ML040770589

Draft Information Request Response to RAI - Attachment 7

ML040770589
Person / Time
Site:	South Texas
Issue date:	04/13/2004
From:	Ann Sheetz NRC/NRR/DLPM/LPD2
To:	Gramm R NRC/NRR/DLPM/LPD2
Shared Package
ML040820686	List: ML040770110 ML040770584 ML040770589 ML040770593 ML040770599 ML040770606 ML040770611 ML040770616 ML040820682
References
Download: ML040770589 (19)

Text

NOC-AE-0300 1659 Attachment I Page 1 ATTACHMENT 1 Response to Request for Additional Information

NOC-AE-0300 1659 Page 2

1. Provide the critical crack size that the master connecting rod will fail due to high cycle fatigue. Give length & depth or aspect ratio.

Response

As shown in the attached photograph of the fracture surface, the critical crack size is about 7 inches in length by about 1 inch in depth (the thickness of the ligament). This determination is based on empirical data obtained from examination of the fracture face.

2. Provide a calculation that demonstrates that the minimal detectable crack size wvill not grow to the critical crack size and fail due to high cycle fatigue during the proposed interval between NDE inspections. The calculation needs to account for the possibility that an accident can occur prior to the end of the inspection interval and that the diesel will perform its mission without failure. The calculation should describe the results, the assumptions and inputs and method used so that an independent reviewer can verify the conclusions.

Response

The requested calculation is presented in two parts. The first part is a classical Paris Law Equation analysis for the initial portion of crack propagation. The second part is an empirical assessment of the failure timeline.

Part I Discussion Understanding the failure mechanism and the timeline associated with crack initiation and subsequent crack propagation is important for two reasons:

1. Unit 1 SDGs 11, 12, 13 and the other two Unit SDGs 21 and 23 are not susceptible to the type of failure that occurred on SDG22. This is based on the connecting rods being crack-free and that the operating hours places the connecting rods well beyond the longest reasonable incubation period plus the time required to grow a hypothetical crack to detectable size.

2. For SDG 22, the shortest possible incubation time and the time required to propagate a crack to critical size is essential for establishing an inspection periodicity which precludes a similar failure on the rebuilt SDG 22.

In the following discussion STPNOC will explain that the specific NRC questions are germane to issue #2 which is not required to support the Safety Evaluation for the 113 day Extended AOT request. However, the rationale for issue #1 is relevant to the request.

In the unlikely event that fatigue cracking of the master connecting rod were to occur, that cracking will occur in the ligament between the connecting rod bearing bore and the articulating rod bushing bore. That ligament is 9 inches long axially and about 1 inch thick

NOC-AE-03001 659 Page 3 between the bores. The fatigue cracking mechanism proceeds in stages. The first stage is initiation during which submicroscopic atomic planar rearrangements and dislocation motion occur. The second stage is initial propagation according to the Paris Law Equation, when an actual crack has formed with a cyclic stress intensity factor equal to or greater than the threshold cyclic stress intensity factor required to drive the crack front across the fracture surface. This regime of cracking assumes an unvarying cyclic stress distribution and is valid for crack growth covering up to about 20% of the final fracture area and is characterized by a rapidly increasing crack propagation rate, da/dN, as the crack length increases.

Testing of materials for fatigue resistance traditionally is done to evaluate the resistance to initiation of fatigue cracks on a featureless (polished) surface. Many decades of testing have demonstrated the concept of an endurance limit. The fatigue limit may be established for most steels between 2 and 10 million cycles (Ref. 10). Typically, if a test specimen has tested for 107 (ten million) cycles or more, it has been shown to be operating at a stress below the endurance stress. Although 10 7 stress cycles is well accepted as the endurance limit, for this assessment assuming that initiation could occur up to twice the time, or 20 million cycles, adds additional margin.

This 4-stroke cycle Cooper-Bessemer KSV engine experiences one stress cycle every 2 rotations, and the peak stress occurs at Top Dead Center (TDC) at the end of the master rod exhaust stroke. This loading is all from the inertia of bringing the master rod and piston to a stop and reversing its direction of travel and is unrelated to the gas pressure loads which depend of engine power output. These diesel engines always run at 600 rpm, and thus accumulate fatigue cycles at 300 stress cycles per minute or 18000 cycles per hour, independent of engine load. Therefore, a crack can initiate and begin to grow up to 1 100 hours0.00116 days <br />0.0278 hours <br />1.653439e-4 weeks <br />3.805e-5 months <br /> of operation (which equates to 20 million cycles).

Once the initiation process has been completed, i.e., a crack-like configuration with a cyclic stress intensity factor AK = 6.2 ksi 4lin has been developed, that crack will propagate continuously at a rate described by the Paris Law Equation, da/dN = A(AK)p where A is a coefficient and P is an exponent, both of which are determined experimentally for a given alloy and heat treatment.

For the connecting rod material as used by Cooper-Bessemer, Battelle determined the coefficient A = 9.77 x 10-12, and the exponent P = 4.12. (February 27, 1990 Battelle Report).

The Battelle Report was reviewed and found to be applicable to the current situation. The details of the experimental determination of the Paris Law Equation parameters and the threshold value for fatigue crack propagation are clearly and completely presented in that reference.

The Paris Law Equation will be valid near the origin of the fatigue crack, as long as the stress field is constant, that is, unchanged by the crack itself. This applies while the crack extends

NOC-AE-0300 1659 Page 4 over less than 20% of the eventual final fracture surface, or is about I inch deep and 2 inches wide at the connecting rod bore surface. The cyclic stress intensity AK can be calculated for the 2003 event directly from the fracture surface. As the attached photographs show the fatigue fracture surface is exceptionally well-preserved and has an excellent set of beach marks preserved on the surface. In fatigue, a beach mark indicates a temporary arrest point for the fatigue crack, usually when the machine is not operating. In the case of the number 9 master connecting rod from SDG 22, the beach marks are in essence a "calendar" engraved on the fracture surface. Groups of beach marks close together represent consecutive monthly 4-hour surveillance runs, and the single large gap between such groups of beach marks represents crack growth during a 24-hour annual surveillance run.

A photograph of the fracture surface was used to measure the crack growth and the number of beach marks. The photograph has a ruler scale at the bottom of picture. The measured crack growth for one group of beach marks is about 3/16 inches. There are 13 beach marks in this length. Thus on average, the fatigue crack grew 0.014 inch between two successive beach marks. This region of beach marks is about 1/2 inch from the origin. Each of these equivalent beach marks was associated with a normal monthly surveillance run, and in the relevant time frame that run was just over 4 hours4.62963e-5 days <br />0.00111 hours <br />6.613757e-6 weeks <br />1.522e-6 months <br /> in duration. Thus the measured crack growth rate per stress cycle, da/dN, is about 0.2 x IOE-6 inches per cycle. The stress cycles are counted from the peak stresses when the master connecting rod is at TDC at the end of its exhaust stroke, 300 cycles per minute at 600 rpm.

As noted above, the February 27, 1990, Battelle report provided the coefficient for the Paris Law Equation for this material, based on tests of actual connecting rod steel. Using this equation and inserting da/dN = 0.2 x I OE-6 inches per cycle, the AK for the crack at that depth was computed to be 11.13 ksi 4in. The AK's for other crack depths between 0.1 inch and 1 inch were computed using the standard fracture mechanics relationship between stress intensity factor K, stress cr, and crack depth a:

K = Ya'a where Y is a coefficient that is unity for ideal geometric circumstances, and near a value of one but varying based on geometric details for specific cases.

For cyclic stress intensity factors for fatigue, the change in stress intensity factor AK is proportional to the change in stress Ao via the modified fracture mechanics equation:

AK= YAa~a The ratio of the square root of crack depth over 0.5 inch was computed for a given crack depth, and this ratio was multiplied times the AK at 0.5 inch crack depth to produce the value of AK for the desired crack depth. This process was calculated for every 0.005 inch of crack depth, and is shown on the attached spreadsheet. This calculation also shows that AK does not reach the threshold value until the crack depth is about 0.155 inches. The Paris Law Equation is then used to compute the average crack extension rate, da/dN, for every 0.005

NOC-AE-03001659 Page 5 inch interval, and this is then converted to the number of cycles, and the number of hours, required to cover each 0.005 increase in crack depth. Finally, starting with the crack at threshold depth, the number of hours for each interval is summed to provide, on the spreadsheet, the cumulative hours for the crack to reach any given depth up to 1 inch.

Several lines are highlighted on the spreadsheet. The first is at a depth of 0.16 inches', the minimum detection limit for in situt NDE UT detection at STP. This depth will be reached after only 30 hours3.472222e-4 days <br />0.00833 hours <br />4.960317e-5 weeks <br />1.1415e-5 months <br /> of crack propagation after initiation is complete. The next highlighted line is at a crack depth of 1/4 inch (0.25 inch). The value of AK has increased to 7.9 ksi 4in, and the crack has reached this depth after a total of 191 hours0.00221 days <br />0.0531 hours <br />3.158069e-4 weeks <br />7.26755e-5 months <br /> of growth post-initiation. The next 1/4 inch of growth, to a depth of 1/2 inch (0.5 inch) requires another 140 hours0.00162 days <br />0.0389 hours <br />2.314815e-4 weeks <br />5.327e-5 months <br /> of growth, indicating some acceleration of the crack growth rate. Another 1/2 inch of growth, to a depth of I inch, uses up just 68 hours7.87037e-4 days <br />0.0189 hours <br />1.124339e-4 weeks <br />2.5874e-5 months <br />, as the AK value has increased to 15.7 ksi 4 in.

At this point in the assessment, the response to the first issue can be determined. Below is a summary of STP diesel engine connecting rods hours of operation:

• SDG 11 1691 hours0.0196 days <br />0.47 hours <br />0.0028 weeks <br />6.434255e-4 months <br />

• SDG 12 1880 hours0.0218 days <br />0.522 hours <br />0.00311 weeks <br />7.1534e-4 months <br />

• SDG 13 21l1 hours

• SDG 21 1802 hours0.0209 days <br />0.501 hours <br />0.00298 weeks <br />6.85661e-4 months <br />

• SDG 22 2116 hours0.0245 days <br />0.588 hours <br />0.0035 weeks <br />8.05138e-4 months <br />

• SDG 23 1834 hours0.0212 days <br />0.509 hours <br />0.00303 weeks <br />6.97837e-4 months <br /> Since the lowest operating hours on any engine connecting rod is 1691 hours0.0196 days <br />0.47 hours <br />0.0028 weeks <br />6.434255e-4 months <br />, sufficient operating time has elapsed such that any defect or condition which could possibly develop into a crack has had sufficient time to initiate and grow to a detectable condition (1130 hours0.0131 days <br />0.314 hours <br />0.00187 weeks <br />4.29965e-4 months <br /> based on 20 million cycles to incubate and crack propagation per Paris Law). Since the inspections on SDGs 11, 12, 13, 21 and 23 have confirmed that no such cracks exist, the 1 An ultrasocni testing (UT) calibration standard was prepared by machining a narrow Electric Discharge Machining (EDM) notch was machined into the crankshaft bore of another connecting rod to simulate a crack in the region near the initiation site of the failed section on the number 9 connecting rod. To ensure the delectability of a crack in the vicinity of the initiation site, the simulated flaw was positioned behind the drilled oil passage at a location just past the direct line-of-sight horizon of the phased-array UT transducer. The UT calibration standard demonstrated the capability to repeatedly detect a crack 0.16 inches deep at this location. Larger flaws positioned further around the curvature of the crankshaft bore or located on the smaller radius of curvature articulating pin bore opposite the initiation site are possible and are more difficult to detect.

Nevertheless, the 0.16-inch simulated defect is conservatively much smaller than any crack which could hypothetically exist in the plane of the initiation site at this point in the operating history. Photographs of the calibration standard are provided in reference 2 of the cover letter.

NOC-AE-0300 1659 Attachment I Page 6 conclusion that the connecting rods are operating below the endurance limit has been demonstrated and that no such cracks could ever develop is supported.

Part 2 Discussion Beyond a crack depth on the order of 1 inch, the third stage of crack propagation occurs with load redistribution along parallel load paths as the crack itself increases the compliance of the ligament, reducing the cyclic stress distribution acting on the crack. This effect modulates or decreases the rate of acceleration predicted by the Paris Law Equation alone and accounts for the long crack growth period experienced with these connecting rods. If the acceleration continued, complete separation of the connecting rod would occur in less than 450 hours0.00521 days <br />0.125 hours <br />7.440476e-4 weeks <br />1.71225e-4 months <br /> of crack propagation. However, this is inconsistent with the experience in 1989 (634 hours0.00734 days <br />0.176 hours <br />0.00105 weeks <br />2.41237e-4 months <br />) as well as the current failure (2116 hours0.0245 days <br />0.588 hours <br />0.0035 weeks <br />8.05138e-4 months <br />). The explanation is that the forces imposed on the fracture surface drop off as the crack grows because there are significant alternate load paths to carry stresses around the affected area (load redistribution) as the compliance of the cracked region increases. Thus the crack growth acceleration decreases considerably as the crack grows, and the total propagation time is on the order of 600 to 1 100 hours0.00116 days <br />0.0278 hours <br />1.653439e-4 weeks <br />3.805e-5 months <br /> after crack initiation.

Employing an analytical fracture mechanics model to evaluate the behavior of event past this point is considerably more complicated because AK is influenced by two opposing factors:

(1) increasing crack size and (2) decreasing stress applied to the crack face. Calculations of crack growth rate and the critical crack size in the ligament between the bores of the Cooper-Bessemer KSV master connecting rod is not necessary because the two incidents that have been associated with the connecting rods, in 1989 and in 2003 yielded experimental verification that critical crack size is 7 inches long by through through-wall (on the order of 1-inch). The ligament length in the axial dimension is 9 inches. The definition of critical crack size is standard definition from fracture mechanics, that is the size of crack for a given stress field, that raises the stress intensity K to a level equal to the critical stress intensity Kic (the fracture toughness) of the material. This large critical crack size is due principally to load redistribution around the ligaments as the crack enlarges and the compliance of the master connecting rod in the vicinity of the ligament increases. This drops the applied stresses considerably and keeps the stress intensity from reaching the critical stress intensity value until the growing fatigue crack is relatively large compared to the total fracture surface.

The direct measurement of the critical crack size in the 2003 event, with corroboration between 1989 and 2003 events, is much better than any calculated approximation, especially in light of the load distribution phenomenon.

There is confirmation of the identification of the sub-critical fatigue crack from the final critical fast fracture in the well-preserved fracture surface. The attached photographs show the excellent beach marks that identify the fatigue crack covering the majority of the fracture surface.

NOC-AE-03001659 Page 7 Therefore, in order to address the issue of establishing an inspection periodicity which precludes a similar failure on the rebuilt SDG22, the time for an assumed crack to grow to critical size is determined from the empirical data. The failure occurred following more than 2100 hours0.0243 days <br />0.583 hours <br />0.00347 weeks <br />7.9905e-4 months <br /> of accumulated engine operation. Subtracting the doubly conservative initiation time (1100 hours0.0127 days <br />0.306 hours <br />0.00182 weeks <br />4.1855e-4 months <br />) and the time required to grow to detectable size (30 hours3.472222e-4 days <br />0.00833 hours <br />4.960317e-5 weeks <br />1.1415e-5 months <br />), the time for a crack to grow from just below the detectable size to critical size is 970 hours0.0112 days <br />0.269 hours <br />0.0016 weeks <br />3.69085e-4 months <br />.

Since a detectable crack of a depth of 0.16 inches will take at least 970 hours0.0112 days <br />0.269 hours <br />0.0016 weeks <br />3.69085e-4 months <br /> to grow to critical size and cause connecting rod failure and in an emergency situation the diesel is required to provide 7 days (168 hrs) of continuous operation for plant safety, the indicated inspection interval would be calculated by subtracting 168 from 970 hours0.0112 days <br />0.269 hours <br />0.0016 weeks <br />3.69085e-4 months <br />. This shows that if the connecting rods are inspected every (970 - 168 = 802) hours, they will maintain at least 168 hours0.00194 days <br />0.0467 hours <br />2.777778e-4 weeks <br />6.3924e-5 months <br /> of run time available, even if called on just before the next scheduled inspection. Therefore, an inspection interval of about 800 hours0.00926 days <br />0.222 hours <br />0.00132 weeks <br />3.044e-4 months <br /> is considered acceptable (Ref. 7, 8, & 9). Per reference 11, inspections will be performed every 500 hours0.00579 days <br />0.139 hours <br />8.267196e-4 weeks <br />1.9025e-4 months <br />.

References:

1.

Materials Technology Report, Investigation of Diesel Generator Engine Connecting Rod Failure - South Texas Project Unit 2, dated December 13, 1989.

2.

APTECH Report, Significance of Over-drilled Oil Holes on Fatigue Life of the KSV-4-2A Connecting Rod in the Standby Diesel Engines at South Texas Project, Dated March 1990.

3.

Applied Mechanics Report (AM-1852-C-1A) titled Finite Element Analysis of the KSV 2A Master Connecting Rod, by Cooper-Besemer Reciprocating Products, Division Cooper Industries, Inc.

4.

Report No. 341B7139 by Battelle titled Failure Analysis of the KSV-4 2A master Connecting Rod to Cooper Bessemer Reciprocating, Cooper Industries, Dated February 27, 1990.

5.

Metals Handbook Ninth Edition, Volume 1, Properties and Selection: Iorns and Steel.

6.

Formulas for Stress and Strain, Fifth Edition by Roark, and Young.

7.

STP UFSAR Ch. 8.3.1.1.4.9

8.

STP UFSAR Ch. 9.5.4

9.

NRC Standard Review Plan 9.5.4

10.

Mark's Standard Handbook for Mechanical Engineers, Eighth Ed., p. 5-9

11.

Letter from T. J. Jordan to NRC Document Control Desk dated December 20, 2003, "Revision to Proposed Emergency Change to Technical Specification 3.8.1.1" (NOC-AE-03001653)

NOC-AE-03001 659 Page 9 4140:Alloy Steel: Effect of.,Moisture.and Dissolved Oxygen on Reversed. Bending FatigueLife, in: Sodium' Chloride A

.Dry Air A

Air, 93% R.H..

70

\\..

Deoeroted3%NQCI

\\

A Aerated 3% NMCI.

u) 6;8A

's

\\

"'5''Q Cl)

A

.A

.30

~

1:

1 I gIr i1 e,

.105.

IQ

1 n*

. of CYCLES T0 FAILURE Atlas of Stress Corrosion and Corrosion Fatigue Curves, (1990 Version), Edited by A. J. McEvily, Jr. -

American Metals International, Page 106.

NOC-AE-0300 1659 Attachment I Page 10 Crack Initiation and Growth Timeline Plotted Along Engine Operating Hours 2 X 107 cycles or 100 hours0.00116 days <br />0.0278 hours <br />1.653439e-4 weeks <br />3.805e-5 months <br /> SDG22 #9 Connecting Rod Failure (2100 107 cycles or 550 hours0.00637 days <br />0.153 hours <br />9.093915e-4 weeks <br />2.09275e-4 months <br /> Detectable Crack (0.16")

1130 hours0.0131 days <br />0.314 hours <br />0.00187 weeks <br />4.29965e-4 months <br /> eCeckp I lDeepl ICrack P

I I

P.-

970 Hours of Growth From Detection Threshold to Failure

.4-Crack Growth Governed by Simple Paris Law Fnistinn Crack Growth Influenced by Load Redistribution

NOC-AE-03001 659 Attachment I Page 1 I Schematic Representation of NDE Calibration Mockup Not to Scale

v i!

i t, p l

C oo-fiws~er rild, utilji in lune i.:uay':-tr' Seicvi.censi

¶kf11r.'e:s.ct!?. CtrrIO5 'MtflK£ Ls~ttU;.flG nl......'.....;.. ci,.2-CridiI*'

I., ~.....t,. i, it

':slnflli, filibo

• zIwSO R T1I31 ct tt l C A F 14 I 0 F SE U PME.4 ';r n1. Tr We Wig v

(:;

jJ (i 3) c

'"Li'Sir-k1-R

. IIT Pa,!ilE pil

___ ____;__.Riro..

I3,il'................

_l2r;

.1

fit:8~~~~~~~~~~~~~~~~~~~~.t...

.-. 8....()l; l

............ m3-F9%vt,...

~s ~s;It.l'

........ : !.., i;.l-el

,l<t

ci(

........... riat.'r.

?

l APOX.'¢, ;1....... QVe~'},L-S3'ir'..t 7?',.......................t.fAt'v....

Ojjil rgql{nc1:std and tem1ered to 1.97-241 rir?.1, sti:rt.izjteeled mu! ultrustz ra10_cnJ4+/-.

I1airiii.1~

LOle s7.

I I I

I.,

,f I

~

11ttr

-- Fi2.- iti et U.514 r e. _

C ITa 1

a fi!

1;?,,- I r

(c-jII i.

, k..

grrrs1444

-4 7

PDRr

. 39 43 la9

.l5 Ib2U

.2 l PY3

.9!1

.
r A

112 YAm;:::r.L r;?rr VV'%i

e.

51/4. -

TJV:_ $P r**

,4it

'-'I.

ii I

.. *...

-4

'fls

.4:

.i*

a

.1

tmDE irVITr 0414)

Mf~ThOY' Sr-zS IMOM:Zvo #'irs I

"T'"

MYtil'

?.?-Yl. C:!:,h nzyi J :';

~~~

• ~~-

.W-........

_,g>*.........

rFri(I'AT.S cf.:T-3t1ir11 CW32)l

'S 0

CM 0 CD -

z 0

0 nri 0

I'D 08 rertl sc EFr teat CLa73*t6I tr.w 7 Thmire r pp Lc-e:l asi tfl/J.

,?..

J52i--IC-I4fl.. p/s 5--:

• e rt lily t t' tJI e (li',s8:.'! A'.

,. J Z7........

as Z:aVo.- )tf IS>@ i n

.. IC It-.:

a : z w ).

1. I..-: !:a-s i

NOC-AE-03001 659 Attachment I Page 13 Or ioi S~11_

17 7 8

19 20' 21'

• 1 1

A s

I 91 hI lot

• t1 hd,,.. t.,.j l

t i 1:j i,Ior

.. i I

I16 I

.H D

22 23 pit.,.

i 24 M...

2 L

I

NOC-AE-0300 1659 Page 14 O7

• • A J*/,

q...PA

.J%.

4..

.-t _!

n I

NOC-AE-03001 659 Attachment I Page 15 fi 1

4tPtA

)J,,Jr

• - ;VAVy\\%t-Vrst;-

JR..

V -.

A 110,"

i£ C -

I 4,. -. '



4 w

a crtr if' a

Fatigue Beach In.

.' III toD I II H 1 1 I.',

Paris Law Equation, from Battelle Report, Feb 27, 1990 for actual connecting rod

material, dafdN = (9.77 x 1OE-12) x (AK*(4.12))

coefficient =

9.77E-12 solve for AK = (da/dN"(1/4.12)) / (9.77 x 10E-12)**(1/4.12)

SORT(2) =

1.414213562 18000 cycles per hour

.014 Inches between beach marks at 112' from origin 4 hours4.62963e-5 days <br />0.00111 hours <br />6.613757e-6 weeks <br />1.522e-6 months <br /> between beach marks 1.94444E407

=.2 x 10E-6 inches per cycle

=

0.023667914 at da/dN =.2 x IOE-6 in.cycle, when crack depth = 112 Inch

=

0.002127391 1/4.12 root of dafdN 1/4.12 root of 9.77E-12 AK @.2x10E-6 da/dN da/dN =

AK= c9/c10 atl/2"deep 11.13 1.9985E-07 use fact that AK is proportional to sqrt(crack depth) to compute AK at 1/4 deep 7.87 4.7927E-08 AK at 1/8" deep 5.56 1.1494E-08 crack depth from origin, inches AK }si sqrt(in) 0.15 6.1 0.155 6.2 da/dN cycles to grow crack hours to grow cumulative hours after inches/cycle depth by O.005 inches by 0.005 in.

AK >= threshold 1.67329E-08 1.79022E-08 298812 279295 16.60 15.52 Note: AK is below threshold value 0.0 for crack depths less than 0.155 Inches 15.5 Threshold AK

6. ----

0.165 0.17 0.175 0.18 0.185 0.19 0.195 0.2 0.205 0.21 0.215 0.22 0.225 0.23 0.235 0.24 0.245

->"&. vik ii _

2"'

S4

3;'.. 6;

]h'3E

';'08' 6.4 2.0363E408 6.5 2.16545E-08 6.6 2.2987E-08 6.7 2.43605E-08 6.8 2.5775E-08 6.9 2.72306E-08 6.9 2.87273E-08 7.0 3.02654E-08 7.1 3.18447E-08 7.2 3.34654E-08 7.3 3.51275E-08 7.4 3.68311 E-08 7.5 3.85763E408 7.5 4.0363E-08 7.6 4.21914E-08 7.7 4.40615E-08 7.8 4.59734E-08

.... ;.iii F... ;:. --*; *'

v%

.... *.iii'iii......i.-.......-...............

i

.i:

ii i

i'>'{:

245544 230898 217514 205251 193987 183617 174050 165205 157012 149408 142339 135755 129613 123876 118508 113478 108759 13.64 12.83 12.08 11.40 10.78 10.20 9.67 9.18 8.72 8.30 7.91 7.54 7.20 6.88 6.58 6.30 6.04 43.7 56.5 68.6 80.0 90.8 101.0 110.7 119.8 128.6 136.9 144.8 152.3 159.5 166.4 173.0 179.3 185.3

.................... '41 27 43

-1:
::

.9

.6 0.255 0.26 0.265 0.27 0.275 0.28 0.285 0.29 0.295 0.3 0.305 0.31 0.315 0.32 0.325 0.33 0.335 0.34 0.345 0.35 0.355 0.36 0.365 0.37 0.375 0.38 0.385 0.39 0.395 0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 OA4 0.445 0.45 0.455 0.46 0.465 0.47 0.475 0.48 0.485

..................... NS....

........................................................ ;7 7.9 8.0 8.1 8.2 8.3 8.3 8.4 8.5 8.5 8.6 8.7 8.8 8.8 8.9 9.0 9.0 9.1 9.2 9.2 9.3 9.4 9.4 9.5 9.6 9.6 9.7 9.8 9.8 9.9 10.0 10.0 10.1 10.1 10.2 10.3 10.3 10.4 10.4 10.5 10.6 10.6 10.7 10.7 10.8 10.8 10.9 11.0 4.99226E-08 5.196E-08 5.40394E-08 5.61608E-08 5.83243E-08 6.05299E-08 6.27776E-08 6.50675E-08 6.73996E-08 6.9774E-08 7.21908E-08 7.46499E-08 7.71 514E-08 7.96954E-08 8.2281 8E-08 8.49108E-08 8.75823E-08 9.02965E-08 9.30532E-08 9.58527E-08 9.86949E-08 1.0158E-07 1.04507E-07 1.07478E-07 1.10491E-07 1.13548E-07 1.1 6647E-07 1.19789E-07 1.22974E-07 1.26202E-07 1.29474E-07 1.32788E-07 1.36145E-07 1.39546E-07 1.4299E-07 1.46477E-07 1.50007E-07 1.53581E-07 1.571 98E-07 1.60858E-07 1.64561 E-07 1.68308E-07 1.72099E-07 1.75932E-07 1.7981 E-07 1.8373E-07 1.87695E-07

• i66 100155 5.56 196.7 96228 5.35 202.0 92525 5.14 207.2 89030 4.95 212.1 85728 4.76 216.9 82604 4.59 221.5 79646 4.42 225.9 76843 4.27 230.2 74184 4.12 234.3 71660 3.98 238.3 69261 3.85 242.1 66979 3.72 245.8 64808 3.60 249.4 62739 3.49 252.9 60767 3.38 256.3 58885 3.27 259.6 57089 3.17 262.7 55373 3.08 265.8 53733 2.99 268.8 52163 2.90 271.7 50661 2.81 274.5 49222 2.73 277.2 47843 2.66 279.9 46521 2.58 282.5 45252 2.51 285.0 44034 2.45 287.4 42864 2.38 289.8 41740 2.32 292.1 40659 2.26 294.4 39619 2.20 296.6 38618 2.15 298.7 37654 2.09 300.8 36725 2.04 302.9 35830 1.99 304.9 34968 1.94 306.8 34135 1.90 308.7 33332 1.85 310.6 32556 1.81 312.4 31807 1.77 314.1 31083 1.73 315.9 30384 1.69 317.6 29707 1.65 319.2 29053 1.61 320.8 28420 1.58 322.4 27807 1.54 323.9 27214 1.51 325.5 26639 1.48 326.9 I....

s;;.

...'C

.. :. i

.: >.. I.::' :  : 'C:::

I..

0.49 11.0 1.91703E-07 26082 1.45 328.4 0.495 11.1 1.95754E-07 25542 1.42 329.8 0.505 11.2 2.03988E-07 24511 1.36 332.6 0.51 11.2 2.0817E-07 24019 1.33 333.9 0.515 11.3 2.12396E-07 23541 1.31 335.2 0.52 11.3 2.16666E-07 23077 1.28 336.5 0.525 11.4 2.2098E-07 22627 1.26 337.7 0.53 11.5 2.25337E-07 22189 1.23 339.0 0.535 11.5 2.29738E-07 21764 1.21 340.2 0.54 11.6 2.34183E-07 21351 1.19 341.4 0.545 11.6 2.38672E-07 20949 1.16 342.5 0.55 11.7 2.43204E-07 20559 1.14 343.7 0.555 11.7 2.47781E.07 20179 1.12 344.8 0.56 11.8 2.52401E-07 19810 1.10 345.9 0.565 11.8 2.57066E-07 19450 1.08 347.0 0.57 11.9 2.61774E-07 19100 1.06 348.0 0.575 11.9 2.66526E-07 18760 1.04 349.1 0.58 12.0 2.71322E-07 18428 1.02 350.1 0.585 12.0 2.76163E-07 18105 1.01 351.1 0.59 12.1 2.81047E-07 17791 0.99 352.1 0.595 12.1 2.85976E-07 17484 0.97 353.1 0.6 12.2 2.90948E-07 17185 0.95 354.0 0.605 12.2 2.95965E-07 16894 0.94 355.0 0.61 12.3 3.01026E-07 16610 0.92 355.9 0.615 12.3 3.06131E-07 16333 0.91 356.8 0.62 12.4 3.1128E-07 16063 0.89 357.7 0.625 12.4 3.16473E-07 15799 0.88 358.6 0.63 12.5 3.21711 E-07 15542 0.86 359.4 0.635 12.5 3.26993E-07 15291 0.85 360.3 0.64 12.6 3.32319E-07 15046 0.84 361.1 0.645 12.6 3.37689E-07 14807 0.82 361.9 0.65 12.7 3.43104E-07 14573 0.81 362.7 0.655 12.7 3.48563E-07 14345 0.80 363.5 0.66 12.8 3.54066E-07 14122 0.78 364.3 0.665 12.8 3.59614E-07 13904 0.77 365.1 0.67 12.9 3.65206E-07 13691 0.76 365.9 0.675 12.9 3.70843E-07 13483 0.75 366.6 0.68 13.0 3.76524E-07 13279 0.74 367.3 0.685 13.0 3.82249E-07 13080 0.73 368.1 0.69 13.1 3.88019E-07 12886 0.72 368.8 0.695 13.1 3.93834E-07 12696 0.71 369.5 0.7 13.2 3.99693E-07 12510 0.69 370.2 0.705 13.2 4.05596E-07 12328 0.68 370.9 0.71 13.3 4.11544E-07 12149 0.67 371.5 0.715 13.3 4.17537E-07 11975 0.67 372.2 0.72 13.4 4.23574E-07 11804 0.66 372.9 0.725 13.4 4.29656E-07 11637 0.65 373.5

0.73 0.735 0.74 0.745 0.75 0.755 0.76 0.765 0.77 0.775 0.78 0.785 0.79 0.795 0.8 0.805 0.81 0.815 0.82 0.825 0.83 0.835 0.84 0.845 0.85 0.855 0.86 0.865 0.87 0.875 0.88 0.885 0.89 0.895 0.9 0.905 0.91 0.915 0.92 0.925 0.93 0.935 0.94 0.945 0.95 0.955 0.96 0.965 13.4 13.5 13.5 13.6 13.6 13.7 13.7 13.8 13.8 13.9 13.9 13.9 14.0 14.0 14.1 14.1 14.2 14.2 14.2 14.3 14.3 14.4 14.4 14.5 14.5 14.5 14.6 14.6 14.7 14.7 14.8 14.8 14.8 14.9 14.9 15.0 15.0 15.1 15.1 15.1 15.2 15.2 15.3 15.3 15.3 15.4 15.4 15.5 4.35782E-07 4.41953E-07 4.48169E-07 4.54429E-07 4.60734E-07 4.67084E-07 4.73478E-07 4.79918E-07 4,86402E-07 4.9293E-07 4.99504E-07 5.06122E-07 5.12786E-07 5.19494E-07 5.26247E-07 5.33045E-07 5.39888E-07 5.46775E-07 5.53708E-07 5.60685E-07 5.67708E-07 5.74776E-07 5.81888E-07 5.89046E-07 5.96248E-07 6.03496E-07 6.10789E-07 6.18126E-07 6.25509E-07 6.32937E-07 6.40411E-07 6.47929E-07 6.55492E-07 6.63101 E-07 6.70755E-07 6.78454E-07 6.86198E-07 6.93987E-07 7.01822E-07 7.09702E-07 7.17627E-07 7.25598E-07 7.33614E-07 7.41675E-07 7.49782E-07 7.57933E-07 7.66131 E-07 7.74373E-07 11474 11313 11157 11003 10852 10705 10560 10418 10280 10143 10010 9879 9751 9625 9501 9380 9261 9145 9030 8918 8807 8699 8593 8488 8386 8285 8186 8089 7993 7900 7807 7717 7628 7540 7454 7370 7287 7205 7124 7045 6967 6891 6816 6741 6669 6597 6526 6457 0.64 0.63 0.62 0.61 0.60 0.59 0.59 0.58 0.57 0.56 0.56 0.55 0.54 0.53 0.53 0.52 0.51 0.51 0.50 0.50 0.49 0.48 0.48 0.47 0.47 0.46 0.45 0.45 0.44 0.44 0.43 0.43 0.42 0.42 0.41 0.41 0.40 0.40 0.40 0.39 0.39 0.38 0.38 0.37 0.37 0.37 0.36 0.36 374.1 374.8 375.4 376.0 376.6 377.2 377.8 378.4 378.9 379.5 380.1 380.6 381.2 381.7 382.2 382.7 383.2 383.8 384.3 384.8 385.2 385.7 386.2 386.7 387.1 387.6 388.1 388.5 388.9 389.4 389.8 390.3 390.7 391.1 391.5 391.9 392.3 392.7 393.1 393.5 393.9 394.3 394.7 395.0 395.4 395.8 396.1 396.5

0.97 0.975 0.98 0.985 0.99 0.995 15.5 15.5 15.6 15.6 15.7 15.7 7.82661 E-07 7.90995E-07 7.99374E-07 8.07798E-07 8.16268E-07 8.24783E-07 6388 6321 6255 6190 6125 6062 0.35 0.35 0.35 0.34 0.34 0.34 396.8 397.2 397.5 397.9 398.2 398.6

_=

_Af.