _ . - - , . T"
BOTTOM OF SUPPORT LEG R1 .317 .208 .519 R2 .326 .176 .209 R3 .373 .257 .239 R4 .429 .297 .929 R5 .705 .504 l'.320 RG ,Boi 572 8 460 It is found that the fully loaded rack, with COF = .8 leads to maximum stress conditions. The criteria that all of the ratios be less than 2.0 is satisfied for the SSE condition tested.
It is noted that the values obtained in the analysis assume 5% structural damping and no fluid damping. We also note that thermal stresses that may be expected to occur have been shown to be very low and do not influence the preceding structural acceptance criteria.
- b. Local stresses in the rack cell wall due to impacts are computed using the impact loads generated from the dynamic simulations. The impact loads generated are less than the values generated with the original Stone &
Webster seismic load. The secondary stress range generated is a self limiting and therefore secondary stress; stress range < 3 S = 60000 psi M
where S M is the stress intensity value for the material.
- c. The maximum displacements occurring in the rack during the SSE motion used herein are summarized below for the simulations performed.
Type C Rack - The maximum corner displacement occurs for a full can with .8 ground coefficient. The value is .795" with 5% damping. The " empty" rack displace-ment under the same condition does not exceed .588".
Referenecc[kA Section 4[ '
- e *
. g ,
- 1. Regulatory Guide 1.29, Seismic Design Classification, Rev. 2,
'. Feb. 1976. .. .
~
- 2. " Friction Coefficients of Water Lubricated Stainless Steels for a Spent Fuel Rack Facility", by Prof. Ernerm Rabinowicz,
~
M.I.T., a report for Boston' Edison Company.
- 3. Regulatory Guide 1.92, combining Modal Responses and Spatial Co.mponents in Seismic Response Analysis, Rev. 1, Feb. 1976.
- 4. "The Component E'lement Me'thod in Dynamics with Application' to Earthquake and Vehicle Engineering" by S. Levy and'J.P.D. Wilkinson, McGraw Hill (1976).. -
General Electric specification 22A5866, Rev. 1,kppendixII, Fuel 5.
Assembly Structural Characteristics.
- 6 .' R.,J. Fritz, "The Effect of Liquids on the Dynamic Motions of Immersed Solids",,
Journal of Engi~cering n for Industry, Trans.
of the ASME, Feb. 1972, pp. 167-173. -
- 7. Regulatory Guide 1.61, Damping Values for Seismic Design of
, Nuclear Power Plants, Oct. 1973. -
. 8. ,J.T. Oden, Mechanics of Elastic Structures, McGraw-Hill, N.Y. , 1967.
'9. R.M. Rivello, Theory and Analysis of Flight Structures, McGraw-Hill M . ~x . , 1969.
- 10. M.F. Rubinstein, Matrix Computer Analysis o'f Structures, Prentice-Hall, Eaglewood Cliffs, N.J., 1966. .
- 11. J.S. Przemienicki, Theory of Matrix Structurhl Analysis, McGraw-Hill, N.Y. , 1966.
- 12. P. Kuhn, Stresses in Aircraft and Shell Structures, McGraw-Hill,
.N.Y., 1956. -
- 13. S.P. Timoshenko and J.N. Goodier, Theory of Elasticity, McGraw-Hill, N.Y., 1970, Chap. 10. -
l', ,14.. U.S. Nuclear Regulatory Commission, Standard Review Plan, NUREG-
. 75/087, Section 3.8,4.
15.
, SRP NUREG-75/087, Section 3.8.5.
- 16. NRC Regulatory Guide 1.124. .
- i
+
i
- d
- I * .
t 1
i r
J e 4
g &
a8"*, .
mm
= .
e
)
f 4
a 3
j -
D I
t * .
i .
1- ,
5 0 g . .
. . e j ee
. e
- e s, .
3 M 4 4
j 26-
. .,g
, ~h-
Type B Rack - Rack B is an isolated rack. The maximum displacement with an empty rack is .554" with 5%
-damping, and the corresponding maximum displacement of a fully loaded rack is .536.
Type A Rack - For a full can, with ground coefficient of friction equal to .8, the maximum displacement is .488" with 5% structural damping. The maximum displacement
, for an empty rack is .508" with 5% damping included.
1 It should be noted that no simulations have been reported for partially loaded racks using the site specific earthquake.
However, for the simulations that.have been run using the new seismic loading, the deflections obtained have been consistently less than the values reported in the initial
, licent.ng document using the Stone and Webster seismic input. Therefore, we can conclude that consistently smaller
, values would also be achieved for partially loaded racke if we used the latest seismic input. Therefore, we conclude that all conclusions drawn concerning the lack of any impacts with adjacent racks carry through without modification and lead to the result that the racks meet all of the criteria for safe operation using either the new seismic specifications as well as the original ceismic specifications.
a
, ew b%
G 4
, . s
References for Section 4
- l. Regulatory Guide 1.29, Seismic Design Ciassification, Rev. 2, Feb. 1976. .
- 2. " Friction Coefficients of Water Lubricated Stainless Steels for
~
a Spent Fuel Rack Facility", by Prof. Ernest Rabinowicz, M.I.T., a report for Boston Edison Company.
- 3. Regulatory Guide 1.92, combining Modal nosponses and Spatial Co.mponents in Scismic Response Analysis, Rev. 1, Feb. 1976.
~
- 4. "The Component Element Method in Dynamics with Application ~to Earthquake and Vehicle Engineering" by S. Levy and J.P.D. Wilkinson, McGraw Hill (1976).
- 5. General Electric specification 22A5866, Rev. 1, Appendix II, Fuel Assembly Structural Characteristics. .
- 6. R.J. Fritz, "The Effect of Liquids on the Dynamic Motions of
~
Immersed Solids", Journal of Engincering for Industry, Trans.
of the ASME, Feb. 1972, pp. 167-173.
- 7. Regulatory Guide 1.61, Damping Values for Seismic Design of Nuclear Power Plants, Oct. 1973.
- 8. ,J.T. Oden, Mechanics of Elastic Structures, McGraw-Hill, N.Y. , 1967.
- 9. R.M. Rivello, Theory and Analysis of Flight Structures, McGraw-Hill N.Y., 1969.
- 10. M.F. Rubinstein, Matrix Computer Analysis o'f Structures, Prentice-Hall, Eaglewood Cliffs, N.J., 1966. .
- 11. J.S. Praemienicki, Theory of Matrix Structural Analysis, McGraw-Hill, N.Y., 1966.
- 12. P. Kuhn, Stresses in Aircraft and Shell Structures, McGraw-Hill, ,
N.Y., 1956. -
- 13. S.P. Timoshenko and J.N. Goodier, Theory of Elasticity, McGraw-Hill, N.Y., 1970, Chap. 10.
O s l .
t i l .
.-N- ,
g 0
, 14. U.S. Nuclear Regulatory Commission, Standard Review Plan, HUREG- ;
75/087, Section 3.8.4.
- 15. SRP NUREG-75/087, Section 3.8.5.
- 16. NRC Regulatory Guide 1.124.
5 e
e a
e
.. . . _ -29 , _
~
d Z ha 3
, gs .
/
' CO U PLIN G ELEMENTS 4
T YP I C A L F U E L A S S E M B L'.
3
% GROUP M ASS H TYPIC AL FUEL RACK MAS S 2 FUEL R AC K B A S E 2
Ay
7
/ t /
p Ax ,.1, ys l y
'T /
/-- + - -4, X B y u s 32
, ! t
, i ; a I I h
,,', sh '
FUE L R ACK SUPPORT
~
1 X /
XB, YB - LOC ATION OF C E NTROI D O F FU EL ROD G ROUP M ASSES - REL ATIVE TO CENTER OF FU EL R A C K lli = U NIT VE C TO R S FIG.A.I DYN A MIC MODEL
._ w
CELLS MODULE B ASE PLATE
,..~ ~ ~ . ~ vy y:
- .t .l
, , jxxxx C522 -?A M 252 C sxg
.. 7
/
x 7
l # l i I , p' 3/4
/Ts 7'/2
~
r y 1 i u >^ /A y
1,2 xggxgg'xgxxs a
15/I 4,< S Q,
h ~A NN NN NN , INNNNNM
// N
/
/ /
/ /
/
/
I..
dl/ 8 4
13 /4 r-s- '
. b
/
/
/ ..
l / / -3/4 TYP.
A //
V l _%NNNNNN! NsNNNWV_-
l i l
F I G. A .2 SUPPORT l
l l
l J
5 Kg , KB,(T Y R) O K:^ 5 S ElSM,C Ko
~
MOTIONS s e4 .
Z k<g> 4 dh ,
A y< py i FUE L ASSEMBLY.
GROUP LUMPED MASE 3
ey % (TYR)
R ACK LUMPED MASS 8 lNERTI A b ~
FOR HORIZONTAL 2 '
~
2 MOTIONS (TYP.) O w w'- K.
V' pg - l 4 I ,
kKs -
Y B + 8 Kf h I \
5
/// / / /
b fijfty ^
K, i Ay - .
FIG. A.3 SPRING MASS SIMULATION FOR A TWO DIMENSIONAL MOTION
- m. . . _ _ _ , , - - - . ., - - - - - , . - _ .,__..
. i 4
v' IMPACT A SPRIN G S f
[J- A S
- c E F LUID DAMPERS RIGID FR A M E X FIG.A.3 i M PAC T S PRI N GS AND F LUI D D A M PERS
. _ . _ _ ~ . _ , . . . . _ - _ - _ . _ . . . . _ _ _ _ . _ . _ , . . _ _ . - . _ . . _ _ . _ _ _ _ _ .
i i Fy yg B L
; J B
--- Fx
~X 7 (a) TOP VIEW Z L, .
I Fz h,/
=-F x
( 3) AXIAL CROSS m u u ,,,,,,, . S ECTION ( B-B l FIG.A.4 (a) HORIZONTAL CROSS . SECTION OF RACK (b) VERTICAL CROSS SECTION OF RACK l . 2
e CELL Z(W) WALLS ' ((C 1 \^///XU^ ' '
/ s 'l )(/(> ('/ 2 C
/ j' '$f',fyfpf77 a j b= NyC
<-t j/ ,
"="# C7 ,
C C A' ,-; y(V) A RIGID PL ATE B /
- f- ;/cg = X (u) n
__ / /
, ?-d e 6<==,
7
/ / _
SUPPORTS-FIG.A.5 ' hMZ a jMy - b C' .
/ /
A'/ /* B C Fx A B FIG. A.6
-. - - . --. . , .-- . .. ~
t t nZ ' NODEI T_
^ /
7-EL.I SEC.I ~ ---- NO D E 2- -/ ,
, - E L. 2 SEC.2 ~ -
NODE 3- EL3
/
S E C. 3 -*- -- NODE 4- : m
- - E L.4 T- -/7 E L.5 S E C.4 -.- ,
'/ /
rz '
/ -
,_/[ S E C' 6
, _ _ _ . S E C. 5 - _,
/- 4 ' g. N O D E 5 k.- ,d- wp E L.7 - ~
2 gROOT OF RACK , -EL8 r S E C. 8 i S E C. 9 N O. 0 F E L E M E N T S = 8 N O. OF S EC TION S' =9 N O. 0 F N O'D E S =5 FIG.A.7
~
l ) , l i 4 Y
~
. b
@ @X g g- @
a = O FIG.A 8 e 0 _ . - _ _ _ - . - ~}}