ML20081J938
| ML20081J938 | |
| Person / Time | |
|---|---|
| Site: | Oyster Creek |
| Issue date: | 06/20/1991 |
| From: | Devine J GENERAL PUBLIC UTILITIES CORP. |
| To: | NRC OFFICE OF INFORMATION RESOURCES MANAGEMENT (IRM) |
| References | |
| 5000-91-2051, C321-91-2172, NUDOCS 9106240280 | |
| Download: ML20081J938 (80) | |
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M Ng gf One Upper Pond Road GPU Nuclear Corporation Parsippany, New Jersey 07054 201 316 7000 TE LliX 136-482 Writers Direct Dial Number.
201-316-7246 June 20, 1991 C321-91-2172 /5000-91-2051 U.
S. Nuclear Regulatory Commission Attn Document Control Desk washington, DC 20555 Gentlemen:
Subject:
Oyster Creek Nuclear Generating Station (OCNGS)
Docket No. 50-219 License No. DPR-16 Oyster Creek Drywell containment
References:
(1) HRC letter dated 2/14/91, " Request for Additional Information on Oyster Creek Drywell Stress and Stability Analysis (TAC No. 79166)."
(2) NRC letter dated 5/23/91, " Request for Additional Information on Oyster Creek Corroded Drywell Analysis (TAC No. 79166)."
l (3) GPU Nuclear letter dated 12/5/90, " Oyster Creek Drywell Stress and Stability Analysis (With Sand)."
(4) GPU Nuclear letter dated 3/4/91, " Oyster Creek Drywell Stress and Stability Analysis (Without Sand)."
(5) GPU Nuclear letter dated 3/20/91, " Oyster Creek Drywell Stress and Stability Analysis (With Sand)
Response for Additional Information."
In the Reference (2) letter, the NRC requested additional follow up information on the Oyster Creek Drywell Stress and Stability Analyses (With and Without Sand) submitted by GPU Nuclear, References (3) to (5).
This information request consisted of five questions on the stress and stability analyses plus a request for the computer model input files in an IBM PC compatible format.
1 Attachment I provides the requested additional information for each of the five Reference (2) questions. Also enclosed is a 5 1/4" high density floppy disc containing the ANSYS input files for the "without sand" computer models.
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June 20, 1991 If you have any questions or comments on this submittal or the overall drywell corrosion program, please contact Mr. Michael Laggart, Manager, Corporate Nuclear Licensing at (201) 316-7968.
Ver tru ?Nyours, l
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J.
C. DeVine, Jr.
Vice President and Director, Technical Functions Attachment JCD/RZ/ pip l
cc Administrator, Region 1 Senior NRC Resident Inspector Oyster Creek NRC Project Manager
-RZ:C3212172
ATTACHMENLt GPU NUCLEAR RESPONSE TO THE MAY 23.1991 NRC REQUEST FOR ADDITIONAL INFORMATIQR ON THE ASME Vill OYSTER CREEK DRYWELL STRESS AND--STABILITY ANALYSES l
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1.
Your response to Question 2 states, "For a vessel that originally complied with the code, increases beyond 1.0 S, in localized areas of undefined size are acceptable." This statement is loose and you
-have applied it throughout the drywell as shown in Tables 5-lb, 5-2a and 5-2b of GE Report Index No. 9-3.
One may conclude from what you have stated and implemented that a corroded drywell has increased its structural capability. Your interpretation of Section NE 3213.10 of the ASME Code is questionable. Without corrosion, you consider the drywell when subjected to internal pressure to be under general primary membrane stress (tensile) and with corrosion you consider it to be under local primary membrane stress (tensile).
NE 3213.10 considers a membrane stress to be local primary, if it is produced I
by pressure or other mechanical loading and associated with a primary or discontinuity ef f ect, resulting in excessive dintortion in the transfer of-- load to other portions of the structure.
NE 3213.10 specifies the region to be considered local over which the membrane stress intensity exceeds 1.1 Sm.
The code gives an example of the discrete regions of local primary membrane.
It is realized that there is no code limit for the extent of the region in which the membrane stress exceeds 1.0 S but is less than 1.1 S Logical judgement is to be exercised in,the interpretation, and tIfe. basis for your judgement should be clearly defined.
Even if your interpretation of NE 3213.10 for application to the corroded oyecer Creek drywell is acceptable for localized areas, it should be demonstrated that the present and projected corroded condition of the oyster Creek drywell falls within the bounda.les established in accordance with NE 3213.10.
Unless and until the staff's concerne as indicated above are satisfactorily resolvod, the staff has reservations on your use of 1.1 S,, as indicated in GE Report Index No. 9.3.
This means that the allowable stresses indicated in Tables 5-3b, 5-2a and 5-2b should be based on 1.0 S, for primary membrane.
RESPONSE
The membrane stress, as a result of internal pressure, is not considered to be a Local Primary Membrane stress per Section NE 3213.TFoi the ASME Ccde. The discussions presented relative to NE 3213.10 are intended to demonstrate that-there are no specific requirements to limit the size of areas which are proximate to areas where the stress is determined to be a Local. Primary Membrane stress. Further, the stress in these proximate areas can be in excess of 1.0 S and still comply with the code rules.
Since NE 3213.10 does not define, limits for stresses between 1.0 S and 1.1 S, a requirement that the drywell corroded condition f all with5 the boun [ aries established in accordance with NE 3213.10 is not meaningful.
Using the specific Local Primary Membrane stress limit would be inappropriate.
In response to an earlier NRC question, "Has the opinion of'the code Committee been solicited regarding this matter?", we stated that "The opinion of the Code committee has not been solicited." Their opinion had --
not been solicited for the-reason that this specific issue was on the agenda of the March ~1,1991 Main committee Meeting.and the letter ballot had not yet closed, so an answer reflecting the Committee's opinion with any certainty could not be given. The Main Committee letter ballot and the ballot of.the ASME Board on Nuclear Codes and Standards have now been closed and the committee position based on this ballot can be provided.
The committee accepts 10% thinning of the drywell by corrosion, and this provision is consistent with the criteria applied in the analyses performed on the Oyster Creek drywell.
i SCT/WP/ MIS /Drywell/l l
e The action proposed at the March, 1991 meeting included the elimination of NE-3319 of the 1990 Addenda and substitution of a general rewrite of the Code acceptance rules applicable to metal containments which are in service.
However, both the existing rule and the proposed rule stated that the containment is acceptable, if the thickness was reduced by no more than 10% or the reduced thickness was shown by analysis to satisfy the requirements of the Design Specification.
Therefore, the Code Committee has formally expressed their opinion in the form of specific actions accepting a 10% teduction in thickness as the result of corrosion, and ASME has formally approved the continuaticn of this position.
Application of thisSection XI provision to analyses crc;h as those performed for the Oyster Creek drywell requires the adopt on of a 10%
increase in allowable stresses for those regions of the drywell not evaluated to the requirements on local membrane stresses.
That is, regions of the drywell where, considering the corroded condition, the computed stress intensity does not exceed 110% of the original allowable strees.
Therefore, the procedure followed in these analyses is consistent with both Section III, which does not limit the size of the region in which the calculated stress intensity resulting from a gross structural discontinuity (such as the corrorion experienced) exceeds 1.0 5, but is less than 1.1 S,,
and the provisions of Section XI (which contains the Code requirements f or components which are in service) which
(
accept 10% thinning as the result of degradation (such as the corrosion experienced).
Specifically, the existing and newly approved Code requirements state:
In IWE-3519.3, the existing provision with respect to the acceptance of base metal subjected to corrosion:
A110wable conditions.
The suspect areas determined under IWE-3519.1 or IWE-3519.2 shall be acceptable if either the thickness of the original base metal is reduced by no more than 10%, or the reduced thickness can be shown by analysis to satisfy the requirement 9 of the design specification.
In IWE-3122.4, the proposed provision with respect to the acceptance of components thinned by corrosion:
Acceptance by Evaluation (a) Components whose examination results reveal flaws or area of degradation which do not meet the acceptance standards listed in Table IWE-3410.1 shall be acceptable for service without removal or repair of the flaw or area of degradation or replacement, if an engineering evaluation indicates that the flaw or area of degradation is nonstructural in nature or has no effect on the structural integrity of the cont air. ment.
When supplemental examinations of IWE-3200 are required, if either the thickness of the base metal is reduced by no more than 10% of the nominal plate thickness or the reduced thickness can be shown by analysis to satisfy the requirements of the deeign specification, the component shall be acceptable by evaluation.
7 SCT/WP/ MIS /Drywell/2
e (b) When flaws or areas of degradation are accepted by engineering evaluation, the area containing the flaw or degradation shall be reexamined in accordance with IWE-2420(b) and (c).
(c) When portions of later editions of the Construction Code or Section-III are used, all related portions shall be met. The engineering evaluation shall be subject to review by the enforcement and regulatory authorities having jurisdiction at the plant site.
The reference paragraphs in both of these provisions are consistent with the practicos applied to the identification and examination of the Oyster Creek drywell.
SCT/hP/ MIS /Drywell/3
2.
The response to Question 3 does not fully address the question regarding possible stress concentrations resulting f rom the corroded condition of the drywell.
This issue should be fully discussed by the licensee.
RESPONSE
Fatigue as well as ductile fracture are addressed in the attached response.
The first attachment has been prepared by Mr. William E.
Cooper of TES, which explains the code provisions for fatigue and the theory and code provisions for ductile fracture.
Section 4 cf this report provides the code rules for protection against ductile fractura.
Table 1 shows the sum of the three principal stresses (hydrostatic s' ',Je per the code rules) for all nodes to evaluate relative to 4 S, =
s. 70 pol.
The model is the asymmetric model without sand (sandbed thick.4 1 is 0.700").
This model was chosen over the pie slice model becaur
't is the more detailed model and thus more accurately descri..a ar f discontinuity effects.
Stresses were computed for accident cord!* ion V-1.
This condition produces the highest biaxial stress state
.tch it the most demanding for ductile f racture evaluation. Hydrostatic a:.resses are computed on both surfaces and all are shown to be below 4 S The m
vast majority are well below 4 S Consequently, ductile f racture is not a concern for the Oyster Creek Er.ywell.
SCT/WP/ MIS /Drywell/4
ATTAC11MENIf_QB_GP_U.tLFlESP_0RS.E IO_QUESIl01t2 R2:C3212172
-TELEDYNE ENGlNEERING SERVICES U. E. Cooper Page 1 June 3, 1991 Project 7377 APPLICATION OF THE CRITERIA FOR THE DEVELOPMENT OF DUCTILE CRACKS TO NRC QUESTIONS CONCERNING CORROSION 1.0 INTRODUCTIp{
Item #3 of the NRC request for additional irformation on the Oyster Creek Corroded Drywell Analysis, transmitted Mal
.., ) il states:
The response to Question J - does no6 /Ully address the question regarding possible stress concentrations resulting from the corroded condition of the drywell, This issue should be fully addressed by the licensee.
This document has been prepared to assist in presentation of a response to this. item.
The first response is based on Section III of the ASME Boiler and Pressure Vessel Code, the Code classifies such stress concentration effects as local structural discontinuities and requires the consideration of such effects only in the performance of a fatigue evaluation.
Fatigue cycling is neither a defined operating condition or to be expected for the drywell.
This Code position is justified by two considerations.
First, the material is considered to be ductile in service, and previous responses confirm that this is-the case.
Second, the Code places a limit on the sum of the principal stresses to protect against ductile fracture The present author prepared that specific rule 'n about 1960 based on the state of knowledge at that time.
Recently, for in-house purposes, the present author has prepared a review of current knowledge with respect to the initiation and propagation of ductile fracture.
That study is abstracted in this document, confirms the conservatism of the Code rule, and summarizes recent developments and the
TELEDYNE ENGINEERING SERVICES W. E. Cooper Page 2 June 3, 1991 Project 7377 anplication of this technology in the French nuclear industry.
The deri-vation of the existing Section III rule is discussed in Section 4.0 of this document, following a review of pertinent background information.
2.0 PURPOSE Standard material tests, such as the tensile test or the bend test, provide information about the behavior of a metal under simple loading conditions with simple geometries.
The theories of elasticity and plasticity, together with finite element analysis programs, permit the results of these tests to be used to determine the stress and strain distribution in complex geometries subject to complex loading conditions.
However, these analyses tell us nothing aoout the potential failure of the structure.
If the structure has, or is postulated to have, a sharp crack present, elastic or plastic fracture mechanics is used to determine the loading conditions under which the crack becomes unstable, based on material properties determined by the performance of specialized tests.
But these analytical procedures, as well as those of elasticity and plasticity, are theories which apply to continuous media, not to the local inhomogeneities which are present in any real material. What stress or strain states are required to initiate a micro-crack in the real material, and to grow such a micro-crack, or a preexisting micro-crack, to a size where fracture mechanics or any other theory of a continuous media becomes applicable?
The literature selected for this review is identified in the References, and was chosen for its usefulness in providing a concise general backg"ound.
The total literature is very extensive, as is indicated by the selected references and by the many works which they reference.
The modern approach applies a continuum description in the form of a damage function without necessarily specifying an accompanying physical process.
In this less physics-specific, or metallurgichl-spv
- approach to constitutive description of damaged materials one postulates a damage function which accounts for the progressive softening of the material
TELEDYNE ENGZNEERING SERVICES W. E. Cooper Page 3 June 3, 1991 Project 7377 with strain or time.
The damage function need not be specifically defined if the behavior under a complex stress state is represented by the behavior in simple tests, such as the tensile test.
This approach is discussed in more detail in 5.2, following a discussion of the basic concepts.
This review is primarily limited to crack growth under simple, monotonic, loading conditions.
Finite element and fracture mechanics crack growth analyses include cyclic and high temperature loading conditions and the effects of corrosive media, and certain of the related fatigue or corrosion tests provide information as to the development of cracks from these effects, but this is done on a somewhat empirical basis.
3.0 BACKGROUND
3.1 Terminoloov This subsection reviews the terminology and concepts used in this l
review,.but is not intended to provide a complete technological background.
Symbols used in the text are enclosed in brackets, [ ].
3.1.1 Stress The general state of stress at a point is a second order tensor which can be defined in terms of six stress components, three principal stresses [oj with i = ;1, 2, and 3], or three tensor invariants.
The 1
stresses must be considered relative to the instantaneous dimensions of the structure, rather than the original dimensions as used in the tensile test,
. and are_ termed "true" or "Cauchy" stresses.
It is useful to consider the.-
- total state of stress as the sum of a hydrostatic stress [ag] and a deviatoric stress, because any change in volume is dependent upon the hydrostatic stress and any change in shape is dependent upon the deviatoric stress.
The hydrostatic stress is completely defined by one scalar l
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TELEDYNE ENGINEERING SERVICES W. E. Cooper Page 4 June 3, 1991 Project 7377 quantity.
The deviatoric stress may be defined in terms of six deviatoric stress components, three principal deviatoric stresses [a'j] or two tensor invariants (the first invariant of the deviatoric stress tensor is zero; the second, generally termed the quadratic invariant, is [J ]; and, the 2
third is finite but not used here).
3.1.2 Strain The general state of strain at a point is a second order tensor which can be defined in terms of six strain components. three grincipal strains [ej], or three tensor invariants.
It is useful to consider the total strain as the sum of an e_lastic strain [ej ] and a plastic strain e
[cjP].
It is also useful to consider each of these strains as the sum of a volume chance plus a shape change, consistent with the way in which the stress is separated.
The elastic portion of the strain is just that considered in elastic analyses, and needs no further discussion.
The plastic portion of the strain is somewhat more complicated.
The plastic strain is generally dependent upon the loading history, a complication avoided in this review by limitation to simple load histories.
Also, there are a number of definitions of finite strain, so that the user must be aware of the specific definition used by an author or by a computer program.
Because in plastic deformation there is no volume change, the total plastic strain and the deviatoric plastic strain are equal, and may be defined in terms of six plastic strain components, three principal plastic strains [ejP], or two tensor invariants (the first invariant of the plastic strain tensor is zero, the second is [I ], the third is finite but 2
not used here).
3.1.3 Stress - Strain Relationships The total stress and the total elastic strain are related by the usual elastic equations, generally using Youna's Modulus [E] and Poisson's Ratio [p]. Alternatively, the hydrostatic stress and volume change may be related by the Bulk Modulus [K] and the deviatoric stress and elastic change in shape by the Shear Moaulus [G].
Recalling that there is
TELEDYNE ENGINEERING SERVICES I
W. E. Cooper Page 5 l
June 3, 1991 Project 7377 no plastic change in volume, to complete the solution it is only necessary to establish a relationship between the deviatoric stress and the plastic change in shape.
This is accomplished by application of the theory of plasticity, which provides this relationship in terms of material properties determined from the tensile test, which may generally be expressed in terms of an exponential relationship between stress and plastic strain or in terms of the Rambera-Osanod equation, lhe uniaxial test results, expressed in terms of true stress and one of the finite strain definitions, usually the true strain, is made applicable to complex states of stress or strain by defining quantities which I will term here the effective stress [a ff] and effective plastic strain [c ff ].
These P
e e
quantities are sometimes termed eauivalent rather than effective, and the term effective is sometimes used to mean a completely different quantity, such as the manner in which the term effective stress is used by Lemaitre in Ref. 9.
The effective quantities, as I have used them, are defined in terms of the invariants J 2 and 1, with coefficients chosen so as to reduce 2
to the tensile test in the uniaxial case.
Because of the constancy of plastic volume, the effective plastic strain can not differ from the numerically, not algebraically, maximum plastic strain by more than 15%,
and the latte" value is often more easily visualized.
3.1.4 Triaxiality Factor Just as the theory of elasticity does not include a means for determining when elastic theory is no longer applicable because yielding occurs, the theory of plasticity can not predict the strains at which a failure occurs.
Although the plastic strains which result from a given loading are not dependent upon the hydrostatic state of stress, oH, the strains at which a micro-crack initiates are somewhat dependent upon this quantity, and the rate at which the micro-crack grows to a size which is treatable by fracture mechanics is strongly dependent upon the hydrostatic state of stress.
TELEDYNE ENGINEERING SERVICES W. E. Cooper Page 6 June 3, 1991 Project 7377 Micro-crack initiation is of general technical intarest, and is discussed in 3.3, but because of the relatively low stresses at which the micro-cracks initiate, and the existence of initial micro-cracks in the structure, the aspect of major engineering interest is the growth of micro-cracks to a structure scale level.
The dependence of micro-crack initiation and micro-crack growth on the hydrostatic stress is found to be expressable in terms of the ratio of the hydrostatic stress to the
/ a ff, Many authors refer to this quantity as the effective stress, OH e
triaxiality factor.
I prefer to define the Triaxiality Factor [TF] as the ratio of the sum of the principal stresses [ajj] to the effective stress, TF = ajj / a ff, because this ratio is unity for the tensile test.
Since e
ajj = 3 aH, the two quantities are easily relatable, my definition being three times the alternative definition.
3.1.5 Plastic Instability There is an important qualification which must be placed on the usefulness of fracture mechanics discussed in the second paragraph of 2.0.
A failure may occur as the result of a plastic instability at loads, or strains, less than those predicted by fracture mechanics.
The occurrence of a deformation instability, which may or may not occur at the same time as the load instability, may also affect the initiation and growth of micro-cracks.
The theory of plasticity can predict the conditions for load and deformation instabilities.
A standard, round, load-controlled tensile test exhibits failure as the result of a plastic instability, and the load instability and deformation instability coincide.
The deformation instability is reflected by local deformation (necking) of the specimen, with a complex state of stress developed in the neck. Micro-cracks initiate, starting at the centerline of the specimen where the triaxiality factor is highest, and grow until the specimen can no longer withstand the imposed load, when fracture occurs.
There is still some question as to the exact mechanism
TELEDYNE ENGINEERING SERVICES W. E. Cooper Page 7 June 3, 1991 Project 7377 which results in the final failure, as will be discussed in 3.3.
- But, similar to the initiation phase, this final phase is of general technical interest but is of less importance from an engineering view than is the growth phase.
An important issue, if the failure strains under complex stress states can be related to some strain experienced by a tensile test, is the specific tensile test strain to be considered. As will be demonstrated later, the tensile test result of use in this regard is the true strain to failure in a tensile test, ET.
Since the uniform elongation in a tensile test is determined by the plastic instability of that specific configuration, that strain is not a logical choice, although it is sometimes used on an empirical basis.
As stated earlier, the theory of plasticity may be used to determine the occurrence of a load or deformation instability.
Such an evaluation, including the effects of the net cross-section, must be performed in parallel with any fracture mechanics analysis to assure that a plastic instability failure does not occur before the crack instability
_ predicted by the fracture mechanics evaluation.
The load and deformation instabilities may not occur at the same strain.
As was demonstrated in Ref. 3 for thin-walled cylinders and spheres, the pressura instabilities occur at considerably smaller effective strains than the uniform elongation strain in a tensile test, but the deformation instabilities occur at higher effective' strains than do the load instabilities.
The load instability is of significance for comparison with the results of the fracture mechanics analysis.
It is possible that the deformation instability would be of interest for consideration with micro-crack initiation and growth, but such studies are limited. Moreover, it is only in the most ductile materials, I know of'one case with very soft aluminum, that the deformation instability is evident in a failed vessel.
Evidently, for most materials, the ductility reduction as the result of the Triaxiality Factor reduces the failure strains to smaller values than those where a deformation instability would occur.
TELEDYNE ENGINEERING SERVICES W. E. Cooper Page 8 June 3, 1991 Project 7377 3.2 Hi stori cal, 3.2.1 Testing Much of the early work on this issue wts conducted with notched tensile specimens.
Some 1923 nominal stress - nominal strain data are shown by Figure 29 of Ref. 11 and are reproduced here as Figure 1.
It is seen that as the notch becomes sharper the failure stress increases and the strain to maximum load and the failure strain decrease.
The Triaxiality Factor increases as the notch becomes sharper.
What would happen if a test could be conducted in pure triaxial tension, where TF = =?
As discussed earlier, there would be no plastic deformation and the term cohesive strenath has been used to indicate the failure value of each of the three stress components. An early attempt to establish this value was performed by Kuntze in 1932.
The results as provided by Figure 38 of Ref. 5 are reproduced here as Figure 2.
Even by these crude tests, the cohesive strength was a factor of 2.5 higher than the strength in tenstori.
There have been many similar tests conducted over the years, but these two figures should indicate that the effect being discussed here i.as a rich and lengthy history of research, but the applications have been generally restricted to problems in metal forming, such as are discussed in Ref. 4.
In the 1940s a number of more careful investigations were conducted.
The notched tensile test was improved by a number of S
investigators, including the results of Lubahn, Ref.12.
- lso, some more elegant tests were conducted by McAdams, as summarized in Section 15-4 of Ref. 17.
Even for very brittle materials, these results indicate that the cohesive strength is twice the tensile strength, so the sum of the three principal stresses at failure is approximately six times the tensile strength. Multiaxial stress conditions have also been tested.
For example Manjoine, Ref. 13, indicates the importance of the shape of the stress-strain curve.
t
TELEDYNE ENGINEERING SERVICES U. E. Cooper Page 9 June 3, 1991 Project 7377 3.2.2 Theory Theoretical developments have not been neglected.
Much of the very basic work was performed by McClintock, and Figure 3 of Ref.15 has been reproduced here as Figure 3 to summarize his early theoretical developments with respect to ductile failure.
Each of the three axes in the triangular coordinate system on the base plane of this figure is proportional to the failure value of one of the three principal strains (since the elastic strains were neglected and the sum of the three principal plastic strains must be zero, any combination of plastic strains can be represented on this or a parallel plane).
The vertical axis represents the ratio of the hydrostatic stress (his a equals my aH) divided by the effective stress (his a-bar equals my a f f).
Therefore, the numerical values on the vertical axis are one-third e
of the Triaxiality Factor as I have defined it.
The shape of the surface which represents these various quantities is dependent upon the shape of the tensile stress - strain curve.
For a point on the surface, as the vertical axis lengthens
.(increasing TF) the horizontal axes shorten,-the plastic strain to failure decreases.
The tensile test is represented by the plane labeled 1/3, so the surface would be at a 'uniaaial principal strain related to the percentage reduction of area in the tensile' test.
If the ratio of hydrostatic stress to the effective stress
. equals three (TF ( 9), the plastic strain at failure is not reduced to zero, although it becomes quite small. As is pointed out by McClintock in Ref. 14,-this result is consistent with some of Hill's simple models, of L
Ref. 8, which predict failure at a value of the hydrostatic stress equal to three to five times the effective stress, which Hill calls the equivalent flow stress.
TELEDYNE ENGINEERING SERVICES L E. Cooper Page 10 l
June 3, 1991 Project 7377 3.3 Physical 3.3.1 Void Initiation I have selected the results from one particular paper to illustrate the physical behavior, Ref. 21, because the discussion provides a good physical description accompanied by test results on a low-yield strength, highly ductile, material with one major source of metallurgical impurities which are well distributed within the matrix.
To this point I have carefully avoided the use of the word void.
In a metallurgical sense, the initi'ating feature at a microscopic level is the formation of voids.
These vofds grow and then coalmce.
It is the coalescence of the voids which creates crack-like micro-defects which, with further coalescence, grow to become the cracks of interest to the application of fracture mechanics.
As noted by these authors, this sequence of events was first identified by Tipper in a 1949 publication.
Although some voids may be present in the virgin material, others result from decohesion of the matrix material from imbedded particles, so the initial void formation is dependent upon the
" cleanliness" of the material. The theories related to this aspect are discussed and tested by the authors, but will not be discussed in detail here.
3.3.2 Void Growth The next step, and that which is specifically considered in detail in this review, is void growth, the aspect really studied by McClintock and others who the authors reference.
All note the exponential amplification of the growth rate caused by the Triaxiality Factor effect, and note that "since stable void growth accounts for much of the plastic strain before failure the ductility of the material often depends strongly on triaxiality."
Experimental data are cited.
TELEDYNE ENGINEERING SERVICES W. E. Cooper Page 11 June 3, 1991 Project 7377 3.3.3 Void Cealescence and Crack Formation Even though the void growth equations can be used to estimate the size and the shape of the voids at failure, there is not sufficient void growth to produce failure by coalescence between the voids in a homogeneous flow field. Therefore, some of the authors conclude that the final stage in the process is a change from a homogeneous flow field to a localized deformation field, and have noted that the tendency in this direction is enhanced for materials which strain-harden at a low rate.
Again, there is a problem, because realistic average porosities do not result in reasonable failure predictions. The apparent conclusion is that the statistical cistributions of the void-forming particles leads to higher than average local void counts with the failure resulting from the local concentration of strains in these regions.
The general analysis can be performed by the normal finite element analysis techniques, but it may be necessary to include the effects of local regions if failures are to be evaluated.
The authors conduct and interpret experiments directed towards all phases of the initiation, growth, and coalescence, and conclude that the " statistics of the inclusion distribution determine the size scale over which void coalescence must occur in order to create a crack like defect",
with the radius of the coalesced void being at least twice the average void spacing.
3.3.4 Experimental Results Although all three stages are interesting, I note, again, that the stage which accounts for much of the plastic strain before failure is that of void growth, and turn to some of the experimental results which contribute to the engineering issue.
The authors of Ref. 21 used two types of tensile test specimens, notched round bars and wide plate, plane strain specimens.
Figure 4 of this review reproduces Figures 3-5 of Ref. 21.
The first of these figures plots the ratio of the hydrostatic stress (their a m
is my aH) to the effective stress (their a is my a ff) versus the effective e
TELEDYNE ENGINEERING SERVICES
- 8. E. Cooper Page 12 June 3, 1991 Project 7377 plastic strain to " failure initiation" (their e-bar, superscript p, is my i
e ff ), where " failure initiation" is defined as "the first formation of a P
e distinct internal crack", so additional strain would be required for complete fracture.
The results for the five specimens are tabulated below, including results from the author's Table 2 and adding columns for the TF which are scaled from the figure:
CODE TYPE Aporox. TF '
r ffP Void Vol.
e Init.
Final A_v_e raac local Fraction AX-P Round, unnotched 1.00 1.35 1.05 1.05 0.052 PL-P Flat, unnotched 1.73 1.73 0.79 0.79 0.037 AX-A Round, mild notch 2.22 2.70 0.56 0.50 0.033 PL-A Flat, mild notch 3.33 3.33 0.37 0.37 0.025 AX-D Round, sharp notch 3.60 3.87 0.48 0.29 0.026 The plotted and tabulated results imply a correlation between failure initiation and stress state, independent of the state of strain.
For reference, the true strain at maximum load (the uniform elongation) for the material is 0.28, much smaller than any of the failure strains with the exception of the last.
-It should also be noted that failure initiation as defined for these tests results in crack sizes which are very small, being less than a millimeter.
The internal failure shown by the second figure is typical of the cracks formed in all cases, except for the unnotched wide plate specimen which is shown by the third of these figures.
Should the initial or final value of the TF be used in the evaluations? TF = 1 is used for the tensile test despite the increased TF which will exist because of necking when the specimen fractures, by 35% in the case of this very ductile material. Use of TF = 1 in reporting the
TELEDYNE ENGINEERING SERVICES
- 9. E. Cooper Page 13 June 3, 1991 Project 7377 results of the tensile test is conservative. With elastic-plastic finite element analyses of structures the instantaneous value of the TF can, and should, be used in predicting fracture strains.
Triaxiality Factors based on elastic computations may be unconservative.
In most structures, which are better typified by the flat plate specimens where the initial and final values are the same, and even in the tensile test for most materials, the change in TF will be much smaller.
4.0 CODE REOUIREMENT ON SUM OF THE PRINCIPAL STRESSES Paragraph NE-3227.4 requires that the sum of the principal stresses not exceed 4Sm.
The derivation of that requirement will be discussed, but some background may be useful.
The Code applies the Tresca Criterion, the behavior under combined stresses is dependent upon the maximum shear stress.
If the three principal stresses are al, a2, and 33, and if a1 ) a2 > a3, the maximum shear stress is one-half of the difference between the largest and smallest principal stress.
The Code multiplies through by two and terms this difference the
" Stress Intensity." Although it is not obvious, the Tresca criterion is independent of the sum of the principal stresses.
Therefore, absent the criterion of NE-3227.4, the Code contains no direct protection against ductile fracture when the three principal stresses are tensile.
This provision was written to provide just such protection, recognizing that significant triaxial tensions could exist, through design or through fabrication or in service, as with the drywell corrosion, and ductile failure prevention had to be assured.
As was pointed out in 3.2.2, it was known that if the ratio of hydrostatic stress to the effective stress equals three (TF = 9), the plastic strain at failure is not reduced to zero, although it becomes quite small.
If strain hardening is neglected, this says that brittle fracture is possible if the
[
sum of.the three principal stresses is equal to nine times the yield lo l'
TELEDYNE ENGINEERING SERVICES W. E. Cooper Page 14 June 3, 1991 Project 7377 strength.
Since the Code stress limit is the lesser of two-thirds of the yield strength or one-third of the tensile strength, the requirement may be expressed in terms of Sm as follows when a factor of safety of 3 is applied:
9S 9 '3S/2]
y m
= 4.5S t+a2+
a
- 3*
FS 3
m The allowable value was rounded down to 4.05m-l 5.'0 PROPOSED IMPROVED CRITERIA 5.1 Format A number of criteria have been proposed to determine the effect of hydrostatic tension on the effective plastic strain to failure. All result in expressions which include the true strain to failure in a tensile test and the Triaxiality Factor, either in the way in which I have defined it or in some equivalent definition, recalling that my definition for the Triaxiality Factor may be written as:
a a+a+#
3a jj 7
2 3
g TF =
=
=
"eff "eff "eff The more common of the proposed criteria are discussed and those
.specifically discussed here are plotted in Figure 5 of this review.
This plot shows the ratio of_ the effective plastic strain to failure to the true strain to failure in a tensile test, e ffP / ET, as ordinate and the e
Triaxiality Factor as abscissa. When the predicted value is dependent upon Poisson's Ratio, I have used p = 0.3.
For the tensile test TF = 1; for biaxial plane strain, such as the unnotched plate test of Ref. 20, TF =
1.732; for plane stress conditions TF f 2,-with TF = 2 for equal biaxial tension; the ordinate is expected to be zero when the TF = =; and, the ordinate can not become negative.
TELEDYNE ENGINEERING SERVICES W. E. Cooper Page 15 June 3, 1991 Project 7377 5.2 Preferred Criterion (Lemaitre)
The higher, bold line, in Figure 5 is a plot of the criterion whict.
I favor, that of Lemaitre, Ref. 9, My preference for the criterion of Lemaitre is related to both its recent date and to the technical approach applied.
Lemaitre's continuous damage mechanics approach deals with the macroscale level of constitutive equations for strain behavior which lies between the microscale, say 10-3 to 10-2 mm where the McClintock and Rice and Tracey analyses apply, and the structure level scale, say 102 to 103 mm.
The approach defines "a damage variable as an effective surface density of cracks or cavity [ void] intersections with a plane." As he points out, "at that macroscale it is difficult to introduce much physics but on the other hand this damage variable is easy to introduce in structural calculations."
By analogy with the toughness criterion of fracture mechanics, wnere the damage strain energy release rate-is represented by the symbol G, Lemaitre's rupture criterion is postulated as:
The damage process gives rise to initiation of a macrocrack for a critical value of the damaae strain enercy release rate, that value being a characteristic for each material.
The damage prccess is shown to be linear with strain, and this conclusion is validated by experimental data.
Specific evaluation of the damage process is not required to apply Lemaitre's concepts here, for he develops the influence of triaxiality in a form which may be written, in the terms used in this review, as:
2 (1 + p) + --(1-2p)
Models are provided for any loading path or for the " radial loading path" considered in this review.
TELEDYNE ENGINEERING SERVICES W. E. Cooper Page 16 June 3, 1991 Project 7377 5.3 Simplest Criterion The lower, slimmer line in Figure 5 is a plot of the criterion:
p C eff 1
e TF 7
I have not-identified a source reference for this criterion because I have used it so long I don't remember the basis.
5.4 Other Criteria A nt'mber of alternative criteria have been developed and will be identified, but not discussed as they were in the original document.
These are contained in Refs. 1, 2, 4, 6, 7, 10, 14, 15, 16, 19, 20, and 22. All indicate the same trends as shown by Figure 5, but there are differences in the predicted curves because of the developing knowledge.
6.0 FUTURE TREND - DAMAGE MECHANICS 6.1 Introduction.
The trend is well summarized by W. G. Knauss and A. J. Rosakis of Cal Tech in their role as Guest Editors of Volume 42, 1990 of the International Journal of Fracture, see their Preface.
The new approach attempts "to describe the complete material response in its transition from -
the continuum to the damaged and failing material," and is " distinguished by a fully non-linear description of the material and failure process, and wherein the crack or ' law provides only the high stress or strain field gradients within which a local,. material-based, failure criterion can be satisfied at the crack tip."
l
_ __= _
TELEDYNE ENGINEERING SERVICES W. E. Cooper Page 17 June 3, 1991 Project 7377 Each of the major approaches has been developed in France. However, an EPRt Report, Ref.18, describing the French Approach to PWR reactor pressure vessel integrity, clearly brings the potential advantages of a part of the work described in the reference to the attention of the USA.
All of the approaches have been developed in association with the performance of finite element analyses with an element size near the crack tip which is_ representative of the metallurgical process zone, and all apply what I would term a local approach to fracture, although the "name" local approach is used only with the methods of 6.3.
In considering ductile fracture, both the 6.2 approach and the alternative 6.3 approach develop a material constitutive law which combines the strengthening as the result of strain-hardening and the weakening as the result of damage. The original 6.3 approach applies a critical value of void growth, and requires the sequential release of nodes as the crack grows.
Only the 6.3 approach has a consistent associated criterion for brittle fracture, and this is summarized in 6.3.
6.2 Lemaitre's General Acoroach to Fracture Initiation Lemaitre's recent work (Ref. 10) provides what the editors of Volume 42 of Fracture describe as an alternative and less physics-specific view which derives basically from a continuum description in the form of a damage function without necessarily specifying an accomoanying physical p rocess.
In this approach to constitutive description of damaged materials one postulates a damage function which accounts for progressive softening of the material with strain or time. This is the approach reflected, perhaps unknowingly, by many of the proposals discussed in the previous text.
Ref.10 continues the development of Lemaitre's " continuous damage mechanics" approach, Ref. 9 which is discussed in the previous sections, but broadens the applicability to cover other potential failure mechanisms, not just ductile fracture.
In principal, he recognizes that L
TELEDYNE ENGINEERING SERVICES W. E. Cooper Page 18 June 3, 1991 Project 7377 failures will initiate in local regions of the material and seeks a formulation which permits one to apply a post processor to the results of a normal finite element analysis to evaluate the initiation and propagation, to structural scale, of a crack.
He does this by assigning a degraded property to the local region, specifically by reducing the yield strength to the endurance limit on the basis that there can be no damage in the local region if the stresses in the local region do not exceed the endurance limit.
He then develops, in principal, a post processor which imposes equilibrium and compatibility considerations across the border between the local region and the surrounding structure and computes the stress in the local region.
Lemaitre applies this principal to low cycle fatigue and predicts a low-cycle fatigue curve which is similar to the interpretation of such data by Coffin and Manson; and, to high cycle fatigue and predicts the Goodman mean stress correction. He argues that this technique is applicable to other modes of failure.
6.3 The French " Local" Approach to Vessel Intearity The recent EPRI Report (Ref. 18), which has been previously identified, reviews the results of applying conventional fracture mechanics, referred to as the " global" approach, and of statistical fracture mechanics to problems typical of French PWRs and, then, summarizes and applies their " local" approach to the same problems.
The advantages of the " local" approach are striking!
In part, the local approach is quite similar to that of Lemaitre, in that it is recognized that crack initiation and development is a local phenomena and that it is very useful to have consistently-based criteria which account for various failure modes, although the present approach has been limited to brittle fracture and to ductile crack initiation and growth.
I l
TELEDYNE ENGINEERING SERVICES W. E. Cooper Page 19 June 3, 1991 Project 7377 The major difference from the Lamaitre approach is that this " local" approach includes within the finite element analysis grid elements which are of a size which represent the metallurgical process zone.
In fact, the size of these elements is one of the important variables in the analysis; although guidance is available in terms of the chemical content and heat treatment of the material, the metallurgical structure, and correlations with the fracture mechanics properties K c and J.
I The basic paper with respect to ductile fracture is that of Devaux, Mudry, Pineau and Rousselier (Ref. 23).
The basic approach is very similar to that of Rice and Tracey (Ref.19), in that the equation for void growth is quite similar.
If the ratio of hydrostatic to effective stress is considered to be constant, this void growth equation may be integrated.
Then, dividing by the untaxial value:
p
'eff 1
e exp LO.5(TF-1)]
T This is exactly the Rice and Tracey equation as used by Hancock and Mackenzie (Ref. 6), and again indicates the type of behavior shown by Figure 5.
However, the application of the equation for void growth with this
" local" approach to ductile failure is quite different.
The material property experiment is conducted for the purpose of determining a critical value of void growth indicated by (R/R )c.
For example, the critical ratio o
for SA 508, Class 3, a typical reactor pressure vessel material, has been established.
The structure is fitted with a similar finite element analysis grid, but with the small grid extended from the cracl: tip so as to include the region of ductile crack growth of interest.
The analysis is performed until the critical void growth ratio is computed at the modeled crack tip.
Then, the model is modified by releasing the first pair of nodes beyond the tip and the analysis is repeated. When the critical value is again obtained, the process is repeated.
~
~
TELEDYNE ENGIllEERIflG SERVICES W. E. Cooper Page 20 June 3, 1991 Project 7377 l
An alternative approach, which does not require the sequential release of nodes at the cr0ck tip, has been developed by Rousselier in Ref.
24, and is based on damage mechanics, and he discusses both this and the technir.ue of Ref. 10.
Specifically, the damage variable is included in the constitutive equation for the material, as does Lemaitre. Damage results in the softening of the material and fracture results from the competition between-damage and strain-hardening.
Rousselier develops a plastic potential, which reduces to the usual plastic potential when there is no damage, with the additional term having three parameters which are calibrated by the performance of simple tests with associated finite element analyses.
These techniques have been applied to a number of experiments and practical problems.
Comparison with experiments indicates that the initiation of crack growth is predicted very well, and that subsequent crack growth is adequately predicted.
For example, the J-R curve is very well predicted from the results of material data developed, using a simpler finite element analysis grid, on grooved tensile specimens.
The " local" approach to brittle failure is based on the work of Mudry (Ref. 25) and Beremin (Ref. 26).
An essential feature of this approach is recognition that, since there is always considerable scatter in fracture toughness data, a statistical approach is required.
The classical approach of Weibull is followed and the measure of the material property or of the structural response is termed the "Weibull stress", with the symbol aw used to represent the quantity. As described earlier, the finite element model of the crack tip in both the specimen used to measure the material properties and in the structure contains a very small, square, grid with four integration (Gauss) points in each element at the crack tip.
The Weibull stress is entered into the Weibull distribution function to give the probability of failure, where ao is a material property as:
.m
- W PR " I ~ **P aoJ J
Useful relationships between the quantities used in this approach and and J c, common to conventional fracture mechanics have quantities, KIc I
been developed.
4
TELEDYNE ENGINEERING SERVICES W. E. Cooper Page 21 June 3, 1991 Project 7377
-The" local" approach has been used for the purpose of predicting material behavior under complex conditions based on data from simpler specimens.
For example:
The statistical development of the plane strain fracture toughness as a function of metal temperature using material data from a few grooved tensile specimens - with the results fitting the results of the many fracture toughness tests performed by the HSST program - some of which required Compact Tension specimens several inches thick.
4 The development of the effects of neutron irradiation on the plane strain _f racture toughness based on the effect of neutron irradiation'on the yield strength, with reasonable agreement with surveillance data.
The effects of a liquid nitrogen quenen on the surface of a precracked thick-walled cylinder, with _ excellent agreement with experiment (predicted crack propagation at 170-175 seconds compared to a measured value of 169 seconds), indication that the normal " global" approach gave unconservative answers, and correction of these answers by considering the effects of l
plastic strain on toughness predicted by the " local" approach.
The significance of underclad cracking in the presence of residual and thermal stresses.
The ductile fracture of an austenitic-ferritic duplex welded joint.
The significance of a cladding crack which just penetrates the base metal.
. = _
TELEDYNE ENGINEERING SERVICES W. E. Cooper Page 22 June 3, 1991 Project 7377
REFERENCES:
1.
Brownrigg, A., Spitzig, W. A.,
- Richmond, 0., Teinlinck, D. and Embury, J. D., Acta Metall., 31, 1983, pp. 1141-1150 2.
Coffin, L. F., Jr. and Rogers, H. C., Trans. ASM, 60, 1967, pp. 672-686 3.
Cooper, W. E, The Significance of the Tensile Test to Pressure Vessel Design, Welding J. Research Supp., January 1957 4.
Dodd, B. and Bai, Y., Ductile Fracture and Ductility, With Applications to Metalworking, Academic Press (London), 1987 5.
Gensamer, M., Strength of Metals Under Combined Stress, ASM,1940, p.
106 6.
Hancock, J. W. and Mackenzie, A. C., J. Mechanics and Physics of Solids, 24, 1976, pp. 147-169 7.
Harlin, G. and Willis, J. R., The influence of Crack Size on the Fracture Behavior of Short Cracks, Intl J. of Fracture, 42, 4, April 1990, pp. 341-356 8.
Hill, R., Mathematical Theory of Plasticity, Oxford,1950 9.-
- Lemaitre, J., A Continuous Damage Mechanics Model for Ductile-Fracture, J. Engrg. Materials and Technology, ASME, January 1985, pp.
83-89 l
10.
- Lemaitre, J., Micro-Mechanics of Crack Initiation, Intl. J. of l
. Fracture, 42, 1990, pp. 87-99 11.
Low, J. R., Jr., Direct Loading of Metals, in Properties of Metals in Materials Engineering, ASM,1948, pp. 59 12.
Lubahn,'J. D., Notch Tensile Testing, in Fracturing of Metals, ASM, 1948, pp.90-132 l
l 13.
Manjoine, M.
J., Multiaxial Stress and Fracture, in Fracture, an _ _
Advanced Treatise, Vol. 3, Engineering Fundamentals and Environmental Effects, Edited by H. Liebowitz, Academic Press, 1971, pp. 267-311 l
14.
McClintock, F. A., A Criteria fcir Ductile Fracture by the Growth of l
Holes, J. Appl. Mechanics, ASME, June 1968, pp. 363-371 15.
.McClintock, F. A.,
local Criteria for Ductile Fracture, Inti J. of g
l Fracture Mechanics, 4, 2, June 1968, pp. 101-130 l
l
TELEDYNE ENGINEERING SERVICES
- 8. E. Cooper Page 23 June 3, 1991 Project 7377 16.
McClintock, F. A., Plasticity Aspects of Fracture, in Fracture, an Advanced Treatise, Vol. 3, Engineering Fundamentals and Environmental Effects, Edited by H. Liebowitz, Academic Press, 1971, pp.48-277 17.
Nadai, A., Theory of Flow and Fracture of Solids, McGraw-Hill,1950 18.
Pellissier-Tanon, A.,
Grandemange, J., Houssin, Buchalet, C.,
French Verification of PWR Vessel Integrity, NP-6713, EPRI, February 1990 19.
Rice, J. and Tracey, D., On Ductile Enlargement of Voids in Triaxial Stress Fields, J. of Mechanics and Physics of Solids, 17, 1969 20.
Corten, H. T. and Sailors, R. H., Relationship Between Tensile Properties and Microscopically Ductile Plane Strain Fracture Toughness, STP 605, ASTM, 1976, pp. 34-61 l
21.-
Thomson, R. D. and J. W. Hancock, Ductile Failure by Void Nucleation, Growth and Coalescence, Inti J. of Fracture, 26, 2, October 1984, pp.99-112 22.
Weiss, V. and M. Sengupta, Ductility, Fracture Resistance, and R-Curves, STP 590, ASTM 1976, pp. 194-207 23 Devaux, J. C., Mudry, F., Pineau, A. and Rousselier, G., Experimental H
and Numerical Validation of a Ductile Fracture Local Criterion Based on a Simulation of Cavity Growth, Nonlinear Fracture Mechanics:
Volume 2 - Elastic Plastic Fracture, ASTM STP 995, 1989, pp. 7-23 24 Rousselier,13., Devaux, J. C., Mottet, G. and Devesa, G.,
A Methodology for Ductile Fracture Analysis Based on Damage Mechanics:
An Illustration of the Local Approach of Fracture, Nonlinear Fracture Mechanics: Volume 2 - Elastic Plastic Fracture, ASTM STP 995, 1989, l
pp. 332-354 25-Mudry, F., A Local Approach to Cleavage Fracture, Nuclear Engineering and Design, 105, 1987, pp. 65-76 l
26 Beremin, F. M., A Local Criterion for Cleavage Fracture of a Nuclear l
l Pressure Vessel Steel, Metallurgical Transactions,14A, November 1983, pp. 2277-2287
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TABLE 1 Dystcr Creek taw Data for Accident with Pressure at 62 psi - No Sand - Hydrostatic Stress (Sam Sa, Sy, S2) inside modes Outside Modes Radiat Meridionat Hoop Radial Heridional Hoop Mode x
Y Theta Node S3 SY S2 Hydrostatic hode SX St SZ Hydrostatic (inch)
(inch) (degrees)
(psi)
(psi)
(psi)
(psi)
(psi)
(psi)
(psi)
(psi) 3 247.08 106.93 36.00 1
792.66 -10715.00 -3044.40 -12966.74 3 12534.00 42743.00 16590.00 71867.00 5
248.68 108.10 36.27 4
210.83 -7194.20 -1933.60
-8916.97 6 -3592.30 38545.00 11030.00 45982.70 8 350.28 109.28 36.54 7 -142.29 105.19 1008.90 761.42 9 963.33 30821.00 11219.00 43003.33 11 351.87 110.46 36.81 to
-3.73 5967.30 4109.70 10073.27 12 -240.90 24404.00 10348.00 34511.10 14 253.45 111.66 37.08 13
-67.77 10646.00 6983.80 17562.03 15 58.44 19538.00 10540.00 30136.44 17 255.03 112.86 37.35 16
-20.34 14300.00 9749.70 24029.36 18
-10.31 15852.00 11066.00 26907.70 20 356.61 114.06 37.62 19
-39.06 16923.00 12330.00 29213.94 21
-10.40 13126.00 11907.00 25022.60 33 258.18 115.28 37.89 22
-17.63 18739.00 14613.00 33334.37 24
-8.71 11295.00 12953.00 24239.29 26 259.74 116.50 38.16 25
-24.25 19816.00 16544.00 36335.75 27
-22.58 10176.00 14100.00 24253.42 29 261.30 117.73 38.43 28
-13.34 20317.00 18155.00 38458.66 30
-22.00 9684.80 15305.00 24967.80 33 262.85 118.97 38.70 31
-15.70 20320.00 19450.00 39754.30 33
-32.13 9683.20 16508.00 26159.07 35 264.39 120.21 38.98
~ 34
-9.94 19943.00 20470.00 40403.06 36
-34.19 10091.00 17691.00 2T747.81 38 265.93 121.46 39.25 37
-9.58 19259.00 2'244.00 40493.42 39
-39.65 10807.00 188t31.00 29598.35 41 3G7.47 122.72 39.52 40
-6.30 18352.00 21819.00 40164.70 42
-42.00 11761.00 1992S.00 31647.00 44 269.00 123.99 39.79 43 5.35 1T285.00 22237.00 39516.65 45
-46.03 12881.00 20984.00 33818.97 67 270.52 125.26 40.06 46
-4.84 16119.00 22547.00 38661.16 48 4 0.00 14108.00 22007.00 36065.00 50 272.03 126.54 40.33 49
-3.32 14910.00 22796.00 37702.68 51
-52.89 15385.00 23014.00 38346.11 53 273.54 127.83 40.60 52
-4.92 13707.00 23030.00 34732.08 54
-58.63 16658.00 24015.00 40614.37 56 375.05 129.13 40.87 55
-1.29 12569.00 23301.00 35868.71 57
-59.86 1'40.00 25031.00 42851.15 59 376.54 130.43 41.14 58
-5.32 11541.00 23650.00 35185.68 60
-67.77 18985.00 26067.00 44984.23 62 278.04 131.74 41.41 61 2.92 10695.00 24130.00 34827.92 63
-66.27 19934.00 27142.00 47009.73 65 379.54 133.07 41.68 64
-4.55 10076.00 24781.00 34852.46 66
-79.29 20636.00 28253.00 48809.71 l
68 281.03 134.41 41.96 67 11.85 9803.40 25659.00 35474.25 69
-70.90 21042.00 29404.00 50375.10 71 282.52 135.75 42.23 70
-2.79 9914.30 26770.00 36681.51 72
-92.37 21015.00 30546.00 51468.63 I
74 384.01 137.11 42.50 73 29.00 10577.00 28186.00 38792.00 75
-70.T3 M530.00 31690.00 52149.2T TT 285.48 138.47 42.78 76
-1.16 11800.00 29867.00 41665.84 78 -109.08 19379.00 32728.00 51997.92 80 286.%
139.83 43.05 79 57.06 13840.00 31901.00 45798.06 81
-60.86 17588.00 33673.00 51200.14 83 388.42 141.21 43.33 82 2.20 16612.00 34104.00 50718.20 64 -131.88 14833.00 34264.00 48965.12 86 289.88 142.59 43.60 85 74.59 20487.00 36129.00 56690.59 87
-29.56 11283.00 34098.00 45351.44 89 291.33 143.98 43.87 88 TT.10 25087.00 35755.00 60919.10 90 -144.30 6500.20 308T2.00 37227.90 93 292.77 145.37 44.15 91 -289.08 30694.00 28926.00 59330.92 93 44.83 1345.50 20928.00 22318.33 95 294.21 146.77 44.42 94 981.58 30078.00 12763.00 43822.58 96
".040.80 2428.30 4981.30 8450.40 98 294.65 147.04 4'. 49 97 1175.50 16090.00 8864.90 26130.40 99 -322.66 6056.80 5757.90 11492.04 101 295.08 147.31 44.56 100 144.38 T229.00 6104.20 13477.58 102 -920.46 9373.40 6680.80 15133.74 104 296.51 148.72 44.83 103 37.48 8131.50 6961.90 15130.88 105 28.17 11092.00 8097.30 19217.47 107 297.92 150.14 45.10 106
-6.04 9535.60 7987.70 17517.26 108
-32.2s 9858.90 8361.50 18188.19 05-Jurv 91 NANtDSUM.natt Pagg 1
Dystsr Creek Raw Data for Accident with Pressure at 62 psi - No Sand - Hydrostatic Stress (Sun Sa, Sy, St)
Outside Wodes Inside modes Radial Meridional Hoop Radiat Meridional Hoop mode x
Y Iheta Mode SX ST 52 Hydrostatic Mode SX ST S2 nydrostatic
(!nch)
(inch) (degrees)
(psi)
(psi)
(psi)
(psi)
(psi)
(psi)'
(psi)
(psi) 110 299.33 151.56 45.37 109
-33.71 10502.00 8888.80 19357.09 111
-57.85 8742.90 8660.00 17345.05 113 300.74 152.99 45.65 112
-1.14 11329.00 9750.20 21078.06 114
-30.65 7914.20 9051.50 16795.05 116 302.13 154.42 45.92 115
-20.36 11890.00 10490.00 22359.64 117
-51.49 7363.20 9440.70 16752.41 119 303.52 155.87 46.19 118
-6.30 12305.00 11159.00 23457.70 120
-41.48 6967.90 9860.60 16787.03 122 304.91 157.31 46.47 121
-13.61 12554.00 11729.00 24269.39 123
-48.21 6711.00 10270.00 16932.79 125 306.28 158.77 46.74 124
-2.15 12688.00 12225.00 24910.85 126
-49.31 6591.20 10673.00 17214.89 128 307.65 160.23 47.01 127
-28.44 12714.00 12630.00 25315.56 129
-41.37 6573.90 11060.00 17592.53 131 309.01 161.70 47.28 130 18.06 12474.00 12934.00 25426.06 132
-44.48 6837.20 11483.00 18275.72 134 312.35 165.36 47.96 133 7.61 12021.00 13497.00 - 25525.61 135
-33.92 7344.20 12307.00 1 % 17.28 137 315.65 169.06 48.64 136 3.99 11540.00 13832.00 25375.99 138
-44.32 7889.00 12914.00 20758.68 140 318.91 172.81 49.31 139 6.37 11055.00 14001.00 25062.37 141
-51.02 8438.10 13359.00 21746.08 143 322.12 176.58 49.99 142 8.27 10670.00 14089.00 24767.2T 144
-53.37 8882.90 13660.00 22489.54 146 325.28 180.40 50.66 145 11.00 10457.00 14158.00 24626.00 147
-53.14 9159.70 13829.00 22935.56 149 328.40 184.25 51.34 148 16.14 10484.00 14247.00 24747.14 150
-49.04 9245.90 13868.00 23064.86 152 331.48 188.14 52.01 151 2.98 10717.00 14325.00 25044.98 153
-27.88 9206.10 13800.00 22978.23 l
155 334.51 192.07 52.69 154
-10.07 10776.00 14256.00 25021.94 156
-33.26 9324.90 13716.00 23007.64 l
158 337.49 196.03 53.36 157 2.62 10459.00 13978.00 24439.62 159
-40.48 9655.40 13655.00 23269.93 161 340.00 199.45 53.94 160 7.24 10091.00 13660.00 23758.24 162
-53.02 9973.30 13590.00 23510.28 164 342.48 202.89 54.52 163 0.T2 9882.20 13379.00 23261.92 165
-54.79 10206.00 13481.00 23632.21 117 344.93 206.36 55.10 166
-2.52 9789.00 13152.00 22938.48 168
-56.77 10347.00 13348.00 23618.23 170 347.34 209.85 55.68 169
-4.94 9770.80 12977.00 22742.86 171
-57.10 10413.00 13213.00 23568.90 i
173 349.71 213.36 56.25 1 72
-6.64 9799.10 12848.00 22640.46 174
-57.49 10425.00 13087.00 23454.52 l
173 352.05 216.90 56.83 175
-7.05 9854.40 12758.00 22605.35 177
-56.48 10401.00 12977.00 23321.53
(
179 354.35 220.46 57.41 178
-7.09 9922.90 12696.00 22611.81 180
-55.47 10358.00 12885.00 23187.53 182 356.62 224.05 57.99 181
-7.09 9995.10 12654.00 22642.01 183
-54.83 10310.00 12811.00 2306o.17 185 358.85 227.66 58.57 184
-6.90 10063.00 12625.00 22681.10 186
-54.11 10266.00 12753.00 22964.89 188 361.04 231.29 59.14 187
-6.94 10120.00 12604.00 22717.06 139
-54.07 10230.00 12709.00 22884,93 131 363.20 234.94 59.72 190
-6.76 10162.00 12588.00 22743.24 1' d 52.67 10210.00 12678.00 22835.33 194 365.32 238.61 60.30 193
-8.22 10177.00 12569.00 22737.78 1M N.62 10220.00 12660.00 22827.38 l
197 367.41 242.31 60.88 196
-7.82 10149.00 12545.00 22686.18 th 33.75 10275.00 12662.00 22883.25 l
200 369.45 246.03 61.45 199
-7.71 10083.00 12521.00 22596.29 20'
-54.22 10361.00 12679.00 22985.78 203 371.46 249.76 62.03 202
-5.79 9990.30 12508.00 22492.51 m
52.97 10476.00 12713.00 23136.03 206 373.43 253.52 62.61 205
-6.12 9668.80 12511.00 22373.68 207
-50.30 10618.00 12766.00 23333.70 209 375.36 257.30 63.19 208
-0.82 9736.50 12543.00 22278.68 210
-56.63 10790.00 12838.00 23571.18 212 377.26 261.09 63.77 211
-5.41 9628.90 12603.00 22226.49 213
-22.79 10983.00 12944.00 23904.21 215 379.11 264.91 64.34 214
-48.02 9179.50 12568.00 21696.48 216
-9.73 11689.00 13252.00 24931.27 Page 2 NAMYDstst.hatt 05 h 91 l
}yster Creek aaw Deta for Accident with Pressure at 62 psi - No Sand - Hydrostat c 5 tress (Sun Sa, Sy, Sz1 Outside modes inside hodes Radiat toeridional hoop andial esceidian t woop Mode X
Y theta mode SX SY S2 Nydrostatic made SX SY
$2 mydrostatic (inch)
(inch) ( *grees)
(pst)
(psi)
(psi)
(psi)
(psi)
(psi)
(ps6) tpu )
213 380.93 768.74 64.92 217
-14.72 TF18.20 12328.00 20131.48 219 - 76.M 1L 92.00 13884.00 26999.66 221 382.71 272.59 65.50 220
-6.42 6338.80 12208.00 18540.38 222
-75.59 14620.00 14698.00 29242.41 224 383.49 274.32 65.76 223 10.69 5464.90 12172.00 1764 T.59 223
-55.93 15502.00 15229.00 30675.07 227 384.26 276.04 66.02 226
-10.15 4796.80 12250.00 17036.e5 228
-61.53 16159.00 15737.00 31834.47 230 385.03 277.78 66.27 229
-5.46 4223.70 12439.00 16657.24 231
-62.86 16770.00 16306.00 33013.14 233 385.79 279.51 66.53 232 24.39 3711.50 1273T.00 16472.89 234
-35.T3 17270.00 16930.00 E164.27 236 386.54 281.25 66 79 235 130.33 4023.00 uS89.00 17542.33 237 -487.09 16259.00 17054.00 32825.91 239 386.75 282.00 66.90 238 50.63 10276.00 15475.00 25801.63 240 -288.91 14306.00 1a797.00 30e14.09
~41 295.17 19835.00 18657.00 38787.1T 243 511.86 119e5.00 16604.00 29080.86 242 386.97 282.74 67.00 245 387.40 253.76 67.15 244 -150.32 22295.00 19588.00 41732.68 246 12.15 9398.80 16027.00
?5437.95 248 387.82 284.77 67.30 247 1.27 21743.00 19773.00 41517.27 249 -103.66 9672.00 16357.00 25v25.34 251 388.24 285.79 67.45 250 8.41 21390.00 19532.00 41330.41 252
-23.32 10195.00 16778.00 26947.68 254 388.67 286.80 67.60 253
-16.03 20922.00 20010.00 40915.97 255
-68.66 10588.00 170e9.00 27608.34 257 389.08 287.82 6T.75 256 1.26 20518.00 20084.00 40603.26 258
-46.06 18040.00 17402.00 28395.95 260 389.50 288.84 67.90 259
-7.69 20096.00 20113.00 40201.31 261
-57.99 11453.00 17662.00 2V057.01 263 309.91 289.86 68.05 202
-4.89 19699.00 20124 00 39818.11 264
-50.97 11868.00 17900.00 29717.03 266 390.32 290.88 68.70 265 0.91 19313.00 20111.03 39424.91 267
-60.45 12259.00 18101.00 30.'*9.52 269 390.73 291.90 68.35 268
-28.36 18945.00 20069.00 38985.64 270
-36.13 12640.00 18286.00 3G889.87 2 72 391.13 292.93 68.50 271 24.63 1a330.00 19959.00 38313.63 2 73
-66.07 15270.00 18510.00 31713.93 2 75 392.28 295.87 68.93 2T4 2.33 17509.00 19773.00 37284.83 2 76
-44.99 14123.00 18819.00 32897.05 278 393.40 298.82 69.34 ZTT 5.60 16314.00 19534.00 36353.60 279
-58.78 14848.co 18987.00 33776.22 281 394.50 301.77 69.79 280 0.96 16489.00 19259.00 35578.96 282
-57.65 15395.00 19060.00 34397.35 284 395.58 304.74 70.22 283
-0.38 155!9.00 19069.00 34987.62 285
-58.94 15777.00 19065.00 34783.06 287 396.64 307.71 70.65 286
-0.80 15682.00 18892.00 34573.20 258
-56.12 16011.00 19029.30 34983.58 290 397.67 310.69
?1.08 289
-2.29 15551.00 18765.00 34313.71 291
-54.97 16137.30 18974.00 35054.03 293 398.68 313.e4 11.51 292
-1.29 15502.00 18/,86.00 34186.71 294
-53.84 16188.00 18912.00 35046.16 296 399.67 316.68 71.94 295 2.31 15543.00 1865T.00 34202.31 297
-49.04 16180.00 18841.30 34971.96 299 400.64 319.68 72.37 298 6.67 15702.00 18677.00 34385.67 300
-45.34 16146.00 18755.00 34855.66 302 401.58 322.69 T2.80 301 11.30 15978.00 18732.00 3 721.30 303
-31.12 16121.00 18650.00 34739.88 305 402.51 325.71 73.23 304
-5.76 16184.00 18751.00 34929.24 306
-40.89 16123.00 18570c30 34652.11 308 403.41 328.73 73.66 307 T.89 16085.00 18660.00 34752.89 309
-33.95 16112.00 18553.00 34631.05 311 404.28 331.76 74.09 310 9.26 15865.00 18514.00 34385.26 312
-41.00 16095.00 toS50.00 34606.00 314 405.13 334.80 74.52 313 2.81 15767.00 ta191.00 34160.8*
315
-45.28 16131.00 18528.00 34613.72 31T 405.97 337.84 74.95 316
-1.32 15756.00 15302.00 34056.68 318
-50.14 16186.00 18496.00 34631.86 320 40C.77 340.89 75.38 319
-4.04 15780.00 18251.00 34026.96 321
-53.03 16214.00 18465.30 34625.97 323 407.56 343.95 75.81 322
-4.68 15809.00 18236.00 34040.32 324
-53.52 16196.00 18438.00 34580.48 l* age 3 aANb5Wt.W1 05 Jun 91
e t
j 0pster Creek Ram Data for Accident with pressure at 62 psi - to Sand - It:-1 estetic Stress (Stan Su, Sr. 50 -
]
Outside bodes Inside Modes padiet ; steridienst recp Radial. steridienst moap tode N
Y 1hete. Wade SM SY
$2 Wydrostatic made SE SY
$2-wydrostatic (inch) '(inch) (dmerees)
(psi)
(psi)
(psi)'
(psi)
(psi)
(psi)
(psi) igi) 326 - 40s.32 347.01 76.24 325
-2.12 15446.00 18257.00 34100.88 327
-50.72' 16117.00 18416.00 34502.28 329 409.06 350.08 76.67 32B 0.41-15905.00 18306.00 1 34211.41 330
-47.37 16050.00 15393.00 34395.63 i;
332 -409.77 353.15 TT.10 331 a..m Me23.co 18t3es.80 34407.as 333'
-44.36 '15965.00 1 362.00 342s2.u 335 410.47.' 3 %.23
. 77.53 334' 10.02 4 228.00 18647.80 34795.02 3M
-32.25.15922.00 18314.00 34203.5
' 5.2s %392.es ta5 %.es 349s2.72 339
.-42.96 15947.00 182s2.00 34186.04 338 411.14 359.31 77.96 337 f
341 411.75 362.40 75.39 348 2.85, 4321.00 18668.00 34791.05 3Q.
-41.27 15978.00 18280.00 34225.73 l
344 412.41 365.49 78.82 343 4.4 4 145.00 14MT.00 34516.13 345
-46.15 15990.00 18294.00 34237.85 367 413.01 368.59 79.25 346
-1.29 16e66.00 14274.88 34318.71 348
-49.13 2019.00 13275.00 3 442.a7
' 350 413.54 371.69 79.as 349
-2.91 15996.00 18193.es 34186.09 351
-49.96 16062.00 18239.0c 3 Q51.05 353' 414.14 374.a0 -
30.11 352
-3.45 15968.88 18120.00 34004.55 -
354
-51.15 16117.00 18205.00 3 Q 70.85 I:
3%
414.67-3TT.91 80.M 32
-4.99 15953.98 18863.00 34011.01 357
-53.44 16159.00 18168.00 3473.56 i
359 415.17 381.02 80.9T '
358
-6.63 15953.00 18024.00 33970.37 360
-54.82 M178.00 18133.00 34256.1a l-362 415.66 3e4.14 31.40 361
-6.77 15958.00 18000.00 33951.23 363
-54.82 *161TE.00 18101.00 3 Q24.12 i
M5 4 4.12 387.26 81.83 364
~6.39 15968.00 179e5.00 33964.61 366
-M.03 16 %7.00 18075.00 ' 34187.97 364 44.%
390.38 a2.26 MT
-5.77 15981.08 17978.80 33953.23 369
-53.35 16145.00 18053.00 34144.65 i
3 71 4 4.97 393.51 32.69 370
-4.82 14400.00 17976.00 339T1.18 3 72
-51.75 16117.00 18036.00 34101.26 l
3 74 417.M 396.64 83.12 373
-6.18
%e22.e0 1M75.es 33990.82 375
-52.77 16096.00 18023.00 34066.23 I
3 77 417.72 399.78 83.55 376
-6.95 16037.es 17974.se 340e4.05
' 378
-54. 0 160es.00 18015.00 3404a.94 I
300 418.07 402.91 83.98 379
-5.99 %048.00 17979.80 34012.11' 361 4 3.57 16079.00 18006.00 34031.44 383 414.39 406.05 34.41 382
-4.30 M066.98 17968.00 5 330.20 384
-51.58 16068.00 1 M9T.00 34013.c 3e6 414.68 409.19 84.e4 385
-6.91 M4444.00 17966.00 34043.09 387.
-53.27 16069.00 17991.00 34006.73 389 418.95 412.33 85.27 386
-6.3e 16082.00 17957.0G 34032.70 390
-53.27 16084.00 '17986.00 3401).73 392 419.20 415.48 85.70 391
-5.82 % 067.08 17945.00 34006.18 393
-53.45 M096.00 17983.00 34025.55 395 419.43 418.63 86.13 3M
-6.46. 16059.00 1 M30.Se 33906.54 396
-53.s5 M106.00 17978.00 34030.15 396 - 419.63 421.75 86.%
'397
-6.68 %055.00 17925.e0 33973.32 399
-54.13 16113.00 179T.00 34029.87 401 419.81 424.93 a6.99
- Je
-6.93 Me54.ee 17919.00 33966.37 402
-%.42 16118.00 17965.00 34023.5a 404 419.96 428.08 87.62 483
-T.18 M055.00 1M14.00 33961.82 405
-54.62. *.6119.00 17960.00 34G24.3d 407 420.09 431.23. 87.85 406
- T.09 %054.00 1M11.00 33961.91 408
-54.43 4120.00 17955.00 34020.57 y
. 413 420.29 434.38 88.28 489
-T.06 Me61.00 17908.00 33961.94 411
-54.44 412G 00 17950.00 34015.56 l
413 420.28 437.%
88.71 412
-T.05 M065.00 17907.80 33964.95 414
-54.45 16119.00 17945.00 34009.55 416 420.34 440.69 39.14 415
-T.05 M070.00 17905.80 33967.95 41T
-54.4 16117.00 17940.0G 34002.58 4t9 429.37 443.85 89.57 418
-6.96
%CT4.00 17903.00 33970.04 40
-54.30 16115.00 17935.00 33995.70 j
422 420.39 447.00 90.e0 421
-6.76-16079.00 17901.01 33973.24 43
-54.05 16113.00 17929.00 33987.95 l
425 420.37 450.15 90.43
_424
-6.99 M004.00.17898.00 33975.01 426
-54.26' 16112.00 17922.00 33979.T4 428 Q0.34 454.31 90.86 42T
-F.11
% 009.00 17893.00 33974.84 49
-54.42 16110.00 17915.00 33970.59 5
'431 420.28 4%.46 91.29 430~
-T.1T 4 092.00 17806.00 3393D.d 432
-54.37 4107.00 1790s.00 33960.63 j.
1]re4 mmostm.wt 05
- 91
,i
. Oyster Creek Raw Data for Accident with Pressure at 62 pst - to Sand - urdrostatic stress (sum sa, sy, sa)
Outside Wodes inside m
- s Radiat Meridional hoop Radial peridional hoop tode X
Y 1hete Node SX 51 12 Nydrostatic Mode 5X SV
$2 MW rostatic i
(irmh)
(irth) (degrees)
(psi)
(psi)
(psi)
(psi)
(psi)
(psi)
(psi) spsi) 434 420.20 459.62 91.72 433
-6.57 16095.00 178T7.00 33965.43 435
-53.59 16103.00 17901.00 33950.41 437 420.09 462.TT 92.15 436
-6.32 16095.00 17868.00 33956.68 438
-53.16 16099.00 17894.00 33939.84 440 419.M 445.92 92.58 439
-5.49 16093.00 17859.00 33946.51 441
-52.07 16098.00 17887.00 33932.93 443 419.81 469.47 93.01 442
-4.37 16092.00 17852.00 33939.63 444
-50.T4 16101.00 17881.00 33931.27 446 419.63 472.22 93.44 445
-3.73 16097.00 17867.00 33940.2T 447
-49.27 16121.00 17875.00 33947.73 449 419.43 475.3T 93.87 448 1.41 16109.00 1'544.00 33954.41 450
-45.48 16171.00 17872.00 33997.52 452 419.20 478.52 94.30 451
-3.35 16135.03 17845.00 33976.65 453
-53.63 16229.00 17874.00 34049.37 455 418.95 481.67 94.73 454
-2.60 16137.00 17838.00 33972.40 456
-50.00 16223.00 17875.00 34048.00 458 418.68 484.81 95.16 45T
-2.54 16112.00 17824.s0 33933.46 459
-48.46 16180.00 178,'O.00 34001.54 461 418.39 487.95 95.59 460
-4.22 16102.00 17816.00 33913.75 462
-50.87 16166.00 17864.00 33979.13 464 418.0T 491.09 96.02 463
-5.56 16102.00 17813.00 33909.44 465
-52.26 16163.00 17860.0c 33970.74 44 7 417.72 494.22 96.45 466
-6.30 16106.00 17815.00 33914.70 468
-53.2) 16162.00 17857.00 33965.73 470 417.36 497.36 96.88 469
-T.07 16110.00 17819.0c 33921.93 4 71
-54.15 16160.00 17855.00 33960.85 4 73 416.9T 500.49 97.31 4 72
-6.97 16113.00 17824.00 33930.03 4 74
-54.12 16156.00 17856.00 33957.88 474 416.56 503.62 9 7.74 475
-T.15 16114.00 17827.00 33933.85 477
-54.34 16153.00 17857.00 33955.66 479 416.12 506.74 98.1T 478
-T.05 16114.00 17830.00 33936.95 480
-54.44 16150.00 17859.00 339 %.76 482 415.66 509.86 98.60
'.81
-T.06 16111.00 17832.00 33935.94 483
-54.24 16149.00 17861.00 33955.76 485 415.17 512.98 99.03 484
-6.98 16109.00 17832.00 33934.02 486
-54.1.
16148.00 17862.00 339 n 84 488 414.67 516.09 99.46 487
-T.10 16105.00 17831.00 33928.90 489
-54.28 16145.00 17864.00 33957.T2 41 414.14 519.20 99.89 490
-T.18 16100.00 17829.%
33921.82 492
-54.37 16150.00 17866.00 33961.63 494 413.58 522.31 100.32 493
-T.20 16093.00 17826.00 33911.80 495
-54.40 16153.00 17868.00 33966.60 497 413.01 525.41 100.75 496
-T.19 160tu.00 17824.00 33a02.81 498
-54.35 16157.00 17871.00 33973.65 500 412.41 528.51 101.18 499
-T.23 16076.00 17821.00 33889.77 501
-54.31 16163.00 17876.00 33984.69 503 411.78 531.60 101.61 502
-T.28 16065.00 17820.00 33877.72 504
-54.50 16170.00 17883.00 33998.50 506 411.14 534.69 102.04 505
-T.14 16054.00,17822.00 33868.86 507
-54.39 16178.00 17892.00 34uts.61 509 410.47 537.77 102.4T 508
-6.94 16043.00 17826.00 33862.06 510
-54.29 16155.00 17904.00 340*,4.71 512 409.77 540.85 102.90 511
-6.66 16034.00 17835.00 33862.34 513
-53.97 16101.00 17920.00
%C57.03 515 409.06 543.92 103.33 514
-5.70 16030.00 17850.00 338T4.30 516
-53.64 16193.00 17940.c0 34079.36 518 408.32 545.99 103.76 517
-4.06 16042.00 17876.00 33913.92 519
-55.15 16186.00 17960.00 34090.85 521 40T.56 550.05 104.19 M
-5.18 16084.00 17919.00 33997.82 522
-55.38 16150.00 17974.00 34068.62 524 406.77 553.11 104.62 523
-5.05 16150.00 17975.00 34119.95 525
-53.61 16080.00 17978.00 34004.39 52T 405.97 556.16 105.0L 36
-4.46 16237.00 18035.00 34267.54 528
-53.41 15988.00 tiv70.00 33904.59 530 405.13 559.20 105.48 529
-3.48 16350.00 18093.00 34439.52 531
-52.56 15875.00 17946.00 33768.44 533 404.28 562.24 105.91 532
-2.77 16491.00 18143.00 34631.23 534
-51.77 15738.00 17e96.00 33582.28 536 403.41 565.27 106.34 535
-1.91 16662.00 18174.00 34834.09 53T
-50.23 15581.00 17813.00 33343.77 539 402.51 568.29 106.TT 538
-1.90 16857.00 18173.00 35028.10 540
-49.54 15407.00 17689.00 33046.46 Page 5 kAMDSLM.w 1 CFJun 91
Oyster Creek Raw cate for Acciernt with Presswe at 62 psi - so sard - nydrostatic stress (sus sa, sy, sa)
Outside modes Inside modes Radial steridional
- oop Radiat steridionat moop mode X
Y 1heta made sX sY 52 pydrostatic mode s1 ST 52 nydrostatic (inch)
(incM (desrees)
(psi)
(psi)
(psi)
(psi)
(psi)
(psi)
(psi)
(psi) 542 401.58 5T1.31 107.20 541
-1.22 17068.00 18124.00 35190.78 543
-47.43 15227.00 1751T.C0 32696.58 545 400.64 574.32 107.63 544
-2.69 17270.00 18007.00 35274.31 546
-46.54 15058.00 17298.00 32309.47 548 399.67
$77.32 108.06 547
-3.14 17431.00 17804.00 35231.86 549
-44.19 14930.00 17039.00 31924.81 551 398.68 580.32 108.49 550
-T.21 17498.00 17494.00 34984.79 552
-44.05 14878.00 16748.00 31581.96 554 397.67 583.31 108.92 553
-T.88 17412.00 17081.00 34485.12 555
-38.81 14956.00 164 %.00 31353.19 557 396.M 586.29 109.35 556
-10.37 17091.00 165T0.00 33650.63 558
-34.79 15217.00 16116.00 31300.21 560 395.58 589.26 109.78 559
-9.96 16480.00 15953.00 32423.04 561
-24.17 15751.00 15828.00 31554.84 563 394.50 592.23 110.21 562
-8.62 1U52.00 15221.00 30764.38 564
-23.24 16672.00 15615.00 V263.76 566 393.40 595.18 110.64 565
-26.42 14248.00 14388.00 2C609.58 567 0.32 18240.00 15561.00 338o n.=
569 392.28 598.13 111.07 568 43.95 12461.00 13531.00 26035.95 5 70
-42.45 20557.00 15732.00 36246.55 5 72 391.13 601.07 111.50 5 71 T1.68 11355.00 13087.00 24513.68 573
-36.04 22716.00 16076.00 38755.96 575 390.73 602.10 111.65 5 74 9.90 11529.00 13147.00 24685.90 5 76
-96.18 23096.00 16167.00 391a:. 82 578 390.32 603.12 161.80 577
-8.98 1205T.00 13354.00 25402.C2 579
-29.60 22304.Jo 16058.00 38332.40 581 389.91 604.14 111.95 580 3.33 12563.00 13592.00 26158.33 582
-41.50 21619.00 159e5.00 37562.50 584 3 M.50 605.16 112.10 583
-2.25 13001.00 13833.00 26831.75 585
-40.68 20988.00 15955.00 36902.32 587 389.08 606.18 112.25 586
-6.45 13388.00 14081.00 27462.55 588
.T.06 20430.00 15963.00 36345.94 590 388.67-607.20 112.40 589 6.22 13745.00 14347.00 28098.22 591
-34.46 19955.90 16018.00 35938.54 593 388.24 608.21 112.55 592 420.40 14015.00 14593.00 28587.60 594
-61.45 19501.00 16082.00 35521.55 l
596 387.82 609.23 112.70 595 12.92 14338.00 14890.00 29240.92 597
-28.81 19198.00 16221.00 35390.19 599 387.40 610.24 112.85 598 25.87 14456.00 15134.00 29615.87 600
-17.39 18780.00 16329.00 35091.61 602 38o.97 611.26 113.00 601 0.33 15183.00 15560.00 50743.33 603 -597.87 17667.00 16057.00 33126.13 605 386.88 611.39 113.02 604 204.33 18286.00 165T3.00 35063.33 606 261.05 17220.00 16228.00 33709.05 608 386.11 613.20 113.29 607
-42.86 19409.00 1T200.00 36566.14 609
-84.09 16169.00 16213.00 32297.92 C1I 385.33 615.01 112.56 610
-8.55 1958T.00 17591.00 37169.45 612
-43.03 1594T.00 16521.00 32424.97 c15 384.54 616.81 113.83 613 4.30 19728.00 17928.00 37660.30 615
-36.23 15920.00 16831.00 32714.77 417 383.74 618.61 114.09 616
-14.81 19718.00 18177.00 37880.20 618
-55.74 15922.00 1T100.00 32966.26 620 382.93 620.41 114.36 619 1.03 19673.00 18393.00 38067.03 621
-42.34 16024.00 1727.00 33348.66 623 382.11 622.20 114.63 622
-10.92 19547.00 18545.00 38081.c8 624
-55.C2 16140.00 17591.00 336 5.98 626 381.29 623.98 114.90 625
-2.22 19403.00 1866T.00 38067.78 627
-47.91 16299.00 17800.00 34051.09 on 380.45 625.77 115.1T 628
- T.53 19224.00 18747.00 37963.47 630
-53.65 16458.00 17972.00 34376.35 437 379 il 627.55 115.44 631
-3.04 19044.00 18802.00 37842.96 633
-50.08 16629.00 18122.00 34700.92 035 378.76 629.32 115.70 634
-5.65 18858.00 18826.00 37678.35 ou
-53.01 16790.00 18243.00 34919.99 o38 377.91 631.09 115.97 637
-3.65 18682.00 18833.00 37511.35 639
-51.46 169".8.00 18342.00 35238.54 641 377.04 632.86 116.24 MO
-5.07 18516.00 18820.00 37330.93 642
-53.03 17090.00 18418.00 35454.97 644 376.16 634.63 116.51 M3
-4.36 18%T.00 18796.00 37158.64 M5
-52.45 17221.00 18476.00 35M4.55 MT 375.28 636.39 116.78 646
-5.26 18234.00 18763.00 36991.74 M8
-53.39 1T336.00 18515.00 35797.62 hAN fD9At.4A1 05-Jure 91 page g a
k e ster Creek Ram Data for Accident with Pressure at '62 psi - no Sand - mydrostatic Stress (sum Sa, sy, 52) r
{
thatside hodes Inside modes Radial fearidionet moop Radial w idional mooo sede X
Y 1hete mode
' SK ST 52 bydrostatic_
mode 51 ST
?Z mydrostatic (inch)
(inch)' (degrees)
(psi)
(psi).
(psi)
(psi)
(psi)
(psi)
(psi)
(psi) ese 374.39 ' 638.14 117.05' M9'
-5.09 18119.00.18724.00 ' 36837.91 651
-53.19 1T437.00 18540.00 35923.81 p
653 -3T3.49 639.e9 '117.31 652
-5.49 18822.00 18681.00 36697.31 6%
-53.71 1F523.00 18551.00 36020.29 0% 3T2.58 - 641.64 117.58
.%55
-5.79 17941.00 18656.ee = 36571.21 657
-53.62 17594.00 18551.00 36091.38 i
l ' 659 371.67 M3.38 - 117.85
.'658
-6.18,178 5.80 1859e.00 36458.90 660 754.04 17653.00 18543.00 36141.96 662 - 370.74 M 5.12 118.12
'641
-6.76. 17822.00 18543.00 36358.24 M3
-53.4T 17700.00 18528.00 M1T4.53 M5.. 369.81 64.85 110.39
- 666
-5.08 17T79.e0 18498.98 M271.92 au
-55.33 17737.00 18507.00 M188.67
- 668 368.8T 648.58 118.66..667 3.41. 17811.88.18475.00 36289.41
- 669
-61.21 17707.00 18464.00 M109.79 CT1 368.00 648.72 118.68
> 670 8.00. 177e0.e8 184M.00 36252.80 672
-e9.27 17T43.00 18469.00 M142.73 i-675 MT.64 650.82 119.00-673
-5.M 17699.00 18396.00 360e9.36 675
-54.63 17821.00 18454.00 M 220.3T CTT _3M.48 652.91 119.33 676
-T.52 17706.88 18360.00 36058.48 678
-53.52 17814.00 18410.00 M170.48 600 M5.30 654.99 119.66 679
-T.% ' 1TT12.00 18323.00 M027.4 6G1
-53.99 17806.00 18368.00 M120.c1 4
683 M4.11 657.06 l119.98 6e2
-7.63 ' 1TT14.08 18284.00 35990.3T 604
-53.47 17802.00 18329.00 36077.53 I
6e6 362.91 659.13 120.31-
. 6e5
- T.M IT70s.80 18243.00 35963.96 687
-52.52 17805.00 18295.00 3606T.48 esp M1.70 661.19 120.63
' 6e8
-6.57 17600.0e 18199.0e 35002.43 690
-51.66 17819.00 18266.00 36031.34 692 360.47 663.25 120.96 691
-5.81 17659.00 18153.00 35006.19 693
-50.31 17851.00 18245.00 36045.69 4
695' 359.24 665.30 121.29
. 694
-4.79 17612.00 18108.00 ' 35715.21 696 4 9.52 17909.00 18232.00 36c91.48 695 357.99 667.34 121.61 697
-5.31 1550.80 18062.00 35606.69 699
-47.35 18009.00 18233.00 36194.65 791 3 %.73 669.37 12!.94 700 '
1.66 17469.00 18021.00 3% 91.66 702
-48.42 181M.00 18249.00 36364.58 i:
Fe4 355. 4 671.40 122.26 703 9.30' 17440.00. 10005.80 35445.30 705
-59.20 182T1.00 182M.Mi 36475.80 787 3 %.17 673.42 122.59-706
-1.14 1504.00 18031.00 35533.86 108
-51.66 18'89.00 18255.00 36392.34
}
718 352.88 675.43 122.92 709
-4.45 17593.09 18079.08 3 % 67.55 711
-46.83 18026.00.18237.00 36216.1T i
713 351.5T 677.43. 123.24 T12
-4.32 17670.00 '18132.08 35797.68 T14
-49.41 17913.00 18232.00 36095.59 i
. Tie' 350.26 679.43' 123.5T T15
-5.42 ITT35.00 18108.80. 3591T.58 TIT
-50.22 17836.00 18239.00 36024.78 719 348.93 681.42 123.89 718
-5..*1 17791.00 18245.00 36030.29 720
-51.09 1T781.00 18254.00 35983.91 T22 347.59 683.40 124.22-T21
-S.29 17838.co 18299.00 361%.T1 723
-51.96 ITT38.00 18273.00 35959.M T25 346.24 655.37 124.55 T24 ' -6.4 17876.00 18350.00 36219.54 726
-52.47 17705.00 18293.00 35965.53 j
72s 344.es - 687.34 124.87 727
-6.42 1790s.es 18394.00- 36295.58 T29
-5 ?.82 17678.00 18313 00 35938.18 T31 343.50 6w.30 125.20 TSO
-6.28 17935.00 1M3e ce M35s.n 732 52.72 iT657.00 18329.00 35933.za i
T34 342.12 691.25 125.52 T33
-6.43 17959.00 18457.J0 M409.57 T35
-53.00 17639.00 18340.00 35926.00
{
737 340.M 693.19 125.e5 736
-6.4 17981.90 18474.88 36448.54 T38
-53.11 17621.00 18344.00 35911.89 740 339.32 695.13 126.18 T39
-4.62' 10001.00 '186e0.08 36(74.38 741
-53.26 17605.00 18339.00 35890.T4 T43 337.90 697.05 126.50 74 2
-6.73 18019.00 18475.G3 36487.27 T44
-53.31 17589.00 18326.00 35061.69 1-
'T4 3M.47 698.97 126.83 745
-4.99 18034.00 184%.00 36483.01 747
-53.39 175T4.00 18305.00 35325.61 l
741P 335.03. 700.P8 127.15 T48
-6.91 18043.00 18425.00 36461.09 750
-53.10 1T564.00 18275.00. 35785.90 j'
'752 333.58 702.79 127.48 751
--T.05 '18043.00 18379.00 36414.95 53
-52.08 17563.00 18240.00 35150.12 i
'55 332.i2 704.68 127.81 754 6.87 ie028.se lesi9.00 36340.i3 r56
-52.i2 17573.00 18200.00 35720.8s t
i f
jrase T mantosuu.w t 05-Je 91 I
i t
O sy, sa)
Raw Data for Accident + ith Pressure at 62 pst - no Saruf - mydrostatic stress tsua su, syster Creelt Inside modes Outside modes Radial steridional Moop Radiat Meridional Mory Node X
Y Theta Wode sX 57
$2 Nydrostatic hade SX ST 52 Mydrostatic (inch)
(inch) (dega.es)
(psi)
(psi)
(psi)
(psi)
(psi)
(gui)
(psi)
(psi) 58 330.65 706.57 128.13 757
-6.44 17992.00 18246.00 36231.56 759
-51.04 17596.00 18158.00 35702.96 761 329.17 708.44 128.46 760
-5.4T 1F932.00 18163.00 36089.53 762
-49.29 17639.00 18117.00 35706 71 764 327.67 710.31 128.78 763
-4.60 17843.00 18073.00 35911.40 765
-47.69 17710.00 18079.00 35741.31 767 326.17 712.17 129.11 766
-3.2T 17729.00 17978.00 35703.73 768
-45.07 17826.00 18049.00 35829.93 770 324.66 714.02 129.44 769
-1.18 17587.00 17878.00 35463.83 771
-43.52 18016.00 18031.00 36003.48 T73 323.13 715.87 129.76 772
-2.53 17412.00 17775.00 35184.47 774
-38.69 18321.co 18034.00 36316.31 T76 321.60 717.70 130.09 T75 12.05 1T195.00 17674.00 34884.05
/TT
-42.50 18749.00 18063.00 36769.50 T79 320.05 719.53 130.41 778 9.25 17101.00 17627.00 34737.25 780
-67.19 19031.00 18085.00 37048.81 782 318.50 T21.34 130.74 781 6.95 1T223.00 17665.00 34894.95 783
-48.36 18845.00 18062.00 36858.65 785 316.93 T23.15 131.0T
/84
-1.71 1T410.00 17747.00 35155.29 786
-38.19 18453.00 18022.00 36436.81 l
788 315.35 724.95 131.39 787
-1.22 17566.00 17834.00 35398.78 789
-43.84 181 5.00 18010.00 36141.16 791 313.T7 T26.74 131.72 790
-3.86 17694.00 17921.00 33611.14 M2
-45.71 17999.00 18021.00 35974.30 794 312.17 728.52 132.04 793
-4.67 1 TNT.00 18009.00 35801.33 795
-47.77 17894.00 18050.00 35896.23 797 310.56 730.29 132.37 796
-6.26 17873.00 18095.00 35961.T4 798
-49.99 17830.00 18c90.00 35870.01 800 308.94 T32.06 132.70 799
-6.79 17923.00 18179.00 36095.21 801
-51.%
17795.00 18141.00 35884.67 803 307.32 733.81 133.02 802
-T.T5 17946.00 18257.00 36195.25 804
-53.01 177M.00 18198.00 35923.99 806 305.68 T35.55 133.35 805
-T.00 17950.00 18328.00 36271.00 807
-52.8i ITT75.C") 18260.00 35982.17 809 304.03 T37.29 133.68 808
- T. 3 T 17939.00 18392.00 36321.63 810
-53.47 17780.00 18325.00 36051.53 l
812 302.38 739.01 134.00 811
-6.38 17924.00 18450.00 36367.62 813
-53.22 17791.00 18390.00 36127.78 815 300.71 740.73 134.33 814
-6.88 17908.00 18503.r3 36404.12 816
-54.08 17800.00 18451.00 36196.93 818 299.03 742.44 134.65 817
-5.37 17899.00 18556.00 36449.63 819
-53.07 17803.00 18510.00 36259.93 821 297.35 744.13 134.98 820
-6.T3 1T899.00 18606.00 36498.27 822
-54.71 17793.00 18562.00 36300.29 824 295.65 745.82 135.31 823
-4.38 17919.00 18660.00 36574.62 825
-52.80 17769.00 18608.00 36324.11 827 293.95 747.50 135.63 826
-T.09 17954.00 18713.00 36659.91 828
-55.75 1772Lc0 18641.00 36306.25 f
l 830 292.23 749.16 135.96 829
-3.05 18021.00 18773.00 36790.95 831
-52.20 17654.00 18466.00 36267.80 833 290.51 F50.82 136.28 832
-8.06 18108.00 18829.00 36928.94 834
-57.46 17551.00 18670.00 36163.54 8M 2S8.7T 752.47 136.61 835
-1.75 18237.00 18890.00 37125.25 837
-50.25 17430.00 18660.00 35039.75 139 287.03 754.11 136.94 838
-T.42 18383.00 18939.00 37314.58 840
-61.05 17260.00 18616.00 3*,816.%
l 842 285.28 755.74 1.'T.26 841
-T.37 18582.00 18983.00 37557.63 843
-40.96 17080.00 18554.00 35597.04 845 283.52 757.36 13T.59 844
-0.45 18694.00 18977.00 37670.55 846
-62.?e 16962.00 18 80.00 35379.72 848 280.5T 760.02 138.13 847 16.38 18922.00 18910.00 37848.38 849
-52.16 16725.00 18280.00 34952.84 851 277.60 762.66 138.67 850
-6.88 19346.00 18774.00 38113.12 852
-42.65 16281.00 17906.00 34144.35 i
854 274.61 765.27 139.21 853 7.13 19731.00 18474.00 38212.13 855
-28.4T 15923.00 17402.00 33296.53 857 871.59 767.85 139.75 856
-14.29 19903.00 17894.00 37782.71 858
-30.52 15742.00 16749.00 32460.48 860 268.55 770.40 140.29 859
-6.38 19728.00 16988.00 367D9.62 861
-9.50 15978.00 16007.00 31975.50 863 265.48 TT2.92 140.84 862
-42.77 18895.00 15655.00 34507.23 864
-11.81 16828.00 15230.00 32046.20 Ob Jun 91 RANTDsLM.hm1 Page 8
- ster Creek Raw Data for Accidmt unch Pressure at 62 psi - so Sand - mydrostatic stress (sus sa, sy, sa)
Ntside modes trande modes Radiat Meridierat Noop mediat meridional woop made x
v Theta made su sf 52 Nydrostatic mode sa ST 52 wydrostatic (irch)
(anch) (degrees)
(psi)
(psi)
(psi)
(psi)
(psi)
(psi)
(psi)
(pse) 866 262.39 775.41 141.38 865
-40.00 17171.00 13931.00 31062.00 867
-7.87 18679.00 14613.00 33254.11 869 259.28 777.88 141.92 868
-89.63 14122.00 11840.00 25872.37 870 48.82 21801.00 14410.00 W 39.82 8 72 256.14 780.31 142.46 871
-58.94 9823.50 9781.70 19546.26 8 73 -310.17 26332.00 14802.00 4c823.&3 875 252.98 782.72 143.00 874 359.85 8626.20 9661.70 18647.75 876
-50.37 25342.00 14486.00 39777.63 878 251.48 783.85 143.26 ST7 225.88 2891.00 8434.00 11550.88 879 438.66 10570.00 10438.00 21446.66 881 249.98 784.97 143.51 880 -184.41 2278.40 8693.20 10787.19 882 -203.76 6178.30 9221.40 15153.94 864 247.27 786.96 143.97 883 21.49 3098.90 9796.30 12916.69 885
-40.20 6633.60 10155.00 16748.40 887 244.55 788.92 144.43 836 30.81 3240.10 10702.00 13972.91 888
-67.10 6540.80 10920.00 17393.70 890 241.81 790.57 144.89 889 5.53 3606.10 11730.00 15341.63 891
-88.77 5947.50 11601.00 17459.73 893 239.05 792.79 145.34 892 32.08 4440.70 12957.00 17429.78
- 94
- 74.61 4978.90 12241.00 17145.29 896 236.28 794.69 145.80 895 5.96 5715.90 1 316.00 20037.86 897
-97.41 3490.70 12758.00 16151.29 899 233.49 796.57 146.26 895 102.13 7545.50 15864.00 23511.63 900
-41.46 1486.20 13160.00 14604.74 902 230.69 798.42 146.72 901 -136.13 9861.80 17393.00 27118.67 903 -140.63 -1023.50 13357.00 12192.87 905 225.09 801.86 147.52 904 -213.46 11889.00 19371.00 31046.54 906 -219.01 -3497.90 14251.00 10534.09 908 221.39 805.68 148.32 907 -250.59 12398.00 20521.00 32668.41 909 -211.32 -4468.70 15309.00 10628.98 til 217.22 809.87 149.09 910 -179.99 11045.00 20596.00 31661.01 912 -248.06 -3696.50 16312.00 12367.44 C14 213.41 814.38 149.85 913 -105.28 8705.20 19796.00 28395.92 915 -216.74 -1968.30 16956.00 14770.96 C17 209.99 019.19 150.57 916
-27.06 6110.70 18411.00 24494.64 918
-1 74.74 50.75 17073.00 16949.01 920 206.97 824.26 151.25 919 35.86 3778.20 16736.0C 20550.06 921 -125.37 1895.60 16677.00 18447.23 923 204.38 829 57 151.89 922 78.80 2000.60 15033.00 17112.40 924
-81.25 3300.70 15885.00 19106.45 926 202.23 E35.08 152.47 925 100.49 8tA.95 13493.00 14462.44 927
-48.44 4164.60 14865.00 18981.16 929 200.55 840.74 153.01 925 109.48 321.90 12224.00 12655.38 930
-24.70 4522.30 13785.00 18282.60 932 199.34 846.52 153.48 931 97.90 202.21 11252.00 11552.11 933
-19.52 4514.90 12780.00 1 7275.38 935 198.61 852.38 153.90 934 95.70 323.18 10558.00 10976.88 936
-1.34 4326.60 11946.00 16271.26 938 198.37 858.28 154.25 937 118.21 596.18 10127.00 10841.39 939
-65.05 3767.20 11207.00 14909.15 941 198.31 858.7?.
154.23 940 -130.53 398.14 9964.20 10231.51 942 -178.04 3311.70 11009.00 14142. 2 944 198.32 860.78 154.39 943 28.54 178.35 9844.40 10051.29 945 164.09 6104.80 11780.00 15068.89 947 198.32 862.78 154.50 946 220.67 1546.70 10300.00 12067.37 968 320.74 16277.00 14800.00 31397.74 950 198.32 863.78 154.55 940 75.55 776.69 10142.00 10994.24 951
-242.46 18466.00 15408.c0 33629.54 953 198.32 864.78 15*.61 952
-61.81
?840.80 10965.00 13743.99 954
-13.01 16182.00 15c37.00 31206.00 956 198.32 865.78 154.66 955 15.70 4808.60 11916.00 16740.30 957
-38.57 14335.00 14814.00 29110.43 959 198.32 866.78 154.71 958
-25.04 6396.40 12786.00 19157.36 960
-55.11 12671.00 14717.00 27332.89 962 198.32 867.78 154.76 961
-4.87 7793.70 13661.00 21449.83 963
-41.62 11304.00 14763.00 26025.38 965 198.32 868.83 154.82 964
-13.60 8947.60 14504.00 21438.00 966
-53.43 10126.00 14907.co 26979.57 968 198.32 869.*8 154.87 967
-9.02 9903.80 15300.00 25194.78 969
-49.01 9173.10 15132.00 24256.09 C71 198.32 870.93 154.93 970
-10.26 10647.00 16025.00 26661.74 9 72
-53.63 8420.80 15408.00 23775.17 page W mANYosUM.W 1 05-Jun-91
- Oyster Creek Raes Data for Accident esith Pressure at 62 psi - to Sand - Nydrostatic Stress (Las Sa, Sy, Sz)
Outside modes inside modes Radial Iteridionet hoop Radiat Meridional poop mode X
Y 1hets Eade su ST S2 Nydrostatic kode sa ST 52 Nydrostatec (indi)
(inch) (degrees)
(psi)
(psi)
(pal)
(psi)
(pse)
(psi)
(psi)
(psi)
(T4 196.32 871.96 154.98 9 73
-T.65 11212.00 16680.00 27884.35 95
-53.48 7853.30 15724.00 23523.82 TTT 196.32 873.03 155.04 976
-T.22 11620.00 17260.00 28872.78 9 78
-55.34 7440.30 16058.00 23442.96 980 196.32 874.08 155.09 979
-5.24 11897.00 17768.00 29659.76 981
-56.41 7160.90 16399.00 23503.49 9El 198.32 85.13 155.15 982
-6.78 12062.00 18205.60 30262.22 964
-55.46 6991.60 16736.00 23672.14 966 198.32 876.18 155.20 985 1.17 12136.00 18576.00 30T13.17 957
-61.33 6921.30 17060.00 23919.97 909 198.32 877.23 155.25 908
-16.75 12127.00 18874.00 30964.25 990
-44.71 6933.30 17375.00 24263.59 i
'992 198.32 878.28 155.31 991 7.13 11867.00 19070.00 30%4.13 993
-72.64 7186.30 17711.00 24824.67 995 196.32 880.55 155.42 994
-2.17 11464.00 19396.00 30857.03 996
-64.47 5 79.70 18285.00 25800.23 998 198.32 882.81 155.53 997
-3.37 11105.00 19591.00 30692.63 999
-61.88 7932.00 18697.00 26567.12 1001 196.32 885.00 155.64 1000 0.08 10727.00 19665.00 30392.08 1002 - M.80 8304.20 18996.00 27235.41 1004 196.32 887.34 155.75 1003 1.24 10375.00 19657.00 30033.24 1005
-M.82 8650.20 19198.00 27783.38 100T 196.32 889.61 155.86 1006 2.10 10075.00 19601.00 29678.10 1008
-M.91 8944.00 19321.00 28200.09 1;10 198.32 891.88 155.97 1009 2.39 9636.60 19522.00 29360.99 1011 - M.47 9175.00 19385.00 25496.53 1013 198.32 894.14 156.08 1012 2.32 9659.00 19438.00 29099.32 1014
-M.00 9346.80 19405.00 28687.50 1016 198.32 8 %.41 156.19 1015 2.07 9535.70 19358.00 28895.77 1017
-63.45 9463.20 19398.00 28797.75 1J17 196.32 896.67 156.29 1018 1.70 9456.80 19289.00 28747.50 1020
-62.98 9534.90 19375.00 28846.93 1022 196.32 900.94 156.40 1021 1.33 9412.00 19234.00 28647.33 1023
-62.55 9572.60 19345.00 28855.05 1025 198.32 903.20 156.50 1024 0.9T 9391.00 19192.00 28583.97 1026
-62.22 9586.30 19314.00 28838.08 1028 196.32 905.47 156.61 102T 0.67 9385.20 '19162.00 28547.8T 1029
-61.97 9584.80 19285.00 2880T=84 1031 196.32 907.T3 156.71 1030 0.43 9387.70 19142.00 28530.13 1032
-61.79 9575.00 19261.00 28774.21 1034 196.32 910.00 156.81 1033 0.26 9393.10 19130.00 28523.36 1035
-61.67 9562.40 19244.00 28744.73 1037 198.32 912.27 156.91 1036 0.16 9397.90 19124.00 28522.06 1038
-61.61 9'50.40 19233.00 28721.79 1040 196.32 914.53 157.01 1039 0.13 9399.90 19123.00 28523.03 1041
-61.59 9541.30 19228.00 28707.T1 1043 196.32 916.50 157.11 1052 0.14 9398.50 19126.00 28524.M 1044
-61.62 9535.60 19230.00 28703.99 1066 198.32 919.06 157.21 1045 0.21 9394.2q,19134.00 28528.41 1047
-61.68 9532.90 19238.00 28709.22 104')
196.32 921.33 157.31 1048 0.34 9388.90 19146.00 28535.24 1050
-61.80 9531.30 19251.00 28720.50 1052 198.32 923.59 157.41 1051 0.51 9385.50 19164.00 28550.01 1053
-61.97 952T 80 19269.00 28734.83 1055 196.32 925.86 157.50 1054 0.72 9388.50 19139.00 28578.22 1056
-62.19 2518.00 19290.00 28745.81 1058 196.32 928.13 157.60 105T 0.96 9403.40 19222.00 28626.36 1059
-42.48 9496.20 19312.00 28745.72 1061 198.32 930.39 157.69 1060 1.20 9436.9C 19265.00 28703.10 1062
-62.83 9455.90 19133.00 28726.07 1064 196.32 932.66 157.79 1063 1.41 9496.40 19316.00 28813.81 1065
-63.21 9359.60 19346.00 28672.39 1067 198.32 934.92 157.88 1066 1.55 9589.40 19374.00 289M.95 1068
-63.63 9289.70 19346.00 28572.07 II70 198.32 937.19 157.97 1069 1.4T 9722.20 19432.00 29155.67 1071
-63.92 9149.80 19322.00 28407.88 1:73 198.32 939.45 158.06 1072 1.34 9898.50 19483.00 29382.84 1074
-64.33 8966.40 19265.00 28167.07 10 4 198.32 941.72 158.16 10 5 0.03 10116.00 19512.00 29628.03 10TT
-63.60 8741.40 19161.00 27838.80 1279 198.32 943.98 158.25 1078 1.03 10366.00 19501.00 29868.03 1080
-65.51 8484.40 18996.00 27414.89 p.g,13 hANtD5 W.4A1 EMI
Oyster Creek Raw Data for Accident eith Pressure at 62 psi - no sand - rydrostatic stress (s as sa. sy, sz)
Ostside modes inside modes Radial seeridional moop Radial meridional moop mode X
T Theta made sx sY s2 Nydrostatic med su sf s2 Mydros m ic (inch)
(inch) (degrees)
(psi)
(psi)
(psi)
(psi)
(psi)
(psi)
(psi)
( us) 1082 196.32 946.25 15e.34 1081
-1.37 10660.00 19432.00 30090.63 1083
-63.51 8183.50 18749.00 26868.99 1065 196.32 948.25 158.41 1084
-T.3T 10917.00 19294.00 30203.63 1086
-57.69 7920.70 18458.00 26321.01 1088 1M.32 950.25 158.49 1067
-4.88 11060.00 19039.00 30094.12 1089
-60.68 7772.30 18112.00 25823.62 1991 196.32 952.25 158.57 1090
-12.45 11080.00 18649.00 29716.55 1092
-53.15 7746.70 17711.00 25404.55 1094 196.32 954.25 158.65 1093
-3.40 10907.00 18109.00 29012.60 1095
-61.93 7915.70 17267.00 25120.77 1097 196.32 956.25 158.72 1096
-4.25 10M O.00 17460.00 23125.75 1098
-60.20 8148.80 16758.00 24846.60 1100 196.32 957.20 158.76 1099
-8.87 10384.00 17071.00 27446.13 1101
-51.82 8435.80 16544.00 24927.95 1103 196.32 958.16 158.79 1102
-6.61 9935.70 16624.00 26553.09 1104
-58.19 8879.50 16361.00 25182.31 1106 196.32 959.11 158.83 1105
-4.65 9375.90 16136.00 2550T.25 1107
-51.90 9444.50 16211.00 25603.60 1109 198.32 960.06 158.87 1108
-12.59 8677.30 15604.00 24268.72 1110
-59.16 10129.00 15093.00 26162.84 1112 196.32 961.01 158.90 1111 2.35 7856.30 15051.00 22909.65 1113
-42.49 10977.00 16040.00 26974.51 1115 196.32 961.97 158.94 1114
-27.39 6837.20 14445.00 21254.82 1116 - 71.01 11939.00 16029.00 27896.99 1118 i96.32 962.92 158.97 1117 22.86 5735.00 13872.00 19629.86 1119
-19.57 13155.00 16150.00 29285.43 1121 198.32
%3.87 159.01 1120
-42.39 4257.00 1320T.00 17451.61 1122
-83.07 14384.00 16290.00 30590.94 1124 196.32 964.82 159.06 1123
-51.31 2955.90 12660.00 15564.59 1125
-95.31 16106.00 16658.00 32668.69 1127 196.32 965.78 159.03 1126 568.23 3M4.90 13008.00 17261.13 1128 385.44 19182.00 176M.00 3T233.44 1130 198.32 965.88 159.08 1129 -381.01 4991.30 13116.00 17726.27 1131 728.22 9784.80 14966.00 25479.02 1133 196.32 966. 6 159.10 1132 -835.32 5163.30 13029.00 17356.96 1134 -139.81 4164.50 13027.00 17051.69 1136 195.32 966.63 159.11 1135 -3a2.45 4958.80 13104.00 17680.35 1137 770.5 7 9807.60 14984.00 25562.17 l
1139 196.32 9M.73 159.11 1138 554.90 3642.80 12990.00 17187.70 1140 379.42 19214.00 17671.00 17264.42 1142 196.32
% 7. 73 159.15 1141
-52.96 2959.80 12664.00 15570.82 1143 -100.16 16083.00 16651.00 32633.84 1145 196.32 968.73 159.19 1144
-40.84 4361.00 13246.00 17566.16 1146
-78.9 7 14310.00 16284.00 30515.03 1148 196.32
% 9.73 159.22 1147 22.03 5845.20 13940.00 19807.23 1'49
-19.58 13033.00 16148.00 29161.42 i
1151 196.32 970.73 159.26 1150
-28.07 6970.50 14543.00 21485.43 1152
-70.64 11790.00 16040.00 27759.36 1154 196.32 9T1.73 159.30 1153 2.66 7999.00 15176.00 23177.66 1155
-41.39 10816.co 16071.00 2ss45.61 1157 196.32 9 72. 73 159.33 1156
-13.16 8814.80 15751.00 24552.64 1158
-59.28 9967.30 16146.00 26054.02 1160 195.32 9 73.73 159.3T 1159
-4.60 9500.00 16302.00 25797.40 1161
-51.08 9293.90 16289.00 25531.82 1113 198.32 974.73 159.40 1162
-5.99 10038.00 16804.00 26836.01 1164
-58.82 8/46.20 16463.00 25150.37 1166 196.32 975.73 159.44 1165
-11.21 10459.00 1T260.00 27707.80 1167
-49.06 8326.20 16671.00 24948.14 1169 198.32 976.75 159.47 1168
-1.53 10681.00 17647.00 28326.47 1170
-62.44 8098.90 16915.00 24951.46 1172 198.32 978.93 159.55 1171
-2.52 10837.00 18322.00 29156.48 1173
-61.88 7939.70 17496.00 25373.83 i
1175 198.32 981.13 159.63 1174
-11.24 10950.00 15877.00 29815.76 1176
-53.37 7827.10 17989.00 257c2J3 1178 198.32 983.33 159.71 1177
-1.63 10885.00 19273.00 30156.37 1879
-58.54 7895.00 18423.00 26259.46 1181 196.32 985.53 159.78 1180 0.77 10745.00 1953T.00 30282.77 1182
-59.07 8052.30 18783.00 26776.24 j
1184 198.32 987.73 159.86 1183 6.15 10606.00 19708.00 30320.15 1185
-59.08 8220.20 19056.00 27217.12 11*J 198.32 989.94 159.93 1186 5.28 10493.00 19810.00 30308.28 1188
-62.85 8356.10 19231.00 27524.25 Page 11 hANTD5 tat.bsL1 05-As* 91
- Oyster Creek Raw 9mta for Accident with Pressure at 62 psi - No seruf - Hydrostatic stress (som sa. sy. sm) l inside modes l
Outside Modes Radiat Meridionet Moop Radiat Meridional Noop mode X
Y Theta made sX SY 52 Mydrostatic made su sf 52 Mydrostatic (inch)
(inch) (degrees)
(psi)
(psi)
(psi)
(psi)
(psi)
(psi)
(p.i)
(psi) f 1190 198.32 992.14 160.01 1189 5.49 10416.00 19848.00 30269.49 1191
-63.09 8430.To 19307.00 27674.61 j
l 1193 198.32 994.34 160.08 1192 4.45 10403.00 19834.00 30241.45 1194
-63.83 8419..o 19294.co 2TM9.27 1196 198.32 996.54 160.16 1195 3.07 10475.00 19775.00 30253.07 1197
-63.81 8335.80 19191.00 27462.99 1199 198.32 998.74 160.23 1198 0.86 10613.00 19661.00 30274.86 1200
-63.4T 8193.10 18995.00 27124.63 1202 193.32 1000.94 160.30 1201
-2.22 10780.00 19472.00 30249.78 1203
-61.68 8024.30 18706.00 26668.62 1205 198.32 1003.15 160.3T 1204
-4.73 10921.00 19180.00 10096.2T 1206
-60.51 7883.00 18329.00 26151.50 1208 198.32 1005.35 160.45 1207
-13.02 10958.00 18754.00 29698.98 1299
-52.74 7847.00 17580.00 25674.2T 1211 195.32 1007.55 160.52 1210
-3.18 10791.00 18163.00 28950.82 1212
-62.46 8014.50 17378.00 25330.04 1214 198.32 1009.75 160.59 1213
-l.99 10575.00 17455.00 28028.01 1215
-62.48 5232.80 16796.00 24966.32 121T 198.32 1010.70 160.62 1216
-10.60 10312.00 17067.00 27368.40 1218
-49.88 8499.50 16573.00 25022.62 1220 198.32 1011.66 160.65 1219
-5.98 9865.00 16618.00 26477.02 1221
-58.67 8943.80 16386.00 25271.14 1223 198.32 1012.61 160.68 1222
-4.69 9307.00 16128.00 25430.31 1224
-51.69 9509.40 16235.00 25692.71 1226 198.32 1013.56 160.71 1225
-12.47 8610.50 15584.00 24192.03 1227
-59.17 10194.00 16115.00 26249.83 1229 198.32 1014.51 160.74 1228 2.45 7792.00 15041.00 22835.45 1230
-42.39 11042.00 16062.00 21061.61 1232 198.32 1015.47 160.77 1231
-27.39 6775.50 14435.00 21183.11 1233
-11.07 12003.00 16051.00 27982.93 1235 198.32 1016.42 160.80 1234 23.02 56T6.30 13862.00 19561.32 1236
-19.42 13219.co 16173.00 29372.58 1238 198.32 1017.37 160.83 1237
-42.44 4231.00 13199.00 17387.57 1239
-83.29 14446.00 16313.00 30675.71 1241 198.32 1018.32 160.86 1240
-51.64 2904.10 12655.00 15507.47 1242
-95.36 16168.00 16683.00 32755. M 1244 198.32 1019.28 160.89 1243 5T0.34 3643.00 13008.00 17221.34
!245 386.94 19248.00 17695.00 37329.94 1247 198.32 1019.38 160.89 1246 -383.32 4957.20 13117.00 17690.88 1248 T30.62 981T.20 14987.00 25534.82 1250 198.32 1019.75 160.90 1249 -840.08 5131.70 13032.00 17323.62 1251 -143.11 4177.70 13043.00 17077.59 1253 198.32 10c).13 160.91 1252 -384.54 4928.00 13109.00 17652.46 1254 772.92 9839 20 15008.00 25620.12 1256 198.32 1020.23 160.92 1255 557.06 3609.30 12996.00 17162.36 1257 381.02 19215.00 17704.00 37360.02 1259 198.32 1021.23 160.95 1258
-53.35 2929.80 12675.00 15551.45 1260 -100.T2 16129.00 16684.00 32712.28 1262 198.32 1022.23 160.98 1261
-41.12 4344.40 13265.00 17568.28 1263
-79.38 14344.00 16318.00 30582.62 1265 198.32 1023.23 161.01 1264 22.05 5844.30 13968.00 19834.35 1266
- 19. 5 13055.00 16183.00 29218.25 1268 198.32 1024.23 161.04 1267
-28.27 6986.20 14580.00 21537.94 1269
-71.06 11797.00 16076.00 27801.94 1271 198.32 1025.23 161.07 1273 2.62 8033.40 15223.09 23259.02 1272
-41.65 10807.00 16108.00 26873.35 1274 198.32 1026.23 161.10 1273
-13.2T 8869.80 15808.00 24664.53 1775
-59.75 9938.80 16182.00 26061.06 1277 198.32 1027.23 161.13 1276
-4.73 9578.10 16369.00 25942.37 1278
-51.20 9244.50 16324.02 25517.30 1280 198.32 1028.23 161.16 1279
-5.72 10141.00 16881.00 27016.28 1281
-59.95 8673.co 16494.00 25107.05 1283 198.32 1029.23 161.19 1282
-12.92 10590.00 17346.00 27923.08
- 284
-47.21 8227.40 16698.00 24878.19 1286 198.32 1030.23 161.22
'1285 0.72 10824.00 17739.00 28563.72 1287
-66.6T 7989.30 16940.00 24862.63 1289 198.32 1032.65 161.29 1288
-2.33 11020.00 18477.00 29496.67 1290
-64.06 7791.20 17567.00 25273.24 1292 198.32 1035.08 161.36 1291
-13.42 11210.00 19077.00 30273.58 1293
-54.33 7601.40 18059.00 25606.07 1295 198.32 1037.51 161.44 1294
-4.49 11215.00 19472.00 30682.51 129c
-63.13 75 %.30 18447.00 25980.18 05 - Jure VI hAMDsuM.utt Page 12
Oyster Creek Raw Data for Accident with Pressure at 62 psi - me sand - mydrostatic Stress (Sun Sm. Sy. 5 0 Outside modes inside tades s
Radial Meridional No@
Radial Meridional Moop Mode X
Y Theta Wode
$1 SY S2 Nydrostatic Wode SM ST S2 wydrostatic (inch)
(inch) (degrees)
(psi)
(psi)
(psi)
(psi)
(psi)
.(psi)
(psi)
(psil 1298 198.32 1039.94 161.51 1297
-3.04 11143.00 19689.00 30828.96 1299
-6' 15 7669.80 18707.00 26312.65 1301 198.32 1042.36 161.58 1300
-1.28 11059.00 19756.00 30813.T2 1502
-65.18 7754.30 18822.00 26511.12 13u4 198.32 1044.79 161.65 1303
-1.87 10991.00 19687.00 30676.13 1305
-63.73 7823.10 18793.00 26552.37 1307 198.32 1047.22 161.72 1306
-2.65 10927.00 19484.00 3040S.35 1308
-63.39 7886.90 18629.00 26452.51 1310 198.32 1049.65 161.78 1309
-10.35 10817.00 19134.00 29940.65 1311
-55.45 7998.20 18353.00 26295.75 1313 198.32 1052.0T 161.85 1312 1.29 10574.00 18631.00 29206.29 1314
-66.46 8242.80 17990.00 26166.34 1316 198.32 1054.50 161.92 1315 5.35 10391.00 18045.00 2S441.35 1317
-69.56 8427.50 1T512.00 25869.94 1317 198.32 1055.47 161.95 1318
-12.52 10216.00 17751.00 27954.48 1520
-47.97 8606.70 17336.00 25894.T3 1322 198.32 1056.43 161.97 1521
-3.10 9852.00 17399.00 2T247.90 1323
-61.32 8968.20 17196.00 26102.88 1325 198.32 1057.40 162.00 1324
-3.33 9408.00 17015.00 26419.67 1526
-53.67 9419.30 17082.0C 26447.63 1328 198.32 1058.36 162.03 1327
-9.80 8861.30 16598.00 25449.50 1329
-60.84 9955.40 16990.00 26884.56 1331 198.32 1059.33 162.05 1330 3.29 8221.50 16169.00 24399.79 1332
-46.03 10615.00 16949.00 27517.97 1334 198.32 1060.29 162.08 1333
-22.36 7441.10 15697.00 23115.24 1335
-71.28 11354.00 16936.00 28218.72 1337 198.32 1061.26 162.11 1336 21.5C 6603.10 1525T.00 21881.68 1538
-26.02 12293.00 17029.00 2929%.98 1540 198.32 1062.22 162.U 1339
-38.11 5486.70 14741.00 20189.59 1341
-83.69 13222.00 17128.00 50266.31 1343 198.32 1063.19 162.16 1342
-32.69 4492.20 14332.00 18791.51 1344
-83.42 14557.00 17417.00 31890.58 1346 198.32 1064.15 162.19 1345 442.39 5212.70 14648.00 20303.09 1547 291.16 17052.00 *8233.00 35576.16 1349 198.32 1064.25 162.19 1348 -328.91 5962.00 14641.00 20274.09 1350 372.08 8524.T0 15T11.00 24607.78 1352 198.32 1064.50 162.19 1351 -1013.40 5727.20 14364.00 19077.80 1353 - TT.32 3503.20 14077.00 17502.88 1355 198.32 1064.75 162.20 1354 -331.91 5939.70 14633.00 20240.79 1356 431.09 8542.00 15734.00 24707.09 1558 198.32 1064.85 162.20 1357 43T.98 5173.50 14634.00 20245.48 1359 288.88 17091.00 18244.00 35623.88 1361 198.32 1065.85 162.23 1360
-35.14 4463.00 14326.00 18753.86 1362
-86.69 14578.00 17426.00 31917.31 1364 198.32 1066.85 162.26 1363
-36.80 5482.20 14752.00 2019T.40 1365
-81.25 13235.00 17146.rKs 30299.75 1367 198.32 1067.85 162.28 1366 21.00 6602.90 15283.00 21906.90 1368
-26.11 12297.00 1N57.00 29327.89 13TO 198.32 1068.85 162.31 1369
-23.20 7438.30 15T38.00 23153.10 1371
- 71.09 11361.00 16980.00 28269.91 1373 198.32 1069.85 162.34 1372 3.64 8214.70 16225.00 24443.34 1374
-45.34 10633 00 17015.00 27602.66 13D 198.12 1070.85 162.36 1375
-9.97 8830.50 16670.00 25490.53 1377
-60.70 9990.io 17080.00 27009.90 1379 198.32 1071.85 162.39 13T8
-2.74 9355.10 17102.00 26454.36 1380
-53.32 9477.70 17198.00 26622.38 1382 198.32 1072.85 162.42 1381
-3.17 9773.00 17501.00 27270.83 1383
-60.31 9053.30 17339.00 26331.99 13P5 198.32 1073.85 162.44 1354
-9.%
10109.00 17869.00 2T968.04 1386
-49.74 8720.10 17507.00 26177.36 1388 198.32 1074.85 162.47 1587 3.59 102TT.00 18184.00 28464.59 1589
-65.40 8552.50 17705.00 26192.10 1391 198.32 1077.07 162.53 1390 5.06 10444.00 18762.00 29211.06 1392 62.86 8398.10 18174.00 26509.24 1394 198.32 1079.28 162.59 1393
-5.56 10680.00 19280.00 29954.44 1395
-56.96 8'90.30 18554.00 26687.35 1597 198.32 1081.50 162.64 1396 0.81 10838.00 19680.00 30518.81 1398
-63.51 8038.30 18865.00 26839.79 1400 198.32 1083.71 162.70 1399 2.30 10996.00 19973.00 109T1.30 1401
-64.60 7864.40 19074.00 26873.50 1413 198.32 1085.93 162.76 1402 2.74 11223.00 20173.00 31378.74 1404
-67.32 7633.40 19150.00 26716.08 Page 13 mANYDsuM.w )
05-Jun 91
i t
e l
l 4
r i
Oyster Creek Rau Data for Accident.with Pressure at 62 psi - No Sand - Nydrostatic Stress (sem Sa, Sy, 52)
Outside Emdes lesside hodes
{
j Radial. 80eridionet -Noop Radiet leeridionet Noap
- Hode X
Y Theta mode LSE
$Y
' SZ hydrostatic mode
- 5E SY S2 hydrostatse
'I (inch) (inch) (dooroes)
(psi)
(psil (psi)
(psi)
(psi)
(psi)
(psi)
(psi) 1406 '198.32 1088.M ' M2.81
. M85 1.86 11M5.00 20277.00 31823.86 MOT
-68.16 T311.00 19069.00 26311.84 I
Me9 198.32 1990.36 - M2.87 Mes ~
-0.85 11963.00 20263.00 32225.95 1410
-68.21 6893.00 18808.00 25632.79 M12 198.32 1992.57'- M2.92 M11
-4.54 12444.00 20092.00 32531.46 M13
-64.%
.6410.50 18351.00 24696.54' MI5 198.32 1994.79 M2.98 14M
-T.14 12914.00 19T10.00 32620.90 M16
-65.20 5935.70 17684.00 23554.50 M14 198.32. 109T.00 M3.83 MIT 3.09.1339T.00 19006.00.324a6.09 M19
-73.67 5460.50 16764.00 22150.83 M21 195.32 1998.00 M3.e6
. M2e
-14.21 1MFs.ee 18T25.80' 32384.79 1422.-
-42.%
5183.a0 16248.00 213as.84 i
M26 198.32 1099.00 M3.es M23
-3.62 ; 1MTT.se 18234.00 3190T.38 M25
-62.60 5181.70 15744.00 20063.10
+
{. M2T 198.32 1100.00 M3.11
'1426
-T.98 13573.00 17646.80 - 31211.10 1428
-53.74 5290.00 15221.00 20457.26 M30 Sws.32 1101.00 M3.13 M29
-10.91 13334.80 M958.00 30281.10 1431
-56.%
5524.20.M672.00 2013v.24 L
' M33 - - 195.32 1102.00 M3.15 M32 -
-T.60'12943.00 M170.00 29105.40 1434
-47.9T 5926.60 14121.00 19999.63 l
l - M36 198.32.1103.00 M3.18 1435
-17.57.12345.00 15267.00 27594.43 M3T
-59.9T 6505.30 13567.00 20012.33
}
1439' 198.M 1104.00 M3.20 1438
-8.14. 11551.00 M267.00 ' 25809.86 1440
-27.38 7341.50 13061.00 203T5.12 I
M42. 198.32 1105.00 163.23 1441
-9.90 10642.80 13M0.00. 23572.10 1443
-94.11 8378.00 12555.00 20338.89 i
M45 198.32 1106.00: M3.25 1444
-89.32 9127.90 11912.00' 2C'750.58 1446 16.81 9844.30 12233.00 22154.11 I
M48 198.32 1107.00 M3.28 M47 -142.54 5755.00 100TE.00 15690.46 M49 15.19 12862.00 12316.00 25213.19 l
M51 198.47 1108.25 M3.29 1450 -307.51 -1962.90 7935.20 5664.79 M52 -263.96 13606.00 11511.00 24853.02 M54 -. 19s.63 1109.50 M3.31 M53 244.a2 -4429.70 5360.50 1175.62.
M55
.Tz.s4 M279.00 10x2.00 25M8.M 97 91 85 88 3
3 84 3
1175.50 30t a4.00 36129.00 60919.10 12534.00 42743.00 34264.00 T1867.00 h
k
[
t I
t l'
f 6
\\
i i
}
t f
i I
J t
b c
Y
.. _. _ _ _ _ _. _.. _ -. - ~ _ _ _
3.
In GE Report Index No.
9-3, Section L.2.2, comparisons of circumferential and neridional stress magnitudes with the large and small displacement options should be provided from the sandbed region up to the knuckle region of the drywell.
The amount of stress reduction obtained as a --result of the large displacement method appears to be too high for the small deflection calculated; the results of these calculations should be further investigated. Also, show mathematically as in the case of beams and flat plates, that consideration of large deflection decreases the stress in the drywell shell which is in membrane tension under internal pressure for i
regions of the shell away from discontinuity.
j
RESPONSE
The results of the large and small displacement analysis have been reviewed.
Figures la through le show comparisons of the calculated stress-and displacement results from these analyses extending into the cylindrical region. These plote clearly show that the large displacement approach affects stresses and displacements only in the sandbed region.
Ti.e - largest percentage difference in the magnitudes of the circumferential membrano ctress in the sandbed region is = 8% (at node 66 in Table 2).
The attached analysis by Mr.
W.
E.
Cooper provides_ mathematical displacement solutions.for plates and shells.
This analysis provides expected reductions in stress for problems sim.ilar to the oyster creek drywell.
It shows that reductions in hoop stress of 13% (100-87) would not be unusual. Therefore, the calculated reduction of 8% is reasonable and well within the theoretical prediction.
I 1.
l r
l l
5CT/WP/ MIS /Drywell/5 f-L
ATTACHMENT FQBSPUN RESPONSE TO QUESTIQN 3 RZ:C3212172
R Circumferential Membrone Stress (ksi) oz
-wC M
N N w
w v o
I o
N A
cn cc o N A
cn cc o N A
cn oc o
E i
J t
i i
i i
l i
i
.1 i
I I
o h
Sandbed Region (0.736")
O oo w,
Lower Sphere (1.154")
oe M
o.
+a E
o a
w 2-r-
w
~.
E E
5 C
c e
c 2
v, c
=
0 Qb E
O Mid Sphere (0.770")
9 9
$N Eb n
n o
G Equoter o
G 2
a
?
o-X o
ss m
e
.p c) w a
m e-e en Mid Schere (0 770")
LO o-C O
C g
U w
if CD 1
(A C
e C
O.
v C C
C E
O'.
4 E
U;De' Schere (0.7 7 '
y
~
C-
~
C Y
no M
g 2-C
~
"+: ie (15C:5 i E_ -
g' k
C C
1
\\
1 l
1 l
l R
Circumferential Mem+ Bend Stress (ksi) o l
t w
n w w N N
N Q
o w
~*
w
- c o N A
e en o N A
e cn o N 4
cn cc o
- E i
1 l_
I I
I I
I I
I i
I i
l o
Scndbed Region (0.736")
O..
-o-1 o
~
Lower Sphere (1,154")
f N
W o-
+
a E
o a-a, M
r en
> Q 9.
c 0
2 o
9 v_
e
=
n o
9-C Mic Sphere (0.770")
o 9
E3 3
O, O
f-c
-.s
~
.e--
c.
c n
n r
a 2
2 e
o-Equotor F.
C i
2
(~)
~
3 3
C
.m.
G
.P m
d.'
n
[
G l
8 Mic Spnere (0.770")
e o-o l
O
~
w*
en CL U
~Q CL cn e
D "v~~'
c o-m
*
p.m e 9
+ cr.
V; Pef 50her6 (C.7^T,
y
= =.
O.
O C
y"'**
mum P'**
gam * *
"g 8
C_ =
w F # s *. P,! e f, J( h^
i 3
_,'*.*f7 ' (A
=*
\\
i l
~
R Meridional Membrane Stress (ksi)
Et wo
--.---.w oI o-N uA & c) N cc e o - N uA e c) N oc e o
- E I
i i
i i
i i
i i
i i
i_ i i
i i
i i
i o
Sondeed Region (0.736")
-,o-o Lower Sphere (1.154")
p N
nt o-
+
E c
~
ct, r-w 9.
o 2
E O
9 u
0 O
W o-E-
O Mid Sphere (0.770")
o.-o o--
f_ $_
n.
3*
O i
o c
~
n n
O l i e
'i M
A 9
o-EQuctor
$s
% F X
C
'1 is
~.
5 Q O
~
~
e e
M d
o e
Mid Sphere (0.770")
1 d
v.-
h o-o o
-n B
m V
C l
O e
C O-l T &
C
~
E ll w
hy Uppe' Sphere (C 72: ;
il o-C C
11 A
l m
Q g-
~
N[
re.,:
e ( i6:5 5-Cy w (C is:
11 f
i i
9
,n.-..
~
l l
R Meridienci Mem+ Bend Stress (ksi)
E:
Nrn w
N M
N M
ot o
N A
cn Cc O
M A
Cn CC O
N A
7 E
I i
l i
i i
i l
i i
i i
l O
Sandbed Region (0.736")
8 O
O O
Lower Sphere (1.154"
'P" O
w Q
Q o.
+
5 3
3
,yo n
m.a 2.
e O
a c
2 w.
O o
5' 5
C (f.
e
=
m
=
9.
O Mid Sphere (0.770")
o 9
0 Z
w w
9 s
I E j
LS C
C n
n 9
o.
Equotor 11 3
T M P
F C
E.,
5..
\\
a.
i
-s
=
r t
p" m
t.r.
Mid Sphere (0.770")
U T
V-
'd c
o Vs x
v m
o N
.M C
C O
c-C V.
O O=
l P
~
O C
C w
C l
=.'
~.
r w
n*
UPCe' Sphere (0.'22 g
5 C=
n C
v e
a->,
M e
C~
i re
- f l [ [ "* [ *~; '
+ -
s g.
O I
!) " :: t ' C #.4:
ll
- x 9
9
R Radiol Displacement (inches) oZ N
9 o
o o o o o o o o
o o o
c o
o o o 9
L L
L L
O k k k b P w
a e co w w a
en cm u
x o N A
cn co
- E I
i i
i I
i i
i i
i i
i i
l o
2-Sandbed Region (0.736")
_.o-O Lower Sphere (1.154")
C w
+
n o..
5-o a
r e
E E
3 C
9 u
i h
x o-8 tr E
o u;c spnere (0.770")
9 9
J v
2 w
.v.
s T.
t e
a o
n p
n n
E Eouctor 4
G
- 9. O F
O E
E L
C C,
a B
2 m
-M
>=4 S
3 Mic Sphere (0.770")
C p
o-c, a
s H
(A c
C C
C e
C o-0 (f.
~
e b.
m J.
e y~
C x
u: e* Spnere (C 72:
j m-M yms.
A eg W
L M
Ye s.*.t a,
W C,#
t' f 642 Il I*
X 0
9
T/\\BLE 2 Of11th CittK CtfWELL ANALYll$
(ACC0bi7.WK1)
Circumferential Stress Distribution f or accident case (ho land, we f ransition with 4 without Large Disp.)
D i s t anc e f rom t avat or t o sot t ern o f landbed:
395.77 (inches)
Memorano uom. + lend.
Meecrone mem. + tend, tacial Circumfe**ntial C i r cumf erent i s t weridional me r i di or.a t D I solac eaent Angle MeridlDhal
$trell 44 )
$treet (kli)
Strett (kli)
Strell (kli)
( b4hel) ggggw g [ g g gng g Equator From I.0.$8 w/o L.D w L.D.
w/o L.D w L.D.
w/o L.D = L.D.
w/o L.D s L.D.
w/o L.D u L.D.
N ode (degreet)
({nches)
OTCt14 CVCt1ML QYCR1M CYCt1ML OYCRIN QTCR1ML CfCR14 OYCR1mL CYC#1m ofttimt 27 53.99 0.00 3.746 3.756 1, 64 3 1.225 12.432 12.465 5.523 4.131 0
0 40
$2.64 9.90 8.978 8.67 6.439 6.454 12.472 12.473 5. 77 6.699 0.0739 0.0684 53 51.'9 19.79 17.693 16.519 19.414 18.124 12.718
- 12. f.3 19.377 18.792 0.201 0.182 66 49.94 29.69 22.288 20.623
- 24. 772 22.613 13.071 12.9 20.391 18.804 0.2 72 0.245 49.265 34.64 32.9 21.3 24.85 22.9 13.3 13 18.9 17.T 0.28 0.213 79 48.59 39.59 22.970 21.543 24.945 23.128 13.436 13.178 17.628 16.626 0.285 4.
47.505 47.54 22 21 23 22 13.5 13.25 15.2 14.9 0.26 0.45 92 46.42 55.49 19.911 19.481 20.239 19.738 13.647 13.323 13.27 13.244 0.244 0.232 102 45.58 61.65 17.694 17.533 17.802 17.638 11.634 11.355 9. 71 10.011 0.225 0.218 108 43.12 79.68 13.283 13.483 15.396 15.597 9.898 9.692 9.088 9.2 0.192 0.19 112 40.66 9 7. 72 12.292 12.44 14.467 14.534 10.381 10.192 10.17 10.053 0.1 66 0.1 54 116 38.20 115.75 12.771 12.789 15.763 15.524 10.599 10.407 12.191 11.819 0.196 0.192 120 35.67 134.30 12.833 12.808 15.042 14.809 10.411 10.225 11.462 11.149 0.193 0.189 126 33.13 152.91 13.083 13.09. 13.885 13.729 9.642 9.687 9.8 99 9.65 0.182 0.178 130 30.60 171.46 13.045 13.143 13.332 13.343 9.414 9.311 9.487 9.344 0.1 73 0.1 72 138 28.07 190.01 12.884 13.081 12.639 12.874 9.3 04 9.252 8.166 8.28 0.165 0.166 148 25.53 208.63 13.805 13.942 13.442 13.623 9.478 9.447 8.132 8.281 0.178 0.179 161 23.00 227.17 17.565 17.379 17.699 17.492 12.269 12.248 12.605 12.545 0.216 0.213 170 17.25 269.32 19.450 19.289 19.569 19.392 15.1 D6 15.095 15.381 15.342 0.23 0.227 1 79 11.50 311.47 18.118 18.219 18.055 18.169 15.355 15.354 15.17 15.213 0.205 0.206 1 68 5. 75 353.62
'8.647 18.564 18.699 18.609 15.522 15.525 15.678 15.646 0.206 0.204 197 0.00 395.77 17.684 17.777 17.627 17.T32 15.635 15.64 15.461 15.501 0.154 0.181 400 5. 75 437.92 18.47 18.382 18.514 18.419 15.694 15.699 15.824 15.811 0.156 0.185 409 11.5 480.07 18.006 17.904 18.05 17.94 15.679 15.684 15.854 15.828 0.17 0.169 l
418 17.25 522.22 15.812 16.029 15.692 15.922 15.939 15.942 15.538 15.593 0.128 0.131 l
427 23 564.37 17.787 17.604 17.824 17.544 16.79 16.791 16.861 16.872 0.143 0.144 436 28 601.02 19.131 18.644 19.188 18.921 17.342 17.347 17.552 17.489 0.151 0.148 445 33 637.67 18.616 19.t3 18.653 18.696 17.209 17.297 17.408 17.428 0.135 0.136 454 38 674.32 17.081 17.343 16.879 17.172 17.288 17.293 16.701 16.818 0.106 0.11 4 63 43 710.96 20.305 19.856 20.652 20.152 17.24 17.252 18.099 17.974 0.142 0.137 4 72 48 747.63 14.941 16.831 16.744 16,653 17.2D4 17.232 17.165 17.166 0.0857 0.0861 l
481 53 764.28 10.844 11.244 10.921 11.304 10.938 10.951 10.264 10.322 0.0258 0.0332 490 56.72 811.55 15.54 15.525 17.12T IT 4.241 4.235 8.461 8.15 0.104 0.105 499 823 18.021 17.879 19.533 19.315 3.455 3.451 8.609 8.353 0.12 0.12 l
508 834.5 16.408 16.318 16.474 16.379
- 2. 772
- 2. 773 3.551 3.517 0.0966 0.0989 517 844 13.182 13.198 12.342 12.415 2.362 2.364
-0.146 0.094 0.0718 0.0768 526 858.28 13.2 13.276 12.74A 12.832 5.571 5.575 4.052 4.085 0.0698 0.071 535 912 19.635 19.589 19.647 19.639 8.919 8.926 9.084 9.088 0.088 0.0684 544 966 18.017 17.998 18.02T 18.007 8.9 54 8.942 8.962 8.967 0.0864 0.0874 PL018 ACC0miT:
A a
ACCONTTE:
A A
ACCDNITC t A
A ACC0kT101 1
A ACCOstTI:
a a
a 2
ACCONTTFt
~_
- ~ - - - -
. - - - =..
TELEDYNE ENGINEERING SERVICES 5
W.
E.
Cooper Page 1 June 4, 1991 Project 7377
' i COMPARISON OF LARGE AND SMALL DISPLACEMENT SOLUTIONS FOR PLATES AND SHELLS
REFERENCES:
1.
M.
Hetonyi, " Beams on Elastic Foundation",
U.
Mich. Press, 1946 2.
S.
Timoshenko, " Theory of Plates and Shells", McGraw-Hill, 1940 INTRODUCTION I
The usual small deformation theory will significantly overestimate the otrasses in a beam, plate, or shell subjected to in-plane and lateral loediage if the lateral displacement exceeds one-half of the thick-nees.
Such a lateral displacement was calculated in the sandbed region of the Oyster Creek Drywell under certain loading conditions, co the calculations were reperformed using large displacement theory.
Some have expressed surprise at the resulting reduction in the calc-ulated stresses.
The purpose of this analysis is to show that similar l
reductions occur when the two solutions are compared for simpler structures which characterize the drywell.
It may be desirable to first point out that an axisymmetric shell subjected to axinymmetric loadings behaves as a beam on an elastic l
foundation, with the hoop stiffness of the shell providing the elastic foundation and the product EI replaced by the plane strain equiv-l alent J
2 D = Eh
/ 12(1 - p
)
This is shown by Ref. 1 for cylinders, page 30, and for spheres, page 163.
Further, the equations for a cylinder may be used to approximate tho behavior-of a very thin sphere if, as shown by Ceckeler, the ophere is replaced by a cylinder of the same radius and thickness (Ref.
1, page 167).
When the beam on elastic foundation approximation is used, the beam stresses represent the meridional stresses in the shall, the hoop bending stress is Poisson's ratio, y,
times the meridional bending strees, and the hoop stress is computed from the lateral deflection and the meridional average stress using Hooke's law end the definition of the hoop strain, so thats i
L
TELEDYNE ENGINEERING SERVICES W.
E.
Cooper Page 2 June 4,
1991 Project 7377 o
- = E"
+yo a
h
,R, l
where the subscripts h and 1, respectively, represent the hoop and longitudinal directions; o is the symbol for stress; 6 is the lateral (radial) displacement; E is Young's modulus; and, R is the radius of the shell.
As mentioned earlier, the hoop stiffness of the shell provides the clastic foundation.
In particular, the modulus of the foundation is given by the equation Et k :=
a 2
R where t is the thickness.
For very large diameter thin-walled shells, then, the hoop stiffness becomes negligible and the shell behaves as a plate in plane strain without an elastic foundation.
Two approaches are used in the following computations.
First, the corroded sandbed region is represented as a Geckeler cylinder of radius, length, and thickness of the approximate dimensions subjected to the design pressure.
Small and large displacement solutions are obtained using the equations available from Ref.
1.
Second, the wide flat and curved plate solutions of Ref. 2 are used to demonstrate the type of additional reduction which is obtained when the spherical curvature is actually considered.
CONCLUSIONS The computations included here indicate that use of large displacement colutions for the oyster Creek drywell is required if the stresses are not to be significantly overestimated.
Use of the largo displacemnt colutions are expected to reduce the membrane hoop stress by between 10% and 20%.
Additional arguements justifying the use of large displacement colutions, and the type or error which result if they are not used, are given in Chapter-IX of Ref.
1.
TELEDYNE ENGINEERING SERVICES W.
E.
Cooper Page 3 June 4,
1991 Project 7377 GENERAL QUANTITIES The material properties and the dimensions of the sandbed region are 6
E := 30*10 Young's modulus, pai.
p := 0.3 Poisson's ratio P := 62
. internal pressure, psig.
R := 420 Radius, in.
t := 0.7 Thickness, in.
L := 70 Sandbed length, in.
CYLINDER SOLUTIONS The procedure used is illustrated by the discussion which starts on page 138 of Ref.
1.
From the discussion on page 139, axial load offects must be considered unless 0.5 2
"1" 3
R*P
< 1.0 o
,2,
2 2
,1 - y,
Et In this case 0.5 2
"1" 3
RP 0.675
=
,2,
2 2
,1 - y,
E't Therefore, the large displacement solution is required.
To show the difference, the large displacement solution will carry the subscript 1 and the small displacement solution will carry the subscript 2.
TELEDYNE ENGINEERING SERVICES W.
E.
Cooper Page 4 June 4, 1991 Project 7377 The terme k, alpha and beta becomo E*t k :=
k=
119.048 2
R 0.5 3*
,1 - y,,
3 R*P a
- =
+
a
= 0.091 1
R*t 2
1 2*Ea t 0.5 7
.3+
,1 -
0.075 a
- =
a
=
2 Rt 2
0.5 3
,1 - p,,
3*R'P
= 0.054 4
- =
1 1
R*t 2
2*E t 4
- = a 4
= 0.075 2
2 2
The beam equations of Article 35 of Ref. 1 are to be used.
Because the bottom end of the sandbed region is constrained by concrete and the top and matches with a shell of considerably larger bending stiffness, the equations for a fixed-fixed beam will be used.
The equation for maximum deflection is:
l l
"V y
r* Mw-*e
-w-m-
-r
-w w
w,w_.w-w_a-a m
" E L E D YliE E t4G I!1E E RI!1G SERVICES W.
E.
Cooper Page 5 June 4, 1991 Project 7377 "a L'
~
L' a L'
~
L' C2 := a cosh ein
+
sinh cos o
2 2,
,2
,2,
'p. L' "a L'
'4 L'
'a L'
+ a ein conh
+ p cos sinh 2
,2,
,2,
,2,
C1 :=
C2 o f sinh (aL) + a* sin (AL),
p-6 :=
-(1 - C1) o k.
For the case where largo deflections are being considered, theon become:
"a L'
"s L'
'a L'
's L'
1 1
1 1
C2
- = a
- conh
- sin
+0 sinh con 1
1 2
,2 1
, 2 2
"p
. L' "a
L'
's L'
'a L'
1 1
1 1
+a sin cosh
+ 4 cos sinh 1
2
, 2 1
2 2
C1
- =
C2 C2 1.648
=
1 0
sinh"a L'
+a e in 's L'
1 1
1 1
1 1
C1
= 0.104 1
P
'l - C1 6
= 0.467
~
5
- =
1
,k, 1,
1
l l
TELEDYNE ENGINEERING SERVICES W.
E.
Cooper Page 6 June 4,
1991 Project 7377 For the case where only small deflections are being considered, those becomes "a
L'
'S
- L'
'a L'
'A L'
2 2
2 2
C2
- = a cosh ein
+A sinh cos 2
2 2
2 2
2
, 2 "g
. L" "a
L'
'E L'
'a L'
2 2
2 2
+a sin cosh
+ 4
- cos sinh 2
2
, 2 2
2 2
C2
= -0.379 1
j C1
- =
~4 L
2
- C2 2
2 0
sinhfa L'
+a ein
~
[2 2
,2 C1
-0.054
=
2 P
~1 m
~
8
- =
C1 6
0.549
=
2
.k, 2,
2 The equation for the hoop stress in the vessel, as shown previously, is dependent on the radial deflection and on the longitudinal streso.
Noting that the longitudinal stress in the Ceckeler cylinder is as given below, the hoop stresses in the two canes are:
PR 4
1.86 10 o
- =
o
=
1 2t 1
1 4
o
- =
E-
+po o
=
3.89 10 h1
,R, 1
h1 2
4 o
- =
E-
+po o
=
4.478 10 h2
,R, 1
h2 o
h1 0.869
=
a h2 Therefore, the hoop stress with the large deflection solution will be about 87% of the hoop stress with the small deflection solution.
l l
TELEDYNE ENGINEERING SERVICES W.
E.
Cooper Page 7 June 4,
1991 Project 7377 WIDE PLATE EQUATIONS The hoop stresses in the previous computations are higher than would be expected in the Drywell because the effects of meridional curvature have been neglected.
As an analogy, the hoop stress in a sphere is only one-half of that in a cylindev because of the meridional curvature.
To demonstrate the effects of such curvature, the Ref.
2, Chapter 1 equations for a simply supported wide plate NOT on an o3astic foundation are applied with and without considering the effects of curvature.
In both cases the available solutions consider the case where the ends of a simply-supported wide plate are not permitted to char.ge the distance between them, so the average beam stress, that due to the normal loading which prevents this relative motion will be computed to provide a comparison with the meridional stress in the sphere.
An additional flat plate solution is obtainea for the case where the plate edges are fixed but the longitudinal membrane stress is limited to that which can be developed by the sphere.
The wide plate considered has the material proporties and dimensions previously described.
Therefore 3
E't 5
D :=
D = 9.423 10 12*
,1 - p,
If NO IN-PLANE LOADS were present, the maximum lateral displacement would bei 4
5*P*L 5
- =
6 20.57
=
0 384*D 0
The longitudinal membrane stress would be zero and the membrane hoop stress would be
~6 O
6 1.469 10 o
- =
E' o
=
h0m
,R, h0m
TELEDYNE ENGINEERING SERVICES W.
E.
Cooper Page 8 June 4, 1991 Project 7377 Consider first the initially curved plate solution given by Article 7 of Ref.
2, because it reduces to the flat plate solution.
In order to identify these a)1utions, the subscript 3 will be used for the initially curved plate case and the subscript 4 for the initially flat plate.
The initial curvature wi.'.1 be represented by an initial maximum deflection represented by the symbol
'p'.
The solution proceeds as follows:
p := 1.48 2
3- 'e + 6 0,
First :=
2 t
Using the HATHCAD solve block procedures Guess a := 10 Given 2
2 2
3 p - (1 +al First =a-(1 + a)
+
2 t
a
- = Find (a) a
=
- 10. 2 'e 3 3
3 n
5.022 u
- =
a u
=
3 23 3
3 The tensile stress required to keep the points from having relative motion ist 2
Eau 2
3 "t'
4 2.772 10 o
- =
~
2'
,L, 13m
+
o
=
13m 3
,1 - p,
TELEDYNE ENGINEERING SERVICES W.
E.
Oooper Page 9
.Nne - 4, ' 19 91 Project 7377 Tae lateral deflection from the original position is.
6 a
p O
3 6
- =
'~
u.485
=
3 1 + a 3
3 3
and the mt.rane hcop stress which would exist in the sphere is:
-6 1
3 4
o
- =
E-
+ y*a o
=
4.294 10 h3m
,R, 13m h3m The solution for th i.11 ally flat plate follows from the same squations, but with:
P := 0 2
3
.p+6 0,
First t=
2 t
Guess a
a= 10 Given 2
2 2
3 p - (1 + a)
First =a-(1+.a)
+
2 t
l-r
- = Find (a) a
=
13.075 li 4
4 w
i u
- =
a u
=
5.68 4
23 4
4 2
E*u
,,2 4
t 4
3.545 10 o
- =
2'
,L, 14m o
=
14m 3
,1 -y.
a TELEDYNE ENGINEERING SERVICES W.
E.
Cooper Pago 10 June 4, 1991 Project 7377 The lateral deflection from the original position ins 6
a
- P O
4 6
- =
6 1.461
~~
~
=
4 1 + a 1+a 4
4 4
and the membrans hoon stress which would exist in the sphere is:
4 5
a
- =
E-
+yo o
=
1.15 10 h4m
.R, 14m h4m
-Reference 2 provides the' solut. ion f or a fixed edge plate in Article 3.
The subscipt 5 will be used.to identify this case.
In order to obtain the proper longitudinal stress:
o
- = a 4
15m 1
o
=
1.86 10 15m r
i a
~
L 2'
15m u
- =
3
,1 - p,-
u
=
4.114 5
t 3 E
5 Therefore:
4 u
u u
PL 5
5 5
14 6
- =
+
5 384*D 2
sinh"u tanh "u 4
5
,5,,
u 5
6 1.544
=
5 The membrane hoop stress in the sphere is then:
A
TELEDYNE ENGINEERING SERVICES W.-E.
Cooper Page 11 June 4, 1991 Project 7377 6
5 a
- = 3a
+pa h5m R
15m 5
1.159 10 a
=
h5m DISCUSSION The five solutions may be compared as follows:
Case 1
2 3
4 5
Equations used Shell Shell Beam Beam Beam
' Hoop stiffneas Yes Yes No No No Edge conditions Fixed Fixed Simple Simple Fixed End in-plane motion Yes Yes No No Yes Large displacements Yes No Yes Yes Yes Meridional curvaturs No No Yes No No
" Radial" displacement 0.467 0.549 0.485 1.461 1.544
" Hoop" stress, kai 38.9 44.8 42.9 115 116
" Longitudinal" stress 18.6 18.6 27.7 35.5 18.6 l
j.-
TELEDYNE ENGINEERING SERVICES W.
E.
Cooper Page 12 June 4,_1991 Project 7177 As noted previously, Case 1 gives a hoop street which is but 87% of that for Case 2.
Therefore, tSe large displacement solution gives a hoop stress which indicates about the same benefit as was determined by CE in their analysis of the Oyster Creek Drywell.
However, also as previcasly noted, the calculated hoop stresses are considerably higher than those computed by GE..
This is to be expected because the beam on olastic foundation equations used in the analyses of these two cases dod not consider the effects of meridional curvature.
Cases 3 and 4 were performed to investigate the type of effects which result from the meridional curvature, Case 3 considering the carvature and case 4 considering an initially flat wide plate.
The effect of the curvature is very significant, the " hoop" stress considering curvature being but 37% of that obtained neglecting the curvature.
These solutions do NOT have an elastic foundation, so that the hoop stiffness of the actual sphere is neglected.
Also, these solutions have simply-supported ends which are constrained from relative in-plano motion, therefore generating a higher longitudinal stress than can actually be-generated.
Both effects were considered in Case 5,
where the edges were fixed and relative in-plane motion considered.
The results from case 5 are very similar to those of Case 4, so the comparison of Cases 3 and 4 is considered to be pertinent to the present issue.
This is not to say, however, that one would expect as dramatic an effect of curvature on the GE calculations, because the curvature was included in both the small and large deflection GE enalyses.
However, some additional effect of curvature would be expected.
Therefore, basea or. _ these analyses and previous experience with this issue, _a range of possible effects has been stated in the con.clusions.
- ~_
4 4,
.In GE Report Index No.
9-3, Tables 3~3 and 3-4 indicate the large concentrated loads consid6 red in the analysis; however, these loads-are uniformly distributed along the circumference of the pie slice finite element model at various elevations.
Sinco the stresses in the corroded regions of tt., drywell are close to the allowables, what effect would a more re?.ined treatment of these loads have on the stress evaluation? -Tl is question should be addressed for all drywell regions (i.e., cylindar, knucklo, upper sphere, middle sphere,.ower sphere, and sandbed). It should considet stresses directly under the load (if corrosion in this area is present), aa well as the effect on the stress distribution at further distances from the load.
RESPONSE
The " concentrated loads" referred to in the question are due to penetrations, upper and lower beam seats.and other miscellaneous appurtenances, most of which are not really concentrated. Referring to Tab' e 3-3, 2,015,050 of th9 2,184,150 lbf shown in the Dead Weight column is distributed either uniformly or at 20 locations spaced evenly around the circumference of the shell. Also, 762,000 lbf of the 862,000 shown in the Misc Load column is also cistributed.
Therefore, 2,777,050 of the 3,434,350 lbf Total Load (column 4) or elt of the total aediticnal weight load is. distributed. The remaining 657,300 lbf are concentrated loads due to penetrations and the equipment hatch.
The 657,300 lbf for concentrated loads was derived from another drywell containment during the analysis for restart performed by CBI in 1987.
In the current GE work, this load was judged to be small and that Erefinement of these loads reflecting the specific Oyster Creek penetrations was not warranted. The specific Oyster Creek penetrations-have been reviewed relativo to the analysis and the - loads used are conservative.
For example, the analysis includes 169,100 (64,100 + 105,000) lbf for the equipment hatch and personnel lock assembly while the actual assembly at Oyster Creek weight. 70,000 lbf.
The specific response to this question is divided into two parts, local and global. Locally, all penetrations six inches and larger were located in the areas of corrosion (see Table 3).
Calculations for all were reviewed and ample margins exist such that the thicknees loss indicated does not threaten code compliance.
Globally, the egalpment hatch and personnel lock' assembly were analyzed as a concentrated Icad (actually distributed over the reinforcing ring) and uniformly distributed over the circu.nference of the shell using a
-180' finite. element model.
The analysis shows'that concentrating the load increases the meridional stress by 204 pai and hoop by 160 psi in the sandbed region. -This includes the fact that the actual assembly weights 70,000' vs. 169,100 lbf used in the GE repart. The next heaviest penetrations are main steam and feedwater with combined loads of 23,300
-lbf.
(The penetrations are combined for this analysis because they are l
close together).
This analysis shows that concentrating the loads increases the meridional stress by 81 psi and hoop by 66 psi in the sandbed region. The calculated hatch assembly stresses do not add to the main steam and-feedwater stresses since thay are=1ocated 90* apart from one another. The remaining penetrations are either located higher up in the drywell and/or deliver less load.
Therefore, concentrating these loads will result.in increases less than 81 and 66 phi.
Also, since the penetrations are scattered on'the shell surface, these increases will not -
r l
be cumulative.
These stresses are in the order of 1% of the allowable and are, therefore, judged to be insignificant.
I SCT/WP/ MIS /Drywell/6
ATTACHMENT FOR GPUN RESPONSE IQ_QllESll.ON 4 R2:C3212172
=.
~i IABLE 3 0.C DRYWELL PENET1ATIONS IN AREAS OF CORROSION Drywell Penetration /
Latest Nominal Thickness Region Location Measurements Near Shell Loss penetrations Thickness cylinder X38-six 3"4 0.643" El. 73'-9" &
72'-11" 0.640" X70- 16 4 0.629" 0.011 El.79'-6" Knuckle No penet, located in thj - region Upper X12A, X128 0.719" 0.003 Sphere 22"4 El. 62' X8, 26" 0.717" 0.005 El.58'-3" 0.678" 0.044 El. 62,"4 X63, 14
- 0. 7' 2 "
0.713" 0.009 X9, X10, l
22"4 El. 62' l
X71, 8"4 0.713=
o, cog El.59'-3" L
Middle X13A, X13B 0.753" 0.017 l
Sphere X14A, X14B 96"p x li "
s Insert Pl.
140 1"4 pipe 0.770" El. 49'-3" 0.775" X24, 6"4 El. 47' Lower X49, 94"4 GB analysis I
Sphere &
El. 15'-7 "
captures the vent Sandbed opening and sandbed corroded region i
i a
5.
In GE Report Index No. 9-3, Section 3.2.3, it is indicated that the neismic loads are imposed on the pie slice model by applying forces at four elevations of the model and matching stresses at selected elevations with those f rom the axisymmetric model. How sensitive are the calculations to the location and number of elevations c..,sen to match the strernes?
How well do the stresses compare at other elevations in the drywell?
RESPONSEt Figure 3 shows a. comparison of the axisymmetric 2D model meridional stresses to those predicted by-the four point loading in the pie slice model.
The stress magnitudes include the inertia and displacement effects. Although the results plotted here are for the "with" sand case, the meridional stresses at the four locations in the 2D model are virtually identical to the "without" sand case.
The four pointe seler:ted for the equivalent loading are indicated by (+).
The plot shows that at the intsrmediate points (diamonds) the agreement is good.
The difference shown in the lower spherical regica is mainly due to the fact that the 2D model does not include the vent line whereas the pie slide model does. This comparison clearly shows that the method
)
used in applying the seismic loading in the pie slice model was reasonable and conservative, j
1 SCT/WP/ MIS /Drywell/7
l l
ATTACHMENT FOR GPUN RESPONSE TO QUESTION 5 l
l l
l l
RZ:C3212172
iMeridional-Seismic Stress Comparison
.Betweenn 2-D and 3-D Analyses;
~1.5 3_'O Results { + 4 Pcints at wiuch Stresses were Mott. bed 1.4 -
o Other Points 1.3 *
[ 2-D Results 2-D = AXISDDIETRIC MODEL c
1.2 -
j; 3-D = PIE SLICE }DDEL 1.1 -
usy' 1-e e
e:
u Ei 0.9 -
E t
E 2e in c.
t c v> ~
e, u,
'E
' O.8 -
t I>
0N Lhj nd h !!
o
-c o u o a
t' 3 <>
=m 0.7 -
e i-Sc is
-8 6 26 Ce 15 Eo 1
0.6 -
_O 0.5 -
c O
15 0.4 -
.o
'C O.3 -
0.2 -
)
0.1 -
0
,,,,,,i.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
2 32 62 ~ 95 131 191 215 242 302 383 461 542 005 665 725 845 881 '341 9//10'3/121/133/1446
~2-D Node. Locatiori H W RE j SEISCOMP.DRW.
_-.~.
..- -...... - -...... - - ~-. - -.
6.
In order to examine your analysis uore closely, the staff is requesting you. to provide the ANSYS input file for both the axisymmetric and pie slice ?aodels.
It would be convenient if this
-information-is provided on a high density 5 1/4" floppy disk for an IBM PC.
RESPONSE
The disk and indices are provided.
a 2
f scT/WP/ MIS /Drywell/8 2
ATTACHMENT FOR GPUN RESPONSE TO QUESTION 6 l
I l
R2:C3212172 l
l
(
SUMMARY
OF OYSTER CREEK DRYWELL FINITE ELEMENT ANALYSIS RUNS FOR WITHOUT SAND CASE The following ANSYS input files are provided for the Oyster Creek Drywell Analysis.
Two models were used: Axisymmetric and Three Dimensional Pie Slice.
The following unit load cases were analyzed using the axisymmetric model: temperature gradient, seismic inertia, seismic displacement.
All other load cases and combinations were analyzed using the pie slice model.
The input files for the temperature gradient and seismic displacement load cases are described under the heading Axisymmetric-Static.
The heading Pie Slice Model contains the description of input files for the pie slice model.
The input files for the seismic inertia load cases are described under the heading Axisymmetric-Dynamic.
Axisymmetric-Static These runs were made on ANSYS version 4.1 on a VAX computer.
The input files on the disk are under the directory 'AXISYMM'.
File \\T210.F40 - Input file for the temperature gradie.it case.
File \\0THERLOA.F40 - Input file for the seismic displacement case. Also has the pressure and weight case inputs.
File \\HYOROLOA.F40 - Input file for the post-accident condition seismic displacement.
Also has the weight case.
Pie Slice Model These runs were made using ANSYS version 4.4a on a 386 PC computer.
The input files for this case are under the directory 'PISLICE'.
Run OYCRIA.DAT - This is a stress analysis run for the-0yster Creek Drywell with sand in the sandbed and a corroded thickness of 0.700 inches. This run contains six load steps.
The first four load steps are to determine the resulting stresses when unit loads are applied-in the meridional direction at four different elevations.
- These load steps are used to match the meridional stresses for the 2-0 axisymmetric analysis to simulate the
- seismic loads (note that the seismic inertia stresses for the with and without sand cases were essentially the same at the four elevatior.s where unit loads were applied).
The fifth and sixth load steps are to investigate the stresses due to pressure and weight loads.
Run OYCRIM.DAT - This run is the small displacement stress analysis of the drywell for the accident case with no sand and a corroded sandbed thickness of 0.736 inches.
Run OYCRlhl.DAI - This run is the large displacement stress analysis of the drywell for the accident case with no sand and a corroded sandbed thickness of 0.736 inches.
_1 1
Run 0YCR10.DAT - This run is the stress analysis of the drywell for the post-accident condition with no sand and a corroded sandbed thickness of 0.736 inches.
Run OYCRIP.DAT - Inis run is the eigenvalue buckling analysis for the post-accident condition which determines the buckling load using the FILE 03.DAT file from Run OYCR10.DAT.
Run OYCRIS.DAT - This run is the stress analysis of the drywell for the refueling condition with no sand and a corroded sandbed thickness of 0.736 inches.
Run OYCRIT.DAT - This run is the eigenvalue buckling analysis for the refueling condition which determines the buckling load using the FILE 03.DAT file from Run 0YCRIS.DAT.
Run OYCRICC.DAT - This run is the eigenvalue buckling analysis for the refueling condition with asymmetric boundary conditions which determines the buck'ing load using the FILE 03.DAT file from No OYCRIS.DAT.
Axisymmetric-Dynamic These runs were made using ANSYS 4.3 version on a VAX computer.
The input files are listed on the next two pages are stored in the disk under the directory 'AXIDYNM'.
2 l
l
.f u
i f
t I
r m -
E M
ANE L
i T
T T
T T
T T
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A A
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A A
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W W
W W
W W
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N N
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D D
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ANALYSIS DESCRIPTION C HPUTER PUN DESCRIPTIO9/ OUTPUT FILE ANSYS INPUT FILENAME
- 3. FLif0DED WITh SAND 3.1 Eisen/ Response Spectrum /
DISKOS:[ CHEEK.KIF. OYSTER.DYN)WATSSELYN.OUT
\\SDWAT\\ FILE 1,DAT K,1,Z Directions /Modai 3.2 Double sum of modest DISKo$:[ CHEEK.KKF. OYSTER.DYN]WATSSEPOST1.f*JT iSDWAT\\ FILE 2.DAT SRSS of X,Y,Z Direction of Input Motion Colinear Responses 3.3, Static - Missing Mass DISKOS:[ CHEEK.KKF. OYSTER. STATIC]WATSSESTA.OUT
\\SDWATiFILE3.DAT Contribution of Truncated Higher Frequency Modes 3.4 SRSS of Response D!SK05:[ CHEEK.KKF. OYSTER. STATIC]WATSRSS.OUT MDWAT \\ FILE &.DAT Spectrum & Static DISKO5:(CHEEK.KKF. OYSTER. STATIC]WATSRSSI.F34
- Colinear Responses 4 FLOODED WITHOUT SAND 4.1 -Eisen/ Response Spectrun/
DISKOS:[ CHEEK.KKF. OYSTER.NOSAND]NOsWATSSEDYN.OUT
\\NSWATLFILE1.DAT K,Y,Z Directions /Modai 4.2 Double sum of modest DISKOS:[ CHEEK.KKF. OYSTER.NOSAND]NOSWATSSEPOST.OUT
\\MSWAT\\ FILE 2.DAT SRSS of X,Y,Z Direction of Input Motion Colinear Responses 4,3 Static - Missing Mass DISKOS:[ CHEEK.KKF. OYSTER WOSDST]NOSWATSSESTA.OUT
\\NSWATtFILE3.DAT Contribution of Truncated Higher Frequency Modes 4.4 SRSS of Response DISKOS:[C:iEEK.KKF. OYSTER.NOSDST]NOSWATSRSS.OUT
\\NSWATiFILE4.DAT Spectrum & Static DISKOS:[ CHEEK.KKF. OYSTER.NOSDST]NOSWATSRSS.F39
- Colinear Responses ANSYS Binary output flie.
This flie can be read as a
- FILE 12.DAT*