ML20148F718

Rev 1 to Stress Intensification Factors for Lateral Branches Fabricated from `Welded-In Piping to Be Used in ASME Class 3 & ANSI B31.1 Pipe Stress Analysis

ML20148F718
Person / Time
Site:	Comanche Peak
Issue date:	04/21/1982
From:	Arena G, Raghavan L STONE & WEBSTER ENGINEERING CORP.
To:
Shared Package
ML17303B208	List: ML20148C865 ML20148F051 ML20148F081 ML20148F113 ML20148F150 ML20148F186 ML20148F215 ML20148F252 ML20148F335 ML20148F444 ML20148F459 ML20148F492 ML20148F524 ML20148F648 ML20148F718 ML20148F789 ML20148F820 ML20148F863
References
RTR-NUREG-0797, RTR-NUREG-797 75, 75-R01, 75-R1, NUDOCS 8803280267
Download: ML20148F718 (28)

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CA LCUL ATION TITLE (Indicative of the Objectivelt Streer,TuttasMication Factors for Lateral Branches

{} I - NUCL E A R Fa ricated fece N ded-In" Piping to be used in ASME Claso SAFETY RELATED

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Calculation Titla Stress Intensification Factors for Lateral Branch Conn.

i This calculation has been reviewed in accordance with DfrP 8.26 and was found to be adequate. The method of review utilized was (circle one):

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= theoretical limit pressun of plane -

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d and r

= mean diameter and mean radius of pr

= experimental limit pressure of con. -

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Cs and Cas

= theoretical limit couple of plane 7

= thickness of pipe of connection 1.

= thickness of branch

. pipe and plane branch respec. ~

s/S -

= elanac boop asresa ratio (d/t)/

tively io (D/T) p

= experimental pressure in connec. -

tion

._ i

= experimental limit couple of plane ii

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= constant fillet radius of external C

1s surface ofintersectma of tees and -

pipe

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fillet radius at external erotch of. Cis

= stable experimental in plane limit tee couple Ar = p*(1 - y)= crossectional ana of reinforcement [ Cor

= stable experimental out of plane is due to fillet in horizontal piane

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limit couple

,a p.anda.

= external fillet radius of lateral '- ICoe

= unstable experimental out of. plane where crotch makes an acute and plastic couple obtuse angle, respectively C,6

= theoretical limit couple of plana.

er

= average yield strength of connectaas pipe at constant internal pressure -

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= theoretical elastic boop strain due

= theoretiesi elastic axial strain due..

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pipe with closed ends having di-s*

pipe with closed ends having di-mensions of the branch or pipe, s es mensions of branch or pipe, re T respectively as l

spectively f es

= referring to en, or ene l

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= experimental elastic boop strain due to internal pressure l

' a./e,

= elatic stress ratio in thin plane pipe exposed to axial force and band. fu

= axial force acting on branch due to' ing C

...A differences in magnitude of faecae

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= elastic stress ratio in thin branch i

constituting the limit couple, i

l due to F, and Cir are, ser

=, theoretical elastic extremum Axial Du

= nominal diameter of pipe ed welded strain due to an external couple se having dimensione of branch and

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= referring to c,, orter s

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= experQnental axial strain due to ex-a, ternal couple measured at 90 deg to neutral axis nr F,

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NPcs)- 7 5 - x 6 Pa g s (3 STRESS INTENSITICATION FACTORS (SIFl FOR UNREINFORCED LATERAL BRANCH CONNECTIONS

1.0 OBJECTIVE

Paragraph NC 3650 of the ASME Section III, (12)*, code provides a method of analysis of class 2 and 3 piping products. The analysis utilizes Stress Intensification Factors (SIF) along with some simple equations to establish acceptable limits on stresses.

Figure NC 3673.2(b)-1, (12)*, provides SIF's for commonly used standard piping products. For non-standard piping products NC 3673.2(b), (12)*,

states that SIF may be taken as C K /2 where C2 and K2 are class 1 2

stress indices given in Table NB 3682.2-1, (12)*.

Lateral branch con--

nections are not among the components for which SIF or C2 and K2 stress indices are available. Thus, code evaluation of lateral branch connec-tion by simplified analysis is not possible.

The p.upose of this calculation is to establish a method to derive an appropriate SIF for use in the evaluation of lateral "stub-in" branches using NC-3650 rules, (12)*, based upon the results of a published lit-erature survey.

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• Numbers in () indicate reference numbers listed in Section 3.

B2-12241-9

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• STATIC 4/80 3.

DIRECT - this indicates the step is to be analyzed in the increments given on the data card, breaking the step into fractions, e.g.,

0.7, 0.8, 0.9, 0.95, 1.0 indicates increments will be used applying to 70%, 80%,

90%, 95%, and 100% of the load history (as defined on the loading cards).

4.

TIMEP is the period of this analysis step.

Default value is one which means that normalized time is used.

Note:

this time period for static analysis is not accumulated over different steps.

The time period must be non-zero.

5.

NUMBER - this parameter is used to initiate the automatic load incrementation option and to suggest the increment size.

For example, NUMBER = 5 will make the first increment equal to 0.2 of the total time.

However, the program will now adjust the time increment based on the number of cycles needed in each increment with the limitation being that the time increments will not be larger than 0.2 of the total time.

Note:

NUMBER and DIRECT are mutually exclusive parameters.

mc 6.

CUTMAX - the maximum number to times the suggested uniform increment size may be subdivided.

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7.3.2-3

• STATIC

STONE & CEBSTER ENGINEEQlNG CORDORATION CALCULATION SHEET a sne es CALCUL ATION IDENTIFICATION NUMBER J.O. O R W.O. NO.

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8 1.

It is reasonable to assume that unreinforced lateral branch I

8 connection behavior would also be indicative of reinforced

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Interal branch connectiton behavior.

e 2.

Bending moment stress indices (c and k.,) are same for,

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2 tubular joints (no hole at the intersecEien) as well as pipe branch connections.

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1. 3 3, All other assumptions are noted in the body of the text.

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References:

1. Markl A.R.C., "Fatigue Tests of Piping Components"- Transactions ASME, April 1952, pp. 287-303.

2. Schroeder, J., Srinvasaich, K.R., and Graham, P., " Analysis of test data on branch connections exposed to internal pressure and/or external couples", Bulletin No. 200, Welding Research Council, New York, 1974.

3. Kuang, J.G., Potvin, A.B., and Leick, R.D., "Stress concentrations in Tubular Joints", Paper No. OTC 2205, Off-Shore Technology conference, Houston 1975.

4. Hsiao C. and Kahn. A.S., "Stress intensification effects in unreinforced oblique branch intersections due to external

- moments" - PVP Volume 50 ASME, New York 1981.

5. Wichman, K.R., Hopper A.G., and Mershon, J.L., "Local Stresses in spherical and cylindrical shells due to External Loadings" Bulletin No. 107, Welding Research Council, New York.

6. Visser W. " On the structural design of tubular joints" OTC 2117 Proc. Sixth Annual Off-Shore Technology Conference, Houston (May 6-8, 1974) Volume II pp. 881-894

7. Reber, J.B. Jr. "Ultimate Strength Design of Tubular Jofnts" OTC 1664 Proc. Fourth Annual Off-Shore Technology Conference O~

Houston (May 1-3,1972) Volume I pp. 447-458

8. Beale L.A. and Toprac, A.A. "Analysis of in-plane T,Y, and K Welded Tubular Connections" Welding Researen Council Bulletin 125 Oct. 1967 pp. 1-30.

9. Gurner, T.R., "Fatigue of Welded Structures" Second Edition 1979

' Cambridge University Press.

10. Khan, A.S. and Hsiao C., "Strain Field in the intersection region of two obliq'uely inclined straight cylindrical shells, An Experi-mental Study". Submitted for publication in "Experimental Mechanics".

11. Mikhopad'hyay.5,30h..y., *Bouwkans J. G., "Fatigue Behavior of

~

Tubular Joints-in offshore Structures", OTC 2207, Seventh Annual'

- Of fshosa Technology Conference, Housten (May 5-8, 1975).

l

12. ASME Boiler and Pressure vessel Code,Section III 1980 Edition.

13. ANSI B1171, American National Standard Code for Pressure Piping, Power Piph2g,1977 Edition.

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ec 4.0 ANALYSIS O

Stress intensification factors (i) for various piping components are, in large part, based upon tiarkl's (1)* approach and test data generated by his work.

The Mark 1 cyclic moment fatigue tests did not cover lateral branch con-nections and code does not provide either 'i' factors or C, K2 stress 2

indicies for lateral branch connections. Several authors have investi-

)

gated this problem and references (2)*, (3)*, and (4)* are some of the significant published reports.

VRC Bulletin 200 (2)* reports and analyzes test data on branch connec-tions including unreinforced laterals exposed to internal pressure and/

or external couples. Tests wer-conduc.ted on plain pipes, tees (normal branch connections) and 45' late.rals, to determine "limit loads" of the components when subject to internal pressure, in-plane and out-of-plane bending moments. No fatigue tests were conducted.

Figures 1and2f(2)*,showresultsofin-planecoupletestsona45' lateral and a 90* nomal branch connection, both of identical dimensions except for the angle of branch connection. Table 1, (2)*, summarizes the data and test results as well. From these figures and table, it is clear that the limit load for the lateral is higher compared to that of 90* tee indicating that the laterals are plastically stronger than The same conclusions are arrived at for out-of plane couples as tees.

observed by test results shown in figures 3, 4, and 5 and Table 2, (2)*.

O However, as observed in the Pe/PyP column in Table 1, (2)*, the follow-ing is concluded:

1.

Laterals are plastically. stronger than 90* branch connections when subjected to external bending moments.

2.

Laterals are plastically weaker compared to tees when exposed to internal pressures.

Conclusion 2 is drawn as a point of interest since in class 2, 3, and f

B31.1 stress analysis, the pressure loading terms are not intensified.

l The branch construction need only meet the local pressure reinforcement requirements stated in the applicable codes.

While reference (2)* conducted tests on 45' lateral branch connections only reference (3)* reports results of tests conducted on tubular l

joints laterals with angle of branch connections ranging from 0* to 90*.

Reference (3)* presents the finite element model analytical results as l

well as results of experimental investigations and provides stress concentration factor (SCF) for radial thrusts loads, in-plane, out-of-plane bending moments applied to both nomal and lateral branch connec-l tions. The SCF value reported does not represent maximum or peak in the joint, but rather the equivalent of the maximum primary stress l

plus secondary membrane plus bending stresses as represented by the C 2 stress indices of NB 3650.

i O

Numbers in () inficate reference numbers listed in Section 3.

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J.G. Kuang, et al, (3)* performed a parametric study to best fit the h

experiment.a1 results to those arrived at by finite element analysis.

The following parameters that govern the stress distribution in branch connections were chosen: the run thickness to diameter ratio T/D, the branch the run pipe thickness ration t/T, the braach to run diameter ratio d/D, and most significantly to our current investigation, the angle of branch connection. The T/D and t/T ratios govern the stress i

distribution by influencing the radial flexibility of the run pipe

'(Figure 6), (3)*, and by bending stress in the branch at the intersee-tion. The d/D ratio and the angle of branch connection influence the i

stress distribution by the load transfer mechanism.

Veen a tee is subjected to axial branch loading, the load is transferred to the run primarily via local bending and punching shear. As a result if the branch is inclined at other than 90' only the component of the load normal to de run wall is of primary concern, as the horizontal component is transferred by compression or tension in the run.

l Reference (3)* developes empirical equations to derive SCF's based on the parameters discussed a mve. The applicability and accuracy of the empirical equttions develcr.ed were verified by comparing the test re-sults to results obtained by the empirical equations. Figure 7(3)*

shows good agreement between the experimental and analytical results.

The empirical expression for radial loads, ig-plane, and out-of plane bending loads contain a multiplying ters sin 0 where 9 is the angle, of branch connection, (see Table 3] and 'a' is a constant grester than This indicates that the maximum stress for the branch connection zero.

0 and SCF increases as the angle e increases, 0'i e 190'.

Severalotherresearchers' investigations,(6)*,(7)*,and(g)*9 term have resulted in empirical equations for SCF's that include a sin reinforcing the conclusion arrived at in reference (3)*.

Table 4, (9)*,

also indicates the agreement between the results arrived at by various authors.

f Reference (3)* imposes a set of limitations on geometric parameters to minimize dispersion between experimental Snd analytical results. !fost l

important of them are:

0.2 g t/T g 0.8 0.3 g d/D g 0.8 0'

g6 g 90' As sentioned earilier, the SCF derived in reference (3)* is akin to ce stress indices of the code. From reference (3)* it is clear that the for laterals are lower thean 90' branch connee-SCF and therefore, C2 tions. By considering the geometry, branch and lateral connections for laterals indices and thus the product of C K2 must have similar K2 will always be lower than that for branches. Therefore stress intensi-fication factor 'i' which is equal to C K /2 (NC 3673.1(b)) for laterals 2 2 will always be lower than that for 90' branches.

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• Numbers in () indicate reference numbers listed in Section 3.

B2-12241-9

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15 - n PA y, n While it is true that Reference (3)* deals with tubular joints, (no O

hole at the run-branch intersection) the same cone 1=sions are arrived at by C. Hsiao and A.S. Kahn (4)* for piping intersetions.

C. Hsiao, et al, present the result of finite element investigation of 6 x 3 branch connections for three branch sogles, namely 30', 60', and 90',

subjected to in plane and out-of-plane loads.

The output of the finite element analysis in the form of membrane stresses and bending moments in the local coordinates are properly com-bined to obtain total stresses at the run/ branch pipe intersection.

These stresses are divided by "beam type stresses"

( = M/Zr) for the known applied in plane and out-of plane soment to obtain a "stress ratio". Here M is the applied soment and Zr the elastic section - med-ules of the run pipe. The stress ratio thus obtained are compared to the experimental data, (10)*, for in-plane and out-of-plane loadings available for 30' and 60' branch connection angles. Figures 8, 9, 10, and 11, (4)*, exhibit good agreement between the experimental and analytical results. Reviewing figures 12 through 20, (4)*, indicate that the stress ratio increases with the increase in the angle of branch connection thus confirming results of reference (3)*.

Reference (II)* provides a basis to evaluate the fatigue capacities of a lateral in comp:rison to a 90' branch of equal size under equiva-lent loading conditions. Figure 21 results' indicate a trend to initial failure (crack initiation) occurring at 90' branches sooner than at equivalent laterals and complete failure (through-wall crack) predomin-antly occurring in 90' branch: connections. The tests were run using O

stress ranges above those alleved by the piping codes for a 7,000 cycle life. The laterals withstood greater than 7,000 cycles in all cases. These trends indicate that a lateral is less sensitive to cyclic damage than its equivalent 90' branch.

O Numbers in () indicate reference numbers listed in Section 3.

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SUMMARY

OF RESULTS O

1.

Under a single load to failure, the lateral brancheonnection is stronger plastically than the normal branch connection.

2.

Under cyclic loading the lateral branch connection has greater fatigue strength than a normal branch connection.

3.

Laterals are plastica 11y weaker compared to tees when exposed to internal pressure.

4.

While reference (3)* tests are on tubular joints 'the results are appl.icable to branch connections considering the similar conclu-sions arrived at in reference (1)* and (4)*.

5.

Reference (3)* imposes geometric parameter limitations for the empirical expressions for SCF to be valid. However, it is reas-ocable to assume that the dispersion between experimental and analytical results for tees and laterals will be in the same dir-ection so that the laterals SCF's will always be lower than that of tees even outside the geometric limitations.

s O

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• Numbers in () indicate reference numbers listed in Section 3.

32-12241-9

PAG,E. 1S 6.0 CONCI.USIONS O

1.

In a piping analysis a lateral branch connection can be safely analyzed siMlar to a normal branch connection for class 2 and 3 and non-A.-E ipes.

2.

In general the results of this investigation indicates that unre-inforced fabricated lateral connections are stronger than corres-ponding 90' connections. It is expected that this same conclusion could be drawn for reinfored lateral connections as well. However, until more data becomes available to cenfirm this it is recoamended that a factor be applied for additional conservatism in the calculation of stress intensification factors (SIF) for laterial connections.

The SIF for either an unreinforced or reinforced cent.ections may be determined by calculating the SIF for an equivalent 90' connee-tion and increasing it by 25 percent.

3.

The above must be subjected to the following restrictions:

a.

The branch connections must meet all the pressure reinforce-ment requirements of NC 3643 of ASE Section III or ANSI B31.1 Paragraph 104.3.1.

b.

The branch connection angle (the angle between the run and ~~

r 0

_ bra _n.ch pipe axes) is between 45' and 90' both inclusive 1

c.

ASE Section III code version is limited to the sunner 1981 addenda and earlier. Winter 1981 addenda requires that pres-sure terms be modified by "B" indices.

4.

The use of lateral branch connections vould be restricted to ASE Class 2 and 3 and B31.1 systems; insufficient data exists to draw conclusions for Class 1 applications.

O Numbers in () indicate reference numbers listed in Section 3.

32-12241-9 J

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37.7 4.26 1.9 0.47 4

35 l'1%s breach. pipe ansk e of al! latersh to 45 de6. The arternal rainfor

=t of Ti and T was more than a 111et.Tb hmat --

q pressee ps of P was 2.09 kaL TMbds. 2 SEF 1 T*J8W 2 4 k tt

-Dete en Umrt Cowpie Tests of Ptain Pipes and in. Plane Cavoie Tests a3 No. of Tig. No.

• Cannast.

e C,_, e, C a sC.L*.

.P dsel far w

er pse Cs or Ces p Ce er Con ts y ny,,

d D e Af Cs pu saaes asse dess 23 No.*

D T S is n

(Ash (As0 (sn.hp)

(as0 (sn.hp)

P.

21 28.7 43.0 36.9 0.86 2

37 88 Pe 41 28.2 1.38 31.8 0.75 26.5 0.83 0.66 2

38 P.

81 27.7 24.6 23.8 0.96 2

39 4 Tg 0.52 24 ' 1 0.14 R 31.6 7.3 0

6.6 sk 0 0.91 0

2 40 as T., 0 75 25 1 0 37 3 ST $2 4 22.1 0

18.5 e 0 0 84 0

2 41 4

T.e 1.0 25 1

0.28 4T N25.0 42.6 0

27. 0 = 2 0.64 0

4

42. 8. 44 to y,

o.;5 25 1 TT 35 4.

24 2 - 0 23.0

• 0 0 96 O

?

A 30 Ta 0.75 26 1

0.27 4T 37.5 3.1 25.4 1.0 12 0 a 0 0.47 0.32 2

44 To 1.0 27 1 0.25 4T 26.2 1.9 N.6 0.5 19.2 a 0 0.49 0.28 2

47 3L J

j s The branch. pipe angle e of alllaterale is 46 de6. Cg of P. is 27.8 la.. hip.

3 l

33 i

34 TQQ 1

33

~

.Oeta en Owt.ef. Mane Unitt couple Tests and Plast 6cel4 UneteMe Ovt.ef. Mane Canapte Tests 3,

N) of Tig. No.

• Comanet.

o

'y d

D e

Af er er p s, Ces p

Ces C__,,se ICoe I.Ctf dal for erpspr a.

(Ash (As0 (in.4 p) (he0 (ia.hp) Cea (in-Up)

Cea soses smet data 3e No.

• D 7'

S Ef T.

05 25 1

0 14 ?T 33 6 78 56 0.72

>7. 8 2

50 s.7 0.45 1

41 Tie 0.7 34.5 0.55 0.22 3.5T 29.5 20.2 1

40

-* Y.

0 63 22 1

6T 33 2 16 1 -

14.4 0 to T.

1 25 1

0.07 Ir 31.4 54.0 32.0 0.69 1

54 d'

Tie 1

42 1

0.34 fr 24.1 23.1 11.0 0.49 3

55,57 To 0.7 34.6 0.58 0 044 ST 31 0 18 21.8 1.0 70 0M S

'A.

et el iThe branch. pipe angle e of alllaterals is 48 deg.

-- " - : n _ _

43 es l

l

.-. - - _ _ _ ~ _. - -.._..__ -,-.

STONE & CEBSTER ENGINEEQlNG COQDORATION CALCUL ATION SHEET

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TA B t E &

(,/t.e p 3

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C ALCUL ATION 10EN TIFIC ATION NUH8ER J. C. O R W. O. N O.

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i t ym-i.m(g""c2M(g)""(qT""Aw me

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si

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l T,%.,c 0.%) (Vpf* (9 T"**'[*/7) '"3 0

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s = p,. g %,. m..+,,,

STONE & CEBSTER ENGINEEGING COAPOR ATION CALCULATION SHEET a seso es CALCUL ATION IDENTIFICATION NUMBER b

J.O.OR W.O.NO.

OlVISION D GROUP CALCUL ATION NO. ' OPTIONAL TASK CODE PAGE 0

M o.470 1eCt hip LS.)

75 XIe

. i i i i.,

i I

i 4

i i i ;

1 i i !

i ;l l l j !

3

, i t

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3 6 t i !

i.

i 4

i i

2 i

i

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j i i i i i e

i i l i i i e t

i i

7

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so Table 7.2 is

'3 SCF in chord SCF in brace le

- ~ - ~

~

Formula

1. = U.3

$ = 0.55 4 = 0 8 4=03 $ = 0.55 / = 0.8 Analload on the brace 87 Gibsicin 5.25

? 38 4 08 5.79 6.20 5.24

~

9 Kuang 5.92 4.58 3.06 8.36 6.27 3.97 Yvordswonh 5.87 6.66 4.98 4.70 5.20 4.14 i.

& Smedley In. plane bending 4

E'

~~~l Gastem 2.03 2.03 1.85 2.03 2.0:

1.83 Kuang 1.59 1.55 1.53

.59 2.06 1.78

-~

~

~~~ ~~~

Wores=onh 2.! 4 2.23 2.04 2.35 2.40 2.:9 l

as

& Smedley Out ofplane bending Gibstem 2.91 4 60 4.3:

2.78 4 64 4.93 8S

' ' - 'l Kuang 2.44 3.94 3:10 3.15 5.12 4.60

~

se Word 6*ont 2.87 5.09 5.8T~

2.81

4. 1 4.70 at 3

a 5<. dw s

3.

St TA6LEj__k 5'

55 34 RU_. ; _.9_.... PA 4 E. t&&.

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3?

1 I

3.

40

.i 4I

- - ~

43 44 48 1

STONE & CESSTER ENGINEERING CORPOR ATION CALCULATION SHEET a mo u C ALCUL ATION 10ENTIFIC ATION NUMBER

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J. O. O R W.O. N O.

OlvlSION O GROUP CALCUL ATION NO.

OPTIONAL TASK CODE PAGE E9 c. A'7 c i l. c l M%B )

"75

)(G i i i i iii ii i

> i.

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80 L

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,. _ _J N. P L A. u r_. Ale 4 7 c.co fi.e.s-.

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=

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STONE & CEBSTER ENGINEEQlNO CORD 00ATl0N CALCULATION SHEET wo n C ALCUL ATION IDENTIFICATION NUMBER J.O. O R W.O. NO.

OlVISION O GROUP C ALCUL ATION NO.

OPTIONAL TASK CODE PAGE lb E9 c. A 7 o, i o l NPLCs)

~7 7 X(o a

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1 STONE & CEBSTER ENGINEEalNG ConPOR ATION CALCULATION SHEET' C ALCUL ATION IDENTIFIC ATION NUMBER d

J.C. O R w.0. N O.

CIVISION Ts GROU.P C ALCUL ATION NO.

OPTIONAL TASw CODE PAGE 5 9 e A 7o-.i el NPLfh) 1.r-X(s O = 48 Bf d = is ri l

t = 4 411 N REF t, 3

$4 (s.,ioy l

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3 a

i 4.83 4 l5 4:41 LC

• . rig. Ica. Influence of 1/0 on the SCF of a typical

f. joint.

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Fi 11. Comoarison of e sper ie en ta l and empir.

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e STONE & UEBSTED ENGINEERING CORPOR ATION j

CALCULATION SHEET

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CALCUL ATION IDENTIFICATION NUMBER O

J.0. O R W.O. N o.

OlvlSION G GROUP CALCUL ATION NO.

OPTIONAL TASK CODE PAGE 59c 47ost el NFLe) 7 5' X(o i

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Offt. 54fif E W = 84134 9G1

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18 i

.a 16.4

64..

l..I l.l.6 187..

g, Sl11 AIE1 f M IIE ifft.5(cfl. (as i to El 22 P14vre 1.3.

Ingl.no 10441r4 results f or 60' 1.atar.ettice (out. aide outf ace).

23 Fm ugs e

gg

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STONE & CE85TER ENGINEE%ING CORPOR ATION CALCULATION SHEET

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& acts as CALCUL ATION IOENTIFICATION NUWBER J.O. O R W.O. NO.

OlVISION O GROUP CALCUL ATION NO.

OPTIONAL TASK CODE PAGE I--

O 5~t) o. 4 7 c..e l NF L6,)

7 s-X6

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• 12 al.a te.s 74.3 nei.6 ur.e is etsTants rami fu inftstetim (m )

O-Pissrs 15. Inglane laading results for 30' intersectise (outside surf ace).

to

_ F 140 Re: do i

_ ~-

at II j

N.

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,, "t l'n/'. I risiin t1 t

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n 7-

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it.e te.s 74.4 ici.s str.e 3e sistascz taas is tenastctie (= 1 3,

40 en F1 pere 16. Out-of 91ame laading reemits for 30' intersection (owtaide surf ace).

e,

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=

_.. ~ ~ ~ ~

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i.

STONE & CEBSTER ENGINEERING CORPOR ATION CALCUL ATION SHEET

& 20 GS CALCUL ATION IDENTIFICATION NUMBER J.0. O R W.O. N O.

OlVISION O GROUP C ALCUL ATION NO.

OPTIONAL TASK CODE PAGE M

@ O s A7 O s t. c)

NP c/6) 75 X,lo i

I i

i i i 4

I i i ii,I i

I i !

@EF.* 4 N ii) 8 l l I !

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7L2 10L4 EEF.0 214 50.4, _

es DIETANCE FMOM TM NTERSECT1CN (sun) _

• F1gste 11. In-91ase 1 Wing roamits f or 90' intarsectise (outside sarf aae).

I kk 88

~ ~ -

g.

34 (eres/r )

~

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l J

(r /F )

I" ay e

$Q 270*

t?

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g

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i 214 S0.5 7L2 10L4 12 7.0 152.4 17 7.8 40 OtSTANCE FROW TW. HTERSECTICN (son) et

~ ~ ~ ~

~'

Chit-of.91ame loading results f or 90' intersectism (outsige surf ace).. '.

et

- ~ ~

Fisvre 12.

15

.=

F140RE

- ~ ~ ~ ~

~

42 es

STONE & CESSTER ENGINEERING CORDOR ATION

• c>

CALCULATION SHEET 4 seio es C ALCUL ATION IDEN TIFIC AT10N NUMBER J.0. 0 R W.0. NO.

OlVISION Ca GROUP C ALCUL ATION NO.

OPTIONA TASK CODE PAGE O

' $ C i 4'7 0 e t

• C )

NF C.8.b 3 "75 K

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ie Fipts 17. Cannetase of the esarse and fine meshes fer the case of ta-plane t aading as o' lias.

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3s 214 SO.4 7L2 10LS IIFA 3'

OtSTANCE FMOW TM NTTJtSECTION (sum)

F% 0 R.E I E i

40 risure 18. IaMame loadias results ter 90* intersection (inside surfaa.).

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48 43

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STONE & CEBSTER ENGINEEGING CORPOD ATION e'

s.

CALCULATION SHEET

& Sct6 48 C ALCUL ATION IDENTIFICATION NUMBER J. 0. O R W.O. N O.

OlVISION En GROUP CALCUL ATION NO.

OPTIONAL TASK CODE PAGE E9e Ate.g.et eJPub) 77 xle I

I i i i ! i l i i i i 8

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Figure 19. Det-of-plane la*== results for 90' intereaction (Laside entf ace).

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