ML20032E889

Forwards Valve Operability Analysis Performed by Posi-Seal Intl Inc,Manufacturer of Butterfly Valves Used for Facility Containment Purge & Vent Valves.Valves in Svc at Facility Meet Operability Criteria Established by Guidelines

ML20032E889
Person / Time
Site:	Brunswick
Issue date:	11/17/1981
From:	Utley E CAROLINA POWER & LIGHT CO.
To:	Ippolito T Office of Nuclear Reactor Regulation
References
NO-81-1887, NUDOCS 8111230448
Download: ML20032E889 (59)

Text

7 Carolina Power & tirght Company November 17, 1981 File: NG-3514(B)

Serial No.:

NO-81-1887 Office of Nuclear Reactor Regulation f

>E @

ATTN:

Mr. T. A. Ippolito, Chief g

/ h' )y Operating Reactors Branch No. 2

'gy 'gpp,

/

United States Nuclear Regulatory Commission b

Washington, D.C.

20555 4'O

/g (Q

No,,g/Sg',*,

BRUNSWICK STEAM ELECTRIC PLANT, UNIT NOS. 1 AN' ?E 7

DOCKET NOS. 50-325 AND 50-324

'g

-g-LICENSE NOS. DPR-71 AND DPR-62 g /p CONTAINMENT PURGE AND VENT VALVE OPERABILITY I\\ \\ y

SUMMARY

In our letter to you dated December 7, 1979, Carolina Power &

Light Company (CP&L) stated our intent to verify the operability of our containment purge and vent valves at the Brunswick Steam Electric Plant by analysis, and in the interim, to limit the travel of all butterfly valves greater than 3 inches nominal diameter to less than 50' open.

DISCUSSION The valve operability analysis was performed by Posi-Seal International, Inc., manufacturer of the butterfly valves used for our containment purge and vent vr.1ves.

The analyses supplied by Posi-Seal include both a seismic analysis and an operability analysis. These analyses are attached and are summarized below.

The operability analysis compares the torque requirements of the valves under the maximum differential pressure condition of 47.3 psi to the guaranteed capability of the actuators to close the valves. The

/f;;03q effects of the concerns listed under the Operability section of the

" Guidelines for Demonstration of Operability of Purge and Vent Valves",

Items 1 through 8, are taken into consideration in the analysis. The results demonstrate the capability of the valves to operate under all postulated operating and accident conditions.

8111230448 811117 m.m.

ma mw-DR ADOCK 05000 2

. ayettevine street. e. o 804 1551. Ralei;;h. N C. 27602 m,_

The seismic analysis concentrates on the external scis,1c loading imposed during a design basis accident (DBA) einac this is the only loading beyond normal operating loads added during a DBA. This is based on the fact that the wafer-type butterfly valve body used at Brunswick is always loaded in pure compression, and the transmission of external piping loads is done by the bolting between the piping flanges where the valve is installed. The results establish the adequacy of design for seismic events.

United Engineers and Constructors, our architect-engineer for the Brunswick site, has analyred the subject valves with regard to sealing integrity after closure and long-term exposure to the contain-ment environment.

Since the Brunswick units use water from the sup-nression pool for containment spray (no chemicals added), radiation, relative humidity, and seal shutoff capability were the primary consider-ations in seal performance. This analysis concludes that the subject valves will seal and maintain shutoff over the lifotime of the plant and following a design basis accident.

CONCLUSION In summary, it can be concluded that the containment purge and vent valves in service at Brunswick meet the operability criteria estab-lished by the guidelines for valve operability.

We will continue to observe the provisions of the interim position while we are awaiting your concurrence to remove the travel limitations on the containment purge and vent valves, and to reenergize those valves that were de-energized due to their inaccessibility for the travel limitation modification.

Please advise us of your concurrence so that CP&L may return all the containment purge and vent valves to full operability.

Please contact us should you have any questions regarding this information.

Yours very truly, y isC I) ), -

m D Gb,O An E. E. Utley l

Executive Vice President Power Supply and Engineering & Construction WRM/lr (7132)

Attachments u

ATTAClEENT 1 BRUNSWICK STEAM ELECTRIC PLANT UNIT NOS. 1 AND 2 V,U.97, SIZING CALCULATIONS FOR CONTAIm!ENT PURCE AND VENT VALVES

POSI. SEAL INTEftNATIONAL, INC.

ENGINEERING CALCULATIONS Titto VD.hMf SI2 it f, C-g.t rcht LTLO. N

- eage !

i cate. By

7. M. 47 checked By _2

.ran_ _/.9.2p_ 'f.

..f'OS(

SEM A E'FER c.v CE. :

......n.-..-.

9 780' z

LM>r TEO Ed Q(NESR S $ CVWCr'R,uC 70R.5

~

CAROLItJR P'clug 2

$ LIC,(4r Co.

BRM U.swick STEAM ELEC-Mtt c PC-At'Jl'

~~

^^

~

u sst r.s i f 2.

• ~ '

UC $ C P O.

95~2 7-0/ - 2 %2 ' 570

'i E N c t.; c C u R E S :

I. POSI-S EA L

TCCMurCM, 50, U. Fi~tM No.

I A p r+'r*ED MilY ? ?.

v

~~

z. CLcestuG. T o R Q t.t G 5, c o m P Gt M ?'(L.

Pit tor o a t-

.OR?'d'O 12./ (G/79.

5.

8 E TT(S P0B 0 TAnh1 Acrc.tn 7 cn. parn. ' yegy, S

~

y u%

s e

e eu..e -

W6*W*

.e

..e.

. eem

's a

.a t

j.

{

1

POSI. SEAL INTERNATIONAL, INC.

~

~

ENGINEERING CALCULATIONS i

Title Page J-Calc. By Checked By bd

/%

27

.1.

• s

' '......._..._..[._._..__....

I

__ A uA t. Y'St.S.

- =

n i

AS SrATS tu Cucc OSU/2E

(.

r W C C Lctsruc TO/?.QtAl' ' (S;.

C A c-c is c-A TED AS FOt t.O uv S I

^

0 T~~ =

T

-t-X e E (AP)C 5) e

.dR x

~

v, E '+ T3 (6P)~- %(4 P) GF I

n.

~

~

.a.......

T =-

'C t. O StuC.

'I'OR C l.t2 fu - e. Or D ' = "V A t. V C PACkfAlGr TO' R.Ql. fC ~

/ o - c.y K =- VR L v'E 'SSkT~ruk TORQ7UC.

tu - c B TJ = VAtV[' 56* A at A)g f A.tc. t'/o u rokq9L4C jg. c 5 y =

vne.e Hy.o copy unmte nrque --

w -ta i

N0 r5 '

/g E Yr3 TS YlftCtisfldstT~

Yl/E 90* V A L-M TR.R VSL

$, RESIST 3 CL 0.S t"Cr Mo rtoa.

i Tu

.Eyis r.s - tout-r stiA sua ritt Les r 5~

• of

. r4AUSL uNt tLL

.SSe rt AJC, 7tSC.

(

REs19 r3 C L 0,$ fuG. f@Yrou.

&~

EY( Y$

'YttR 0 a; Ho a r VME 90*

UA L. VC.

1-Yft A VE!

Bct T~ ^ v/WL E'S to/77f bP.

Tj RCSIS r.S C L. O S suG M:nou,

m.

Th C x?S r.s Ytttracte r rtis 90*

V A L. V~C TR.A-G'6L B u t-VA &tCS wa rt4 o P $ veut Art LE.

T. f3.$/ $ l'S Ct OSto a Ma rco u.

A 9

Tr.. APPkOACffE*S 2EKO ("o)

/7S VALVC APFCActfCS i,

F nc1 T~

Pcst reo v.

,.x' ab" J

w j&

POSI. SEA 1. INTERN.TIONAL. INC.

ENGINEERING CALCULATIONS O

Page Title

@ d

~u.-

/3[k/79-Calc. By Checked By_

/

REQ 'D @

R/lTE D ITE14 val.VE ACTunTOR "Q"y?'" ll'[$

g n

l

/ g "- / 0 732. C - SR 80

$2.00 4 n z.

2 2.o'*-tco 73 2. C-SR 60 81.00 5 (1) 3 2.0 "-15 0 73 2 C - 5 A 80 8260 S'II I 9-8- ts~o CS S20 SR 60 1300 t ie-G N

2.0" 1s~0 73 2 C - SR Go 8200 ynI 6

/ S"- / ro 73 2, C-S R 80 220o 9/32.

7 2.4"-/S'O 73 2. C-S/t 60 9200 7 8 92.

0 4 "- / S* O CB 417-SR 80 700

+ 83 4

+ "- ts'o c3gir-SR90 700 4 g3 nseca.

To s u ct.o s v.n e 3.

D Toaque is GAL.cuin T*EP A T 47.3 PSI AP m

-w-Ms 1+

+

,=,.r

-g--m

,tw4, er w-M+

.g

-c.pg

--w.-

,.-p gy

e EETTIS ROBOTARM' vat.VE ACTUATORS - SPRING RETURN o

TORQUE OUTPUT ALL PUBUSHED TOHOUG ARE GUARANTEED tHNIMt3M VALUES CB SERIES SPRING RETURN OPEH ATING PRESSURE - LDS.*SO. lHCH ACTUATOR 40

$3 60 70 83 90 sco WlODEL C&3:5(4 ENDING 200 20) 300 300

_4m __.

400 egy)

C S4:5s4 EnorNG 350 350 Sm 50)

(78 7ao ggn CS42359 END:NG AT 400 60) 63)

_Av) 800 tory)

CS52044 FNO:NG

.f 90 600 1000 100)

(133))

13a3 g7m Ca525 SR rNoiNo wo 900 i300 i303 in 17 y3 2:00 l

3x0

n00 m3 l car 25sa FNoinG um ir00 2500 2m RACK &. PINION SPRING RETURN

.e OPER ATING PRESSURE a LDS.eSO INCH 40 53 60 70 83 90 100 125 150 175 l 200 225 l 250 l 3010LSR l END 225 420 45d 450 515 710 750 10C0 1000 100) i 1350 1350

4. 1300 HEAVY DUTY - SCOTCH YOKE ~

SPRING RETURN OPER AllNG PRESSURE - LBS /SO INCH 40 50 60 70 to 93 100 125 150 175 200 725 253 521C-SR EN3 830 830 1250 1250 1600 ifio 2010 250) 3130 3130 4170 72iC.5R END 1710 1710 2570 2570 3423 34?O 4200 SY3 6MO 72?C-SR ENO 3150 3150 4750 4750 6W 63C0 79CO

_ _ ~

732C SR ENO 3500 3530 6150 6150

. (820h e200 1030) 10?M 15500 v

HEAVY DUTY - SCOTCil YOXE SPRING RETURN with HYDRAULIC OVERRIDE or SPEED CONTROL OPER AllNG P74E3SURE LDS.?SO. INCH 40 53 CO 70 to 53 l 100 125

'53 175 200 225 250 522C 5 4 H ENO 630 630 1250 1750 WA 1660 m'3 2600 3130 3'19 4170 7720 59.H END 1710 1710

,_2570 2570 34M 3420 4 2 -J S3'A F.120 3500 [ 35T 1500 353) 6150 61A 6150 E201 8200 503h 732C-SR H ENO T. SERIES SPRING RETURN OPERATf*dG PRESSURF LDS./SO. INCH 40 50 60 70 80 93 103 125 150 175 203 225 250 T 310A?R ENDING

.$.}

..$.)

b

_d l 4l

')

b

.b

..b M

.1I M

1470 5170 5 510 7630 9 570 9 570 13400 M 203 20 200 21 000

.,.100 23100 4150 5 510 9 570 9 573 13403_

13 400 19 000 20 2tv) 27 000 2S.100 28100 T^312 A'OR ENDING

',l 2,,,j

,2,j

,,[,,j 1,]

d J.j

,,1,,,j 8) 3 T 316iOR ENO:NG 9 570 13400 17000 20 MO 20 200 24 000 23100 23131 23 100 T-410-SR ENO%G 13 20) 19 303 24 500 ' 73 400 29 400 31800 41 300 T 412-SR E NGIN*"

13310 13300 19 903 -20 800 M 47)

M 40)-

41 300 46 30) 55 700 55 700 T 416.SR ENO:NG 8 ASO 13 309 19 90) 24 400 29 *M 20400 34 000 45603 55700 19 900

?) 400 29 400 41 390 43500 55 700

-55 700 T 420.LR ENO:NG b

b 3-26 300 26 30) 33903 43 000 49 000 41 T3_.ETQJ_u 81 600 92500

_111 l00 t il 000 111000 T 516A SR E*40tNG b

T.520 A-SR ENO!NG 35100 44 C00 49 W 41000 (1CCC 61 533 81 '00 1110ro 1110M b-T 61C A-SR Ef.D'.NG

- 63 300 63 371

_9 WO IN oro iM OM 1720M 177 0v) 1770 0 59 000 63 W T 220A-SR END:NG

- e 5103 3i SCO IM tDO I?10M G 000 177 000 4)(0) 61 M3 61 D)

(

~

~j Pvt.tMR IN $V ALL GOUARE IS

• LEGE40 5

!PehNG fJI2 AND A10$T GE f#ICJIED EXAf :Pt E. T 413 5A%

C0%AT 01CTOW FOa !JWNG DETu~es AC70ATO 3 CAnnLE OF FPOOu0tNG ENO:NC TOTOUES i'4 EXCESS OF t77.0>3 IN (Liss.

4

..n

c=

m 'w.,,)

lp r T~a TECHNICAL BULLETIN NO,1 A t

uqA h;~.id,,.Jl-n J

Operating torque valu-'s mE=F INTERNATIONAL, INC.

and Actuator sizing Innovators in Flow Control ugy 79 m

(

i n

TORQUE VALUES TO OPEN AND SHUT EXAMPLE:

The Posi-Seal Trunnion Valve is a low torque valve A. Requirement - What is the maximum opening which normally reaches its highest torque when torque of a 12" Class 150 valve wits teflon opening. This torque value will vary with the seat chevron packing, a teflon seal ring with rubber material and stem packing selected in addition to.

back-up ring and a maximum AP of 200 PSI.

the maximum operating differential pressure (AP) across the valve.

B. S fution - From Table 1 Torque values to open and shut for standard Posi-Seal Trunnion Valves are listed in Tables 1,2 T = (B) = 70 in. Ibs.

3 and 3, arid are denoted as T, T,, and T.

T, = (G) = 986 in. Ibs.

3 3

10.10 in. Ibs. per PSIAP = 10.10 x 200 =

T and T, torque values are due to the stem T

=

3 3

2020 in. Ibs.

packing and seat material selected and are added~

together to determine preload torque.

Total opening torque = T + T + (T x 3

3 3

PSIAP) = 70 + 986 + (10.10 x 200) = 3076 The static pressure torque factor T

.is the static 3

.in. Ibs.

pressure torque per PSIAP. This factor (T ) is 3

multiplied by the maximum operating AP or maximum line pressure to obtain the torque h

ege@ m mb m @ h value due to pressure.

highest operating torque used in actuator sizing, it To obtain the maximum torque to open or shut is often necessary with flowing liquids to check the T, T, and T AP values are simply added for total hydrodynamic torque. Refer to Section 11 3

2 3

together.

for data on calculating total hydrodynamic torque.

h

Posi-Saal Technical Bulletin No 1A pasa 2 of 12 TABLEI CLASS 150 STANDARD RATING

}

PRELOAD TORQUE = T + T*

STATIC VALVE 3

S!ZE T,

T PR ESSURE 2

TORQUE A

B C

E F

G H

J PER PSI T3 3"

302 28 227 122 73 61 244 280 0.24 4"

338 31 254 218 131 109 436 501 0.50 6"

454 42 340 510 306 255 1020 1173 1.56 8"

529 49 397 902 541 451 1804 2074 3.23 10" 680 63 510 1398 839 699 2796 3215 6.44 12" 756 70 567 1972 1183 986 3944 4535 10.10 14" 832 77 624 2424 14!i4 1212 4848 5575 13.66 16" 907 84 680 3164 1898 1582 6328 7277 19.44 18" 1058 98 794 3994 2396 1997 7988 9186 28.64 20" 1210 112 907 4914 2948 2457 9828 11302

- 40.28 24" 1512 140 1134 7564 4538 3782 15128 17397 77.48 30" 1814 168 1361 11982 7189 5991 23964 27558 147.28 J

36" 2268 210 1701 17426 10456 3713 34852 40080 267.76 42" 2419 672 1814 23795 14277' 11897 47590 54728 390.00 48" 2722 756 2041 30364 18518 15432 61728 70987 569.00 54" 2722 756 2041 39849 23909 19924 79608 91653 734.70 60' 3024 840 2268 49280 29563 24640 985S1 113345 1010 66" 3326 924 2495 59937 35962 29969 119875 137856 1351 72" 3629 1008 2722 71355 428i3 35677 142709 164115 1754 CLASS 150150 PSI RATING PRELOAD = T 4 T, STATIC VALVE 3

SIZE T,

T PR ESSURE 2

TORQUE A

8 C

E F

G i

H J

PER PSI T 24" 1210 112 907 7194 4316 3597 14388 16546 58.96 3

30" 1512 140 1134 12038 7223 6019 24076 27687 123.32 36" 1663 154 1247 17420 10452 8710 34840 40066 196.28 42" 1966 546 1474 23846 14308 11923 47693 54847 317.50 48" 2268 630 1701 31069 18642 15535 62139 71460 477.30 54" 2268 630 1701 39849 23909 19924 79698 91653 612.12 60" 2268 630 1701 49484 29691 24742 98069 113814 760.30 66" 3024 840 2268 59937 35962 29969 119875 137856 1228 72" 3024 840 2268 71661 42097,

35830 143322 164820 1468 Valve torque (opening) = T + T, + (T x PSIAP)

NOTES:

3 3

Valve torque (closing, on-off servicel = T

+T

+

T (A) Asbestos jam packing 3

2

(.5T x PSIAP) 3 3

(b) Teflon Chevron packing Valve torque (closing, modulating service) = T + T, +

(C) Graphite jam packing (T x PSIAP) 3 3

When the operating AP used for actuator selection is T, (E) Urethane seal ring with rubber back-up ring.

Metal seal ring with and without rubber back.

less than the maximum line pressure, contact the up ring, Kel F seal ring without rubber back up factory for sizing torque.

ring (F) Teflon seal ring with Teflon back up ring, Tefzel seal ring with rubber back-up ring (G) Teflon seal ring with rubber back up ring (H) Metal seal ring with Teflon insert and rubber back-up ring (J) Metal seal ring with urethane, Tefzel, or Ke! F insert and rubber back up ring

Rosi Seal Technical Buitetin No 1A paga 3 e n I

TABLE 2 CLASS 300 STD. RATING PRcLOAD TORQUE = T + T,

_ l STATIC 3

' 'ESSU R E VALVE T

T 1

2 SIZE

'iORQUE A

B C

E F

G H

J PER PSI Ta 3"

302 28 227 122 73 61 244 280 0.24 4"

338 31 254 218 131 109 436 501 0.50 6"

454 42 340 510 306 255' 1020 1173 1.56 8"

756 70 567 750 450 375 1500 1725 3.84 10" 907 84 680 1242 745 621 2484 2857 7.64 12" 1058 98 794 1722 1963 886 3544 4076 12.70 14" 1210 112 907 2160 1296 1080 4321 4968 17.71 16" 1361 126 1021 3164 1898 1582 6328 7277 29.16 18" 1512 140 1134 3602 2161 1801 7204 8285 36.90

-s 20" 1814 168 1361 4534 2720 2267 9068 10428 55.74 24" 2117 196 1588 7564 4538 3782 15128 17397 108.46 30" 2722 252 2041 107G4 6458 5382 21528 24757 198.45~

36" 3024 280 2268 16278 9767 8139 32556 37439 333.46 42" 3175 294 2381 23402 14041 11701 46804 53825 503.30 48" 4234 392 3175 30383 18230 15192 60766 69881 871.40 Valve torque (opening) = T + T2 + (T x PSIAP)

NOTES:

3 3

Valve torque (closing, on-off service) = T

+T,+^

T (A) Asbestos jam packing 3

3

(.5T x PSIAP)

(8) Teflon Chevron packing 3

Vaive torque (closing, modulating service) = T + T, +

(C) Graphite jam packing 3

3*

'O 1, (E) Urethane seal ring with rubber back-up ring, When the operating AP used for actuator selection is Metal seal ring with and without rubber back-less than the maximum line pressure, contact the up ring, Kel F seal ring without rubber back-up factory for sizing torque, ring (F) Teflon seal ring with Teflon back up ring, Tefzel seat ring with rubber back up ring (G) Teflon seal ring with rubber back-up ring (H) Metal seal ring with Teflon insert and rubber back up ring (J) Metal seat ring with urethane, Tefzel, or Kel-F insert and rubber back-up ring

~

an:ceg mqenn hi;o 1A pasa 4 cf 12 e-Post-cesg secg e,

I TA8LE 3 TORQUE VALUES (In. Lbs.)

Class 600 Posi Seal Trunnion Valves PRELOAD TORQUE (T + T,)

STATIC 3

PRESSURE VALVE T

T 2

2 SIZE TORQUE A

B C

D E

F.

G H

J PER PSI Ta 3"

342 257 95 120 72 276 0.27 4"

454 340 126 202 121 465 0.63 6"

529 397 147 496 298 1141 1.77 8"

907 bZ 680 252 770 462 W

5Z 1771 4.73 10" 1058 m9 794 294 1234 750 d8 9

2838 8.85 m$

3w*

12" 1361 d$

1021 378 1724; 1034 p

3965 15.89 l

a

<o m

h3

<d2 14" 1512 d2 1134 420 2078

-1247 4779 21.29

$Q 1361 504 2698 1619 40

$Q 6205 33.17 16" 1814 18" 2117 1588 588 3532 2119 8124 50.64 Z

20" 2419 1814 672 4238 2543 9747 69.4 24" 2722 2041 756 6422 3853 14770 118.4 Valve torque (opening) = T3 + T, + (T x PSlaP)

NOTES:

3 Valve torque (closing, on-off service) = T + T, +

T (A) Asbestos jam packing 3

3

(.5T x PSIAP)

(B) Teflon Chevron packing - available on appli-a

^

Vaive torque (closing, modulating service) = T + T, +

cation 3

(T x PSlAP)

(C) Graphite jam packing 3

(D) TeHon jam packing When the operating AP used for actuator selection is less than the maximum line pressure, contact the T, (E) Metal seal ring with and without rubber back-factory for sizing torque.

up ring, Kel F ring without rubber back up ring (F) Tefzel seal ring with rubber back-up ring (G) Not available on Class 600 (H) Metal seal ring with Teflon insert and rubber back up ring - available on application (J) Metal seat ring with Tefzel, or Kel.F insert and rubber back-up ring (urethane insert available on application)

1 Posi-Saal Techicel Bui!stin No.1A pages of12 II. TOTAL VALVE OPERATING HYDRODYNAMIC The total valve operatino hydrodynamic torque TORQUE (TH ) is the summation of three torque compo-r nents. These components are: stem packing torque As previously stated the valve opening torque is (T ), stem beanng friction torque (static pressure normally the highest operating torque used for 3

torque per PSIAP) and the disc hydrodynamic lift actuator sizing and selection. However, when and drag torque. Torque values T and T can be flowing liquids, it.is often necessary to calculate 3

3 found in Tables 1 thru 3.

the total valve operating hydrodynam. torque.

ic Extensive flow testing has shown that the disc The location of the maximum valve operating hydrodynamic lift and drag torque values are torque (total hydrodynamic torque) is a result of dependent upon the direction of flow entering the the overall system operating parameters in addition valve. With liquid flow entering the valve from the to the particular salve disc hydrodynamic torque stem side, with the seal retaining downstream, the characteristics.

disc hydrodynamic lift and drag torque value (T.)

is positive to the full open position acting to return the disc to the shut position. Liquid flow entering When the ratio of thru valve AP to total system the valve from the opposite direction, seal retaining AP is high, generally above 25 percent, the maxi-ring up stream, results in a torque value that mum valve operating hydrodynamic torque will remains positive, acting to return the disc to the occur at or about the 70 to 80* disc open posi-shut position, until about the 70* to 80 open tion. As this ratio decreases, the maximum valve position. At this point the torque value becomes operating hydrodynamic torque will shift towards negative acting to move the disc to the full open the O shut position.

position. With liquid flow in this direction the disc hydrodynamic lift and drag torque values are To allow for system operating variables it is recom.

designated as T. Also, test results have shown that s

mended that the maximum valve operating hydro-flowing liquids in this direction results in a positive dynamic torque (TH ) be calculated at both the T value that is lower than the corresponding T, 7

3 20 and 80 disc open position.

value with flow in cpposite direction.

e e

n n

no, iA paga 6 of 12 Pos.nveel tecnmcai,Lw,.enn By utilizing torque values T, and T a!ong with EX AMPLE; 3

tha applicable disc hydrodynamic lift and drag torque values T, or T listed in Tables 4 thru' 9, A. Requirement - What is the total value hydro-3 tha total valve operating hydrodynamic torque dynamic torque of a 12" CLASS 150 Valve TH, can be calculated as follows:

with teflon chevron packing, flowing water

• " 9 "9

RETAINING RING DOWNSTREAM downstream) with a calculated AP of 10 PSI at the 70 disc open position.

TH = T + (T AP) + (T, AP) G, 7

3 3

RETAINING RING UPSTREAM B. Solution -

TH, = T + (T AP) + (T. AP) G, TH, = T + (T 6P) + (T AP) G,

= 70 + [10.10 (10)) + [692 (10)] 1.0 3

a 3

3 3

TH = Total valve operating hydrodynamic torque, TH, r

TH

= 7091 in. Ibs.

in.Ibs.

r T,

= Packing torque, in. Ibs. Tables 1,2, and 3.

T

= Stem bearing friction torque (static pres-Where --

3 sure torque per PSIAP), in. Ibs. Tables 1,2, T = 70 in. Ibs.

3 T = 10.10 in. Ibs.

3 T, = Disc hydrodynamic lift and drag torque,in.

T* = 692 lbs. Flow into valve with retaining ring G, = 1.0 downstream.

Dise hydrodynamic lif t and drag torque, in.

T

=

3 Ibs. Flow into value with retaining ring upstream.

AP = Dif ferential pressure across velve, PSI.

NOTE:

G, = Specific gravity of liquid at flowing condi.

When in doubt about the maximum total value tions.

Density of liquid at flowing conditions hydrodynamic torque for a specific application, contact Posi-Seal f actory for assistance.

G'=

Density of water at standard conditions e

e

^+-

s--,

~.4-y

p. 9

,7

.- Roe., sal _techm. cal buam.s.m Wo,1A paga 7 of 12 m

re TABLE 4 CLASS 150 STD RATING M

T7'7's f

---szt o w i W

t Y

r.__

I i

W/ kVM i

Seal Retaining Ring Dcwnstream Disc Hydrodynamic Lift & Drag Torque -- T4 VALVE T. VS. OPEN POSITION SIZE 10 20 30 40 50*

60*

70*

80 90 4"

0 0

1 1

3 6

12 16 13 6"

1 2

4 8

13

.27 51 68 56 8"

4 10 16 30 49 100 185 247 204 10" 6

16 26 49 79 161 300 399 330 12" 15 38 60 114 182 372 692 920 761 14" 23 59 94 177 283 579 1075 1430 1182 16" 41 102 164 307 492 1005 1876 2482 2052 18" 64 162 259 486 778 1590 2953 3927 3245 20" 99 248 397 746 1193 2437 4526 6019 4974 24" 214 536 858 1610 2576 5259 9768 12988 10734 30" 462 1156 1850 3469 5551 11334 21049 27988 23131 36" 1884 4710 7537 14132 22G11 46164 85734 113998 94213 42" 2281 5704 9127 17114 27383 55908 103829 138058 114098 48" 3265 8164 13063 24494 39191 80016 148602 197592 163299 54" 7388 18471 29554 55414 88662 181020 336180 447008 369428 60" 11165 27913 44661 83740 133984 273552 508026 675506 558270 66" 14942 37355 59768 112066 179306 366084 679972 904005 747112 72" 22995 57488 91981 172465 275945 563388 1046293 1391225 1149773 CLASS 150 1"50 PSI RATING 10293 l 24" 255 637 1020 1913 3061 6251 11609 15437 12758 30" 857 2144 3431 6433 21016 39030 51897 42890 36" 1792 4480 7168 13441 21505 43907 81542 103424 89607 42" 3202 8007 12811 24021 38434 78469 145729 193772 160142 48" 5412 13530 21648 40591 64946 132598 246254 327437 270609 54" 7336 18341 29346 55025 88040 179749 333820 443871 366835 60" 14428 36072 57715 108216 173146 353506 656512 872945 721442 66" 14942 37355 59768 1120G6 179306 366084 679872 904005 747112 72" 30124 75310 120496 225931 361490 738044 1370653 1822516 1E0G212

1. T values = in. Ibs. per PSit_.P.

~

2. All T. values are positive acting to shut valve.

3. O T values a < 1.

Pos.ps ceal secamcal Bu!ietin No.1A paea a or n a

o y

TABLE 5 CLASS 150 STD. RATING I

}[

'7 T

l FLOW

• i

\\

v

.i I

V/

VUL 4

i Seal Retaining Ring Upstream Disc Hydrodynamic Lift & Drag Torque - T3 T VS. DISC OPEN POSITION VALVE 3

SIZE 10*

20" 30*

40 50*

60 70*

80 90*

3" 0

0 0

0 0

1 1

0

-5 4"

0 0

0 0

1 3

4 0

-13 6"

0 1

2 2

5 13 19

-1

- 56 8"

2 4

8 10 18 46 69

-4

- 204 10" 3

6 13 16 29 75 112

-6

-330 12" 7

15 30 38 68 175 258

-15

-761 14" 11 23 47 59 106 271 402

-23

-1182 16" 20 41 82 102 184 471 697

-41

-2052 18" 32 64 129 162 292 746 1103

-64

-3245 20" 49 99 198 248 447 1144 1691

-99

-4974 24" 107 214 429 536 966 2468 3649

-214

-10734 30" 231 462 925 1156 2081 5320 7864

-462

-23131 36" 942 1884 3768 4710 8479 21669 32032

-1884

-94213 42" 1140 2281 4563 5704 10268 26242 38793

-2281

-114098 48" 1632 3265 6531 8164 14696 37558 55521

-3265

-163299 54" 3694 7388 14777 18471 33248 840G8 125605

-7388

-369428 60" 5583 11165 22330 27913 50244 128402 189812

-11165

-558270 66" 7471 14942 29884 37355 67240 171835 254018

-14942

-747112 72" 11497 22995 45990 57488 '

103479 264447 390922

-22995

-1149773 CLASS 150 150 PSI RATING 24" 127 255 510 637 1148 2934 4337

-255

-12758 30" 428 857 1715 2144 3860 9864 14582

-857

-42890 36" 896 1792 3584 4480 8064 20609 30466

-1792

-89607 42" 1601 3202 6405 8007 14412 36832 54448

-3202

-160142 48" 2706 5412 10824 13530 24354 62240 92007

-5412

-270609 54" 3668 7336 14673 18341 33015 84372 124724

-7336

-366835 60" 7214 14428 28857 36072 64929 165931 245290

-14428

-721442 66" 7471 14942 29884 37355 67240 171835 254018

-14942

-747112 72" 15062 30124 60248 75310 135559 346428 512112

-30124

-1505212

1. T values = in. Ibs. per PSIAP.

3. Negative (-) T values act to move the disc to the 3

3 2.

Except as noted, T, values are positive acting to fuH open (90") position.

shu t valve.

4. O T values a < 1.

3

Poei-Seal Technical Bu!!stin No.1A page 9 of 12 TA8LE 6 CLASS 300 STD RATING f

97. &~ T 7 n

'r gs:t.o w i

n t

y j

I l

nI

%U TWLt1 i

Seal Retaining Ring Downstream Disc Hydrodynamic Lift & Drag Torque - T, VALVE T, VS. DISC OPEN POSITION SIZE 10 20 30 40*

50*

60*

70 80*

90*

3" 0

0 0

0 1

2 5

6 5

4" 0

0 1

1 3

6 12 16 13 6"

1 2

4 8

13 27 51 68 56 8"

1 4

7 11 21 34 57 81 68 10" 3

9 17 27 51 81 136 192 162 12" 7

21 39 60 113 179 298 422 355 14" 9

29 54 84 158 250 416 590 495 16" 12 37 68 105 198 313 520 737 620 18" 28 86 158 244 460 726 1208 1711 1438 20" 30 92 169 261 493 778 1294 1833 1540 24" 41 125 229 355 668 1054 1754 2485 2088 30" 143 429 788 1218 2292 3618 6019 8526 7165 36" 287 861 1579 2441 4596 7253 12065 17092 14363 42" 686 2058 3773 5381 10976 17321 28812 40817 34300 48" 429 1287 2359 3646 6864 10832 18018 255,26 21451

1. T values = in. Ibs. per PSle.P.

2. All T values are positive acting to shut valve.

3. O T values a < 1.

~

- - ~

~

~

Posi-Seal Technical Bui!stin No.1A paga10 of 12 TA8LE 7

-.)

CLASS 300 STD RATING i

@gh'M

.l l

y i

\\

Y

/

l t

l

't// % '/)

t Seal Retaining Ring Upstream Disc Hydrodynamic Lift & Drag Torque - T3 T VS. DISC OPEN POS! TION VALVE 3

SIZE 10*

20*

30 40 50' 60*

70 80*

90 3"

0 0

0 0

0 1

1 0

-5 4"

0 0

0 0

1 3

4 0

-13 6"

0 1

2 2

5 13 19

-1

-56 8"

0 1

2 6

8 10 4

-22

-68 10" 1

3 6

14 21 24 11

- 53

-162 12" 3

7 14 31 46 53 24

-117

-355 14" 4

9 19 44 64 74 34

-163

-495 16" 6

12 24 55 80 93 43

-204

-620 18" 14 28 57 129 187 215 100

-474

-1438 20" 15 30 61 138 200 231 107

-508

-1540 24" 20 41 83 187 271 313 146

-689

-2088 30" 71 143 286 644 931 1074 501

-2364

-7165 36" 143 287 574 1292 1867 2154 1005

-4739

-14363 42" 343 686 1372 3087 4459 5145 2401

-11319

-34300 48" 214 429 858 1930 2788 3217 1501

-7078

-21451

1. T values = in. Ibs. per PSIAP.

3. Minus T values are negative and act to move the 3

3

2. Except as noted, T values are positive acting to disc to the full open (90 ) position.

3 shut valve.

4. O T values a < 1.

3 s

\\

Posi' Seal Technical BuHeHn No1A pago 11 or 12 TA8LE 8 CLASS 600 STD RATING

@ w TM y

QRO W 1 ra i

v i

l W

TWM i

Seal Retaining Ring Downstream Disc Hydrodynamic Lift & Drag Torque - T.

VALVE T VS. DISC OPEN POSITION SIZE to=

20 30*

40 50 60*

70*

80*

90*

3" 0

0 0

0 0

0 0

0 0

4" 0

0 0

0 0

0 0

0 0

6" 0

1 3

3 6

8 13 14 13 8"

0 5

10 12 19 27 44 46 43 10" 1

13 26 29 48 67 107 112 105 12" 1

20 38 43 71 99 158 165 154 14" 2

27 52 SS 96 133 213 223 208 16" 2

36 69 78 128 178 284 298 279 18" 3

43 83 93 153 214 341 358 334 20" 3

41 79 88 146 203 324 340 317 24" 12 166 319 357 587 818 1303 1367 1278

1. T, values = in. Ibs. per PSIAP.

2. All T, va!ues are positive acting to shut valve.

3. O T values Es < 1.

y.

~

a Posi-Seal Technical BuHatin No 1A page 12 of 12

]

TABLE 9 CLASS 600 ST.D RATING i

dgh' M I

lh

• y

\\

Y

/

i

%l 1

57 /

YLf L t

s Seal Retaining Ring Upstream Dise Hydrodynamic Lift & Drag Torque - T 3

T VS. DISC OPEN POSITION 3

VALVE SIZE 10*

20*

30 40 50*

60 70 80*

90*

3" 0

0 0

0 0

0 0

0 0

4" 0

0 0

0 0

0 0

0 0

6" 0

0 1

2 3

2 0

-6

-13 8"

0 2

3 8

9 9

-2

-22

-43 10" 1

5 9

21 24 22

-6

-55

-105 12" 1

7 13 30 35 32

-9

-82

-154 14" 2

10 18 41 48 43

-12

-110

-208 16" 2

13 25 55 64 58

-16

-147

-279 18" 3

16 30 66 76 70

-20

-177

-334 20" 3

15 28 63 73 66

-19

-168

-317 24" 12 63 115 255 293 268

-76

-677

-1278

1. T values = in. Ibs. per PSIAP.

IV. ACTUATOR SELECTION 3

Published torque values for Posi-Seal Trunnion

2. Except as noted, T values are positive acting to 3

shut valve.

Valves include adequate safety factors and do not

3. Negative (-) T values act to move the disc to the require additional safety factors.,However, when sizing actuators for specific valve torque require-3 full open (90 ) position.

ments, decrease the published actuator torques by

4. O T values 2r < 1.

at least 10% to allow for a realistic safety factor 3

in actuator selection. When selecting fail safe Ill. AERODYN AMIC TORQUE actuators, the torque output at the end of the actuator spring stroke (ending torque) should be Aerodynamic torque resulting from gaseous flowis used as the basis for actuator selection. When the negligible compared to Hydrodynamic torque.

However, when in doubt concerning a specific operating AP used for actuator selection is less than maximum line pressure, contact the factory application (such as applications where flow is sonic) consult the f actory.

for sizing torque.

.[._.

--.... _ _ _ _ ____ _ ---. _ --- _ _ ' 0 3 M I -[S t i A l __

U A L U II

'h" G 1? L4 l J LE t3 ITEh!

CLO31r4G TOROUE

- J. - - V ALVE-GI ZE=10 V ALVE-CL AG3= 150 SIEtt DI A.

OlSC DIA.

PRESSURE PACICING 1.75 16.654 47.3 3

I Ti=

1,053.4 T2=

2,396.3 T3=

677.2 TOTAL TORQUE =

4,132.0 i

2 val.VE SIZE =20 VALUE CLASS =150 SIEM D1A.

DISC DIA.

PRLSS'INE P ACl(It4G 2-18 c474

-47.6 3

- T 1 = --1,-20 'M--

T 2,-9 4&-7 T3-95A 4 TO LA! -TURO UE--

Sr110. ~'

l l

I.

VALVE Sl~4E=20 VALUE CLASS =150 l

S T Eli-D I A r--

-D 1 S C---D I sr.

PRL

'NE P AC;'It4 --

2 18.474 47._

3 i

1 T1=

1,20?.6 T2=

2,Y48.7.' T3=

952.4 101i.

TUROUE=

5,110.7 Q,

'J ALUE-. 01Z0.3 - vat L'E Cl 130=150 SIEh DlA.

DISC D1A.

PRL:

'RE PACICING

.875 7.912 47.s.

3 T1=

529.2 12=

540.8 T3=

76.4 TUT cd TOROUE=

1,146.I' F.

VALVE SIZE =20 VALUE CLAGS =150 STEM DIA.

DISC D)A.

1 RE-

' IRE PACl(ING 41 13.4 l4

_3 T.1 =--.-1, 2 0 % $

12-O rM % 7 T7-

?S1 a TOT A!.- T.or:OUE-5,.t10.!L r

6.

VALVE SIZE =18 VALVE CLAS3=150 9T E'4--01 A.

O leC-DT A.

PRi ' JUPE P Af'.M I iiG-1.75 1S.654 47.3 3

.i T1=

1,050.4 T2=

2,376.3 T3=

677.2 TOTAL TUROUE=

4 132.O

1 h h~)'

/%

2. c )T

/

\\

6 I

1 SEAL B EtiR i tJ G 1

y___.

l i

IrLI4 H _ -- - -- _.-

SEAL DEM:Irm a

3._._

t.[L__...____._____.._

cA.,.,i.

iL..,.....,,,.j...

h 1

1

- Li-t

""'-*-'-*weweie m

-h%

O g

1

-l. B j

4

<e,,

1 48

,l! bo e (, j 5 l 4 j j

_--_ _ _ 1 _. __.. _ _. _ _ _ _ __.

-10

..-..~

--.*. mew-w m.

• N,,

I e

-=. -._ -. _ _.

a g

g q

3

-e-=.

-,e

- sa

--....m.-..

l.O

3 f

4 t

l' j

i 4

~ >

i

~

+

i e

i i

C I

4 l

c.'.

'I ;

I.

l i

l l

d..

i,

<.g w w A

U*

4 U

n i

t W

l l

h. '

l i

i l

1 i

i.

I i

l I

f l

.i t

I t

i I

I i

j l

t i

I, i

6 l

t i

t

~d...

c j

i -.;

r I

y 04 I,

h'o '

n' I

l l

j l

l I

i 3

a 3

, l i.

t 6

e a

i-t i

j 4

,2 l

e i

.,,/

h

(

i 4

i

~.

i i.

H g

i w

I Q

I cs i o to e2 i

I d;

I I

N h

l w

1 i

i, i

'l 13 3

i M

i

-)

L j

N l

CI l

0.c i

r.

1 I

i

=

%,#e t'

b i

l N

w i

4 l

{

i l

1 i

i

{

l i

I l'

I i

i I

l f

i ll k

I I

n i

j.

I 1,.

e i

1

.,e J

I l ~i l

l e,.'

~

i i

hN 3

l l

9 Y,I i

n i

a 6

=

i

,* i t w 9

t

~

i U >

C 1

t r 1

i l

4

- i I

i e!

.,M i

M a

l.

MI i

9 5

l t l

e*

• m S,

l $

f*

l a-a a

0,

~~

l j

I Na t

W 9 ;

g

~

't i

i

'J s'

l 1

W M-M i

i 1.,

i i

i c

}

D V.

(gy

(

i a'

l h

I m

~

'e

,e i

l

N b'

i e-

"sl l

A

.c i

3 i

s t

i i

i i

4 2-I

- C'J c - l, qo l

w i

i

- s 2

i es i

l i

' JJ, i

4%,

M iC)_*I

}

2.".

O -

g

_s m

-m i

u

.. i.

o i r i

c j

I i

3 i

I i

)

' *e i

i l

4 l "

o

{

Q: j. !, i m-I.

Q 6

(J 3

1 M

i l J l

4 4

C l

a

n.

cc, I '-2 i

i l

i c,,

i

! *I M

I

• *; C j>

.,'2g OH g

I Ql l

j t

i L' "c Q

l G

I

%~,

l' l

s l

w,.

N w ;

a,.

l

-",,_0 l

m<

s

.,w I

x, i

i

• ..i

.q l

g

._; '_ ) w it i

d'.'

1,,

-- C 7 m

c-i c:

j s

(>

k(2, q.

• ~-

-" n t

x ~

r m e

sn P

g l

t l

e V

l G

D l

l

^

w

.o j

l i

7!

!9 l

I.

ol z

l i

i i

s

'e.

j 1

i 9

s f-g, i

k M

a-I l

l fi l

LJ i t

3

'. 61

_t i

i p

5 I

,(

I 9

e i.. !

H 1

b, j

i

~

i 5

H

~*

i i

t i

i I

1, f

~ ~

__ _~

m

+

9 ATTACIDENT 2 BRUNSWICK STEAM ELECTRIC PLANT UNIT NOS. 1 AND 2 SEISMIC CALCULATIONS FOR CONTAINMENT PURGE AND VFNT VALVES I

--mm.

..-A --..

~

P4

)

... r s 2s n 4

SEISM / C L0 ADS ON Vf-? (_. VES TO5 Wo _ _.

(

.._..... ~....

t.

e.*.

CRL C UL A 7*ED B'

.s n

v y

t..

.... _ _. _. _. _. _..... _ _ _. _.. _ _...... _ =

t

... - _. _. _._ _.. -......... _....... _. _.. _... _. _.. _... _ _. _ _ _... _ _. _ _. _ _. _ _ = = - -..._.._.. _._..__

-y

i. m a-m.,

.y-y.- s n

.. - =.. _

PA %.

? 28 72

.{

. 5 EI5M!C LOADS ON V S !_ V E.S

......... REFERENCE.S

. @). PWG SN C 339..,. l 8." _ ISO L B..

~ 27.s~ woG n

.Dw C, Sk63+O j.

18 -(50LB 2 7 s. Wo a...

................u..

C)

D wa.SK 6 3 '+ 1 20.L 150 !.B 2 25' WO S y

(d)

pWc, Sk & 3 f2, 2 0 "-- l 501 B 2 75~ WOC, Dws.SR. 63++j 29U. ~. l S'O LB 2 7f. WCG,

. (F)

pWC, Sk 6 3 4 3, 2 0."- I 50 Le..._...

2.75~ WCGr

-(J). DW G. $ir C 52 2,

. + "~ l S'O 48 m/.S 1......

h)

D NC,. Sk l*3 2.3.....?. "- l 50 l B. A N S /..

j

. (d.. P WC,. Sk. C3.30, 8,l-l5~C LB

/> N S }...-_.

i

.a._.

=

=

._._.............._p....

......u...

,/

p

Ps 3

' -. r

?l:$/7?.

(

FR 0M A i'R.5vt o us AkSt Ys15 ON D Wc, S/c-60/s

).7~.. l $

0 8 V/0 U.S

. rho T.... TME NAP r&fRM L......... _ _...

P $ 5 f(l$N$Y...$ ?. INS CA? Mr,/ LE VER E.D

.CPERRTOR FOR THE S E_

vat vE S

.. JS. WEl. l...

RB W5 2 S' C PS.

TNERSFGR$, 8. STRr/C RMn!.Ys/S CAW BE R$5D TO DE TER M/NE 7'HD STRESS Wjl WE.S

.W YMS t/RLVES. of. R E F.

62 ). - (/)..

..S E / S M / C.. L 0A.DS FOR

/-7

$ TA r/C

/7NALYSAS._.

.. _.... _.... A RE. FCLIND. L/S/ N G..

3 HOR) 2 CrV TA L A W. p..._ ___.

l t

r

..s...

2.

va a.ric a L.....

l

. P CR_

T//2 S5 CR L Cid t. AT/ON.S

. / 7'. $H6i L. 85 RSS CfME.P.. THa r. TME HGR/2 C// Tr74 FORCE 3

(

../6/.

B O TH 0 R TA C G CNA L.

D /RS C 7/0NS A N D....

~'

THE. VER *r/ CAL.

tor GES A c 7.

.S /m u e_7nNEoys.

(

R NA!. YS /S CF D R A W / N Gs.S

.~d

.S/r G 55 9 S/r C 5 9 0,

.5 /i-c3 4. j.

S4' 634-2.

nHD Sn G 3 9.

L.i

. p. _...

........................._...t.....

i 4

(

V. -

e

P6 +

r

(

z

.S TRESS S A!/it '/S/ 5 O f=

VA L VBS SC S3 3 9, Sd" d 3 +0,

& 3 4- /, C34-2., s7N.b 6*349,

c NOTS:

. A AN?l YS/S l.$

TH& Ss4M.5 f=CA ALL DRR w/Wc5 S l

5/NCE o PER R7'OR.S, BOL T/N Gi A N.D 8 A R c: fr-5 7 ~.S j

.ARE THE S A M E-.

J-..

~3 (~

n

• f stn i

. l

. Q.

oPARATdR l

Q~

f.....

. ws7 = 2 90 LS Q

cG I

j t

I*

l g

- S$. -

nReces:~

x c ps.oren

'P S TEN.'M 4

g

^

4 lbN aom.--

en-r=ucn L

1+ o

~

-3 p

n_..

p

.J l

L[g_.

g

/

N.,.

<.-- 7

/....

.f I.

... l......

........ j,,. j...

.N

/

t

~.

e9 s'~

(.

SE/SM /C L 0 A D.S TR C M GPER n 7cR :

3(290.)

Hcn/ z cMr/)L !

=

870 4.B ny-c4 V E R l'~tC & L.

(2 9 0). =

580 LEs i9i cG 8 0t. Y PA 77E R H C f~

0PE~R P T'OR l'-k$ 'rENER.S

~

g~ ' ~ )), '- ) O

^

/

D ~~2

~,

Hot E.S.

p-y I

\\

/

&g fn, = HC I 2 ON T/7L.

fdoRC 5 (87 0 t Fa., = M c Rl = 0 N TA !.

FG,'.;~.5 N.5 7 0 c.

~

s,.

.c T = TWIST DUE Tc Ho R I .

FOR CES A c r/ N C.; A r~.

.k 'I p

CG> O f " 6 P E R r 9 7 0 R ;..

, v+.

t

..........._...a....

(

.T =.3 7 V 3187.$ ? 8 70 WJ^/ = I O,9 7 S~~. I N-t- 5.. _...

F,f.,+ft 8 7 0 ' +.9 7 0 ',..... l 2. 3 0 L. 5.....

Fpg =

11

..=

=

M A X. S HEM.. FCRCE CN

.A BoLY.

/S..

Sh +

T COS W ~ ~ __

j,yo.y 19 9 7.f(7ay) l l'

~~

1 9 _.._.2.0 3; ( 4).. _ _

.._ 4.-

..(4-) 2.03I

(..

..e.

....,..e..

4e

.%3

Pc g l,

~

(

3 TRESS RRE/?

O l' B ot i' =

3 3 C-

/,y ;-

1 2 s.3 SHSAR

.$ rR E S.S

=

37TO PS I

~

.) 3 't t

l i

n'1AX B Cf. l

TEMS/L E S Ti?L=S S

/N 8 CL 7.*

ca

,.,p.=

-r,,,,,,.,

e (y

f y

l 4

p 4, 7.rc n

r n

e,

~

u

n. =

Hi (3.ro - m c 2. n] = 8 7 o c 3.rc - s s o r s.d) ^~

M

=

1 2 S~o tiv - t.a. - - -

t Fu z.( 3. FC )i ~Fv (4. e~3 e ')= 8 7 c ( 3. 75,) + gg o (9.43g)'

~

M, =

F1

=

fr F 70 /w.L e 1

M, M

i Fv

~Y

=

I 3 R.

Ly

'B "M

~

9;on s- ( 2.)

T +.cs27(2) 4

(

~'

~

Fe n x I 3 s~9

=

40GO pS -

T P/.s!L c S 7~Rss S

=

=-

. 3 3 q.

.3 3 4-e

~

w

PS 7

(*

comswer s rass s :

O' t t

M.9 X SHEAR THEbn y

%an =

T

• T..

~

I L

t o.g o 7m 3

j

'.-5

+(f 9#/

.=

4290 psf s uggf, 5 Q cava t sM7~ rsM.s it.e 57 n es s =. 2 ( 9-2 9 9.).

=

8 5~ G O P Sl

~ pciq opgao7 o q f.5 0L T*

7 437 B RA ck E 7~

S 7'R ESS

/

/

/

Al t

3,19 s

Fnz;/ -/...

l

,A

/.-

91 F

V

/r-7 0C

./

.,,,/,,,....

,m

>{l

,/

Y

.p m*

3, 7.c.,

/

B y

Mg = 51 ( ~7. 04 ) ~ l~y ( 3.19 ) = B 7 0 (~7. 0 6, )- S'N f '3. / 9 f,

{

U

• S33C W~ l B t

Pa P

(

• =

iL (7 o ( ) + r, ( v. 9 3 = ) = s 7 :

(2 ce )+ r90 0 n

~

/v12.

1 1,S~ 3 0 J u-t e

=

T=

Fni (9 9 3 9. )-+ (% ( 3. I T ) = 9 7 0 f*' 4 31) +t'0

(.3.5 T =, / O 975~ /N-t s j

STRESSES Ms 4 '} '3 0 '

ET S=

ME To

,,g-(,,.y(g;y 7,3-(g)(; g) =

210.

P

=

o

.put yc 1% :

S==

2-g

- :(. S)(s.=Y._

5' 0 a.

b !,*

Iv1z g

g 7

1.,

g I I T3 C 2 2. c? O esi Ss y o9

=

=

Fv pc<s ro Fv :

Sv = 2c.sxs s )

=

10 5. 5~ PSI C OM BINS O

'r*E N S /L E 57~RE.$3 :

Se =

S o -tS2.+ % = 210 +* 2 2 ?O + 105.7 = 2 G 0 5~5 PSI SHERR S 7~R ESS ;

~

T' 10975 FcecEs :

F; =

7, g-

7. 5* ~ l 4 C 5~

LB Fr 6

?p 2.

'/

5=\\h g. }t+ f',,

t.

~

A 2

2 F,

(

q FQ cn ssp.c

e e, y

(

i ' O ~1 s

Fa =

j(/ 4 (f + 70 )' i ' h ~

300 63 2

Fe Ss =

=

132 est

. r(ms)

CCM5 tNED 7-E A/S l!- E AND

$ HERR S7 RS c.S :

%=

• - ( l 3 8 l3lC P Ss

=

t E C (,<!! VAL Edr mn;<

TEMS /t E S. MESS l^J B R A C /r5 7' !

2. ( t s t o )

2Czo PSI Se,

l 5 " A c KEY FA S T E NF"8 7.c38

=

1 A

N. / 7

.z' A

Q2

7. FC F

hs N

s.} A tv h

(

% -Ic uNc

~

STRESS f) R E A =. 3 3 4 1Al '

e

PG Io

= -

= (?7c )(7..vc)-(7.c )(3.I9 ) = 4.7

! !- i.=

?

p1,

(

Mz = -( T170 ) (7. rc )-i-( 79c)( 9. cn 9 ) = ; 2.o S o p tg y = ( 970 )( L l9 ) + (% 7 0 )( 9 9 3 9 ) = l c, 7 7 s~ s u - e..

• ./. -

F1'

=-

4 7 '2-La F"' = 2 ( S'* )

I I.

,c.

O l O

p1 t-o 30/2 4.3

=

j~y :

1( 2

)

h_:.w.r-4 i

F;, =-

l + S~

La

=

q 7c~n G- = 2, s- =.F

+ =

t-9

• l S ii n A K f cR c6 :

10 9 75[.?$ = l 0 % C _

'l T Ces 9 LB Pe r f fr = (2. 5 ) r+

= (2.f) 9

(

Faz

+ - <((

Fr/

Y F '......

.i..

t

/

l

.l

[.

F, =

I(Fin.+FrGS ?)t+(fir,+Fr6e.)s, 4

c

.z, i

370 g(ic2c)(.93) + 870t(I020)(.Y7[}

=- 2. 2 i O i

(

~

s w,..+.

e

,.-~-,..-..m.

.,m.-.

n

,.-,~_.-y

f6 ll s

(

S a c 7-STR=SS TENCILE :

F,, + R,1 + /% _

grz + 3 0 t h + lets-T

.339

.339-10970 PSI

=

7 SHEAR Fe 2,-to

~

S

=

CG 2 0 PST J

J 7 :(-

,3 3 t C OM BINE.b STR E SS e'

z.

/ o STo i

+

C C2 0) 25~ CO p..gf

%=

2

=

4 N 9 Ulvnt. EN r TENS /L E STRESS

(+1 AX)

Se, =hCs~fo)=-

l7120 PSI

~

(

~

,.,.y e

y r--

m-ww,s.

--w-

,w--

---r,--,

,-y w-g

-,y-----ei.-

P c; 12 s ?c 770N p

.9

- (. '

~

9.e e h

N 30 n

Fu z

II. 8 l Gt

, 4"p g

i Tv.

_ _s36 s

Q> g x

v 2,' pln Noc E N

7 A

~

l

%3.37F-+ -

y;, = (970 )(lI.91)- [Y?O )( 3 I9 )

S?T0 if/-L.B pt,={ft70 )(lt.91)+(s'80 )(9.c39)

=

I7770 in-te 7' = ( 8 70 X 3.t1)+( 7c )(9.n 9.) = 1097f IN ~ l. 6 A = 3. 3 7 5 ( 7. 0 ) - 2.s'6 >' & - W2.Y =

I 2-0 IW '

= 3.3 vs-(7. o)[ 3.n (.575-/, 3 "

3 I_

(1f

= f g, 2_

l, 2 f, I. cS75~

S' I E W

E=

i 2

TENSit E S7^RESS

• Wir Nft fs, 8 4 50 + I:s 60 g90

+ -

a

+

3-7, gt R

~ f C. *z.

7, I 3 l' O 7

2509 pSj s'-

j 4

e 9

(

ANDL YSIS cf

.pnt) vans; S h 4.3 4 3 i

i s

(.

.M S

g g g Sh

.--,n-.---,..--,---,.,.-___,-.._-_,.,n,_,,,n.,_,,_.__...---_--,----....n..

=,

f~n l *$

1 4

4 (e

DRRwtNG S /r (3 + 5 THE ANG L ' S/S CY TH/.C. DRA W/Ns J.2

/

I Dsw rtc n t.-

To TH6 Pacvtct/s <9NH-ys/.C S X C 5P/

7'//N 7

.THE C P S R A?7~0 R WE/e6 N7" iSCNLY ' ?' 8 LB

/W l- /CC4 C<"

2 8S~

/.

5 INc6 rHE opean7ca t.s traitrsa ryz.

(

A E S PEC r/ VE-Loops

?ND STRE S SC.S wit L BE LOWER.

Th'5REFCR 5, By

/Hs PSC r/eiv TM/ s~

/9SSEM B L.'/

/.5 S8 7~/S i=~/)c 70R y..

G j

e 4

{

G O

e 6e et v-----

- -, - + -,,

.,w+--

w -..,..

,e.-~,

...,,n,

.,, ~

---

,.,,,,..--.--,y-,,,-,-

---e..,

PG t el-(

AN A L Y SJE CF.D R A WIN G e

SH C53 8

=

6 e

e de O

m 9

e e

e 4

e O

e e

~

(

STRESS

.wM YSIS

'f W"' W #

NGT~

7~W /S I? NA Y#I#

l 5/

/!'

R 7o TW c,ys W I 7*H

.OfffE REM pp5 c5 y jgg;.

DIMEWSIO M

• 4["

ig_ '.

, __ a h

o r.e M w A

-& N -9 4 [fc 6

i war SS~ w j

s I

I

.M

[

l t

_ g r_

} 's 1'_.7.

g s

2 Li t_

[

'I 1 go _i 1

g l

.a L

l M

+ l 5.y/ DIA

- A e

j'r

{

i A-a 7-b l

\\

1 i

i.

s I

t

,y 4

.e.

-~.

PG /(

(

S El.5~M /C L C M.P.5 FROM CPEnArGR!

Et GRI 2 ONTA ! :

.3( 5~T.) =

l [3~ 4 3 Fer G fu 2 ( T T.) =

1/0

. LS Fv V ERT I C A L C C R D I N ;;.

'CF OPER R rG R FRS 77?N.ERS ;

4-B OL TS.

Y9 - l[

UNC S TRESS A R E A =. C 7 7 3 I N *-

cc,

'{

/ r

/

li

\\

/

L'

- li-x 4.575 g

y, e

f IY

}

'l 3"

x

+

M, = ( l f' 5~.)(l.3125) + ( l / 0 )(6 8 77) = ] 7.2 1/V-t. O

{ LGS ~)(I,312C)~{lIC}{l,127)=

92 fy-t 3

/v1

=

1.

T = (I d5~ )fl. /25~) + (I CS~)(C. 8 7[] = l 3 2. C IW-L t3

~

i

//1 Pli lv 1

4

=

2 0Q* 9 LS f ara y ~

2-( 3 ) + 'L ( 3. 0 )

if

~

B

(.

~ og 7 TENS /L E S TRE SS =

, o y hy

• 2. S YO PSI

~+

9 y,-

rw-p,yw-ww.yw,wwe,c~

w

.--ir-r-v---w --r e

e rr rre -myy es -- ye-r-c-v--

.w-p.-w w--

p-

-&v-w 1-w=m wei-rr-g

Psi / 7

(

S H5s g :

T Ces 9-7 't*

Gjk1 jn-1.

a' SHEN n LOAD =(,,g; (l 3 20) (,70 ?),

y[1 gg )'+ [g a-)*-

-S HtreK

'. o ep =

( h T) 4

• 7-9

=

2f3 to 1/3 m g

=27CC PS/

5 HEnit S TRE s's

=

i 4

C o mewsp

.s 7 e r s s

( mia y) t.

' s q uiv.n enr rsusus s ressiT

~

.See = z ( z o co )

=

c12 o esi e

b e

9 3

(

o O

a e g

g I

+ ~

~

~

t'Gu /8 Bexk? r

.S.T_R.9..ss

(.375 I'

J./

h

, 3

./

Gs A

/'

k F

d.8l 2 7 v

I I

/

\\;

% 7S*

N/

/

1 3[i

~

7 9.75 y'

/.

/

ar g

(.

Th'E

?ow&R SE c-7/GN of T//C BR,9c frfr'

-/.s ANr9L y2.EO

$/N CK

/ 7'.

Y/ E L D.s '. 7*H E.

l. 0N c; E.s' 7-s Momrur anms Fness-7 7'Ns c e, 77/snareRE -l ~

Al

&f L 7"S._/f/

.T. 'r'.C._ NZM WEST-BR n c M E 7..

4.

STRESSE.S.

M = ((C T N d 5/15)-( /10 y t.11.b)

-(

M, =

l0 0 l

/N-L.8 e

e e e

e o

e 8

4 e

4

-4e

.e e

e e a e

3

. p 9

6

~.,

,e..

a--.

--,m,--,

-. - <,,. - ~ -. - - - - - -...

s

- -, - - - ~ -, ' - -. -,

- =

+-

- -- =

w

~

e e

_Pc to,

(

ivh = 1% (c,2 f u

+ 1% ( c, 9 7F) = I d s' V.Ei2 c)+ti o (<.e r t

2.

..t.M"" /. O

..e.

..i.

T=

fm {l* n S'.h & Sn{(A7[

~;. / 6 S'(/./2S~f t- /CS~ ((!?S

... T. =.

/.3 1 C../N-LS

.....u................a...

. Sressses

.. -................-.......... g

.........,x.,......._.........

. S

. c,.g-(,g (,4 - 9.s-g g,p(c o ) =

A'-2. l

.......... pc<S. To. PT..*.

s o

ivre sV

=(.sXr.oT._ a 17

~

(.

. pus rc,m1.S=-

g-g-

c g

..i l280

c. S z 51 4.17 Sv = zc.sx%

f r.o 2 2 ' O 'l'S I.

pui;? To Fv '

~

. C OM BIN & O

~1"~E.H S IL E S7~REJ~S :

.5~/( psi s=

S, + Sz+.G : <+ 2. -f-S S 2. + 2 2.

=

.f..

....... -........... ~...... - - - - - - - -....... -..............

SHE/?R S7~REs.s ;

7

/ *.>. 2 c '.

/3

. ForcEf :

f;. =

q g-

9. 5-t-S

-6 S.

~

rr + & 9 M,,Y a 2.

2 )

2/

(

p*

rg -

i y

e

.F*1

.cNC.ft.pA..

3 e...'......_._.._..

I l

g

- - -,., -,.. ~, - -. - -

., - -, ~,,

?S 10

?I d 5*

• l':

{

2,) + ( 2

2. 3 C L /3 Fx

\\

/ 39 +

e

$3 =-

99, pSj

.r(r')

CC/v!B INED 7~E NS /! E AND SHEAR S TR E S.S *. '

~

'y; :

ill

+ [ 9 W)*

2, 7 >

r S/

c f

5 QU(V8LEN7~

MRX,

TEH5/t E. STRESS IN BRR c/;-G i **'

~

_$gg = 2 ( 2.7 f ) :

TS' d ps/

1

--1 B R P CA-F 7*

PR5 YEE/ER.S A-4.375'

=j.

\\g f

cs.

N

~

~ 7 312 f M

h

/

M

- \\

H3 s

^

A-56 - 1 3 M ^/c Bot 7'S 4' }'=

C B C S TRE.55 ARER=a/4/C

/U M, = { / 6 S~){T 3127)~ (l i O )ff it 5) =

/ 0 8 l' JN-c. B (l 6 5 )[7.312.7)f(I 10 XG 8 7 s~) =

l 9 G O in - i. O Mt=

T = { l G S' )(i.125) + (/ (S'/C.277h ;

l 3 2 0

/At-cD

,,am

P6 2/

(

. T E N S it E.

S O L T-SrR5ss

( M n yf

~

_. ~

mas

t. o n.O M

L N

\\

,g'J, 1

+'YCos+5*

2

=

1.18 '

L=

2 I

M

/ OS/

I ~' o*

LB F'^>'

2.(3,18)

L(3.t e)

~

~

ik I960

~

308 LS

~

Fm, 1 p., 3)

2. (3.f s)

Fv 110 2 7, s ca

=

=

F,, =

q.

y i

0 T-

$Y

[gjf([

}f y

/4/6

/70 t 3 06 + '2. 9

=

=

3 760 P.Sl

. / 4/6

• ~

)

(

G e

e

+

4 m

vc g

a m-,--

-e-----w----e 4

y

- -- ~

o n

,m-

--e-w

--c----- - -

--w-

ec x2.

(~

S HE A R_:

7 m,

sissa a tes o = 9,2.c, 3

+ p"i

~

. 9-

,=

(13 2 o)

\\k us-)% (i sc)'

~

.9HKAK L 0 Ap =

T

( 2* & 9

1. C Y lE PS R SC LJT i.

h

~

.,7 9;g. = l WO

+

S ttE19 A S 7 8 5.T.5

=

PS/

C O fn B (NEP

.S 7~R E.5 S (t.on y} '

e

. z Y = lI=cce' (l %'-50)z '

=

2.300 PSJ

-F 7

' E Q U l V A l. E N T~

T~B NS /L 5 S 7~RE S.S *.

I 0CC0 PSj

$eq = 2. l'25QQ)

=

(

l 5

i g

s

a

(

j..

Ps 13

(

5 7~R55 5 pr s.E c 7/b st A-A

f. S 77

~

h

~

L c4 g

x a

/d,3/2.f~

k

~

K-fuj Fv En$ 'N y

w, T

Y,

,u-3

~ f,6 m cSXI"Is M, = ( l C s~ ) 00.312 s- )- ( l t o Xirzs-). =

/ 5 7 g ju.eg

~

is = (i cs-)(w.312s) + ( ii o )(c, err) =

2 e s s iu-te

'i~= ( I CF )(I/ 2 5*) + { / G S~ )(f.875~) =

/32o lu-c a

% *) = I. / 5' /N A=

Ts (),75 t

f (I7s**- Ih 47/

E=

3

/4

., 9. f y i

YM '+ ME + fu

= \\/(ind+(urr)'

tIO TEt/stlE sriqESS

=

i

+, ' ' '.

A

, ct 9l

(

=

G29C Psi i

w-+

,-,,ge--

,,w-,- - - - -

---

,.-e

.,,--..nn-

,,,,,-,.-,r--,-

m~

-~

w P4

= ?

[

S H =/= R S Tr?ES S T'

S, =

2-7

/

$sl--

l.

E

~;,., } Q *2.

lN

~

N 2

-. S *? T I320

~

=

l 9- 0 0 pSj 3

.942.

C o m B /A!E.D S t RE3.S i

~

/ 4 0 0)t

39 O

/*S/

c2 96 7:

2 Y

i-S HEs7R SQ Vl/%9L EN Y TErrSith S t r?c-.SS Se q = 2 ( 3 + 40 ) =

692 0 PS I

]

1 e

e s

e e

n

-- -. ~ -

a n

.r

r 3

(

A N /?L Y SIS ci=

.DR/? wisc;s S /r ( 3 2 2-4 S/r ( 3 2. 3 9

O O

+

6 O

O

(-

e 9

0 e

O e

O 9

e r

J e

9 e

4 we

-m em.

ye

PC, c5

(.

STRESS ANAL YS/S Of val-VES Ski 322. $6323 NOTE:

7'7/ /S 19 NRL YS/S

/S S / m /L.R tt 7o THs PRS CE D /tv4.

CME W/TH p/FFs REN7*.

D/MEMS/0/VS.

........... ~

s b.g.T _w

• l L

~

.6 f.

07:RA7*CR WC* T 3 0 L3 I

I 4

w

)

g

+,,

6 g

- 4,"

g%

+

l; l

3

.i

=

4 i'

I M

<r yr

~l DIR.

~~

c

.A l

i l

(

l

-e m

e.

e.

e e....m p--y-

~---ews q-m rw w v-+-,g y

-m-pw y., -,

,------+m w

apo-oew er,-nw

-e,,

-m y-

a

~

r.m ' a

,r

(

S =ISMIC L Onp3 FROM C?sRA70R HQRI 2 ONTAL :

3( $ 0 ) =

10' 4.3 Fo r 4 fm.

V ERT l'C A L 2(30

)=

60 L8 Fv tcaowa ce cuaaran fas wees :.

~': l~~:~:.'..:..."..l'.

.g.' s si r.s.

% - l8.

uac s ragss naen =.cn 2 n '

m m,.

e rm p, -

~

t m

/

I.op l p1 p g{

g 4:zE.

in, =. ( 9 0.)(t. 8 77) + ( 6 0 )Cr +3 2) =. 4-7 s tw La.L

_ m= ( 9 o )Q 67.r)- (f o )(I,2 r~ ) = ' ' _9 3, f 1,y _ i. g _..[

T = (9 o )(i. 2 s-) + (9 0 )(C'A'-38) -

Co3 t u-t_ s A

Mi Fv

-1

./ 9 g

-g pe i.m y z ( 2.2 r ) + 1 ( z.2 5 ) 9

/46

=

2 800 P S'l rsusa.e s r a s.s =

,og z2 C

_m

...p,..--->,.--,.---,,,-,,,,y

-7

,s m--,---%

r>c, a.7

(

inss a :

t' T ccs w.r f=m z,-

sma t os o = z,,,g g., 4

.T. -

(603)6709.

\\l(so.of+ [90.o)'

~

$ H G.9 A' L 0 9p =

7'

. O.nz o 9 9

^

=

1 2. 7 tB 127

= 2.+40 psi seena s r a r s~s

=

, o 5,,_,,-

C O M WEP

'$ TRESS (m A '/)

I

(~

Y.

l $ 8 00 t'

'2 6 / O - psi.

+

299

=

r SQUWAlEN#

t'E NS/L 5 S7~RS S.S R20 PSI S'eq = 2 (2.810 )

=

e e

g e

e n.

(

O O

e E

a gg 9

D pg,-..,

,n.v,.

., ~,.,.,,

?G Q.8 a..

R.c ~

y : r..-- - -. 7.. o. e e c

5 930

-I

/

l ak.

9

/

e

?

61 6

1

~~

/ht

{

F

.r,57 2 y

l J

ff w 2.7S~

\\

f et

,/

7 2.77 p

/

n

/

g

• r i

(

e THE LOWER SEC r/eN ci=-

TM.C B R M cfrf r' M

A N/9L Y2_E D f /N CB

/T Ya f f. D S 7'WA L CN A E.S~ 7~~

P10MCN7~

8 A'n't 5 7ACA-7 7~M.8 CG, 7WEA2 f~CRE IT

.m.

4 A E S &f L T C

/N T//&

NZ/4 A/ES7~. BRac/r2 7-STRESSE.S.

fv1, = ( C70,0 )(5'572)~ { C O. 0 )(I 1 S'~) '

(

r..

M=

?.~2V

/N-L B

/

e es g

e,,

O g-rw.---

,--r.e.m.-

,,,, ~.,.,.,,.. -., -. -

y..y-,,.-w-

,,,,_._,,%-,~.--,,,-...,e-,*

- ~

Pc19

(

Mz=

lA- (5'i~s2 ) + Fv ( 5 p 3 5 ) - 9C. O f's~ *2.h C o. c@ qn 8.2 6

.. J.u - t e

_=

T=

Fm ( I. 25 ) -+ Fm ( T +36

= To. o (1, 2. 5-) t % c(cssa',

......T... =..

6. 0 3....../N-L S S ~i P CSS =S

._............_._........._......____g,.

........ 9 2 -S'~- - =---- ' 'd I 7

- ~ - - - - - - -

. __..'........ pus. To. M..'.

..... S: =

,g = gs-,.- (r. o,)

e.-

s 3, g_

/v12.

b l., *

(h)(9.0 $ =

I* C 7 Dus rc Sz =

? =-

7~

=

g

..n y

g2g N Y S' est

=

.. S,. =

f, 67 f: y

=

'2 0'<0 '7S1

.. P.LG i o );~v :

Sv = 1(+i ( pn; )

3 C OM BINE O T~EN S IL E STRE.53 :

%=

% +Sz+ S = f *2 4-4 9 7 + 2 4 5~ 8 /

psi

=

~......

i.

i SHERR

.S 7*R ESS *

-~,

y'

........._.=....... _.__.

7 g 5-5~, 5 ll0 ForcEf

• f=

LB

~

y 2.

5 t

c

-/-(f.,

,4 ca-r *. 2 2

i

.c

]

L.

F El

.__...._...__._......;_.....z.

...C N C. f 1 A C.....

i i

s.

o e

^

PG 30 Ir 9c 9 oc z

(-

g

\\Ji i 1 0 + T ) +

g -

=/6/

Fe

~

/29 p.sf Se = gg ccMB INED TE NS / L 2 AND SHgA R S TR E S.S '-

5l y=

+ ( l2 9 f

=.

3 1d*

p5j EQuIVnLENT

iviRX, TEN 5/L.E. S TRESS JN 2nRC&Gr-

,$eg = 2 ( 3 / 8 ) :

( 32 ps/

15n p cA-E7 PR S 7*FbMR.S C

- -s;o30 q

A

\\

g.

fP co N

'\\

- 5"g 75"

.:1 m

(

t;n.

A

\\

Myg-@"') t i

I" '

.J s

4-l& -13 Muc' Bot r5 39="pt i

S YRE.55 ARER =al4/C

/U' u, ; (g c:o)ce.srs)-(co o)(1 1.+)=

+ s~ 3 iu-c. a t.

p1x = (9 0.0 )(S;275)+(60.0 f +3 8) =

.8 S~?.in-i B l

T -- ( 9 0,0)(f. 2 r)1(90. 0 )(sW38) =

603 lu-e O l

y

%w

..,e a,

m

---i

-m,

...a

.a

.y D6a.

P m, p l-a s e e 4

9 e

(

nasa s e e r-s russ (mnd e

4 s

.s

'g$

LCAN

^

@Q ~,

4

. *h j.

2.+ 8 '..

[=

Cos +5 2

=

e e 4 g

e e

o e

e b

e 91.S~

L6

~

19.#o x 2.+ o e

S

• • • e m.

854 Mt

/ 72 L3

=

Fu, -

1 (2.+o

2. (2.+ a) i F'

60 0 l T. O LB f

~

't

+- - -

I e

e 5,+ Fm

+ f%.

TENS /LE STRtSS l e. / G r

o 1

ci t 3 + 19 2. + /S'

=

=

1970 PS)

I'f /f

.i e.

i t

e l

9 O

y j.

O r

e.--

em**

eems. 6SMFWFG*G W -

,NMW-yw.----y.-,,.,----,-,,--~,-~.,-~-.m,-,

-, - - ~

rr-

PG &*2.

i

~

f u '-

> //

O d g

y' L,

?

D 8x SH.6? R ~LonD =( p p.) 4 (603)

Y{90.0) 4- ( 90.0)

S HEM

t. C a p =

T (I75) 9 9

=

ll8 LB F5 f, BOLY..

//g S/tEnA S 78n-5.5

=

=

c9 3 T PS /_:

./a,/6 ComBrNEP

.9YRESS G.ony)

L.

E Y=

-r. ( %, >-)z 197c

=. / *2 9 0 ess I

j E Q L/ I V A 6 E N 7~~

7"~B N 3 /L 5 S 7"RE $.S '

l l

2 5SO PSI

. $eq = 2 ( l*2 90)

=

1 9.

a-

.J.

b

-%=

--u-e-.

e ee^=

m<*-.e

~t.--

-*-4 w---

---,'s--se

• ---+=.m-

-*--*-e-

-v--

q

--- r

.----- ~

F6 '3 3

(

S T'R E S S p r-S E c 7/c ar A-A Ec+3:

~

4 X

c' I Y.

9 L_

~

A v.s vr (ni-

~

rv_

/

g Y

'37 w,

p Y

- j )f

, cp x 5 " rp 3

k M, = ( 9 0.0 )(9. 8 7 7) f (0.c Z /. 2 s) =

72.3 f g. c. c.

M.,, = ( 9 0. 0 )(

. 8 75) + { 6 0. 0 )(5. ?33,) =

l l 2 <!-~

t y - i. e T= ( 9 0. 0 )( la 2 5') + ( 9 0.0 )(s* so 2 ) =

6' o 3 ju-L a.

/9 =

Yf (l,2 5h25) =

0. 92 IN

[ (l.2S**.-N1$

P=

= o.te iv s

, e 2,

'YlA *+ /d?

'Fu

= \\/(72.3f+O/2W+ d C i

TEt!S /t. E.

STitESS

=

i

. '1;

-,c

.A O-l 8.

-\\,.

7 4 C s'~

t'st

_=

O

PA 3R

/

r 7.- ?.?.;

('

.; s.= a e T

Ss =

Es

. s.g. g..../_f 1,2r'g.,f 1

..,3 g: ;.

a.; _,.

62 7

$3 $

603

=

{C2O est 360 co m ew.o S ren'SS :

7=' c5 'l- (/ 6 20)O

=

4090 esi.

y:

2 s u.ewr<

t 5 ccetget 5 N Y TE WSit A S 74fSS Se q = 2 ( 4 0 9 0) =

2 / S o P.s /

e 9

9 m

6 y

~

'N s.

.g

,_... ; i-99 A

O w

w-g m

.m.-

m_-

.