Pressure Vessel

P

V H T

E e d

ni

withforeword by

P

B

Professor of Chemical Engineering University of Tulsa Tulsa, Oklahoma

E

M

PRESSURE VESSEL PUBLISHING, INC. P.O. Box 35365 “ Tulsa, OK 74153

t t i

oh

FOREWORD

Engineers who design equipment for the chemical process industry are sooner or later confronted with the design of pressure vessels and mounting requirements for them. This is very often a frustrating experience for anyone who has not kept up with current literature in the field of code requirements and design equations. First he must familiarize himself with the latest version of the applicable code. Then he must search the literature for techniques used in design to meet these codes. Finally he must select material properties and dimensional data from various handbooks and company catalogs for use in the design equations. Mr. Megyesy has recognized this problem.

For several years he

has been accumulating data on code requirements and calculational methods. He has been presenting this information first in the form of his “Calculation Form Sheets” and now has put it all together in one place in the Pressure Vessel Handbook. I believe that this fills a real need in the pressure vessel industry and that readers will find it extremely useful.

Paul Buthod

PREFACE This reference book is prepared for the purpose of making formulas, technicaldata, designand construction methods readily available for the designer, detailer, Iayoutmen and others dealing with pressure vessels. Practical men in this industry often have difficulty finding the required data and solutions, these being scattered throughout extensive literature or advanced studies. The author’s aim was to bring together all of the above material under one cover and present it in a convenient form. The design procedures and formulas of the ASME Code for Pressure Vessels, Section VIII Division I have been utilized as well as those generally accepted sources which are not covered by this Code. From among the alternative construction methods described by the Code the author has selected those which are most frequently used in practice. In order to provide the greatest serviceability with this Handbook, rarely occurring loadings, special construction methods or materials have been excluded from its scope. Due to the same reason this Handbook deals only with vessels constructed from ferrous material by welding, since the vast majority of the pressure vessels are in this category. A large part of this book was taken from the works of others, with some of the material placed in different arrangement, and some unchanged. The author wishes to acknowledge his indebtedness to Professor S4ndor Kalinszky, J&os Bodor, Lasz16F61egyhiizyand J6zsef Gyorii for their material and valuable suggestions, to the American Society of Mechanical Engineers and to the publishers, who generously permitted the author to include material from their publications.

The authorwishesalso to thank all those who helpedto improvethis new edition by their suggestions and corrections. Suggestions and criticism concerning some errors which may remain in spite of all precautions shall be greatly appreciated. They contribute to the further improvement of this Handbook. Eugene F. Megyesy

9

CONTENTS PART I

Design and Construction of Pressure Vessels .................................... 11

PART II

Geometry and Layout of Pressure Vessels ...................................... 25’7

PART III

Measures and Weights .................................................................... 321

PART IV

Design of Steel Structures .............................................................. 447

PARTV

Miscellaneous ................................................................................. 465

PART L DESIGN AND CONSTRUCTION

OF PRESSURE VESSEL

1. VesselsUnderinternalPressure_~__~~_~~~~~~~..~.~~~~ti~ti~~~~. 15 StressesinCylindricalShel~Definitions,Formulas,Pressureof Fluid, Pressure-TemperatureRatings of American Standard ,CarbonSteelPipe Flanges. 2.

Vessels Under External Pressure .......................................................... Definitions, Formulas, Minimum Required TicknessofCylindricalSheH,ChafiforDeteminingThicknessofCylindrical and SphericalVesselsunderExternal PressurewhenConstructedof Carbon Steel,

31

3.

Design ofTall Towers .......................................................................... Wind Load, Weight of Vessel, Seismic Load, Vibration, Eccentric Load, Elastic Stability, Deflection, Combination of Stresses, Design of Skirt Support, Design of Anchor Bolts (approximate method), Design of Base Ring (approximate method), Design of Anchor Bold and Base Ring, Anchor Bolt Chair for Tall Towers.

52

4.

Vessel Suppotis ..................................................................................... Stresses in Large Horizontal Vessels Supported by Two Saddles, Stresses in Vessels on Leg Support, Stresses in Vessels Due to Lug support.

86

5.

Openings ............................................................................................... 122 Inspection Openings, Openings without Reinforcing Pad, Opening with Reinforcing Pad, Extension of Openings, Reinforcement of Openings, Strength of Attachments, Joining Openings to Vessels, Length of Couplings and Pipes for Openings.

6.

Nozzle Loads ........................................................................................ 153

7.

Reinforcement at the Junction of Cone to Cylinder .............................. 159

8.

Welding of Pressure Vessels ................................................................. 170 Welded Joints, But Welded Joint of Plates of Unequal Thicknesses, Application of Welding Symbols.

9.

Regulations, Specifications ................................................................... 181 Code Rules Related to Various Services, Code Rules Related to Various Plate Thicknesses of Vessel, Tanks and Vessels Containing Flammable and Combustible Liquids, Properties of Materials, Description of Materials, Specification for The Design and Fabrication of Pressure Vessels, Fabrication Tolerances.

10. Materials of Foreign Countries ............................................................. 194 11. Welded Tanks ....................................................................................... 204

13. Rectangular Tanks ................................................................................ 212 14. Corrosion .............................................................................................. 221 15. Miscellaneous ... ... .... .. . . . ..~...o..o...u,mv..u.mv..~..u...ti..~..~..~..u..~ 232 Fabricating Capacities, Pipe and Tube Bending, Pipe Engagemerit, Drill Sizes for Pipe Taps, Bend Allowances, Lengthof Stud Bolts, Pressure Vessel Detailing, Preferred Locations, CommonErrors,LiRingAttachments, SafeLoadsforRopesand Chains, Transportation ofVessels. 16. Painting Steel Surfaces ..~...o..o...~....a...~.

U.V......O...

247

1NREFERENCESTHROUGHOUTTHISBOOK"CODE"sTANDSF0RASME O O C MI E EC HT AEYNN I GC I FA N BL E O E AR I S ) L (AMERICAN S

N E R P R E VS SE CU S RS SO E E EV C DRL T II FU EO C O LNI N S OET RI US C T IR O N O P R E VS ES SU D SRI F EE V1— LI A SSA , I M O E N S R T I A C N AND NA R D .

1

E

D

S

P

V

Pressure vessels are subject to various loadings, which exert stresses of different intensities in the vessel components. The category and intensity of stresses are the function of the nature of loadings, the geometry and construction of the vessel components. LOADINGS (Code UG-22) a, Internal or external pressure b. Weight of the vessel and contents c. Static reactions from attached equipment, piping, lining, insulation, internals, supports d. Cyclic and dynamic reactions due to pressure or thermal variations e. Wind pressure and seismic forces f. Impact reactions due to fluid shock g“ Temperature gradients and differential thermal expansion

STRESSES (Code UG-23) a. Tensile stress b. Longitudinal compressive stress

c. General primary membrane stress induced by any combination of loadings. Primary membrane stress plus primary bending stress induced by combination of loadings, except as provided in d. below. d. General primary membrane stress induced by combination of earthquake or wind pressure with other loadings (See definitions pages beginn-ing473.)

MAXIMUM ALLOWABLE

STRESS

Sa The smaller of S. or the value of factor B determined by the procedure described in Code UG 23 (b) (2)

S 1.5 Sa

1.2 times the stress permitted in a., b., or c. This rule applicable to stresses exerted by internal or external pressure or axial compressive load on a cylinder.

Seismic force and wind pressure need not be considered to act simultaneously. S.= Maximum allowable stress in tension for carbon and low alloy steel Code Table UCS-23; for high alloy steel Code Table UHA-23., psi. (See properties of materials page 180- 184,)

/

,

STRESSES IN CYLINDRICAL SHELL

Uniforminternalorexternalpressureinducesinthelongitudinalseamtwotimeslargerunit stress than in the circumferentialseam becauseof the geometryof the cylinder. A vessel under external pressure, when other forces (wind, earthquake, etc. ) are not Tn C l factors, must be designed to resist the circumferential buckling o

oh y .d i e od dh t e e tsh ms o tie rdge e qhn uf ei’ rW ei o mo t e hlns t t o . aaeh d ei n n r r g s present, these combined loadings m g o a a hv e e p an rw y vl be n ir a i eed q rt ul ei r l e t t ph w l ah wh a s a ni t t i esact fer a chte t co sisrr yc ui m h f sbe ro ue t n oct ie ak l nl i ln gy p

r

T

ot

m v

c o m p sh r edt s t se r i xev epetu r es a e r t ss n e sse a onudntl trs i r e in pe lt ud r ese e r ss n se a ou l r b dh e t a eb tr lfm oi nlr em eh d u l a y se :

s

F

t

.

D

$

R

M

U

L

A

S

C I R C U M F E R E N T I A LL O N G I T U D I N A L J O I N JT O I N

.

+

O

s, 3 .$

‘

D= P= s, = s* = [ =

S2 ‘

s, ‘/ ~

,R

T

s~ = ~

M I

N O T A T I O N d ie ao vm a eei ts n e s cr e h l f ,e n ot e e x r pt n r e ae pr sl n s a ur l r s e ,

s i

Longitudinal stress, psi 1 Circumferential (hoop) stress, psi Thickness of shell, corrosion allowance excluded, inches

EXAMPLE ;iven

D

=

P= f

=

96 inches 15 psi 0.25 inches

PD s, = ~

s* = $

15 X 96

=

~

= 1440 psi

15 X 96

=

= 2

p

8

8s

lhmi v pt

cr e e h s

2 X 0.25 F s

t s

ou gti

iw o n n pe t d r er a er rewss nl s r at iunc l or r h eni o rc vvb ea ep sp rera osnb x t is fm ao nt ree hdm

H=%

3

w

Hh= C 2

haeat d iwdi b c cd ghaoe u I y ae :

er h i r oet t i ei foc (

ga w l h e t t r

f ,

.

I

P

N

R

1. OPERATING PRESSURE The pressure which is required for the process, served by the vessel, at which the vessel is normally operated. 2.

DESIGN PRESSURE

The pressure used in the design ofa vessel. It is recommended to design a vessel and its parts for a higher pressure than the operating pressure. A design pressure higher than the operating pressure with 30 psi or 10 percent, whichever is the greater, will satis@this requirement, The pressure of the fluid and other contents of the vessel should also be taken into consideration. See tables on page 29 for pressure of fluid. 3.

MAXIMUM ALLOWABLE WORKING PRESSURE

The internal pressure at which the weakest element of the vessel is loaded to the ultimate permissible point, when the vessel is assumed to be:

(a) in corroded condition (b) under the effect ofa designated temperature (c) in normal operating position at the top (d) undertheeffectof otherloadings(wind load, external pressure, hydrostatic pressure, etc.) which are additive to the internal pressure. When calculations are not made, the design pressure may be used as the maximum allowable working pressure (MA WP) code 3-2. A common practice followed by many users and manufacturers of pressure vessels is to limit the maximum allowable working pressure by the head or shell, not by small elements as flanges, openings, etc. See tables on page 28 for maximum allowable pressure for flanges. See tables on page 142 for maximum allowable pressure for pipes. The term, maximum allowable pressure, new and cold, is used very oflen, It means the pressure at which the weakest element of the vessel is loaded to the ultimate permissible point, when the vessel: (a) is not corroded (new) n (b) t

i

h

t

(

te

and the other conditions (c and d above) also need not to be taken into consideration. 4.

HYDROSTATIC TEST PRESSURE

O and one-halfntimes the maximum e allowable working pressure or the design pressure to be marked on the vessel when calculations are not made to determine the maximum allowable working pressure.

If the stress value of the vessel material at the design temperature is less than at the test temperature, the hydrostatic test pressure should be increased proportionally. H

y

d

r t o ss

t bea hc t oi

cnas a d

aul ftc a tl b le re hdil bec

a c t roi e am ol np

le e

ts e n d

.

I t

c

pressure s i e hshall en be: s s ,

t h at

e

t

1

StressValueS Temperature )( M A . W.Press. al l xx o5 w. . StressValueS At DesignTemperature (Or DesignPress.)

V f

e w s tsh me e al xhasr li l s a bn ht g eae aa p ss r l, tse

P

r S i e m r

H

y

d

av

r i

yc

l emwo uweo m ap r br k l el ei si nbs m t gu i r t e lsei h tse dt u o rat ew hb nl ne e :

eh

d

+

e

900 lb

r t o os mt uea l t t ii -c svc h ea m Cs t b sU ef r eo ( Gl

s d- :

e9 e

9

)

A Pneumatic test may be used in lieu of a hydrostatic test per Code UG-100 P s a

tr t e oe s s ot m a t afb lxa s i li sol mhwo uwo m pa r br k l ew ei s t ns h gu r ehe n ro ae pn go t t an v h ec r fh sayb c tsn o f en m e w lpo s ua t it t i ese f dt a c t oh r y s o us r a ap frn e ce si eCct r Uy i f obG , e - d d1 0 n e1 .

t s

5. MAXIMUMALLOWABLESTRESS VALUES

The maximuma

l

a g i it t b u i t l o n g ic t C p U o

s ct g

l l t o ews an vt b s l apr ie e lel r f m uesd i i est f mt sfo ea e dt r e e r nr i t a r ova p 1eb eaT n l m 8 n ga e xa9hn l ie l m c o. o uwm e am p s rb e l ts es ri v e sd eo ce hys o l e i sd n gdnsh er u in ebc t ajlf l l e o clt at p s ed rhd i o n doa g u o u md pi snr ea itls t s ris v se h b hshd ee s t a elna re cl ml c i t ol n ree d i n abC cd & d -r e 2 . 3 , , .

s e

6. JOINT EFFICIENCY The efficiency of different types of welded joints are given in table on page 172. The efficiency of seamless heads is tabulated on page 176. T f o l phl o c aw o i t h i ac kt nm e an s f r e qu u t e nso y st l g f i t l .v o ~o ge hs i t T e

s f

fgen o g t eru am t s icu s nlo at m esr p e uqdw h tu o ei a r ee ld xhsa li l mdw o uw eo m ap r br kl ef ei st n sm gu o r ho e ar a yeph h eTe de f n s lo a rfo hcl m d y d lu i. sl n aeda hr s i c e a f lr l usn ed iur ni aeas tl nugm ao hc ,vl eel i r y n s .

it t h rg se i whs e ger s oiot na ew v hlnte mch ir r l lc un m eh f j ey r en no t ie a il ii lc i t e oen chn y te s l- ao hsn sga hinj lt u fe do f i f n eiia ocl wi ne n cht y ,

f

e l

n e

r

besides the internal pressure additional loadings(wind load, reaction of s t t

a t s

ad cd al l euor ns s g ) i ib t une ed o gin t n dae l inT snr i g ef o ih ani r . s o o e n r sh at rhrai t i eg s t ss i ie phsn er gper o s t nau eq i h niumo n and oe r -c e h ah l s f it t hlr o ne g ihs s t e u sed i nn aea l m .

T

f

o

rf htm g u s l io aeh c serc o r t rda ei nh g ml y : t

PR = 24SE+ 0.4P

Seenotation on page 22.

P=

2SEt R – 0.4t

I

P

N

R

FORMULAS IN TERMS OF INSJDEDIMENSIONS NOTATION P = D

pe o p vt

w S= S

E = J e of f ip i c 1i en a n c t y 7g. r s o e m i s a sg l aul n or R = wex I a bnrr . l as ei d i n i dc u eh s e, r r pke is sn u gs rD = e I ndi i s a i m i n e d t c ee hr , e o rm a ea pl t ps e u ssr at i e= a if t l g h i ,i c e k n n ec s hs , e C = C o rAa r l ol ois wi .n ao nnc c eh .

A

CYLINDRICAL SHELL ( t

R e

PR f= SE– O.6P

P

LS

EO

A N

s t su i at t ll hr s l e i yog h seo ev S ns e arn en p r ep c e a d i g n g e . 2 W [ w h t h aiehe c x ok. lhcnn o ete isl ae n s nd r oa P e d x 0 i c S u. et f es 3 o drgE r 8 hsm i i u5 t C A po h 1p s e db nah dep - ei ap x l l i 2e

SPHERE

HEMISPHERICAL

PR ‘= 2SE–0,2P

2 s

s e

s

M G )

SE t = m-m

1. U

B

e s

p=

gi m ne g s . slhs ie f l v , a e se l de .

HEAD

2SE t R +0.2t

r 1-

R

-1 -–

f

1. F h

w e i aos at t o t h t s ej h hi o t s i e[ h h a 2 W t w h t h aiehe 0 S . t f 6 o gE r I s b -ah p ap3

. .

Ih r d loua r t aisu e gnft fhg si i ol a et f it e eeld hfno f l si e m h fa e s d n e c x 0k. l cnnR o. ePe e sl e 3xs d 6 hm i ti uC 5 lvA, a epo hse p l li , e l d e .

thce i , e n e c thac if { es n c . 6e c 5s e e nd n n de ei

2:1 ELLIPSOIDAL HEAD

I

b

0

“

PD ‘= 2SE– O.2P 1. F

a 1

/1 = 1>/4

e l l ih po m a i i on 4 (

P= -Dy;jt

sw e o t ia hrd rado leta smh r t , a ehi j e o o nxt t 2 1 os hihC d r A e aspo espr e nd n : , de ei c ) .

E D

ED P =

S= 1 5 E = 0 j s

S

AI

G T

X NA

p d pe r s p 7s vt5 o 1p @5 6l . e . f f oi8 s cp oo s ia hh n h e

:

E = 1

j . e of 0f oi is c0 ei n ea , n m tc l y e s f h e a d s ni rnc a hs d ie i8 ds u es * e is sg ui R n=r 4 ie 9 i e ni f A dnc i hsa mie e6 dst e e r * rsSa 0 e l 0 s Dtiu= s e wq [ u h i ai irc ken ln d ec s lhs , e 5a 7 0t 0 ”e= r I F C = 0 . nc A 1o c ra 2r hl. ol e5so iws o u n n c e oi 5t e - ne x, c a ym i n ef i d . r eHe t tnm sl e i f l * s dac .o crd oi r o ngo d d vi e nt a di ot n e w t c i o r a rhlt ol so ihw o ea n n c e l l

SEEDESIGNDATAABOVE SEE DESIGN[),N”f’A AIK)VE

I)c[crmincIhc rcquird lhicknms, 01”o shell ,=

I(K) x 48.1?5

=

().325 in.

fhwrmine the maximum:Ill(nv;IbleIf(whingpressure, P I’br().5()() in thi~k kh{.11wtlrn Ihc tIS 10 a ax l i l pmo r wu e am s bs l u e r The m

L

‘a AX D

4

,

‘

L

3(D,/f,.)

=

“

s a v s forauthickness, ml ~., e u e The valuesof B s b determined h a by thel followingprocedure: 2 D e t t eL., r andmthe iratios , n .L/Dl e and , 1 A

s l%

D1/te 3. Enter chart UGO-28(page42) at the wdue E a 5 wn L/Dl t h e of LJDI (.L/D&)( h o or0 i tz tov n t is greater than 5 M line representing~it. From the point of intersection move vefically to determine factor A, 4. Enter the applicable material chart at the value of A* and move verticallyto the line of applicable temperature. From the intersection move horizontally and read the value of B.

te

a

L

I

a DI

‘1 NOTATION A = factordeterminedfrom fig.UGO-21L0(page , B = fhctordetermined from 3 charts (pages 4

5 C4

o

t m m p2 a u ax h tl i . l ewmo

owu e arm

pressure,Pa.

4 7 ) c lh l I eu Pa fdis s f e e mdt at dl h l ep f er has etr si sn ( aa g xl r d )e e e t ,e ds s i pe gr hs o nmust ci ,be e repeated gd e u n r Dl = outside diameter at the increasing the thickness or decreasingL b

a = o

D s= E = L = Le = P =

h

o t

ian n pdn eeg

large end, in. outside diameter at the small e i n modulusof elasticityof material (page 43) length of cone, in. (see page 39) equivalent length of conicalsection, in.(L/’2)(l+D~/Df) external design pressure, .

t

h

i ic

k

n

effectivethickness,in. = t Cos a

n

●F

v

d

. oa A f ol

at ut l l e ol r t sia e h n fp

g

cable line, the value of P can be calculated by the formula: Pa = 2A E/3(D,/t,.) For cones havingD A ratio smallerthan 10, see Code UG-33(~(b) W

HI G

ER

ETN A 6 a TH

E S RA 0

The thicknessof the conesshallbe the sameas the required t h i f c a kf nh e o lt se s

Pa = flbum allowable workingpressure, psi t = minimumrequired te =

using of stiffeningrings.

e

sn s d , P c

i

o w oa t. mc

e h qt i l u a co a r hfu hl g t e ot he nr ef e .

r a o d v er eiq i dun o f ate o ctr y j l u i nSn cp d t 1 eu ar e e

coe i n n h . g5

37

E

X

DESIGN DATA F’ = 15 psi external design pressure Material of the cone SA 285-C plate 500 F design temperature CONICAL HEAD

a =2n

D( = 9 i

e2 6 g. D, =r. O e

d

e5

Determine the required thickness, t Length, f. =( D1/2)hncx=48/.4142= 115.8,say 116in 1. Assume a head thickness, t, 0.3125 in. 2. fe = t cosa=O.3125x .9239 = 0.288; / )l= 1 X +D(1 + 0/96) 6 D = 58 1/ L, =L/2 ( L, /~, =58/96 =0.6 L), Ite = 96/,288 = 333 cf ph r 4 a oa r mt 2g , 3. A =0.00037 ( 4 ~

=

(5

c, f

2ph r 04 a. 0oa r

mt g3

s

L (1 A7 2

1

w e

,

e

) )

4 X 5,200 = 20.8 psi. . 3(333) Since the maximum allowable pressure is greater than the design pressure, the assumed plate thickness is satisfactory. 4B

5 p,, =

3(D,/t@)

=

CONICAL SECTION (See design data above) DI = 144 in. D

e

L

D, =96 in.

a =30 d

t t e r r em tqi h nu i eic e

rk

e ne e e d s

L n= [ (gD r D t J )h / 2=], / 2t a n4 a= /

g s

. i 45

m 1

Le=(L/2)(1 L

w

1 t i m

s

4n .

6

.

0 i . 3 n7 ~ X( O ) . . 8 3. 6 , 76 =5 0 . 3 2 4

+ D~\Dl)=41.6\2 X

+ 9

I

$

S

O

, 7 17

a

2 t =tC

.

’

6 = /3 1 4 4 4. ) 6 Le/D[ = 3 4 . 6 7 / 1 4 4 = 0 . 2 4 1 D1/te= 1 4 4 / 4 0 . 3 2 44 =

4

3. A =0.00065 (from chart, page42J

4 B= 8( , c f 6 ph r 04 a. oa0 r mt 3g 2 1 4 4 94 6 4 X8 6 2 5. pa = 4B = 3 X (144/0.324) 4 4 3(DJr J s i . = 25.8 p an xah cl i l mpeo ruw e P. eam is sbgreater ls ethan u r de the ep rs e i s

P, the assumed thickness is satisfactory. EXAMPLES

7

&

, 0

sg

u

39

E

P

X

FORMULAS

7 L J

o T

R

L

Use L in calculation as shown when the strength of joints of cone to cylinder does not meet the requirements described on pages 163-169 It will result the thickness for the cone not less than the minimumrequired thickness for the joining qdindrical shell.

7 H

Use L in calculationas shownwhen the strength of joints of cone to cylinder meets the requirements described on pages 163-169

r L. 1 -a

40

E

P

DESIGN OF STIFFENING

X RINGS

NOTATION A : Factor determined from the chart (page 42) for the material used in the stiffening ring. A, = Cross sectional area of the stiffening ring, sq. in. DO= Outside Diameter of shell, in. E = Modulus of elasticity of material (see chart on page 43) 1, = Required moment of inertia of the stiffening ring about its neutral axis parallel to the axis of the shell, in.4. f’,, = Required moment of inertia of the stiffening ring combined with the shell section which is taken as contributing to the moment of inertia. The width of the shell section 1.10 @ in.4.

L, = The sum ofone-halfofthe

distances on both sides of the stiffening ring from the center line of the ring to the (1) next stiffening ring, (2) to the head line at depth, (3) to a jacket connection, or (4) to cone-to-cylinderjunction, in.

P = External design pressure, psi. t

= Minimum required wall thickness of shell, in.

I. Select the type of stiffening ring and determine its cross sectional area A II. Assume the required number of rings and distribute them equally between jacketed section, cone-to-shell junction, or head line at % of its depth and determine dimension, L,. 111.Calculate the moment of inertia of the selected ring or the moment of inertia of the ring combined with the shell section (see page 95). IV. The available moment of inertia ofa circumferential stiffening ring shall not be less than determined by one of the following formulas: D02L,(t+A~L)A ~, = Do’L,(t+A]L)A {,= ~ .s 10.9 The value of A shall be determined by the following procedure: 1. Calculate factor B using the formula:

“’[*J 2. Enter the applicable material chart (pages 43 -47) at the value of B and move horizontally to the curve of design temperature. When the value of B is less than 2500, A can be calculated by the formula: A = 2B/E. 3. From the intersection point move vertically tothebottom of the chart andreadthe value of A. 4. Calculate the required moment of inertia using the formulas above. If the moment of inertia of the ring or the ring combined with the shell section is greater than the required moment of inertia, the stiffening of the sheH is satisfactory. Otherwise stiffening ring with larger moment of inertia must be selected, or the number of rings shall be increased. Stiffening ring for jacketed vessel: Code UG-29 (f)

41

E E DATA: S

D

P= D.=

1 9 L H M T E= M o 1 = 0

p

I

G

X N

,e

xs dt e epi r r s5ne . asi sl g u rn e . i o u nd t i sao. t m i s 6 de , ht e ehe r l fl e . eo t nv gfe ths ra h st n t ef ot ge i al e l nmn 4n igf t O ie n=e 5n o i et 2 e e l a l i :pd s o s i d 1 a l a o t t es tr i i rf haf S el - in i f ne ng 3 g A 6 e m p 5e r Fa t 0 u r e 0 ° o o de l u a ols m t u ai sct2 ie7 t ,rf y0i p 0a@05l f , ‘,s 0 ( 0 c 0 i0 s h p 4 a 3g n e ) i . t h 5 i o csn 0 k nh 0 e se. s l f l

I A a z =

II. U s o h

o n6 x 4 g s3 i 4 .

. ae

- s l .e5n l e /e 0q n , 3

cf 1 t . .

2 s s t ii fr fn e i ngq i n nu g ag pb ea o t cn wet e -de td e eh ni hp r ( e f i as gLj =du1 e in. rf s e e) 9 ,

m o oh m i ne o e tne III. T selected angle: 11.4in.

1. T

n : 7

v

o aF h a

lc

t

r t

uo e r

B= 3/4[PDOjct

t e1

i 3f

=

3/4 ~5 X 96/(0.5 + 3.03 ~1961

= 2095 2 S t

2

t i v no a B hi c l l . e u e e h 5 a0 0 n ,

e

A = 2BiE. = 2 X 2095/27,000,000= 0.00015 IV. The required moment of inertia:

I

[1102L$(r+ A,\Q4] , = 14 S m e S t i a S p

962X 196X (0.5+ 3.03/ 196)X 0.00015 = g 97 in ~ = = . . 14

t i r e n qm h cu o io eim r ene e( de ni 9 r ) it ts . im fnt 9a a t l7 h l ” e ahs o o i m n oe te ns r et t al hi ef( na1c i t fg) ete vd l. nei ae h s 1 4 s ” de q su t a i t f ef el n y e d . i r f fm ei b ns in unt algbg a bj sut e cyTe c kes r tl hiab con lo g ni . us d t d t ir te im q ho u no on i i mr n o e ee d rn t t i a f . a g fe es ~ t 9 i 5r f - cof 9ae e l7i cn ui l narn tg i o ng s .

i l ds

ed

4

2

owl

Cacml

.

001

0

1

SA

SL

A

THE VALUES OF FACTOR U

I

FS

O

REM F

UV DL E ANO U SS

A

S NE E X R D L T SPEE R R

E N R

U

e Uolwj

-

I

I

I

I

n r I I I

i

z

I I 1 I

I \ \ w

II

111111

I

# , I l

w

8

Pa

E

45

46

..

t

t 1

I 1

I 1 I I I I

1 I

1

1

I

1

\

,

,,

,

I

\ I \

e Ho13vd

.

Y-RII\]

, I I

I I ! 1 I I I

I I

I

I

t

I 1 I

I

.

u)

.

!

Ua

E

4

48

E

P

CONSTRUCTION

X

OF STIFFENING RINGS

LOCATION Stiffening rings may be placed on the inside or outside of a vessel.

SHAPEOF RINGS T

r

m i b h o nr e ac g t oea a ns og y u s let eafn rc h t

i e ro y n r s

.

CONSTRUCTION I i p r e ft ue rp a ilb tc l ssoae n st t a rcoe ou emc pst o is innt ge -s s et c ti ri of n f i e r at ut hs hs t easai tnr r nd us n ac hg trT ua dr r p ae f le th a sl ns. h oo oi ei ni n oe t d i f f oih rc u o l h t l i eseel ts ri aus n c fh vtgb ua a ry pba leel uo sct n,as ue t shoc s t a i td r j t t t u ich yus or not vht ase t g Fhu o l reh e ed a li o avfrl eme t . ge s rt s ee m a xp e i r m o i uos rsm io b uul c ne r d n ei eat 1a s–f 2 si u g l bnn te t nac w t s a h t h r e T ni c lh benhe l l idg aimie t i . vn s ae tnmr eeh tde o i t m cr f aibe l ie h c o o t pu ui ls he act T tt s ti f eeo ccen hbtsnf .i col a i ne ansu o rs mn t ot e ee l a t b u h tn t -t weo e igld pd en e ltd h a e c r e n .

n r

r a

DRAIN AND VENT S b d a

t

i r f pf i o f dt r i ah ma t d n a on

F r

t m s iC

ao Fn

e li ntn aei r gc no h ehsso rd i is z nd hhoe nea het aaof l gl oa l tv s l ae ln t a oo ia t nm t a nf gr v eh Poe r do a nct o et hi pt c o r aa 3.lani l y e ob t oe a l rh1% t i t ed noitn e ahm ma ct ed ot t i hse a l rht i o s fe a tc e tf s oef ct deo hrns cd tFei tt iisA eo gns s u. r e . xah oi s m r l uhreu mn ees u pblc pf efo lor c tg te ai d s u t oei Ug Gg d., u’ e 2 re 9 .e 2 .

is a f ef

e

WELDING According to the ASME Code (UG 30): Stiffener rings may be attached “to the shell by continuous or intermittent welding. The total length of intermittent welding on each side of the stiffener ring shall be:

1 f r o i t oo n u nt ghl. s r t i s ode no hehe t, s o aan tu c s it hrln cs ue mi ff ed er ee o t v e sh s e fle ; 2 f r o i t oi n no t ghs.v r esi n nlshd et s e o ee o t fh l e o h,st nac t i i s rn rh ce f e o tr v e e n s hc s e e f l e . W c h o r ea r l o rl si o t i ebw op a nr n o ct v es i t di rfes ho fdse e , bin ah i t ne antg t the shell with continuous filleto or seal weld.ASME. Code (UG.30.) M S pa 1 tf i n 8t f e x

a rt rt

cx oe o1e

i ri ri

n. n2 n

a

lc g

g a rn l ar n l

4 1 F

E T t

X

A

f t

h

F iA g u r e i M R P LO : T 1 G I E UN Sx 3 Il Sf D %wE f 4wE i R II NN S? Gx 2I l SD

iB

g

o lg6 ec l ” o lg6 ec l ”

u

r

e

te” l . t r te“ l . tr

w t l h e ei s g b -e nhl esl tit a dzt e osel h m ols at hae fl t o l s l en1l hiose wt i o cvh k w e n o es seta s sia t f e jlf f le o n l hie r r n tt e .

i

d d

n /f ge

49

CHARTS FOR DETERMINING THE WALL THICKNESS FOR VESSELS SUBJECTED T U T C

~“

F

V

t s c ih t ah n rw r digt i i asef a f, l set trss h e uih nc mckt nbe ea ds vs aeo s i d c h bh a d ree a v t iee a esl c oc s pown er tdd da i n emcn ehtse o Ait h gh S e no S o e V dc D tI e i i 1v I ,o i nsI i ,o n .

1

30 040“

50

602

70

”80 090 100 110 120 130140

150 160170

180 190200

SPHERICAL, ELLIPSOIDAL, FLANGED AND DISHED HEADS (Specified yield strength 30,000 to 38,000 p i n sc l u is

i

v

,e

)

T f t r i e hq hnut hi e oi r d1c Deke aedn t e Res2d rEs m : t inc n . aet th vh e a , a. r hr o R 3 M v e o r t t t i ev cfm ,ap .llee lr4 yaM i t uh nroo oer i e za ovr n, tt a. ele nl y a I

t

R

D.

= R = F F F

e qh u t ih e ir ci e k ad n e h e m i so ph h e etr i i c ar a nlr d 2 e l l o i h:p s 0 oe i .r d a1 a9 f l a a od n ih g n s et r i hda

= Outside diameter of the head, in.

s dn s , . has i s d i , i d eu n e s , . l dx Ds 0 ncedd hsrdrs ai i,o RmW=Do dd e w i e u nn s

,

50 CHARTS FOR DETERMINING THE WALL THICKNESS FOR VESSELS SUBJECTED TO FULL VACUUM 323.

525.

5m.

502

475.

475

a

m

6a

Qo.

e a

37s

375

35a

350.

s

225

3m.

2m.

27s

27s.

Zm.

m

225

2Z-3.

2ca

a

175

r?s.

Isa

(5a

1=

123.

Im

Ice.

-Q5

L

!Ea

I

D

!

5

14

l

Isa

1

3

laa

1

2

I la

,

Ioa

I

m

90.

m.

m

70.

n).

30.

a

3a

30.

Q.

a

2a

m

m.

m.

la

3

d

5

67*9

2

1.

3

*

5

C Y L I N DS R I C H A LE (

S facing page

f

0

7

a

o ,..

L

e xe p l a o en a t i o nr )

!0.

L

51 CHARTS FOR DETERMINING THE WALL THICKNESS FOR VESSELS SUBJECTED TO FULL VACUUM 525”

\

10

Is

,Xl

.25

.32

.sS

.4

.5s

.50

.%

.(M

.05

.70

75

.s0

.03

.90

.95

!.00 S5

Soo.

X0.

4?5.

415

492.

441

-Q5

45.

-QO.

-no.

3n

3T5

330.

330.

325

325

o ~. n 2

X 7

’

5

.

2?s ?3a

—’2EQ. 2?5.

2ZS

ma

290.

ITS.

17S

,3.

Isa

125

!25

ICo. .10

. 15

.20

.2s

.=

,35

.Q

.65

.542 .55

.m

.63

.m

.75

.m

.55

.90

.s5

ICC.. ,.m

t =

C Y L I N DS R I H C A LE (

S

p

ye

T f 1 E 2 M M 4 M 5 E 6 M 7 M

t

t

= =

L

= L eo t 1 D i t 2 T g 3 T d l p

T

l h v h c h v

ir3e e e d0 t nl 3 , g d8t0p

hi , 0n

L

0sc 0 l 0u ois 0 i

v

,e

P J “ Bo H Y D R O CP AR L P o J “ g S ia

)

r i e sq hn ut hhi o i rdce e ke dn l e s l s : n c o t ( h wf e p a. e ar act r vr i g ont aL ehg l ) u t e e o or i z t ocv n t ur .a eel prl ry evDs e e n ot si n g . e o r t t t i ev c m a p lle l r ya ti u ro e n e o or i z a ov rn t D.a el e nl y o a /d d t n a h t a bt a ev o . or raD vh t l eo u t e / e f t o or i z t ocv n t D.au el l ry v o e e o r dt i va c roa . lt e l v ewyn o at han l d du e e f

o s ih e ln l f , . oeg v hst s e ehs st c efasteat li l e okra o l nt r ehf , og l n e l h oss e w t et t att nwa !c e.nohe t ieg h ne np e on e hte t al o ths d nfu eio es hrs h r a in u e ni s r go e sn de t , . r d e ih ab s t et ae at. t se naw t ck e snej etw a i nr fc fi ei ye nonn ti ng n g i f s ht t c ar noe t. ceohfn es tti mi her f er tf rt e hisnf tei nt ane hg n o i thirdl of t n h n u d eeie h s ep l t n e h d , . vn bs

h

C o p y r i g

c s i i tf

L

i pe s gag

e N a. A s C eSe.A , dod M . . d.nC wde FE hn V eid aTe a hn rsi ” c d s kt n es e RO BC O E5N SN S 5 IM N 1G , po 2 9a 51 7. , y7 6 . . m A.np pl , i tp f. . r..i P, oeA r daVe c H seh sD s ueeo Hsr s Yeie D a g Rl nO d,C ”A N o v1 ep 2 m 9 b 6e 7 r 5 6 . . h t e d

52

D

T WIND

T LOAD

The computationof wind load is based on Standard ANSIiASCE7-93, approved 1994. The basic wind speed shall be taken from the map on the following page. The basic wind speed is 80 mph. in Hawaii and 95 mph. in Puerto Rico. The minimum design wind pressure shall be not less than 10 lb.hq. ft. When records and experience indicates that the wind speeds are higher than those reflected in the map, the higher values of wind speed shall be applied. The wind pressureon the projected area of a cylindrical tower shall be calculated by the following formula. F=qz G CjA~

(Table 4) ANSI/ASCE 7-93 STANDARD (References made to the tables of this standard) Projected area of tower, sq. ft. = @x H) Shape factor = 0.8 for cylindrical tower (Table 12) Gust response factor = (G~& GZ)* When the tower located: in urban, suburban areas, Exposure B; in open terrain with scattered obstruction, Exposure C; in flat. unobstructed areas, Exposure D. (Table 8)

= Velocity pressure, 0.00256 K, (1~2 IESIGN WIND ‘ R E Sl S m projected

a

o t

U

R kEb ,

I I

*See tables below for values of q and for combined values of Gh, G,& K,

Wind speed, mph. Importance factor, 1.0 (structures that . represent low hazard to human life in event of failure). Velocity Pressure Exposure Coefficient* Exposures B, C & D (Table 6)

VELOCITY PRESSURE, q Basic wind speed, mph, Y Velocity Pressure p 0.00256 V2,q

70 13

80 17

90 100 110 120 130 21 26 31 37 44

53

DESIGN OF TALL TOWERS WIND LOAD (Continue~ COEFFICIENT G (Gust r Abo?eE~~~~d,il. 0-15 20 40 60 80 100 140 200 300 500

f

EXPOSUREB 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.4 1.6 1.9

c

w

E

EXPOSUREC 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.9 2.0 2.3

The area of caged ladder maybe approximated platform 8 sq. Il.

C EXPOSURED 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.4

as 1 sq. ft. per lineal il. Area of

Users of vessels usually specifi for manufacturers the wind pressure without reference to the height zones or map areas. For example: 30 lb. per sq. fl. This specified pressure shall be considered to be uniform on the whole vessel. The total wind pressure on a tower is the product of the unit pressure and the projected area ofthetower. With good arrangement of the equipment the exposed area of the wind can be reduced considerably. For example, by locating the ladder

90 degrees from the vapor line. EXAMPLE: Determine the wind load, F DESIGN DATA:

t w b v d

s

V D

vessel height, H Diameter of tower, D Height of the tower, H The tower located in flat, unobstructed area, exposure

= 1 =

= = = ..

m 6 fi~ 80 ft. 6 ft. 80 ft. D

The wind load, F=q x G x (9.8xA qf t r a= psf ob l2m e G from table = 1.8 Shape factor = 0.8 Area, A = DH = 6 x 80 = 480 sq. ft. F =26X 1.8X 0.8X 480= 17,971 Ibs.

6

W

MAP

S

(miles per hour)

.

r-v

—

(q 90

i

u

j-----

---

i i ---- =“r ~-i_.. _.T‘-.’ i----

m

. .. . .. . ... ...

my ,-—---- —-/

‘&—— ,, ~ A

I L

A ‘

S

K

’,

A

i

.- \kl

2

.

M

W

S

(miles per hour)

NOTES:1 V 2 3 4 5 6

a a f a l s ts ue r asp3 et t -a.e ms g i ebel fre edl o ox cs p uva tooCa 3 t n. sae ea ud sg r s ro neo r c yi w a a ipn r ono bt0 au b . iah l n i0l t y 2 f . L i i n t ne br peeow l tasa t. cwiri poo eni an ecn t c n oee pud t dra bs l e s . C ai t u o wt s i hc oisp o. in m n e nont eu oerne f tudeoa Adri g nsi laoi udnaos v ns i s ks ef W s f iHp i a8ena fw o Pe . daRu di n9i em or ii r s 0p tdc r o h o s 5 . W l hr o eo et c cei r o nr h.a r de r 5 idi la 0wcgs is-a rhnptyi seee b uhearnh dr s a esd e, l W s m i pb a sent b sac e . uo db nm d e cs ye to te adawat sn noe te eit el ncainnh nor l en e at ds oe

56

D

T WIND

T LOAD

l a i a o l tm n e a erb dn to ads ht st es ASA ao nA58.1-1955.This ed d da rn d Computationof w b b s s o u l ti es u s tic e oa loe f t om ldc d ron enu e e n i ts rg di ne s standardis o T t

w m

T a

t

p o t

rih fh

ae 3 s fn ls e ua de r g tbe v r f o tteo0 U v. u l nSo en h i ti ds t a a ap hc a e i p g nn e eg .

ohr e t e

b a hg e b t i lw l epvo re i h eew f s v nss au he r ode e ai si o g bg u rhf os t ot i r n d be i t c ma a t s eah d p y e . W C

P

H

E

SR I l

RI

E

I I 20

E p SW N S TU H H DR O ER EIH Z O w●NN T EA L O SC QTSO IU R SEO C A TN AR N * G E U L R A R G H M AT R A E A P S 2 3 3 4 4 o 5 5 0 5 0 2 2 0 5

. doe

vs u

o

0

5

30 to 49 I 25 I 30 I 40 I 45 I 50 I 55 I 60 [ 50 to 99 100 to 499 I 30 I 40 I 45 I 55 I 60 I 70 I 75 I

EXAMPLE F

t

T a

v m

I I F w

wi

p

rinh

P e

fs nd sm eur d r a e o

ie i h ns tt s oe r a 3 I r t e km

t t

h h c

y p

ez ez

hli hfi

w p

.

enpe i dO le ekr s dl aw a ht oi ohie tm wian , p c ri h m e h s n ss n e 0aeh a t d w rai p . rnihe es f sp v ns a au he rr od ez i s ioa o ug r n rs h

t o g 3e nfh hen 2t s l o3g t r 4nh fen 3t o l

ape ts s f n b 0e .q t 5 pe s m t f 0b oe 9 q . t 0

. .

r r

. .

. .

l i ton d t or i v ch wra as l e ebl hm suur al eebt si ls p f lh l i a0 ee a td c t .p t h y oe 6 ri ie d s ni s f z uf d rewo reb 1e n ain n 1t e l lp ssn f l r bee se 5p qde tc 8 t .i vr e .

I m e q a u i a p na m t e f tnty trta st c hi o i eahe f a( a cc ct t oB r ro d o uir wnt n0g e f l c . loy )l U e s

m

dw v t iieo sen a rtc bs r tl s eeh a h i v8on dpe ro si5 c sra l e l .

o sv e eu s s rss u pe sfa elmlf acs nl ui fyo aft c tw y u rp e r rri hs w e s in rs t eu h d re o l sp p p .s l f reTb : e q h t0 r t t e h n ez c h i oo emg ano h e rF et ae e xs a a3 or m p e p c r i se f sib hecs odu na r st eibl du e ln r oeei t d f w o v ohr hee m o s snl ee

Relationbetweenwindpressureand windvelocitywhenthe horizontalcrosssection is circular,is givenby the formula: w

Pw= 0.0025 X VW* E W

X

A

M

Ph

= we

Vw = w P

L

p v

r i l e pe s s n fs W u b dre e i ml o n c i p dt

qe t y

E

o

1i m v n e 0 el p d o xa pcf 0er i eht r s y st u s r e : .x Vwz= 0 2 p0 op2 e r s uq5u a r ne f o o dt po r5ne ts hs ue rpe r o j e oc ft ea dc a yr el ai n d r ae a h s oe 3s f i ea g gle b h r t oot e uf v0 nt ed .

Pw= 0 v

T t w o hp tri eo a s tne s l i ou t d r p we r o oehtn du r pu sr cneh ea t st i s f ue n p r o a j oe t cr t t eoW ed hgw ai ea r or f r aet no . gto ee hmq edu n t hit ep mx e pf h ne o a o t rw c eb ihr e anca do f neu s di cd F en eer ea dxb l aby ol .m o p tc l l a er ta , i hd n 9 d e f g t rvr e l a e o0h i s p nm o e e r .

M

W

P

57

.

58 D

E O ST

IT

AGO

NWL

EF

LR

S

WIND LOAD

~ =

v=

t

N O T A T I O N W o ti v w de i hnst si e suh f l etfta e t l ic hot E E f f o it cw i jee no hl c iy d n e f t e d s L a ef rv e tm r , . D i f s b t t ras naeu cocc eons tn s mii df d eoe roean H,HIHZ= L oe v noe v g ss e te sfs ch e st f il e ot r l n M =M a mx o(i t mbm uf el a ma hn s t t be t MT =M oa h mhe f el i n g ~t t h b t t , - ~ = r oea v dei a si s u n en s l f , R =M vt o m ra a eo lat s es cu rsp t t i e rau fs l e a =S s v =T s olh te ab rl , . f =R e dt q h ui c ci o kr ren e rxe docsi sl ,iu od nen

h,

T J_

-

t=R2nSE

P.D, h,)

= = = =

r

~z

hr(V-

-

D2 t Y~ I I 1

D]

i

E G

X

D

e

L S U S T M

h2

HI

i

A tt

! :)

x

> 4

’

D,

k 4u z %

P

~l

2 5

1

II = ~

-

e r 6 o X 2n =7 1 08 2 8 6 , 0 1 e r 3,960 o Xn78 = 308,880 1a 0 l M,4 69 f l 78 , 0 0 a hlt n n t t gi o te e mnn t e = . 5 X

X4 X

=

~ ‘ H13 B

S

T

S

a h

T b t b t s

‘

eL

for X S ‘is

MX = [F, X X + (V -~j X (X – H/3)]

H

4

X

se

ae

r

s aih ht t esh oo e har esit zre osa sin e at shl a ml e i o a t a h oT t swr i ee al he n ro fgp au. a lad eat ir t n e o ht th a s o dph h wei due e ae to e that fg e aloading r ar m

are shown in Fig. (a) and (b). A portion Ft of total i o D s a i m d a hi i go c nr r si g az e ofm in Vt sois aassumed ml r ito becappliedeat the top of the tower. The remainder of the base shear is distributed throughout the length of the tower, including the top. O

v

e

r

t Mu

r on

i mn

g e

n

t

The overturning moment at any level is the algebraic sum of the moments of all the forces above that level.

NOTATION C = Numericalcoefficient = (need not exceed 2.75)

1 7?/3

Outside diameterof vessel ft ;=NumeticalcOef ficient ‘:””: = Efficiencyof weldedjoints =

F, = Total horizontal seismic force at top of the vessel, lb. determined from the following formula:

(b)Seismic ShearDiagram BaseS

h

e

a

r

F, = 0.07 TV (F,,need not exceed 0.25V) = O, for T lot) w h e n = M r e a o t t d a o i i h w u n se n rf R = T h i o c s k i k n e i s s r n t f , t wind p r e p s s u r s e , Pw =

E G

i

v

6i = 30,000,000 = 48 ft., Oin.

= 2 f

E H

= ~ = 30 p = 1 i = 0

I R t

T f

m 4

.i

e t

Dn

A

M

P

L

e : t t e m r am dxi he n i f e lA me n. , .

AM=

3

X

n ) ohn

td t fd i ah r e f

E cu et mi o

n

:

I

PJI,H (12H)3 8EI

30 fx 2.5 x 48 (12 X 48)3 s n ‘ = 8 x 3 20 . , 0x 01 0x M3, 0 x 00 2 .0 1 n 2 5 .

axh l i l d m o e wuf e6lai meb ncp l t1e ci f oo hhn e ee0 48 X 6 n8 8 . 8= ~ ’ o . = 2 ( i ) r . ” a

S t ia dcn e htf cdl uen ece aot e xit l ol ocen s a t i s f a c t o r y .

t d ih e

, .

ti s

= 1 .

g r h0

i 31

. 31

.t f :

e t s h i i og tc ns k eine kde m s e it i d t s ,

A m e f ct a hl c douo e l fad l twei cnr t tg t hi ho ni o,ech t kt n n i eo n esh c sw s gt ba i S Sn Tv .O t “ e v, SC1ea n Mh m y e9ob.f “ uCnter a 6rhl t c Touo t8l Dado te i f wnr l. gAe H y d r oP c r a or kcb oe ns s i n g

69

D

E O ST

IT

AGO

NWL

EF

LR

S

COMBINATION OF STRESSES T

s

t

i r h ne

bsd t s up e r c es evdh i de o s ul cyso rel shallbe aiy bd investigatedin ei dn g s

combinationto establishthe governingstresses. C o m b oi nw a lt i i(o neo a nr t v e sh s e le :

t aol hf dqoi u dn aa pressure tkr dee and r ) weight n , a of l

Stress Condition A w + S + S – S

i dt dt dt

ns d w t rw e t ri p e t rw ee

Ae l e —o S d es + o S. . eh —o S t

i a rt d ui s s n ur n s e s s t u si sg

C o m b oi nw a lt i i(o neo a n r t v e sh s e le : S A windward side

t

+ Stress due to wind – Stress due to ext. press. – Stress due to weight T s

B r

e

T

s

e rw ri rw

t aol hf dqoe u dx aa ptkr

w i a r td d e u is s n e p e u nr s e s t se ee u si sg eh deer

e o os o

aer ) w sn , sa eo ul n i r

t r e s s Condition At leeward side – Stress due to wind – Stress due to ext. press. – Stress due to weight

s so e

e

t s wu ham ei et a s a dr h h bw d o e e u sef ierl a t e r .

tnnl h tqd o udn a o dak es ci dmo u lc ts a nt uoe o t u sr h g diw n otoe e e di ha r et rnl h r qw uhod a i ki rc e ah

sn tdc i ra b n eu cg css e nsse t r bdih sc ui y tam y m wla rt i l siz s f u wl rto ei i an or g t l nh m q o u d a ak r e d . t

s r h be hc s a s l a cae tu sl fl

ao l tl leelh odo c wa it t nie

1.

At the bottom of the tower

2. 3.

At the joint of the skirt to the head A t A c

4

1.

s t t t

p o s s h id i t e t i g evn a en ot sn ts ei ne sgo h adn i t ecid go vnm e penor T e st s s i e u m om t a s t ti ior hne w ds ish f tceee aes t o t nch eo s m e ip r ir oge osn sv i e or r n

I i a t t g r

T

e dt .dt dt

s

t

b

oh h o ad

f r uh er

i

fe e

l

ii n t ne i go

n

D D D

U s v

tn d h di f ce ef o en s rrd t ie w et n i toeo n t h si v , g ae chh eso nt ss en qfte ue e ln ct o r n dae i a t s di oi s l rfn B fs e es r ds e e inuoe dt r.r e eo sid c ,i nts mi gta o n nt ie n us is n noe otd e le x er s pt t n rer ae r ls n s a ur l r e . a n a ot l a n t d mb

tn l t n

:

t s

t s hs se br e hem s ox ra a ei tm l f i o n l l ce leh o do n wd

r r oe id c i nst mi ga o n r ei n. s g p r e ir a n . t ig o

s

dr th e

2 3

F H

ue ut uo

ht t t te s otj eha mho e d i lo en l ni aog . t m eh t e is ot c t ekfv rn ee shrs s

og n

et

nr g

ys zt i r ohrn et g nt g ao eut w h vnl e a f ld r rl o iseab odt r ui oa o xs hk i ,tt m hrhas u ebeen e m applied. os rs y

ns

70

C

O S

O

(cont.)

The b t T t

e mn od d im t wn e ig dun i e ct rf ne et a bosr di ont s toght t ot tm o h e om ot t w p h e t l h r hui ca,c a k sbt n d e el eae s c as r cs ec oan r sod ei e n d g l y . A aa F b i B aln gc oe u n var de t ne f i i te edn i t di ds hn t fs a oot nd r ce w e o t t o f o wh wa hc p o eef it e rh r cit i craa hkd i ne neq su sa t e s . * 1 1 6 . .1 1 (. 1 9 . 1 ) . 1 1 . 1 2 . 3 . 0 0.5 0 m 1 . 0 3 . 1 1 2 .2 . 2 . 2 8. 2 9 . 3 0 . 3 2 . 3 4 . 4 6 . 4 8 . 5 0 .

0.53 0.51 0.50 0.48 0.46 0.44 0.42 0.41 ().39 ().37 ()6 0

0

0: , 8 0 8 ;

10

i

s 57 7

93

STRESSESIN LARGEHORIZONTALVESSELSSUPPORTEDBYTWO SADDLES EXAMPLECALCULATIONS (cont.) TANGENTIALSHEARSTRESS(S,) SinceA (48)>IV2(60/2),the applicableformula: ‘,=%L*H)=

1“’’;”:?*OOO

doesnot exceedthe s

tv

( :::3”.4:1

)=’$’mPsi

of r ashellmaterialmultipliedby e l s us e 0.8; 17,500x 0.8

= 14,000psi.

CIRCUMFERENTIAL STRESS Stress at the horn of saddle (S4) Since L (960)> 8R(480), A(48) > R/2 (60/2), the applicable formula: s4=-

4

Q

.—3K6Q

t

A/R =48160 = 0.8; K = 0.036 (from chart) s, ‘–

300,000 4 X 1 (24 + 1.56 d-)

3 X0.036X 300,000 = –18,279 psi – 2t

S4 does not exceed the stress value of shell material multiplied by 1.5; 17,500 x 1.5 =26,250 psi Stress at bottom of shell (Ss) K, Q Ss =— . r~ +1 ~ . S =–

x 300,000 1(24 + 1.56

I I

cl? .OL

-.94

1.13

L .90

I

1

1

1.22 1.47

1 la

I

1 cc

1-1/4 IQ 1-2 A u

1-1/2 1-5/8 1 9 1A 1-d/+ 506 0 -

]

..-l/ 1

I

u-l/

./

1 -1”

1

I

I

718

1-1/4 1-1/2 ‘

1-1/8 1-1/4

16500 1-3[8 20000 1-1/2 23750 1-518 32350 2 4 5 6 8 .

.69u /

/

5

: 7/8

63’75

.4U Al .U4

Arm of Mo~ent

B

●

710 1060 1600 -%/

Rdl;d cut

.

.

1.44 . -1.75 : 2.12

1 1-118 ‘m I

2

1-3175

-1 .

Z.Y4

I I‘ 3.06

1--‘!LB 13.62 2 II4.06 —.

I

i

m

ei l ni

-

2 1 4 5- 9 2 3 -34 / 5 6- 3 31 35 / 1 - 6 39 / -66 1 1 5- 48 2 / 1A 12— 7. . 5-7/;6 ;:;f ‘:” I‘ 8: l

82 . 3 85 . 4 88 . 4 89 .

I

A d

,

s ni

oc nl hs

e

s n

.

J

. 3 .4 .8 .6 Q .

6 / /

0

120 LIFTINGATTACHMENTS (cont.) RECOMMENDED MATERIAL: A 515-70, A 302 or equivalent. The thickness, and length of the lifting lug shall be determined by calculation.’ WELD: When fillet welds are used, it is recommended that throat areas be at least 50 per cent greater than the cross sectional area of the lug. To design the lugs the entire load should be assumed to act on one lug. All possible directionsof loadingshould be considered(during shipment,storage, erection, handling.) When two or more lugs are used for multileg sling, the am gle between each leg of the slingand the horizontal should be assumedto be 30 degrees. EYE - BOLT

r w

Threaded fasteners smaller than 5/8” diameter should not be used for lifting because of the danger of overtorquingduringassembly. Commercial eyebolts are supplied with a rated breaking strength in the X direction. For loadingsother than along the axis of the eyebolt, the following ratings are recommended. Theseare expressed as percentage of the rating in the axialdirection. 100%0 Y = 33% 20% w = 10% z=

EXAMPLE: An eyeboit of 1 in. diameter which is good for 4960 lb. load in tension(direction x) can carryonly 4960x 0.33 = 1637lb. load if it acts in directiony. The abovedimensionsandrecommendationsare takenfromC. V.Moore:Designing Lifting Attachments,Machine Design, March 18, 1965.

● Assuming shear load only thru the minimum section, the required thickneas may be calculated by the formula: R I

6

P t = 2S (R-DIP)

see page

where

t = required thickness of lug, in. P = load, Ibs. S = allowable shear stress, psi.

for designofweldand lengthofW.

121 SAFELOADSFOR ROPESANDCHAINS

The stress in ropes and chains under load is increasing with the reduction of the angle between the sling and the horizontal. Thus the maximum allowable safe load shall be reduced proportionally to the increased stress. If the ailowable load for a single vertical rope is divided by the cosecant of the angle between one side of the rope and the horizontal, the result will indicate the allowable load on one side of the inclined sling. Example: The allowable load for a rope in vertical position is 8000 lb. If the rope applied to an angle of 30 degrees, in this position the allowable load on one side will be 8000/cosecant 30 deg. = 8000/2 = 40001b. Forthetwo-rope sling the total allowable load 2 times 4000 = 8000 lb. The table shows the load-bearing capacity of ropes and chains in different positions. Multiplying with the factors shovm in the table the allowable load for a certain rope or chain, the product will indicate the allowable load in inclined position.

FACTORSTO CALCULATESAFELOADSFOR ROPESANDCHAINS

.

L

A

A

A

&

Angle of Inclination

9(30

600

450

300

1(-JO

On One End

1.00

0.85

0.70

0.50

0.17

On Two Ends

–

1.70

1.40

1.00

0.34

122

O

P

externalpiping is connectedto the vessel,the scope of the Code includes: (a) the weldingend comection for the first circumferentialjoint for welded connections (b) the first threadedjoint for screwedconnections (c) the face of the first flangefor bolted, flangedconnections (d) the first sealingsurface for proprietaryconnectionsor fittings CodeU-l(e)(1) SHAPEOF OPENINGS: Openingsin pressure vessels shall preferablybe circular,ellipticalor obround.An obroundopeningis onewhichis formedby twoparallelsidesand semicircularends. Theopeningmadeby apipeor acircularnozzle,theaxisofwhichisnotperpendicular tothevesselwallorhead,maybeconsideredanellipticalopeningfordesignpurposes. Openingsmaybe of shapesotherthan the above. (See CodeUG-36.) SIZEOF OPENINGS: Properlyreinforcedopeningsare not limitedas to size,but, whenthe openingin the head of a cylindershell is largerthan one half the inside diameterof the head, it is recommendedto use in place of heads, shell reducer sectionsas shownin the Code FigureUG-36, NOZZLENECK THICKNESS(CodeUG-45) For vesselsunder internalpressurethe wallthicknessof openingnecks shall not be less than: (1) the thickness computedfor the applicableloadingsin UG-22 on the neck (pressure,reaction of piping, etc.), plus corrosionallowance. (2) forotherthan accessandinspection openingsshallnotbe lessthanrequired for the applicableloadingsand not less than the smallestof the following: (a) the thickness of the shell or head (to which the opening is attached), required for internal pressure (assuming E = 1), p a

b nf

w c

evu e ol ei n d, cs

tle s rt ad e 1e

c o l r a r oul s l i ihl s / ns o a e n1 s n

i tn h h i i omcs kut e naw m e np s dp sa ac i or lf lrd a pr l oul l so e w (b) t m i soa The minimumthicknessof a pipe (ANSI/AB36.1OM)is the nominal thicknessless 12.5percent allowabletolerance(see page 140).

I

1

—

123

I

O

All pressure vessels for use with compressed air and those subject to internal corrosion, erosion or mechanical abrasion, shall be provided with suitable manhole, handhole, or other inspection openings for examination and cleaning. The required inspection openings shown in the table below are selected from the alternatives allowed by the Code, UG46, as they are considered to be the most economical. INSIDE DIAMETER OFVESSEL

1NSPECTION OPENING REQUIRED

over 12 in. less than 18 in. I.D.

two - 1% in. pipe size threaded opening

18 in. to 36 in. inclusive

min. 15 in. I.D. manhole or two -2 in. pipe size threaded opening

I.D.

over 36 in.

I.D.

min. 15 in. I.D. manhole or

two -6 in. pipe sizenozzle

INSPECTION OPENINGSARENOTREQUIRED: 1. for vessels 12 in. or less inside diameter if there are at least two minimum % in. pipe size removable connections. 2. for vessels over 12 in. but less than 16 in. inside diameter, that are to be installed so that they must be disconnected from an assembly to permit inspection, if there are at least two removable connections not less than 1% in. pipe size. UG46(e). 3. for vessels over 12 in. inside diameter under air pressure which also contain other substances which will prevent corrosion, providing the vessel nontains suitable openings through which inspection can be made conveniently, and providing such openings are equivalent in size and number to the requirement of the table. UG-46(C). 4. for vessels(not over 36 in. I.D.) which are provided with teltale holes (one hole min. per 10 sq. ft.) complying

withthe provisionsof the CodeUG-25, which are subject only to corrosion and are not in compressedair service. UG-46(b).

The preferablelocation of smallinspectionopeningsis in each head or near each head. In place of two smaller openingsa singleopening may be used, provided it is of such size and location as to afford at least an equal view of the interior. Compressed air as used here is not intended to include ~ which has had moisture removed to the degree that it has an atmospheric dew point of -50 F or less. The manufacturer’s Data Report shall include a statement “for non-corrosive service” and Code paragraph number when inspectionopeningsare not provided.

NOZZLENECKTHICKNESS The wall thickness of a nozzle neck or other connection used as access or inspection opening only shall not be less than the thicknesscomputed for the applicableloadingsplus corrosion allowance.

.1

2-

O

4.

W

R

P

Below the most commonly used types of welded attachments are shown. For other

typessee Code, Fig. UW-16.I.

125 B

O

the e

l

o

W

w

R

THREADED AND WELDED FITTINGS

T

F

I BGH USE R T L E HE M SOC OOO HW M UM WS TO E N S OT YLW Y EPE C O N N E C S T CI O FN SO UE. W I F D-~ G 1E T E6HO .Y. 1EP

N

O

T

A

T

I

a=~ t o ( = 1

O

) w .h

N i3i tc 7 sh , m 5e. r via , hel

- t i s 1 mm o /at ht loe 41 li r = the smallestof t, t. or 0.375in.

+

o

LE D D R ER

t

se

rl

se

e t

sn s et

n

,

.

f , . r

.

b= no minimumsizerequirement c = the smallest

d=t

t

h

o to 1 i i o cSh k1 pn

1 n ew cse i i 6s a

f r 2 . plf h n 0l e

,

.

e = the smallestof t o 3/4in. , i aos nn cn e , t = t h i o vc k we n l es ac s sos e lr ae r l f lolls ois w t =n o t mh i io fc n ki wan. tl el ct sa o sie r a nrl l fol gs ois wil aos nn cn e

T

S

w

N

s

d ehi e h

O ~EF

.

fzla

ti eem e nd i es r rn ehd qi u im e r e u me em n t s .

A PE C E

IAS

N N GG

E

.

THREADED AND WELDED FITTINGS T

F

I BGH U$E R T L H EE M SOC OOO HW M UM WS TO E N S OTYLW Y EPE LE D D S E C O N N E C S T CI O FN SO UE. I1WF D O- G E T 1TE O 6 Y .H . PE R ER S

SEENOTATIONON FACINGPAGE: GJ

a I

I

318in. min. t

t 7:

Dm

= o

ud — .

a it

o asp

m+i 3 exidi t e e .

pr/ -

n

f e

%+ s

d

4

3i i .

z

FITTINGS NOT EXCEEDING 3 IN. PIPE SIZE. In somecasestheweldsare exemptfromsizerequirements,or fittingsandboltingpads maybeattachedtothevesselsby filletwelddepositedfiomthe outsideonlywithcertain limitations(CodeUW-16 (f) (2) and (3)) such as: 1. The maximumvesselthickness:3/8 in. 2. Themaximumsizeofthe openingis limitedtothe outsidediameterof the attached pipe plus 3Ain. 3. Theweldthroatshall bethe greateroftheminimumnozzleneckthicknessrequired by the CodeUG-45(a)or that necessaryto satisfythe requirementsof UW 18for the applicableloadingsof UG 22. 4. Theweldingmayeffectthe threadsof couplings.It is advisabletokeep the threads aboveweldingwith a minimumY’in. or cut the threads after welding. 5. Strengthcalculationof attachmentsis not requiredfor attachmentsshownin Figs. A, C and E, and for openings: 3 in. pipe size fittingsattachedto vessel walls of 3/8 in. or less in thickness,2 in. pipe size fittings attached to vessel walls over 3/8 in. in thickness. (Code UG36(c)(3)).

ne

128

1 SUGGESTED MINIMUM EXTENSION OF OPENINGS

The tables give the approximate minimum outside projection of openings. When insulation or thick reinforcing pad are used it may be necessary to increase these

dimensions. OUTSIDEPROJECTION,INCHESUSINGWELDINGNECKFLANGE NOM. PRESSURERATINGOF FLANGELB PIPE 900 I 1500 2500 300 600 150 SIZE 2 3 4 6 8 10 12 14 16 18 20 24

6 6 6 8 8 8 8 8 8 10 10 10

6 6 8 8 8 8 8 10 10 10 10 10

6 8 8 8 10 10 10 10 10 12 12 12

8 8 8 10 10 12 12 14 14 14 14 14

8 8 8 10 12 14 16 16 16 18 18 20

8 10 12 14 16 20 22

OUTSIDEPROJECTION,INCHESUSINGSLIPONFLANGE PRESSURERATINGOF FLANGELB NOM. PIPE 1500 2500 900 600 300 150 SIZE 2 3 4 6 8 10 12 14 16 18 20 24

6 6 6 8 8 8 8 10

8 10 10

6 8 8 8 10 10 10 10

1

1

1

10 10 10

10 10

12 12 12

6 6 8 8 8

12

8 8 8 10 10 12 12 12 12 12 12 12

8 8 10 12 12 12 12

8 10 10 12 12 14 1

INSIDE EXTENSION a &

a P

c

c t ti

- S f d n -lc E e uM o i sue n tx hi t m te tnxu stf meir eon i ns n pi of e ooo rn tupt hc u e r t vh of aew t eu o rle o e d o o i p n t r u g hr

129

R D

F

I

O P

Single, welded openings not subject to rapid fluctuationin pressure do not require reinforcing if they are not larger than: 3 inch pipe size - in vessel wall 3/8 in. or less. 2 inch pipe size in vessel wall over 3/8 in. (Code UG-36 (c) (3). Largervesselopeningsthantheaboveshallbereinforced.Therules for reinforcementof openingsare takenfromthe Code,UG-26 throughUG-44,andareintendedtoapplyprimarilytoopeningsnot exceedingthefollowing: Forvessels60in.indiameterandless:%thevesseldiameter,butnot > to exceed20 in. Forvesselsover60in.indiameter:%thevesseldiameter,butnotto exceed40 in. Largeropeningshouldbegivenspecialattentionas describedin CodeAppendix1-7. Fig.A Hereisgivena briefoutlineofreinforcement designforbetterunderstanding oftheprocedure describedin thefollowingpages. Thebasicrequirementis thataroundtheopeningthevesselmustbereinforcedwithanequal amountofmetalwhichhasbeencutout for the opening.The reinforcementmaybe an integral part of the vessel and nozzle or may bean additionalreinforcingpad. (Fig. A.) This simple rule, however,needs further refinementsas follows: 1.

It is not necessaryto replacethe actuallyremovedamountof metal,but only the amount which is requiredto resist the internalpressure.@). This requiredthicknessof the vessel at the openingsis usually less than at other points of the shell or head.

2.

The plate actually used and nozzle neck usually are thicker than would be required accordingto calculation.The excessin the vesselwall (Al) and nozzlewall (AJ serveas reinforcements.Likewisethe insideextensionofthe opening(Aj) andthe areaof the weld metal (AJ) can also be taken into considerationas reinforcement.

3.

The reinforcementmust be within a certain limit.

4.

The areaof reinforcementmustbe proportionallyincreasedif its stressvalueis lowerthan that of the vessel wall.

.5.

The area requiredfor reinforcementmust be satisfiedfor all planesthroughthe center of opening and normalto vessel surface.

The required cross sectionalarea of the reinforcementshall then be: The required area for the sell or head to resist the internalpressure, (A).From this area subtractedthe excessareaswithinthe limit(Ai.4zAj AJ). If the sumof the areasavailable for reinforcement(AJ+A?+Aj +A,) is equalor greaterthan the area to be replaced, (A), the opening is adequately reinforced. Otherwise t difference must h be supplied by e reinforcingpad (AJ). Somemanufacturersfollowa simplepracticeusingreinforcingpadswith a cross-sectionalarea which is equal to the metal area actually removed for the opening.This practice results in oversizedreinforcement, butwiththeeliminationof calculationstheyfind it moreeconomical.

E

f

130 REINFORCEMENT FOR OPENINGS DESIGN

FOR INTERNAL

1

PRESSURE

(continue@j 1.

u

d

D

I-Q--l E ~

f

0.8D

,

NC!?@ r

AREA OF REINFORCEMENT

For vesselsunder internalpressurethe total cross-sectional area required for reinforcementof openingsshall not be — less than: A = d XI,, where d= the insidediameterof openingin its corrodedcondition, inches. t, = the requiredthicknessof shell or head computedby the applicableformulasusingE = 1.0whenthe openingis in solidplateor in a categoryBjoint. Whenopeningpasses throughanyotherweldedjoint, E= the efilciencyof that joint. When the opening is in a vessel which is radiographicallynot examined,E = 0.85 for type No. 1joint and E = 0.80 for type No. 2 joint. When the opening and its reinforcement are entirely withinthe sphericalportionof a flangedanddishedhead, t, is the thickness required by the applicable formulas usingAl= 1. Whentheopeningis ina cone,t, isthe thicknessrequired for a seamlesscone of diameter,D measuredwhere the nozzle axis intersectswith the wall of the cone. Whentheopeninganditsreinforcementare ina2: 1ellipsoidal head and are located entirelywithin a circle the centerof whichcoincideswiththe centerof the head and the diameter of which is equal to 0.8 times the head diameter,t,is the thicknessrequiredfor seamlesssphere of radius 0.9 times the diameterof the head. If the stress value of the opening’smaterial is less than that of the vesselmaterial,the required area A shall be increased.(See next page for examples.) 2. AVAILABLEAREASOF REINFORCEMENT i the vessel wall (t—t,)d or ’ Area of excessthicknessin ) (t–t,)(t,, + ~2

use the largervalue, square inches, If the stress value of the opening%material is less than that of the vessel material, area AI shall be decreased. (See next page for examples.) h,)5t or Areaof excessthicknessinthenozzlewall (’t,,— (L-t,,,) 5t,,use — the smaller value, square inches.

Area ofinside extension ofnozzle square inches (t,,-@2h.

ud

Area of welds,square inches. IfthesumofA, A2AJandA~is lessthanthe area forreinforcementrequired,A the differencemustbe suppliedby reinforcingpad.

f

131 . .

REINFORCEMENT FOR OPENINGS DESIGN FOR INTERNAL PRESSURE (continued) G

3. LIMITSOF REINFORCEMENT xx

Themetal usedas reinforcementmustbe located within the limits. R n k trn The limitmeasuredparallelto the vesselwall~= dor R. + t. + t, use larger value. t Y The limit measured parallel to the nozzle wall Y= 2.5 tor 2.5t., —, R 1, use smallervalue. troy When additional reinforcing pad is used, the limit, Yto be d measuredfromthe outsidesurfaceof the reinforcingpad. + Rn=insideradius of nozzle in corrodedcondition,inches. NOTATION: t= thicknessoftheves- For other notations,see the precedingpage. selwalllesscorrosion allowance, 4. STRENGTHOF REINFORCEMENT inches. If the strengthof materialsin AI Az Aj AJ and A5 or the t,= seepreceedingpage materialofthe reinforcingpad are lowerthanthat of the vessel 1.= nominalthickness material,their area consideredas reinforcementshall be proof nozzlewallirrespectiveofproduct portionately decreased and the required area, A in inverse formles~co~osion proportionincreased.Thestrengthofthe depositedweldmetal allowance,inches. shallbe consideredas equivalentto the weakermaterialof the tm= requiredthickness joint. Of;fy:;:sno=’e It is advisableto useforreinforcingpadmaterialidenticalwith the vesselmaterial. h= dist~nce riozzle projectsbeyondthe No credit shall be taken for additional strengthof reinforceinnersurfaceofthe ment havinghigher stress value than that of the vessel wall. vesselwalllesscorrosion allowance, EXAMPLES: inches. 1. a. The stress value of nozzle material: 15,000psi. c = corrosion allowThe stress value of shell material: 17,500 psi. ance,inches.

d= seeprecedingpage.

H

fn(f-1, )

r

f“ Im TF \

I

-------

P t. x t,

Itr

I

Ratio 15,000/17,5000 = 0.857 To the required area, A shalI be added: + 2tMX (1Q 0.857)

b. From the area AI shall be subtracted: (1— 0.857) —2t. 2. Usingidenticalmaterialforthevessel andreinforcingpad, the requiredarea for reinforcementis 12 square inches. If the stress value of vessel material= 17,500psi., the stress value of the nozzle material= 15,000psi., ratio 17,500/15,000= 1,167 Inthisproportionshallbe increasedtheareaofreinforcing pad: 12x 1.167= 14.00square inches.

,

132

REINFORCEMENT FOR OPENINGS DESIGN FOR INTERNAL PRESSURE (continued

DESIGN FOR EXTERNAL PRESSURE. The reinforcement required for openings in single-walled vessels subject to external pressure need be only 50 percent ofthat required for internal pressure where t,isthewall

thicknessrequiredbytherulesforvesselsunderextemalpressure.CodeUG-37(d) (l). REINFORCEMENTOF OPENINGSFOR EXTERNALPRESSURE. The cross-sectionalarea (A)of reinforcementrequiredfor openingsin vesselssubject to externalpressure: /4=

dxt ~

where ii= Diameter in the givenplane of the openingin its corrodedcondition,inches. 1,= The wall thicknessrequired for externalpressure,inches. F = Factor for computation of the required reinforcement area on different planes (as the pressure-stress varies) when the opening is in cylindrical shell or cone and integrally reinforced. For all other configurations the value of F = 1

—

1-JJ

REINFORCEMENT OF OPENINGS EXAMPLES EXAMPLE 1. t“ tr

Rn ~ I

tr

I I “

T * + h

w

P? d

DESIGNDATA: Insidediameterof shell: 48 in. Designpressure:250 psi at 200°F. ShellMaterial: SA-285-C n S 13,800 psi = t= 0.265 in. , The vessel is spot radiographed t No allowancefor corrosion Nozzle material:SA-53-B S=15,000 psi. tn=0.432 in. Nozzle nom. size: 6 in. Extensionof nozzle insidethe vessel: 1.5 in. h = 2.5t~= 2.5 x 0.432 = 1.08in. The nozzle does not pass through seams. Fillet weld size: 0.375 in.

Wall thicknessrequired: for shell,t ‘SE

—.

for nozzle, tm=~*p

6P =

250 X24 = 0.440 in. 13,800X 1.0-0.6X 250 X 2.88 = = 0.048 in. 15,000X 1.0-0.6X 250

AREAOF REINFORCEMENTREQUIRED A,= dt, = 5.761 x 0.440=

2.535 sq. k.

AREA OF REINFORCEMENT AVAILABLE A,= (Excess in shell.) Larger of following:

(t–tr)d = (0.625-0.440) x 5.761 or (t-t,) (...+ ~ 2 = (0.625-0.440)x (0.432+ 0.625)x2=

1.066Sq.in. 0.391 sq. in.

Az = (Excessin nozzle neck.) Smallerof following: (tn–tm)5t = (0.432—0.048)x 5 x 0.625 = 1.200 s i (tn–tm)5tn= (0.432-0.048) X5 X0.432 = (No credit for additionalstrengthof nozzlematerialhaving higherstress valuethan that of the vesselwall.)

q

n

0.829 sq. in.

Aj = (Insideprojection.)t. x 2h = 0.432 x 2 x 1.08= 0.933 sq. in. A,= (Area of fillet weld) 0.3752

0.140 Sq.in.

Aj = (Areaof fillet weld inside)0.3752

0.140 Sq.in.

TOTALAREAAVAILABLE Sincethis area is greaterthan the area required for reinforcement,additionalreinforcementis not needed.

3.108 sq. in.

.

.

134

REINFORCEMENT OF OPENINGS EXAMPLES EXAMPLE 2.

DESIGN DATA: Inside radius of shell: R =24 in.

t“ tr I ~

tr

J

Designpressure:P = 300 psi at 200° F. Shellmaterial: t= 0.500 in. SA-516-70plate, n S = 17,500psi The vessel is spot examined There is no allowancefor corrosion Nozzle nominal size: 6 in. Nozzle material: SA-53 B S = 15,000 psi. t.= 0.432 in.

T

Extensionof nozzle insidethe vessel: 1.5 in. Fillet weld size inside:0.500 in.;

! h

Fillet weld size outside: 0.625 in. Ratio of stress values: 15,000/17,500= 0.857

Wall thickness required: Shell, t,=

‘R

Nozzle, t,.=

sap

SE - 0.6P

=

300 X 24 = 0.416 in. 17,500X 1-0.6X300 300 X 2.88 = = 0.058 in. 15,000X 1.0-0.6 X 300

-. Since the strength of the nozzle material is lower than that of the vessel material, the required area for reinforcement shall be proportionally increased and the areas available for reinforcement proportionally reduced. AREA OF REINFORCEMENT REQUIRED 2.397 sq. in. ~ = dt, = 5.761 X 0.416=

Area increased:+2tnxt,(1-15,000/17,500) = 2 x 0.432x 0.416 (1-0,857)= 0.051 sq. in. 2.448 sa. in. AREAOF REINFORCEMENT AVAILABLE Al = (Excess in shell.)Largerof the following: (1- t,)d= (0.500- 0.416)x 5.761= 0.484 s i o q n . (t-t,) (t.+ t,)2=(0.500-0.416) x (0.432 + 0.500)x 2 ‘O.156sq. in. (1-0.857)= Area reduced:-2 x t.(t-t,) -2 x 0.432x (0.500-0.416)(1-0.857)= -0.010 sq. in. 0.474 sq. in. A2=(Excess in nozzleneck.) Smallerof following: (t.- t,n)5t= (0.432-0.058)5X 0.500= 0.935 (t.- t,n)5tn= (0.432-0.058)5 X 0.432= 0.808 Area reduced: 0.857 x 0.808 = 0.692 sq. in. Since the strength of the nozzle is lower than that of the shell, a decreased area shall be taken into consideration. 15,000/17,500 = 0.857, 0.857 X 0.808 = ,43= (Insideprojection.)tnx 2A= 0.432 x 2 x 1.08‘0.933 Area decreased0.933 x 0.857 =

AJ‘(Area of fillet weld)2 x 0.5 x .6252x 0.857= ~j ‘(Area of fillet weld inside)2 x 0.5 x .5002x 0.857 = TOTALAREAAVAILABLE Additionalreinforcementnot required.

0.692 sq. in. 0.800 sq. in.

0.334 sq. in. 0.214 sa. in. 2.514 SCI.in.

.

135 REINFORCEMENT OF OPENINGS EXAMPLES EXAMPLE 3.

t“ trn

tr t r # h

+ t

d u

DESIGNDATA: Insidediameterof shell:48 in. Designpressure:300 psi at 200° F. Shellmaterial:0.500 in. SA-516-60plate, The vesselfidlyradiographed,E = 1 There is no allowancefor corrosion Nozzlenominalsize: 8 in. Nozzie material:SA-53B, 0,500 in. wall Extensionof nozzle insidethe vessel: 0.5 in. The nozzledoes not pass throughthe main seams. of fiilet welds 0.375 in. (Reinforcement pad to nozde neck.)

Wall thicknessrequired: Shell t,=

‘R SE– O.6P =

Nozzle, t,. =

SAP —.

300 X 24 = 0.486 in. 15,000X 1-0.6X300 300 X3.8125 = 0.077 in. = 15,000X ].0–0.6 X300

AREAOF RE~FORCEMENT REQUIRED A = dx [,= 7.625 X 0.486=

3.706 sq. in.

AREAOF REINFORCEMENT AVAILABLE AI = (Excess in shell.)Largerof the following: 0.106 sq. in. (t -t, )d= (0.500 - 0.486) 7.625= or (t - [, ) (t. + t) 2 = (0.500-0,486)(0.500+ 0.500)2 ‘0.028 sq. in. Az =(Excess in nozzle neck.) Smallerof following: @-t,.)5t = (0.500-o.077)5x 0.5 = 1.058or 1.058sq. in. (tn–tr.)5t. = (0.500-0.077)5X0.5= 1.058 0.500 sq. in. A3= (Insideprojection.)L x 2h = 0,500 x 2 x 0.5 = 0.141 sa. in. AJ ‘ o f w 0 (The area of pad to shell weld disregarded) 1.805 SQ.in. TOTALAREAAVAILABLE Thisareais lessthantherequiredarea,thereforethedifferenceshallbe provided byreinforcingelement. itmaybeheaviernozzlenec~ kirgerextensiono fthenozzle insideofthevesselor reinforcingpad.Usingreinforcingpad,therequiredareaof pad:3.706–1.805=1.901sq,in. UsingO.375in.SA-516-60plateforreinforcing padthe widthofthe pad 1.901/0.375=5.069in. Theoutsidediameterof reinforcingpad: Outsidediameterof pipe: 8.625 widthof reinforcingpad: 5.069 13.694in.

136 STRENGTH OF ATTACHMENTS JOINING OPENINGS TO VESSEL At the attachments, joining openings to the vessel, failure may occur through the welds or nozzle neck in the combinations shown in figures A and B.

a b

The strength of the welds and the nozzle neck in those combinations shall be at least equal to the smaller of:

P c P

1.

2 T

1. Thestrength intensionofthecross-sectionalareaofthe

considered,or o p s o sfa i a bt i l elementof lhe u s reinforcementbeing r f e h

r a o

un g

The allowablestressvalueof the weldsis the stressvalue of the weakermaterialconnectedby the weldsmultiplied by the followingfactors:

a i &

2. hdThe strengthin tensionofareaxf (A = ~ f less the .@ @ ) strengthin tensionofthe excessinthe vesselwall @j.

e b c

Groove-weldtension Groove-weldshear Fillet-weldshear

0.74 0.60 0.49

Possible pathsoffailure The allowablestressvalueof nozzleneck in shear is 0.70 times the allowablestressvalue of nozzle material. 1. Through@and@ 2. Through@@ and@ The strengthof thejoints shallbe consideredfor its entire d @ 3. T h r a o u ng h @ lengthon each side of the plane of reinforcementarea. EXAMPLE3 A = 2.397 sq. in. AI = 0.484 sq. in. b d.= 6.625 in., outside diameterof nozzle ;“% a dttr=6.193 in., mean diameterof nozzle 8 S = 17,500psi allowablestressvalue of vesselmaterial S.= 15,000psi allowablestressvalue of nozzle material Ft A G= 0.432 in. wall thicknessof nozzle. dm c ‘* t = 0.500 in. wall thicknessof vessel 0.375 in. fillet weld leg. ~heckthe strengthof attachmentof nozzle load to be carriedby welds. Loadto be carriedby welds (A-AI)S = 2.397-0.484 x 17,500= 33,478 lb. STRESSVALUEOF WELDS: 0.49 x 17500= 8575 psi. Fillet-weldshear 0.74 x 17500= 12950psi. Groove-weldtension 0.70 x 15000= 10500psi. Stressvalueof nozzlewall shear STRENGTHOF WELDSANDNOZZLENECK: ~ xweldIegx8575= 10.4065xO.375x8575 =33463lb. a. Fillet-weld shear ~, Xt. X10500=9.72x0,432X10500 = 44090lb. b.Nozzle-wall shear c Gr~ove.weldtensi~n~. xweidleg x 12950-10.4065X().50()X” 12950=67382lb. POSSIBLE PATHOFFAILURES: 33463+44090= 77553lb. 1.Througha.andb. 2.Througha.andc. 33463+ 67382=100845lb. Both pathsarestrongerthantherequiredstrength33478lb.

,

127/

STRENGTH OF ATTACHMENTS JOINING OPENINGS TO VESSEL

EXAMPLE4 DESIGNDATA A= 3.172sq.in.,A,=0.641sq.in.,A.F0.907sq. in. = 1

2i o . u d 8 t i n 4osa r mei5 i edn p. tf e oe r rac

i

n f gd

8.625in.outsidediameterof nozzle.

C L

h s the

t e of r a ce t

T OB

C

A

RB

8 i .m d 1 i e noa2 n m ao 5e z t . nze rl e f . S = 1 7p a , l l 5s o s v0w t ao0r vab leim e le as s ut s s e e re S 1 5p a . , l l 0s o s v0w t = ao0r nab leiomle sa z ut s z e e rl t =0 i .t h 5i o vc n 0k w e n 0es a s . s s l e f l l . t =0 i . t h 5i o cn n 0k w o.n 0ez a s . zs l l f l e . 0 i .l o f 3 - w i n 7e a l 5e l . eg l f t d 0 i .l o f 2 - w i n 5e d l 0e l . eg l f t d i . t h 2i o rc n e5k i nn p0ef os . r s ac i n f gd t, = 0 nt ka go cn t h ohm ez n z t l e f . W D R

I EO E EL D

D

SY

:

(A–A,)S = (3.172—0.641) 17,500= LOADTO BE CARRIEDBY WELDSa, c, e: (A2+21“OS= (0.907 + 2 x 0.500x 0.500) 15,000= STRESSVALUEOF WELDS: Fillet - weld shear Groove- weldtension

44,293 lb. 21,105 lb.

0.49 x 17,500= 8,575psi 0.74 x 17,500= 12,950psi

STRESSVALUEOF NOZZLEWALLSHEAR: 0.70 x 15,000= 10,500psi STRENGTHOF WEL~S ANDNOZZLENECK: a. Filletweldshear ~ x weldlegx 8,575= 13.55X0.375X8,575= 43,572lb. b. Nozzlewallshem ~ x tnX10,5OO = 12.76X0.500X 10,500‘66,990 lb. c. Grooveweldte~ion @ x weldlegx12,950= 13.55X0.500x 12,950=87,7361b. d. Filetweldshear Z#2Xweld1egx 8,575= 20.18X0.25X8,575= 43,260lb. e. Grooveweldtension ~ weldlegx 12,950-13.55 x 0.25x 12,950=43,868lb. POSSIBLEPATHOFFAILURE: 1. Throughb andd 66,990+ 43,260 = 110,250lb. 2. ThOU@c andd 87,736+ 43,260 = 130,996lb. 43,572 + 87,736+ 43,868= 175,176lb. 3. Througha, c ande Paths 1.and2. arestrongerthanthetotalstrengthof 44,293lb. Path3. is strongerthanthe strengthof 21,105lb. wi d sl et l 43,260 r ee llb. nis tgreater g d than t hthe reinforcing pad strength of The outerf (dP-do) t. X 17,500= 1.055x 17,500= 18,463lb.

12R .

LENGTH

OF COUPLINGS

AND PIPE FOR OPENINGS

139 LENGTH OF COUPLING

AND P

FOR OPENINGS

140

N

N

T

THE REQUIRED THICKNESS UNDER INTERNAL

FOR NOZZLE NECKS IN VESSELS PRESSURE (Code UG-45)

1 T

a

t

c

f

t

l

i U

p

c

but for other than access and inspection openings, not less than the smaller of the following: 2. The thickness required for the vessel for internal pressure (assuming joint efficiency, E = 1.0), but in no case less than the minimum for shells and heads specified in UG-16 (b); 3. The minimum thickness of standard wall pipe plus corrosion allowance. THE REQUIRED THICKNESS FOR ACCESS AND INSPECTION OPENINGS (manways, handholes) IN VESSELS UNDER INTERNAL OR EXTERNAL PRESSURE. 1. The thickness computed for the applicable load plus corrosion allowance (there is no other requirement). For selection of required pipe under internal pressure, see table “Maximum Allowable Internal Working Pressure for Pipes” on the following pages. EXAMPLES for using the table: 1. Opening Diam: 18” Design Pressure: 800 psig. Corrosion Allowance: 0.125” The Required Pipe for Manway: The Required Pipe for Nozzle:

Sch. 60, Sch. 60,

0.750” Wall 0.750” Wall

2. Opening Diam: 18” Design Pressure: 150 psig. Corrosion Allowance: 0.125” The Vessel Wall Thickness: 0.3 125” The Required Pipe for Manway: The Required Pipe for Nozzle:

Sch. 10, Std. Wt.

0.250” Wall 0.375” Wall

3. Opening Diam: 18” Design Pressure: 140 psig. Corrosion Allowance: 0.125” Vessel Wall Thickness: 0.750” Sch. 10, 0.250” Wall The Required Pipe for Manway: The Required Pipe for Nozzle: Std. Wt. 0.328” + 0.125” Corr. Allow. = 0.453, Min. Wall= Sch. 40 Pipe

h

141

THE REQUIRED NOZZLE NECK THICKNESS FOR VESSELS UNDER EXTERNALPRESSURE(Code UG-45) 1. Thethicknessforthe applicableload t

s

m o t ah f l o

ll l heoe wr

less t i

n f eg

h

:

2. The thicknessof head or shell required for internalp r ue s t s sexternal u i r hen designpressureas an equivalentinternalpressure,but k no case less than the minimumthicknessspecifiedfor material in UG-16(b)(1/16 in. for shells and heads,3/32in.incompressedair,steamandwaterservice,%in.forunfiredsteam boilers),plus corrosionallowance; 3. The minimumthicknessof standardwall pipe plus corrosionallowance. EXAMPLE1. Externaldesignpressure:P = 35 psi. MaterialSA 516-60; S= 15,000 Outsidediameterof cylindricalshell: Do= 96 in. Shellthickness:t = 1 in. The requiredticknessfor 14 O.D., 12 in. long nozzleneck: 1. To withstand25 psi externalpressureapproximately0.05 in. wallrequired,but the thicknessshall not be less than the smallerof; 2. Thethicknessrequiredforthe shellunder35 psi internalpressure(as equivalent externalpressure) = 35x 47 = O~lo in PR ‘= SE - 0.6P 15,000- n “ 3. The minimumthicknessof standard wall pipe: 0.328 in. (0.375 in. nom.) The smallerof 2. and 3.0.110 in. for wall thicknessof nozzleneck is satisfactory. EXAMPLE2. Externaldesignpressure: P = 15 psi. Material SA 516-60; S= 15,000 Outside diameter of cylindrical shell, Do = 36 in. Shell thickness: t= 0.3125 in.

The requiredthicknessfor a 14 in. D.O., 12 in. long nozzleneck: 1. To withstand15psi externalpressureapproximately0.02 in. wallrequired,but the thicknessshallnot be less than the smallerof the following: 2. The thicknessrequiredfor the shell under 15psi. internalpressure PR = 15x 17.6875 = o 0~8 in 15,000-9 “ “ t =SE - 0.6P 3. The minimumthicknessof standardwall pipe: 0.328 in. (0.375 in. nom.) The smallerof 2. and 3. is 0.018 in.,but the thicknessof the nozzleneck shall in no case be lessthan 0.0625 in. UG-45 (a) (2).

142

M W

I

A P

F

The CalculationsBasedon the Formula: P=

23Et D+ 1.2t

P , where

P = The max.allowableworkingpressure,psig. S = 15,000psig.the stressvalueof the most commonlyusedmaterialsfor pipe (A53B,A106B)at temperature-20 to 650°F. For highertemperature see notes at the end of the tables. E= 1.0joint efficiencyof seamlesspipe D = Insidediameterof pipe, in. t = Minimumpipe wall thickness,in. (.875 times the nominal thickness). The figuresunderlinedare the maximumallowablepressurein corrodedcondition for the pipe of which wall thicknessis minimumthe standard wall plus corrosion allowance. NOM. DESIG‘IPE NATION UZE

PIPE WALL THICKNESS NOM. ~ MIN.

CORROSIONALLOWANCE IN.

T=E 3/4

I 1

xX-STG. 0.294 STD. 0.113 X-STG. 0.154 SCH.160 0.218 XX-STG. 0.308 STD. I 0.133 X-STG. 0.179 SCH.160 0.250 XX-STG. 0.358 STD. 0.140

X

1-1/4

1-1/2

2

I

0.191 0.250 0.382 0.145

SCH.160 XX-STG. STD. X-STG. 0.200 SCH.160 0.281 XX-STG. 0.400 STD. 0.154 X-STG. 0.218 SCH.160 0.343 XX-STG. I 0.436

0.095 0.129 0.164 ~‘;:”:g 5392 I 2658 0.257 12153 I 8526 0.099 1072 I I I 288 0.135 4299 2192 100 1985 0.191 6386 4069 2515 0.270 9712 7041 %7 0.116 2847 1261 744 I 0.154 3959 2287 732 0.219 5764 3946 2274 0.313 8820 7423 4842 — .3099 0.123 2362 1126 0.167 3282 1988 774 0.219 4424 I 3059 ! 1779 ] 578 ! 2848 0.334 7194 G 31 0.127 2118 1046 806 0.175 2982 1864 947 0.246 4333 3139 2013 0.350 6481 I 5164 3924 2754 126 0.135 1786 938 852 44 1696 0.191 G 0.300 4215 I 3260 I 2348 1477 2629 0.382 5537 X2 G —

I

I

1’4 252

580

I

I 1494

I 1582 I

I

1648

642 1744

I

143 MAXIMUMALLOWABLE WORKINGPRESSURE(cent) NOM. PIPE SIZE

DESIGNATION STD.

2%

3 . 3

4

5

6

X-STG. SCH-160 XX-STG. STD. X-STG. SCH. 160 XX-STG. STD. X-STG. XX-STG. STD. X-STG. SCH.120 SCH.160 XX-STG. STD. X-STG. SCH.120 SCH.160 XX-STG. STD. X-STG. SCH.120 SCH.160 XX-STG. SCH.20 SCH.30

PIPEWALL THICKNESS NOM. MIN. 0.203 0.276 0.242 I 0.375 0.328 0.552 0.483 0.216 0.189 0.263 0.300 0.438 0.383 0.600 0.525 0.226 0.318 0.636 0.237 0.337 0.438 0.531 0.674 0.258 0.375 0.500 0.625 0.75C 0.280 0.432 0.562 0.71$ o.86f 0.25( 0.27t

CORROSIONALLOWANCE IN. 3/16 o I 1/16 I 1/8 I 1/4 Max.Allow.PressurePsig. 561 1245 577 2707 1971 1261 I 831 1525 2245 2991 3766 2599 3359 — — 5822 4969 Z

l

~ 2398 3597 5113

0.198 1546 0.278 G 0.557 4701 0.208 ~ 0.295 2075 0.383 2739 0.465 I 3379

I

12 556 1116 658 1801 1221 1754 2964 2350 — 3134 4432 3773 78 555 1044 691 1689 1183 2992 3546 4115 — — 137 561 995 730 1616 1168 1802 1350 2= —— I 2890 1- 2412 I 1946

280 908 1490 2412

552 1127

773

425

1767

1401

1042

2X

2044

1673

4394

3880

3379

0.226 0.328

1259 G

902

0.438

2520

1488 2140

0.547

3201

2808

0

.3 .1

0

211 1937

2890 208

0.590

6 39 2 81

111 1175 — 2515

30 5 3 40 6 2 1 96 2 7 0 9 5 6 4 5 45 4 2 3 5

0.378 1793 0.492 2368 0.628 3077 0.756 3767 0.219 777 0.242 861

1485 G 2748 3427 552 634

1181 G 2425 3093 329 411

882 1431 =6 2764 113 190

58~ 112[ F 2440

8 X-STG. SCH.1OO SCH.120

0.500

0.438

1587

1353

1121

892

665

0.593 0.718

0.519 0.628

1896 2319

1658 2075

E 1835

1189

959

=

u

144 MAXIMUM ALLOWABLE WORKINGPRESSURE(con~ NOM. PIPE

S 8

10

12

1

DESIGNATION SCH.140 SCH.160 XX-STG. SCH.20 SCH.30 STD. X-STG. SCH.80 SCH.100 SCH.120 SCH.140 SCH.160 SCH.20 SCH.30 STD. SCH.40 X-STG. SCH.60 SCH.80 SCH.100 SCH.120 SCH.140 SCH.160 SCH.10 SCH.20 STD. SCH.40 X-STG. SCH.60 SCH.80 SCH.100 SCH.120 SCH.140

PIPEWALL THICKNESS NOM. MIN. 0.812 0.711 0.906 0.793 0.875 0.766 0.250 0.219 0307 0.269 0.365 ~0.319 0.500 0.438 0.593 0.519 0.718 0.628 0.843 0.738 1.000 0.875 1.125 0.984 0.250 0.219 0.330 0.289 0.375 0.328 0.406 0.355 0.500 0.438 0.562 0.492 0.687 0.601 0.843 0.738 1.000 0.875 1.125 0.984 1.312 1.148 0.250 z 0.312 0.273 0.375 0.328 0.438 0.383 0.500 4 o.43t 0.593 0.51$ 0.75G 0.65{ 0.937 0.82( 1.093 0.95( 1.250 1.094

I

CORROSIONALLOWANCE IN o I 1/16 I 1/8 I 3/16 i“”;/4 Max.Allow.PressurePsig. 2647 2400 2155 1913 1675 2977 2725 2476 2231 1988 2868 2617 2370 2126 1885 90 264 441 621 228 50 406 585 766 370 193 549 729 ~ 712 532 1263 l= 894 948 ~ 1506 1318 1132 1838 1647 1458 1270 1085 2179 1984 1792 1601 1413 2611 2413 2216 1986 1829 2963 2760 2560 2362 2166 371 222 76 522 540 389 692 91 240 635 483 ~7 333 184 701 549 248 854 398 904 751 486 1059 598 1194 1038 ~ 730 578 ~ 1469 1311 1154 ~ 1820 1659 1500 1341 1184 10 81 54 1530 2178 2 1690 23 10 31 1810 2467 2 1972 2s72 2910 2 2 2 69 202 475 338 49 184 319 456 594 167 303 440 716 577 287 423 561 839 699 407 544 682 962 ~ 585 pJ 863 1146 004 ~ 1173 1031 1460 316 1550 1406 1262 1843 696 2166 2017 1869 1722 1576 2500 2348 2198 2048 1900

145 MAXIMUM ALLOWABLEWORKINGPRESSURE(cont.) NOM. DESIGPIPE NATION SIZE 14 SCH.160 SCH.10 SCH.20 SCH.30. STD. SCH.40X-STG. SCH.60 16 SCH.80 SCH.100 SCH.120 SCH.140 SCH.160 SCH.10 SCH.20 STD. SCH.30 X-STG. SCH.40 18 SCH.60 SCH.80 SCH.100 SCH.120 SCH.140 SCH.160 SCH.10 SCH.20 STD. SCH.30 X-STC SCH.40 SCH.60 20 SCH.80 SCH.100 SCH.120 SCH.140 ISCH.160

PLPEWALL o THICI iESS gOM. MIN. 1.406 1.230 2834 0.250 0.219 m 518 0.312 0.273 625 0.375 0.328 & 0.500 0.438 0.656 0.574 1108 0.843 0.738 1436 1.031 0.902 1771 1.218 1.066 2111 1.438 1.258 2517 1.593 1.394 2809 368 0.250 G 460 0.312 0.273 554 0.375 0.328 649 0.438 0.383 744 0.500 0.438 838 0.562 0.492 0.750 0.656 1129 0.937 0.820 1418 1.156 1.012 1766 1.375 1.203 2118 1.562 1.367 2425 1.781 1.558 2789 T B m 4~ 0.375 0.328 0.500 0.438 668 0.593 0.519 795 0.812 0.711 1097 1.031 0.902 1403 1.281 1.121 1760 1.500 1.313 2078 1.750 1.531 2446 1.968 1.722 2774

ROSIONALLOWANCE IN. 1/4 1/8 3/16 1/16 [ax.All :P s i x E ~ 5 166 43 6 1 398 279 146 6 2 504 384 355 7 4 717 596 617 3 7 C4 861 937 0 1310 1185 1 1263 3 8 1643 1515 1 1595 7 2 1980 1851 1 1990 1 2 2384 2251 2 2275 4 0 2674 2540 2 5 262 157 38 4 1 354 248 130 3 2 447 341 222 2 3 541 434 315 2 4 636 529 407 1 5 729 621 689 7 1015 ~6 974 0 8 1306 1195 1 4 2 1314 1652 1539 1 18 78 77 1658 2002 1 21 09 70 2308 2 1958 2314 25 45 30 2669 2 4 m x 2 3 0 117 1 402 3 7 4 7 284 ~ 5 0 6 0 407 697 ~ 8 0 900 998 1004 1 1 0 1303 1202 1353 1 4 5 1657 1555 1665 1 7 6 1974 1870 2025 2 1 2 2340 2234 2346 2 4 5 2666 2558

146 MAXIMUM ALLOWABLE WORKINGPRESSURE(cont.) NOM. PIPE SIZE

22

24

PIPEWALL THICI JESS MIN. N 0.250 0.219 0.312 0.273 0.375 0.328 0.437 0.382 0.500 0.438 0.562 0.492 0.625 0.547 0.688 0.602 0.750 0.656 SCH.10 0.250 0.219 SCH.20 STD. 0.375 0.328 X-STG. 0.500 0.438 SCH.30 0.562 0.492 SCH.40 0.687 0.601 SCH.60 0.968 0.847 SCH.80 1.218 1.066 SCH.100 1,531 1.340 SCH.120 1.812 1.586 SCH.140 2.062 1.804 SCH.160 2.343 2.050 DESIG NATION

0.250 0.312 0.375 0.437

26

0.500 0.562 0.625 0.688 0.750 0.312

30

0.375 0.500

376 452 G 606 681 761 839 916 275 414 z 625 766 1089 1381 1753 2093 2399 2750

0.219 0.273 0.328 0.382 0.438 0.492 0.547 0.602 0.656

2

0.273 0.328 0.438

275 330 443

3 3 4 5 5 6 7 7

214 289 365 440 519 G 672 750 827 196 334 475 5Z 685 1006 1297 1667 2006 2311 2660 181 244 308 372 438 502 567 633 697 211 267 379

I

T

128 116 202 31 192 278 106 267 136 353 344 431 258 419 332 507 409 496 584 486 G 661 z 649 738 40 117 97 176 255 236 315 395 304 464 384 443 524 6X G 842 924 1214 1131 1048 1582 1498 1413 1919 1833 1747 2223 2135 2048 2571 2482 2393 37 4 5 108 98 7 26 1 171 162 2 90 8 235 225 6 152 4 298 291 2 218 1 364 354 6 281 7 428 419 1 345 4 493 F4 7 410 0 558 548 2 474 7 622 148 204 315

85 141 252

23 78 188

147 NOTE: IF THESTRESSVALUEOF PIPELESSTHAN15,000PSIG. DUETO HIGHERTEMPERATURE,MULTIPLYTHEMAX. ALLOWABLE PRESSUREGIVENIN THETABLESBYTHE FACTORSIN THISTABLE: TEMPERATURENOTEXCEEDINGDEGREEOF 900 950 750 850 1000 650 700 800 – – A 53 B Stress 15000 14350 12950 10800 8650 6500 6500 4500 2500 12950 : 15000 s ’ 14350 + : s 10800 8650 A 106B ‘ 1.000 0.9566 0.8633 0.7200 0.5766 0.4333 0.3000 0.1666 FACTOR Example:

The MaximumAllowancePressurefor 6“ x Stg.PipeWitha Corrosion Allowanceof 1/8” From Table= 1181psi.- at Temperature800°F The Max.Allow.Press.1181x 0.72= 850 psig. Example to find max. allow. pressure for any stress values:

The Max.Allow.Press.1181Psig.From Tables The StressValue 13000psi. For ThisPipeThe Max.Allow.Pressure ~Wo

x 1181 = 1023psi.

w

NOZZLEEN~CMKpTT~CKNESS

I

I

C

O

R

R

O

S

I

O

o

N

0.250$ 0.018

0.3125

J.E. 0.85 0.250

0.250

0.3125

J.E. 1.00 0.213

0.213

0.2660

NOM.

0.280

0.280

0.280

MIN.

0.245

0.245

0.245

1 Requiredfor Loadings(UG-22) 2 Vessel Wall

3 6 in. Std. Pipe

Minimumf 4 I C F *

o

U m

S

&h H

m

pA rS e

nS

f o B ti

Ti

oe Ue l

( Ga l

r

s-d

b1s

st i W s een Sd ara e U mtr , ( vG &e o rUe i e r( lGad

e

-m r

r n e i ht a mh u i ufei cn mr k onen

0

i

bs1 deoz s e zs

0 6

. 0 ) 0 . 06 0 . 2 6 0 5 2

0- rc

b. e1 0

0 . 6 090

06

.)0

2 . 05 2 . 0 5 2 0 0 0 .C 0 kI 0 . 3 1

l cr

e

) .93

30 8

8

148

R

W I

U

T

F

P

P

The required wall thickness for pipes, tabulated on the following pages, has been computed with the following formula: PR ‘= SE– O.6P

, where

t = the required minimum wall thickness of pipe, in. P = internal pressure, psig.

S = 15,000psig.t

s

vt

ohr at

me l c s oe ouh sm u m e sm o f asen tfor t l epipe. yer

A 53 B and A 106 B @temperature –20 to 650°F. E = Joint efficiency of seamless pipe R = inside radius of the pipe, in. For the inside diameter of the pipe round figures are shown. With interpolation the required thickness can be determined with satisfactory accuracy. The thicknesses given in the tables do not include aIlowance for corrosion. For the determination of the required pipe wall thickness in piping systems the various piping codes shall be applied. Selecting pipe,the 12.5% tolerance in wall thickness shall be taken into consideration. The”minimum thickness of the pipe wall equals the nominal thickness times .875.

i

a dl

149 REQUIRED PIPE WALL THICKNESS FOR INTERNAL PRESSURE

1.s. 11AM, 50

PRESSURE PSIG. 100

150

200

250

300

350

400

450

500

0.0

00.0 00.0

020. 030.

30.0 710.0

0500. 0010.

07.0 103.0

8010. 7020.

10. 20.

021. 042.

0.

0.0

00.0

1050.

0520.

0.

0.0

00.0

1070.

5030. 400.

30. 40.

054. 085.

5

0

0,

0.0

00.0

1080.

720.0

0020. 0530.

20.0 307.0

0

0

010.0 320.0

404.0

2050.

501.

096.

0

6

0

0.

0.0

7

0

0.

0.0

01.0 01.0

200. 2020.

030.0 30.0

040. 0540.

500.0 507.0

1060. 9070.

701. 810.

018. 139.

8

0

0.

0.0

01.0

2030.

9

0

0.

0.0

604.0 700.0

0780. 1690.

910. 010.

150. 162.

0

0.

0.0

3050. 3070.

050. 0560.

1

01.0 01.00

740.0 040.0 350.0

060.

817.0

1400.

10.

183.

1

0

0.

0.0

130.

0.0

080,

11.0

120.

310. 410.

104.

0.

750.0 0600

914.0

0

3080. 400.

0570.

1

01.01 02.02

1

0

0.

0.0

130.

0,

0.0

4600 700

17.0

0

402. 403.

580.

1

02.03 02.04

090.

14.0

140.

5120. 6120.

147. 269.

1

0

0.

0.0

. 02 5

0 55

00 .

50.

1.0

150.

720.

270.

1

0

0.

0.0

02. 6

507

0

0.

0.0

02. 7

s08

00. 60.

1.0 1.o

160.

1

480 780

. 270

1 1

0 0

0. 0.

0.0 0.0

03. 8 03. 9

60 602

090 490

10. 6.

1.0 10

280. 90.

820. ~ 020. 3 120.

2

0

0.

0.0

03. 0

613

700

1.

20

2

0

0.

0.0

03. 1

715

7.

2

0

0.

0.0

03. 2

71

00 410

2

0

0.

2

0

0.

0.0 0.0

03. 3 04. 4

718 810

2

0

0.

0.0

04. 5

2

0

0.

0.0

2

0

0.

2

0

2 3

1

0

0.

0.0

2

0

0.

3

0

4

7

126.

291. 21. ( 234.

20.

25.

00.

20.

37.

20

10.

230.

38.

1.

20

20.

230.

39.

710 020

6.

20

30.

3.0

31,

1.

20

40.

30,

32.

812

420

6.

20

50.

3.0

33.

04. 6

814

1.

20

60.

3.0

3S.

04. 7 04. 8

951 971

6.

20

70.

3.0

46.

0.

0.0 0.0

730 030

1.

20

80.

3.0

47.

0

0.

0.0

04. 9

981

40 740

6.

20

9.

340

9.

0

0.

0.0

15. 0

01

050

1.

30

0,

40

0.

0

03

0

150 REQUIREDPIPEWALLTHICKNESS FORINTERNALPRESSURE(cent) PRESSUREPSIG.

1 IAM.

600

650

700

750

800

1

D

).

0.

01

920

0.

0.0

20.0.031 620

82

9

2

0

.3

0.

30

740

1.0

0.0

50.0.062 250

5

9

3

0

.D

0.

50

60

2.0

00.

70.0.093 708

83

8

4

0

.3

0.

70

580

2.0

1.0

01.0.124 31

01

7

5

0

.0

00.

91.

410

12.0

110.

21.0,156 913

48

7

6

0

.0

10.

1.

51.0.187 516

75

6

0

.0

10.

31.

3.0 53.0

130.

7

210 140

160.

81.0.218 029

03

5

8

0

.0

1.0

51.

02.0.249 62

30

5

0

.0

10.

.0

10.

2700

25.0

32.0.280I 24 52.0.311~ 827

4

0

200. 220.

68

1

61. 82. 0

47,0 04.0

280.

9

0610 9280

95

3

1

0

.0

20,

.0

20.

45.0 6.0

83.0 030.

340. 93.

23 315

34

0

620 2540

250.

1

02. 1 2. 2

72

1

0

.0

20.

42. 3

86.0

390.

1

0

.0

20.

62. 4

2460 3280

17.0

310.

3.0 630 .

53. 18.

84 4 64

10 13

1

0

.0

20.

83. s

3100

370.

34.0

48.0

174.

34

06

1

0

.0

30.

03. 6

580.

46.0

0

.0

30.

13. 7

780.

48.0

41.0 43.0

42. 684.

164 895

9

1

3020 3940

1

0

.0

30.

3. 8

090.

40.0

46.0

945.

625

86

1 2

0 0

.0 .0

30. 30.

53. 9 74.00

4760 4680 4510,

290. 404.

43.0 58.0

59.0 5100 S

205. 5.

35 16 8 0.694

79 72

2

0

.

9.01

5700

.

85.

5920

44.0 68.0

16. 76.

0.729 16

0

40. 420.

65.

2

30 40

46

65 58

2

0

.0

40.

34.03

15.

5250

.0

40.

54.04

2

0

0.

40.

56.05

5190.

325. 526.

6470 600

36. 97.

51

0

92.0 16.0

7

2

5170. 5090.

40.0

57.

07 37

4 37

2

0

.0

40.

85.06

5730.

736.

6820

74.0

07.

68

30

2

0

.0

50.

05.07

98.0

67.

98

24

0

.0

50.

25.08

036. 246.

6140

2

650. 6570.

28

17

0

.0

50.

45.09

6490.

464

22.0 46.0

28.

2

7370 5790

78.

15 9

10

3

0

.0

50.

6.00

6210.

675.

720

C 70.

38.

98

30

1.02

850

900

37.0 I

950

1

550

92

3

151 REQUIREDPIPEWALLTHICKNESS FOR INTERNALPRESSURE(cont.) PRESSURE PSIG.

1.s. )IAM.

1100

1200

1300

1400

1500

1600

1700

1800

1900

2000

0.0 70.0

400. 7080.

240. 940.

50.90

035.0

6070.

160.

0

.0 00.

0604.

2

0 .0

1109.

01.09

161.0

2140.

21,

3

0

2039.

12.80

107.0 232.0

8110. 4280.

292. 352.

0

.0

5210, 3610. 210.

631.0 861.0

5

1.0 51.0 92.0

61.80

0

1.0 1.0 10.

1074.

4

.0 .0

20.

2094.

62.70

368.0

0350.

423.

6

0

0520.

27.0

3049.

13.70

394.0

6320.

584.

0

2.0 20.

32.0

7

.0 .0

304.

73.60

429.0

2490.

654.

0

4069.

24.50

465.0

8560.

615.

0

30. 30.

63.0

9

.0 .0

3890. 370.

243.0

8

62.0 03.0 43.0

184.0

4104.

75.50

591.0

4530.

786.

1

0

.0

30.

84.00

4570. 420.

504.0

5079.

35.40

627.0

0600.

846.

1

0

24.01 65.02

2650. 500.

205.0 45.0

86.40

652.0

6770,

917.

0

4.0 40.

5034.

1

.0 .0

690.

078.

0

4.0

4590. 6870.

69.0 486.0

1

0

0.

67.05

3650.

087.0

7604.

47.20 98.20

859.0 985.1

9810 8 598.1

04.

0

59.03 53.04

604.

1

0. 0.

78.0 714.0

3740.

1

36.30 97.30

1951.

270.

1

0

740. 7120.

237.0 748.0

59.11 090.1

91.1 046.1

7201.

330.

0

61.06 75.07

8209.

1

0. 0.

3901.

491.

1 1

0 0

462. 523.

0481.

50.1 190.1 691.1

9161. 5231.

7.0

628.1 869.1 019.1

082.1 118.1

0

5800. 981. 4891.

9391. 0831.

2

79.08 72.09 86.00

24.1

1201.

693.

2

0

80.11 94.12

8951. 2401.

260.1 40.1

1.81

279.1

7371.

754.

0

8.0 8.1

1013.

2

0. 0.

1168.

72.81

305.1

3441.

825.

2

0

0.

8.1

6201

23.1. 7

331.1

9411.

885.

0

.1

9.1

01.

65.1 891.1

321.

2

98.13! 20.14

2178.

73.61

476.1

5581.

956.

2

0

.1

9.1

501.5

951.

024.1

313.

34.61

502.1

2651.

017.

2

0

1.

9.1

091.6

971.

318.

861.

187.

1

0.1

3261. 7241.

663.1

4781.

248.

1

131.7 171.8

4134.

2

1. 1.

84.61 35.41

538.1

2

28.1 43.1 638.1

4180.

95.41

789.1

0852.

219.

2

1

824.1 047.1

46.41 97.31

735.1 8602.

682. 292.

379.

1

1321. 631.

5163.

3

21.19 251.0

1

0. 0. 0.

1. 1.

50. 5.0 6.0 60. 6.0 7.0

0.1 1.1 1.1

.

709.

9741.

518.

109.

I404.

9

152 4

REQUIRED PIPE WALL THICKNESS FOR INTERNAL PRESSURE (cont.) PRESSURE PSIG.

1.s. ‘lM”

2100 2200

2300

2400

2500

2600

2700

2800

2900

3000

1

1.

0.1

161.

141.

205.

1 2 3 4 5 6 7 8 9

911, 2 90.13

6701. 3401.

5011. 5911.

163. 2851.

12.1

261.

121.

316.

20.1

3514.

426.

171. 4 241. 5

2011. 0621.

6281. 6361.

231. 3271.

39.1 487.1

4516.

1371, 141,

5519.

151.

21. 6 391. 7

8331. 6941.

7451. 7531.

41. 501.

586.1

641.

674.1

741.

1681. 147.1

858.

471. 8 51. 9 621. 0

4651. 26.1 086.1

7521. 8601. 8781.

6901. 8741.

763.1 815.1

8147. 9239.

128.1 1.289

96.9 07.9

2789.

9.052

0232.

12.15

18.0

857.1 6182.

9872. 9952.

5293.

08.42

1234.

1.12

290.

6.1

601. 1 781. 2

137.2

27.

2.832

401.

1.

7.1

852. 3

489.2

9042.

0428. 312.

263.2

320.

2.524

511.

1

1.

2.152

622.

022.

262. 132.]

42.

2.

340.2 10.2.

342.2

1

932. 4 012 5

0122.

2

8.2 9.~ 1]

421.2

5125.

28.26

722.

2

1

2.

9.2

6217.

2.527

833.

2

0.2 1.2

242. 8

503.2

1462.

8420. 7524.

695.2 789.2

7120.

2

2. 2.

0392. 1382.

510.2

2

917.2 732.2

0425.

2

082. 6 162. 7

8303.

22.38 2.839

94.3 05.4

2

2

2.

2.2 2.2

629, 573.

868.3 957.3

16.4

2.

2542. 2632,

2.530

2

364.2 135,2

9305.

3

312. 9 492. 0

0038.

22.31

275.

1

0

0.

9.1

1

0

.1

1

1

1.

9.1 0.1

1

1

1.

1.1

1

1

1.

2.1

1

1

1.

2.1

1 1

1 1

1. 1.

3.1 4.1

2

1

1.

5,1

2

1

1.

6.1

2

1

1.

2

1

2

537. 637. 748.

153

N

E

F

M

C

V

P bi t ap d i j n ohn o ie gnz l ixzsy n eo l igtet evc r rs eT ea msth s esl below,to steh hndetermine l e o. de thenozzleloadsisbased inpartontheBulletin107of WeldingResearchCouncilandrepresents a simplificationof it. The vesselsare not intendedto serveas anchorpoints for the piping.To avoid excessiveloading in the vessel,the pipingshall be adequatelysupported.

r{,

FRJW

I 4

A R. *

-—. ———— — - - — — .

, E x t F e or & M nr ao c l m e e s n t s T calculate the maximum forceoand moment, first evaluate ~and y. Then determine

CL2, and A from Figures 1, 2 and 3, for the specified~ and ~ substitute into the

aquationsbelow, and calculateFRRF, fl=.875 ($)

Y=+

Determine CL~and A from Figures 1,2 and 3.

CalculatePressure Stress (~. 0= (q(R.-;) [f a is greaterthan S0,then use S. as the stress due to designpressure. FM= — R; (ST—O)

A4RCM = R~2roSy

Mm =&

S Y –0)

x

Plot the value of FN a FWand the smaller of .~~c~ands MM as A4w.The allowable nozzle loads are bounded by the area of FRF,O,A41w, ~R\f

EXAMPLE: Determine Resultant Force and Moment T= .7511 SY= 31,500 psi@ 460° Rm= 37.5 P = 150 psi S. = 17,500 psi rO= 15“ b= .875(%)= .875 (&)= .35 From Figure2,2= 1,070 From Figure 1, a = 440

y= + = ~= 50 () From Figure3, A = 340

,

154 NOZZLE EXTERNAL FORCES AND MOMENTS IN CYLINDRICAL VESSELS (continued)

;alculatePressureStress 2(150)375 ~ = 14,850psic&=17,500 ‘=%m-3= 75( ~ - 2) Jse o= 24,850in the equationsfor calculatingFRRF and MkM ~alculateAllowableForces and Moments Fw= ~

(~y. @ =(#2(3

psi

1,500—14,850)= 53,214 lb.

~RcM= Rm2~o~y =37.52 (15) (31,500) = ~zo 984 in-lb 9 1,070 z (37.5)2 (15)= (31,500—14,850—l,032,97~ in-lb. M-m= y (sy — ‘-= ~

IL

P f t vl o a oo ah FRF l a t t u sr e meo n afh k fa ~, aQ A 1 ~nT 7 a&f l fLl n odW h Mwol as z.ob a b o b ut r a n o dF’RF, r 0, eh eMm. d e y e a T k n b 6

i

=

h e a rn e rof oe zroa F e =zc2, t l 0l i ae o, nb 0 0f 1 0 i l0? w, b0b oan 0=l ul0s( o lA w p. .a od b l ie l ro eub z o a F. =zc5 t ll t ,i a e oJ 0bn a- n 0 nf s 4 0 2 i0 l , w 0 n0b onb 0 a *ul s l (o ol . w B p. da o b t l ie

* S

O

P

= DesignPressure,poundsper sq. in.

‘ R

=N =M

R

T

= S

T hh

S

=Y S T e m

o

= S p

s

= S p

s

s

T

A

T

oO

Dt Vt

I

O

N

l s l el z ea f

N U

a ob

v ts s oiae t l gl : u

rute

ehae

ps

hn

:

Z

= DimensionlessNumbers

uz R

t za i s odl ni ie d c Au e =hs D i , em e ns N s i ou n lme s bs e e ao S d iah i . n e un c l FRRF s h= l Maximum f e, s Resultant Radial Forc(

r

i ice k n n l e c s l sh , e pounds* s k f M x c t eni , s mC ui@ur l c tum ma f ne r t i t or eM e a nlaytD g e d te r h is a fi R la g R M o , i e n ce hh n- p t o um n d s * p pe r aop t su u r qie n, eu d n a s r cr m Dr ue s ie g e n P sp r te sso s I uo ur e M, n a WdRx e is s Lm uo Mnul g t miMat un d t i ne c h n- p o t u n d, s * qi eu n a r cr e hm o r a f Me Sl a s. pth u e seo r FRF eliu= aM l nl a , dRx e is sF m u poul t omr a u nc nt qi eu n a c r r h eF = .M ’ a xR R ei s mMuMu lo tm i m a en n p o u n d s * e n N s i ou n lm e s bs e r s

~

=D i m

Y a

= D i m e n N s i ou n lm e s bs

e*

ar

bs Uv s

=D i m e n N s i ou n lm e s bs

e

r

s

ao s l l u

u et

ee

REFERENCES: Local Stresses in Spherical and Cylindrical Shells due to External Loadings, K. R. Wichman, A. G. Hopper and J. L. Mershon — Welding Research Council. Bulletin 107/August 1965 — Revised Printing — December 1968.

Standardsfor ClosedFeedwaterHeaters, Heat Exchange Institute, Inc., 1969.

s

155

NOZZLE LOADS Fig. 1 1OJ

9 8 7 6 5 4 3 2

1

,,, , , f,

I 1 !, I

i::: i

,

1

,

I

I I [ WI

,

[ I

, ,

I

,

,

I I I I I

t

I

1 1 I 1

I I I 1 t I I ! I I [ ! ,: I

1 i

I

I 1 1

I I I

I

I

1I I

I

I 1I I I I I ( ,

I

I I I [’1 I I

I

9 ; 6 5 4 3 ,

t

2 a

I :-+-!r i

! { I--+--L

l-l++

-

+--l-%-l-~

-: . .: I

-

,

\. I I :

i I

~i i ~

9 8 7 6 5 4 3 2

,, ; I,

I, ;,I ]02

;

I

1

:

I

I! !;,1

I

,

?

I

,-,4 ----:: : 4-%-4

II

~•••ì´„• i

!

.’ .!””

i!

!:”m!!!-

9 8 7 6 5 4 3 2

1

. .

1,

10

.

,

1 !

1[ I I

.

—

!.

I 1

r

,

t

1

5

6

NOZZLE LOADS Fig 2

!

1 1.11

NOZZLE LOADS, Fig. 3 1OJ 9 8 7 6 5 4 3 2

6 5 4

3 2

A lo] 9 8 7 6 5 4

3 2

]02

9 8 7 6 5 4 3 2

10 0

.05

.1

.15

.2

.25

.3

.35

.4

.45

.5

1

.“,

R T

J

C

U

C

I

P

A the junction of cone or conical section to cylinder (Fig. C and D) due to bending and shear, discontinuity stresses are induced which are with reinforcement to be compensated. DESIGN PROCEDURE (The half apex angle cz~~~~ 184l~o tan 300= 8.94 sq. in. S,E, () u () ? The area of excess in shell available for reinforcement: A,. = (t, / t,)

–A) (t, - ~ %+

(LI t,)

x cos (a – A) (tc- t,) * StC/cos a (0.395/0.36) X COS(30-5) X (0.375 - 0.36)X 484X .0375 + (0.5/0.41) cos (30-5) x (0.5-0.41) x ~84 x 0.5/cos 30°= 0.77 sq. in. A,. - A,, = 8.94-0.77 = 8.17 sq. in., the required cross sectional area of compression ring. Using lfi thick bar, the required width of the bar: 8.17/ 1.5 = 5.45 in. Location of the compression ring: Maximum distance from the junction: a

= 484 x 0.375 = 5.6 in.

Maximum distance of centroid from the junction: 0.25 fi= 484 x 0.4375 = 1.5 in. Insulation ring may be utilized as compression ring provided it is continuous and the ends of it are joined together. Since the-moment of intertia of the ring is not factor, the use of flat bar rolled easy-way is more economical than the use of structural shapes. To eliminate the necessity of additional reinforcement by using thicker plate for the cylinders at the junction in some cases maybe more advantageous than the application of compression rings.

1

R T

J U

D, t-l

L. I

dr

3

!$! ;L w I

I T FIG. F

C E

C P

Reinforcement shall be provided at the junction of cone e o c to cylinder, or at the junction o t l section to cylinder when cone, or conical section doesn’t have knuckles and the value of A, obtained from table E, is less than ct. TABLE E - VALUES OF A P/SE o 0.002 0.005 0.010 0.02 0.04 0.08 0.10 15 21 29 33 A,deg. o 5 7 10 P/SE 0.125 0.15 0.20 0.25 0.30 0.35 57 60 40 47 52 A, deg , 37 6 d f g e r v e ooag Pa l 0t . u/e r re S s f E CX= N

I no t e rt mp ob el ma t f i: iao ann t e rvodm y ae de lei a urt e e

The required moment of inertia and cross-sectional area of reinforcing (stiffening) ring — when the half apex ‘angle a is equal to or less than 60 degrees — shall be determined by the following formulas and procedure.

1. Determine P/SE, and read the value of A from table E. 2.

Determine the equivalent area of cylinder, cone and stiffening ring, ATI,, sq. in. $3:: pa~~ 46 for construction of stiffening ring) 3 FIDI. A~lJ= ~ + ; + A., Calculate factor B B = ~ (~ ,) where F[.= PM+ J tan a

M = -RL tan a + L[ + R{?-R.?

2 2 3RI,tan a 3. From the applicable chart (pages 43 thru 47) read the value of A entering at the value of B, moving to the left to the material/temperature line and from the intersecting point moving vertically to the bottom of the chart. For values of 1?falling below the left end of the material/temperature

line

for the design temperature, the value of A=2WE. If the value of B is falling above the material/temperature line for the design temperature: the cone or cylinder configuration shall,be changed, and/or the stiffening ring relocated, the axial compression stress reduced. 4.

Compute the value of the required moment of inertia

For the ring-shell-cone section: ADI,ZA 71, I’,Y= 10.9 5. Select the type of stiffening ring and determine the available moment of inertia (see page 87) of the ring only 1, or the shell-cone or the ring-shellcone section 1’. For the stiffening ring only: AD[.2A 1[. Is = ~400

164

T

J

R

C

C

(continue~ If 1 or 1’ is less than I, or 1[, respectively, select stiffening ring with larger

moment of inertia. 6. Determine the required cross-sectional area of reinforcement, A,~,sq. in. (when compression governs): A,~ = @fi;;an~

[,@&):]

NOTE: Whenatthejunctionthe compressiveloads determined byPR~2 orPRJ2 are exceeded by~l or~J tensional loads respectively, the design shall be in accordance with U-2 (g) (“as safe as those provided by the Code Section VIII, Division 1.“) Area of excess metal available for reinforcement:

A,~ sq. in.:

A.~ = 0.55 ~D~t, (t, + t. /COS @ The distance from the junction within which the additional reinforcement shall be situated, in. a The distance from the junction within which the centroid of the reinforcement shall be situated, in. 0.25 ~ R,

Reinforcing shall be provided at the iunction of small end of conical section without flare to cylinder.

.~ L~ LL = =I

~

The required moment of inertia and cross-sectional area of reinforcing (stiffening) ring shall be determined by the following formulas and procedure. 1. Determine theequivalentareaofcylinder,cone and stiffening ring, Am

L, L,

“

L,t, An= ~+

I 2.

t L

I R1 A

FIG. G

Calculate factor 1? B . ; ( :~’

Let, ~+A,

)

where Fs = PN +jjtan a RL2- R~2 N=~ + Z+ 6R. tan a

165

R T

J

C

C

(continued) 3. F

t a c ( t r e a p v o B m t t l t t m l a f at i p m v t t b o t nc F v o t l e f n l f t d d t t v o =2 e of B is falling above the materialhemperature line for the design I t v

e

temperature: the cone or cylinder configuration shall be changed, and/or the stiffening ring relocated, the axial compression stress reduced. 4. Compute the value of the required moment of inertia: For the ring-shell-cone section: ~; = AD,2ATS 5.

For the st~~e~~~ ring only:

~.= 1:.0 10.9 Selectthe type ofstiffeningring anddeterminethe available moment of inertia (see page 89) of the ring only, land of the ring-shell-cone section, I! Iflorl’ is

Iessthanl..orli respectively,selectstiffeningringwith largermomentofinertia. 6. Determine the required cross-sectional area ofreinforcement. A,,, sq. in: A~s= kQSR~tan~ SE

metal available for reinforcement Ac,sq. i A.s = 0.55 %

n

[(t,-~ + (tc-tr)/cos ix]

The distance from thejunction within which the additional reinforcement shall be situated, in.G The distance from thejunction within which the centroid of the reinforcement shall be situated, in. 025 G NOTE:Whenthereducersmadeoutoftwoormoreconicalsectionsofdifferentapexangles withoutknuckle,andwhenthehalfapexangleisgreaterthan60degrees,thedesignmaybe basedon specialanalysis.(Code1-8(d)and(e).) NOTATION

A,

a ev = area of excess m reinforcement, sq. in.

af t i

arear of the stiffenlA.a a = bcross-sectional ol l e

ing ring, sq. in. A,,L = requiredareaofreinforcementwhen AT = equivalent area of cylinder, cone and stiffening ring, sq. in. QLis in compression, sq. in. B = factor At.’ = requiredareaofretiorcementwhen D~ = outside diameter of cone or large QLis sq. in. end of conical section, in.

.

66

T

J

R

C

C

(continued) D,, . outsidediameterofcylindricalshell, in.

shelljunctionandone-thirdthedepth ofhead o theotherendofthelarge

D., — outside diameter at small end of conical section, in.

shell.

E

L,

— . lowest efllciency of the 1ongitudi-

naljoint inthe shell,head or cone;E = 1 for butt welds in compression. E

— with subscriptsc, r ors modulus of

design lengthofavessel section, in. forstl~enedvesse[section: distance between the cone-to-small-shell junction and an adjacent stiffening ring on the small shell. unstlflenedvessel o section: disr tance betweenthe cone-to-small-

f

elasticityof cone, reinforcementor shell material respectively,psi. k

— S&L5’RERbut not less than 1.0.

shelljunctionandonethirdthedepth ofheadontheotherend of the small

A

.

shell.

fi

axial load at large end due to wind etc., Ib./in.The value offi shall be taken as positivein all calculations.

— axial load at smallend due to wind,

P

Q~

etc. lb./in. The value of~2 shall be taken as positivein all calculations. I

= available moment of inertia of the

T

— availablemomentofinertia ofcom-

stiffeningring, in4 bined ring-shell cross-section, in4. Thewidthoftheshell whichistaken as contributing to the moment of inertia of the combined section: 1.IO~D,,t IS

.

I,’

= r

L

.

L,

.

required moment of inertia of the stiffeningring, in4.

external design pressure, psi. PRL PRs — +fi Q,= ~ +fz 2 axialcompressiveforce duetopressure and axial load.

RL

outside radius of large cylinder, in.

R,

outside radius of small cylinder, in.

s

allowable working stress, psi. of cone material.

sR

allowable stress of reinforcing material, psi.

s.

allowable stress of shell material, psi.

t

minimumrequired thicknessofcyl-

i wn i da t l hel oof rw u a m q u o oi i mr n o e et ed n r t t c i of ar i o s i o n n , c mr i nb g i- s nh c e el l rd- c oo n e s s t. a ct h t i o cuc k w an oei l s t s ic t ni o n4 , . c o r a r l ol osi wi ao nn c n e a l x eo c i n i o ag nt l n t, he f , . m i r ne q ui i r me d t uoh i cmfk n e I e n g t a h os fl cu oo onr f e f cn a o w cg n ei ce t o , hr a r lo ol uosi w i t oa o d i bs et s at t niw r f c efr e ie e n nin n g g s a ct h t i o cus k w an h ei l s et t, o c i o n n e f , . a l l f o c wo ar rni oo c s e i o e o e

el seo a vin esgg e snt c as ht i he f oa l na a , pdn LL . d l g ee l f in~or stifle-nedvessel section: the — A valueto indicateneed for reinforcedistancebetween the cone-to-large ment, from table E, deg. shelljunction and an adjacent stiffening ring on the large shell.

for umtl@enedvessel section: the distancebetweenthecone-to-large-

ex g

167

R T

J

C

C

E DESIGN DATA DL = 96 in., o Ds = 48

t,

T

~

c fl

o l

c

=

E,, Ec, E

a

d

m a

r

m

o e p

o s

= 100 lb./in., axial load due to wind

A = 30 lb./in., axial load due to wind. LL = 120 in., design length of large vessel section. L, = 244 in., design length of small vessel section. Lc = 48 in. ~ = 15psi, external design pressure F = 48.00 in. outside radius oflarge cylinder LL R “ = 24.00 in. outside rad;us ofsmall cylinder Designtemperature=6500F SS = 13,800 psi. maximum allowableworking stress of shell and cone material. SR = 12,700 psi. maximum allowable working stress of reinforcement material. = 0.25 t t = 0.1875 in. minimum required thickness of small cylinder. t. = 0.25 in. actual thickness of cone. t, = 0.25 in. minimum required thickness of cone. t. =

0

i a

t

o c

JUNCTION AT THE LARGE END 1. P/SE= 15/13,800= 0.0016; from table E A = 4 since A is less than U, reinforcement is required. 2. Assuming As=O, A~~= h/.2+LJd%A. = 120X0.125 +48 X0.125+ O=21 in2. LL RL2-&2 48X 0.5774+ ~0+ 482–242 ~.— RL tan ~ a+— =66.9 2 +3RLtana=— 2 2 3 x48X 0.5774 =

FL=Pk?+fi

tan a = 15 x 66.9+ 100’x 0.5774 = 1061

168

T

J

R CONE TO CYLINDER EXAMPLE

~ = :(~L)

(continue~

= 0.75 x 1061 X96/21 = 3636 TL

3. A = 0.0003 from chart page 43 4. Required moment ofinertiaofthe

combined ring-shell-cone cross section:

ADLATL 0.00035 x 962x 21 = 5.32 ‘L= 10.9 = 10.9 5. Using two 2% x $4flat bars as shown, and the effective width of the shell: 1.10 x ~=

1.1 ~96 x .025 = 5.389 in.,

The available moment of inertia: 5.365 in. (see page 96)

It is larger than the required moment of inertia. The stiffening is satisfactory. 6. T

r

c

a

o r

r

S,E, = 13,800 X k= ~12,700 X

106= 3 ~ 09 0 1063 “ 0

~L= ~ ‘fi ’15 j48+ kQ~RLtan a A,L = I SE

100 ’460

X X

L

s

= 1.09 X 460X48X 0.5774 ~-025( 13,800 X 0.7

15 x48 -460 4 460 )33]=

1.412 in?

The cross-sectional area of the stiffening ring is 2.5 in2.It is larger than the area required. The reinforcing shall be situated within a distance from the junction: m,,

= 448x 0.25= 3.46 in.

The centroid of the ring shall be within a distance from the junction: 0.25 ~

= 0.25~48 x 0.25 = 0.86 in.

JUNCTION AT THE SMALL END 1. The conical section having no flare, reinforcement shall be provided. 2. Asuming A,,= O, ATS= LJJ2 + L~tJ2 + A., A,.,= L.,tl2 + L&J 2 + A.,= 244 x 0.25/2 + 48 x 0.25/2 + O= 36.5 i ~

=

R

8

t +~ ; n ~~

+

+a2 ; ~ ;

“+ +;4 5 : ( X =7

~ 74 x 4 =4 149.72 in. : +

j

169

I

R T

J

F,= PN +fJ t

a

C

E =1

C

(continue~ X 149.7+30X 0.5774= 2263

3 F$.DS = 3/4~22;; :48) = 2232 B ‘? x 3. Since value of B falls below the left end of material/temperature line: A= 2 B/E = 2 X 2232/30X 106= ().()()()14 4. Required moment ofinertiaofthe combined ring-shell-cone cross section: AD.?An = 0.00014X 482X 36.5 = ~ 08 in ~ 1’,,= 10.9 10.9 5. Using 2% x % flat bar, and the effective shell width: 1.1448 x 0.25 = 3.81 in. The available moment of inertia 1.67 in.4 (see page 96) It is larger than the required moment of inertia; the stiffening is satisfactory. 6. The required area of reinforcing: k = 1.09 A,., =-

Q,= ~

+j=

15 zX24 + 30 = 21O lb./in.

kQ,~. tan a = 1.09X 210X24X 0 13,800X 0.7

. ~ 05

inT z3

T

24

Area of excess metal available for reinforcement: A. =~~a ==

.

(tc - t,)+ ~,

(t., -Z)

(0.25 - 0.25) + d24 x 0.25 (0.25 - 0.1875)= 0.153 i

Ar,,-A, = 0.328-0.153 = 0.175 in.2

T

a

of ring used for stiffening 1.25 in.2. It is Iargerthan the required area for reinforcement.

The reinforcing shall be situated within a distance from the junction: G,=d24

x 0.25 = 2.44 i

n

.

and the centroid of the ring shall be within a distance from the junction: 0.25 ~R,,t,,= 0.25424 x o

= O . i

. z

nb s

l

.

8

170

O

P

WELDING V

R

There are several methods to make welded joints. In a .particular case the choice of a type from the numerous alternatives depend on: 1. The circumstances of welding 2. The requirements of the Code 3. The aspect of economy

1. THE CIRCUMSTANCESOF WELDING. In many cases the accessibility of the joint determines the type of welding. In a small diameter vessel (under 18 - 24 inches) from the inside, no manual welding can be applied. Using backing strip it must remain in place. In larger diameter vessels if a manway is not used, the last (closing) joint can be welded from outside only. The type of welding may be determined also by the equipment of the manufacturer. 2. CODE REQUIREMENTS. Regarding the type of joint the Code establishes requirements based on service, material and location of the welding. The welding processes that may be used in the construction of vesselsare also restricted by the Code as described in

paragraphUW-27. The Code-regulations are tabulated on the followin~ the titles: -. DaEesunder a. Types o W eJ l o d i e nf d t s ( J permitted o i byn the Code, t s their efficiency and limitations of their applications.) Table UW-12 b. D

(

eo W s

o J

e Ji

l go

t b u

d ni

f

e nf d t

v

i v

s

s

a

u

c

tain design conditions.) UW-2, UW-3 c. E x a m io nW a t e iJ o l no

d i

e nf d t

s

The efficiency of joints depends only on the type of joint and on the degree of examination and does not depend on the degree of examination of any other joint. (Except as required by UW-ll(a)(5) This rule of the 1989 edition of the Code eliminates the concept of collective qualification of butt joints, the requirement of stress reduction. 3. THE ECONOMY OF WELDING, If the two preceding factors allow free choice, then the aspect of economy must be the deciding factor. Some considerations concerning the economy of weldings: V-edge preparation, which can be made by torch cutting, is always more ec~ nornical than the use of J or U preparation.

[

171 Double V V a

Lower quality weldingmakes necessarythe use of thicker plate for the vessel. Whether using stronger welding and thinner plate or the opposite is more economical,depends on the size of vessel,weldingequipment, etc. This must be decidedin eachparticularcase.

172

T

J

W

JOINTEFFICIENCY,E -

TYPES CODEUW-12

F R g

w an s B as s b rh c o m t

i w

a r

m oe e tl o hs u i t n 1.00 ds e i ue r f la c ci u t k i rs n ig e a am of l v t l e op w l e et i o l n

c ; pN ~ o ia E mo x i a- n m h e r

b us E d x a p

a e de e e

d l d0d e . p fd de r d f .

S i n g l be - j w e ulo d e di t n t t w b a is c tk t i r nh ig 0 p w r h e i m i ac i hn s n p a l w f ea lt c d e i e nr g

c

n .

8

.0

8.

0

.

j

3 S i n g l be - j w e ulo d e di t w i u ot b h a o sc u k t i s t r i

D f

o u l ij

b

l e - f u l o la i e

n t en f g p

l

l nt

—

p

t

t

5 S

i

w

n fg l ie - lf u ll l e t l j o a i n p t p w i l e t lu hd g s

;

S

if

u n l l ; gj i p

w

l e

~ l ol lu

$ea ; i ~ d

n

—

g

s

p

t

173

T

I A

W

L I M I T A T I O N S P PV L A Y R I IN N OG U

C oa

tA Bie

O g ,no

r Cty

N : ,

F

NOTES

S

WELDTYPES

FORTYPE1:N J

J

E ,D

T 2 N YO O P R N E1 C oa tA ie , g 1 no 3 r , ty C: E bx w cw uo e ep ipo t l lft n t fat d— f c i r c u mjo f e oor e n itn i ra nl l t

I t: E t ah a s tbhi t r . lon ys hew p ,o w D ej low d ia h pe n f i d t e r c s thms e beie t t Ct i t a oahe g d d r y n e w y s e p . lr od c i e sn s g e s .

F T J C oa C i r c u mjf e 5 i t a nh 1o d i a m e

E T j sa te tpi re

J

3 YO tA ie g, no rooe nn t i oni a l n n2 i i onv co u8 t e r .

P R2 rB ty : , l vto y . t ken sd

s: oh t h e a t d pb. h e g e Cob b i u t ns t b-e sh w d e a ul y d t ec r o r m p, f m pua li s soe t t i d4n .e et r a t i o n .

3 B j uos bi h ft n f a . t rt lrs e P R Eu n : d oe r v c ae u art sl b , a n rp ol t 1 e nsr t ai r v 8d a. Tgl an l e tse s ys dsh u . g no r t ty w : e l d -h ag cr oo o mv eper sl e e e eb b dlt u u,a a d i lnv o t / ef s iwt rlm 8 l m g. no r. aty r : e i n fC o rT c et mh e ni st hc. k n o t r e i n f h o s r c ne hmf ee n a t e x t f c o l et lh eoi c wkd in ene s g F T 5 YO P R E ( Circumferential ajoints f a t ) t o a P c t l hh r i i- a cM k at n rxe n e isie sm i u ment of heads n o 2 i ov o u te n s ut i rt 4d i . e n 3 c p l/ o . 3 d i t as mn h o e 1 eti t ev l o rh l / eoin s o ct ‘ r t k21v i . . nYe 1 c r lz o / . 3 e / r 1 1 s v o J a o t hti ea mn ci shhtp iht esen r gi c a a l od s a h e xe c l l r u l d se de . J o n t B i w e t ls d es i o hc n i o g owr eu eb bj l luotd eei t dn ( C i r c u mb fj e r eof n [ t i ) a l n o hl a d s s fld a t t t a s c ohhj m a ene onc l t k l v eoo s t i fems p otu tr r f i st i w eh si r e b r e b m c o h v e e i s h n a l g l 5 i i n ot/ m hn iwi c t n kh8 an. n eel s h psr e r oei n mn g i e d g o i l t , n t g i u p l go s u es cm fu euc r o tn m e o pa d l w t t e e o t pd lhi n l l ghd a o ee oe t fp e see n s e ta t s fr a u t F i ssno ni ou o n t 1 t h - t i d 1a i moa 1t hm n e 2e ts h em e r ea wf r e e gc l rhde oi i dpn pgc i h f t po l ol h u e g r e . a g ri t o c o ir r vha e e t c ne J C oa t e i g o n r y t: C m e n d e d . F T 4 YO ( L o n gj i a t nou o d 3i in a)vn t h Ji C oca tA kie ( C i r c u mjb f e nro eo n 5ti i )a i t h J in C oca tBk ie .

F T 6 ( F t a t ta oao h hc t p r t es s nh so r e t q h ui o ci w kr f w i o i l e on sl JointCategory:A

YO P R E ax xha l i l mj o . uw e o am b ch e m o) e r anen t 5dv T fems e f f i cg i e i in t c it v e sh a e b u5e i r vol oe l /oe sn a tt br u 8 i . rf so r w m e eu o lhe ad nu en eo dis s l . st t y j h omade e fh iby arcn or gas t e s s ehl i te dd l n e l weldingprocesses. f : , B

( F a t t bao ohc h h m e ae) p r o e e s s i s t u[si r nhh de o 2 i i v d n i aesna n m oi re 1 r e t q h 1u iw icf rkw iien 4 o o uo h t f s oel i adn na J C oa tA ie g no

nar vt di ee ne rl6 oJ d 4 tnv. oee ir edl es t ls ne l gf d y r. ty :

f ns g . l e oof s f iEt i=c I fi ben jn .c toyu o , i c e o dm tp r r e s s i o n . el h t d e . B

1 . -.

7

4

W

D

WELDED

LOCATIONS

T t j ou hic n enc d roo t ent se sd a p i r r i et e f ja od e moi s ib nig edn t aerl t sne e t dt i t c T s h p r e e q uc si rwi e emaa eh bnl t sio ,a s d t ec oh sn d aei i t t gair ob bnn ur s el , a l t

s o

D C

JOINT

J

O

E N

S D

qin uc o i arni e am pw e l npa ht t s l i y e ay rI s . r ce s mr have tt ei ehdc ri aenic ,ak l n eeo d w .

P W O E N E JI TO G N I Y R AN D PI OT G RE JA P H OI C IH C T Y M R I YNE AF TF I IO CNT I RE EN A I AT C I OA NT N E EG X OA D

a i A ta gD t dl t 1 T d ie A hsc .le eb gn F o snu r l yu w os i ve ei s e l end s c nd tts i s e o n ln s b o ja e f f 1 i ca ih e n.e c n y a 0d d s o 0 . r 9 A c a B to C elb g o u r l y t T r( Tt y( ( d Se w s ( eeni i bgnl e c n dls o uu ds p i t n t g o 1.0 0.9 c o n d t i ti nih o oon o zs zs l ee n s r l bi sec o m t l m eu c no hi d c aaw tmi nb g e r s ) w f h w u i ehn tlt ei n r slc e hc h t s e r a d i o c g ar Aatw p e hi vyge oe l r s y d s se n l i nr s e o ch t o eis o Na n sd o r s m a n) d c a to s o ner vyan . mee l cs e t ss se 0 l 0 . Uw-11 s e o ch t ei o a n sd r s U 1 2 W ( d ) r Joints Band C butt welds C a Ata eB b g o nur y t din t w i ve s e l e s c d cn ts i s ec no n len s se a h s e b onhT a a dy d l s p l1 ein f ee wall UHT-57 (1) or T ( y 2p thickness do not e require ) 2 F r a d e x a i n m a U l

u T ( ol Ty ( . b l 1yp s u 2pe p ) t r Te (o) T t (y 0 0 . i o wg r jae p hol i cdi en dt s m i n a t i o n o s t n d a t o r y ‘ W ( b 1 )

l

2p e t y 1p P C o e U C S e

.

8

8

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f p t

Pt yC1 p U . C8

2 p o ee 8S 5

175 I

DESIGN OF WELDED JOINTS (CONT.) D C

O

E N

S D

P W N O ET JI T N DP I O T G REJ A P HO I C IH GO N IY R A E N A C Y M R I YNE AF TF I I O CNTI RE E I AT CI OA NT N E EG X OA D T M

( 1p ) r y e l l 6e 2.p ) ol pione id ne fr dt ( s 0y gmy rT a op w h yi j ec 0y P3.pC 6e o e ) r ( i n a t i o n U4.p C 0y 5eS ) r ( o s t 0 . 5e T y p ( 5 ) a t o r y . 4e T ( ’ 0 y 6. p ) hs s e e l s i g no e d r e r n a l s ns u rl e y ( c ) o A s i b hn at ls l e I. F e . )u l l ~ N ( p o 1 J W( ( 2 ( 1 aa ) ) ) o B a i C s nb h n t a s l d l e / ef sa s b ec s r soN e( yo l n . s op 1, V e . ) 1r T ( ya . o c 1pt a 0r t al i e n Nt i ( hn ga o 2l . ) 0 ( . 2 9 j l a s l o s u b s Jt a Wn( (c- e 2 s ( 1 ba ) ) ) h b p a o U W 2 ( a ) v h t e re ]intsB andC butt J Dos bi f h n aiut b wls l eu l l el l t d eJl t W d 2 n p e n w e t r e a t o c Di l oi sn id h ns et ls n l e x tt e h tn r d io, hn u hgs ge hnh a e a d n dl s l x e t n h ito t c i k }nr f e rhe s u s a l f de l iey 1 v oe n swo s z }ae z g el lr l rax e p cl h ee t dp t U W( ( 2 d( 1: a x )c)t h )ua . n gb e re c r s o e x r J oo c ai C tf n e mgt e oxs o cr fh y a n gr e rd s ) ) d e s t f a b l r j h i c o aJ at Wie(e da - n 2 p (t2 na p 3 a p n e ) d r s e U t W n- 2 (u a d) ( l b ) (s c ) n J l ( W ( - 4a 1 ) ) r U F u r a d i o e x a m i n m a n d T v ie d e fs e x t p r oe Uw-1 l

$ V a – i r t o U

J Aos b iT h Nn ay t ls p l e e o ( ( e f a x u1 cs t eoe pn ) i t f i T r c ( Type(y c h nr os i m t cai i uk n m le e l s s s t e e l ) . . l B o s b i t h N n a y t l s op l e e . eo s ps e e l .r s ) b te le( o d w 2 U 0 W( ”a - ( 2 F ( 1 r nb 2 ) ) d ) o2 F s m t i pJ e Caof p ci se nutn e t t t r sl a st i ol i n spot e fq uwelds iextending ro ethrough d r No m a tthehentire e r i of the ae l section w m ejoint e tl ar d l W 2 ( b ) J Dof p i e nun e t t r l a s t i ol n w e ex tt le h n rdd oi sn u g g h t e s n ea htt c i t ri eh oe n t e j U o W( ai- ( 2 n ( 2 nbt 3 ) ) d )

nstean f J i ( with d pe sr s e xu c J n i 5 p S n a o(be o i t c oh U l a d e s c o 4n d i

6 U

Aosr

boilers

i

e er Bos s N o(t W iu i t i

1p

e

2

0

PhC

o e

UCS-56

le t d b ei t h. dNn aA yt b w ls op eul l el e t d. j i o s) i h n e t slV nef l s a 1 a a- h s e nh a 1 a d dcl s o . cal g sn o l a s l r u a l d l ie y e de - b f s b p h o g e r a x p c h e e r p t bit h N n a y t l s o p l e e . g 0 i t )np r . r d) 1 hoT e ( v ryw i. he -t 1pe r 1ve e o eu2 y o ~ T n ( 0 sU fW. 2p- mn2 s (n s C o )i U l ( W ( 4 a I ) ) g t n o n :

s b t r o ao e 0e 29

A

176 DESIGN OF WELDED JOINTS (CONT.) D C

O

E N

S D

P W NO E GO N I Y R AN D PI OT G REJA P HOI C IH JI T E T N A C Y I AT C I OA NT N E EG X OA D R I YNE AF TF I IO CNTI RE E M T

l :

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b i t h Nn 1

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w t t h h l a w e e l o o ci a n ; (t P 1) e - e : y 1xp5 i c2 p ee m a .l t h 90 i n s 85 s .8tf e l a s.7o l t 60l e , to P t h h ~ 1 p w oo I t r eei a t n a n d a o0 e y . P l C 1p S9 y . U 2C p l

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9 F c o v

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E F F I C (I E T NB CU YE I SC A L C )EU O L EA D T I O NN S O S E A M H L TE EHSF I S C A A K N Code D E S S UW-12(d) S M E

TYPE OF HEAD H s

p O

h t

T

e e

r h

OFY JOINT

N m i cN a e

Ar

P

o1 00

i l s

E

N

* c a F l ic un l vo a ot il rov n i n g c i r c u ms f e ort , e n rt i aa el s @ s t h io s c ek h an m e sel s e s af s

1

r r d

.0

l

0.0

08 .

.0

2

9 .0

08.

Y .

0

0

.

0

177

EXAMINATION

OF WELDED JOINTS

RADIOGRAPHICEXAMINATION FuUradiographyis mandatory of joints: (Code UW-11) chambersofunjired 1. All butt welds in shells, heads, nozzles,communicating steam boikrs having lethalsubstances. 2 All . 1

1

Exemption: B and C butt welds in nozzlesand communicating chambers that neither exceed 10 in pipe size nor 1 1/8in. wall thickness do not require radiographicexamination in any of the above cases. 3 All categoryA and D butt welds . in vessel sectionsand heads where the design of the joint or part is based on joint efficiency 1.0,or 0.9. (see preceding pages: Design of Welding Joints). 4 All butt weldsjoined by electroslagweldingand , all electrogasweldingwith any

greaterthan 1 radiography,as a minimum,ismandatoryof

B or Cweldswhichintersectthe . CategoryA buttweldsinvessel sections(includingnozzlesand communicating chambersabove10 in. pipe size and 1in.wallthickness)or mmect seamlessvesselsectionsor headswhen the designof Catego~ A and D buttweldsinvesselsectionsand headsbasedon ajointefficiencyof 1.0or 0.9. 2 S . t weldedjoints(~ radiography p isoptionalofbutt o 1 2 w a hn i 1

r c o

) h

required to ~ filly ~diographed. If spot radiographyspeciiled for the entire vessel, radiographicexaminationis not required of CategoV B and C butt welds in nozzlesand communicatingchambers. No Radiography.No radiographicexaminationofweldedjoints is required when the vessel or vessel part is designed for external pressure only,or when the design of joints based on no radiographicexamination.

ULTRASONICEXAMINATION

I f e m r a r te i le etr c wi tn arca ole e ss l l lea wcgn dt w r e ao s sg li da i s d nnt sg h l y p g rat e 1 1 asih s t b esuha /l rtn r aa ns e o lnx2 i .cat al hm l elr yi ot nu ge h hd o eu t i e ln e t n i g r t eh . d t d t ir e t q iu ih.oornr en a md e i onoet gxs r a a m p ia h nwifa c tm ie ob lnt l,a d d lh 2 I a e l be cp ter or bo to aci n en a msce h os r n tdnr iy if ne r rua oi i du c s tv i eo n w e p l r sd o b i uhc ln t er aga ss e o slnx i caf al tm l el eyi h n lno e e td n i g r r rt eh 3 U l t er xa as mo mi n nb i .sa c tu ib oas f n t r i a t d u i yt foo eetg d fr a c p i ohlr hy on s a ru e s i t ec o n sa tho rt uv cm t dei f oen hsn p o s ei n eftoeree rl m rp ars edi tt i a ot b gl er a p

178

B

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B T A IP T E D RI F E FE H E D I TR H E N FI ECI M EK N T E O S 1N S H R O O N E N - FO O T UT R. HT R H PIH NL C N AF U EEOW T RU - E 9D W . ( - C E 1) , 3

T O E

L E OH NT TG ATE T H P HR E A RNF SSEE I D TH B I M O AIN N 3L T I TM LI UM E F B FE STT W A E DET J H ES A U N C R E F TENA WTC EM SH E B. p LAA OE R D N T I IT R T E A L SP HY E OC R N AT EE D D I J TOA I C N E NR T O

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1

APPLICATIONOF WELDINGSYMBOLS WELD

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MEANINGOF SYMBOL

n m

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b

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SYMBOL INDICATES 1/4 IN. INTERMITTENT FILLET WELD. EACH 2 P

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181

C

R

RELATED

Service i

VARIOUS

SERVICES Code paragraph

Brief extracts of Code requirements

A ip r ve lse rf s us uw s r cl e oe i m sl pas r et e r sxiea s hUec -d r e( p , 4t p e r o m t i h ti et t r pe wad h ir ssa ebg i hp r ra n aops hv l i dl ee d w s u i i i n t s t apo ebp chl e t e in o i n n g . V e w s a r s ei e m q l uit si tn rh ih ei omcld kut n m f s 2n ? e e Uh s - s s a C i t an t hb u c i rac so h m tpa e res eo eess ds r bei n hvd i a c r le l p r ow vc io i dr a r e l ot dl sno il who ta n n1e o coh e s a/ t s n 6 -2 t c a l cp h u t l lh a i t caM e k d t nt he i is 3e cs i .kn n1 Ue 1. s 3n s( 6

~ l a mE mx a p c b oa l nne n m o n o x d o g a u s e s m l i q u i dd L s u

To

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3 ht v ii he y d cshr o t ss ht ae te i .sce al tl l sye d 4f gt e d: t e e msh ip n eli r t ag o-t. eFu no rhw e 2e a 5dea t r n 0 t aa r onf el h v td i e 6n eFgo h s h 5 t 2 h. m e e rcs hml a ha ono cli a.oc,y ad c lc i l ni k g e t lan f eol i n wacd o dn ns d ti ror enoe lq gslu ii sirn t eg m

P

M CARBON& LOWALLOYSTEEL*

Form

~ 2

a&: C“S ~z ‘u c1 e E z M .-G 3 m

Specification Nominal Composltlon Number Grade

APPLICATION

c

SA-283

c

Structural uality. For pressurevessel maybeusea withlimitationsseenote: 1

c

SA-285

c

Boilersfor stationaryserviceand other pressurevessels

C - Si

SA-515

55 *

C - Si

SA-515

60 *

Primarilyfor intermediateand high temperatureservice 99 ——

C - Si

SA-515

65

– “ –

C - Si

SA-515

70

– “ –

C - Si

SA-516

55 *

C - Si

SA-516

60 *

C - Mn - Si

SA-516

65 *

C - Mn - Si

SA-516

70 *

C - Mn - Si

SA-105

C - Si C - Mn C - Mn - Si C - Mn

SA-181

C - Mn

For moderateand lowertemperature service 99 —— 99 —— 99 —— For hightemperatureservice For generalservice

SA-53

I LF1 LF2 B

SA-106

B

For hightemperatureservice

B7 *

For hi temperatureservice Bolt2* in. dam. or less

SA-194

2H

For hightemperatureservicenut

SA-307

B*

Machinebolt for generaluse

SA-350

ICr-1/5Mo. SA-193

For low temperatureservice For generalservice

*Forlowtemperature operation seepage185

* Dataof the most frequen~yused materialsfrom ASMECodeSectionII and ~11”

PROPERTIES OF MATERIAL (cont.)

Form

Specification Number

w b e 2

Grade

P Number

Yield Tensile Point Strength 1,000 psi. 1,000 psi.

See Notes

SA-283

c

1

55.0

30.0

1

SA-285

c

1

55.0

30.0

2,6

SA-515

55

1

55.0

30.0

3

SA-515

60

1

60.0

32.0

3’

SA-515

65

1

65.0

35.0

3

SA-515

70

1

70.0

38.0

3

SA-516

55

1

55.0

30.0

3,8

SA-516

60

1

60.0

32.0

3,8

SA-516

65

1

65.0

35.0

3,8

SA-516

70

1

70.0

38.0

3,8

1

70.0

36.0

2,3

1

60.0

2,3

1

60.0 70.0

1

60.0

30.0 30.0 36.0 35.0

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232

F

C

THE TABLES BELOW ARE FOR DATA OF FABRICATING CA}) ACITIES OF THE SHOP WHICH HAVE TO BE KNOWN B T V E D HES S ST I Y GCE EN OLE L HH R U . BEEN M A LEFT OPEN AND ARE TO BE FILLED IN BY THE USER OF THIS HANDBOOK ACCORDING TO THE FACILITIES OF THE SHOP CONSIDERED. MAXIMUM WIDTH in.

ROLLINGPLATES TENSILE STRENGTH OFPLATE p

s

i

MAXIMUM THICKNESS i

NE

MINIMUM DIAMETE; Rni

.

NOTE: FOR MATERIAL OF HIGHER STRENGTH THE THICKNESS OR WIDTH OF THE PLATE MUST BE REDUCED IN DIRECT PROPORTION TO THE HIGHER STRENGTH {

LA

LN I G N

LG

MINIMUM SIZE

MINIMUM DIAMETER in.

MAXIMUM SIZE

MINIMUM DIAMETER in.

LEG OUT

Q

O

MINIMUM DIAMETER in.

LEG IN

3

R

MAXIMUM SIZE

E

4

S

LEG IN

.% Q

LEG OUT

ROLLING BEAMS

MAXIMUM SIZE

ROLLING CHANNELS

MINIMUM DIAMETER

i

FLANGES Q

IN

Q

FLANGES OUT MAXIMUM SIZE

ROLLING FLAT BAR Q

ON EDGE

MINIMUM

DIAMETEllin.

233

F

C NOMINAL PIPE S1z i?

MINIMUM RADIUS in.

SCHEDULE

BENDING PIPES

PLATE THiCK~ESSin.

MiNiMUM PLATE iNSiDE i THICKNESS RADIUS in.

MINiMUM iNSiDE RADiUS

n

BENDINGPLATES WITHPRESSBRAKE

MAXiMUM PLATE MAXiMUM PLATE DIAMETER in. ::AHMoELTEEi: THiCKNESS in. OFHOLE in “ri-ilCKNEss PUNCHINGHOLES

vliNiMUM iNSiDEDiAMETER 3E’VESSEL Accessible FOR iNSIDEWELDING

inches

TYPES OF WELDINGS AVAILABLE FURNACES FOR STRESS RELIEViNG

WIDTH ft. HEIGHT MAX. TEMPERATURE

ft. F.

A

I

LENGTH

ft

234 —

P I s o

b

e

a np

do t ii

A tnu n o gp

IT

B PN UE

bp u

N* EB D D I

oh eet t a br

e c co m t p ari e aos t s nre dn eo, o h s p

paud

EN

G

, ei s er e ht r r a et n t t f i ce

hd nn e sh

ous l esn t si en tt f qr et eup s ad s

l ieh

r tube tends to flatten or collapse. To prevent such distortion, the common

practice is to support the wall of the pipe or tube in some manner during the bending operation.

This support may be in the form of a filling material, or,

when a bending machine or fixture is used, an internal mandrel or ball-shaped member may support the inner wall when required.

MINIMUM R4DIUS:

The safe minimum radius for a given diameter, material,

and method of bending depends upon the thickness of the p

w

i ba

possible, for example, to bend extra heavy pipe to a smaller r

at

pd

pel ho i

i u

standard weight. As a generalrule, wrought iron or steel pipe of standard weight may readily be bent to a radius equal to five or six times the nominal pipe diameter. The minimum radius for standard weight pipe should, as a rule, be three and one-half to four times the diameter. It will be understood, however, that the minimumradius may vary considerably,dependingupon the method of bending. Extra heavy pipe may be bent to radii varyingfrom two and one-halftimes the diameterfor smallersizesto three and one-halfto four times the diameterfor largersizes.

d

d

R (

t 4 3 S

t

aP

f d n

I d i a

i r

R to 4d)

o )( Ee

pd

Hx

2 Pe t

% a ir

MINIMUMR4DIUS

*FromMachinery’sHandbook,

Industrial Press, Inc. - New York

va p

y

235 PIPE ENGAGEMENT LENGTH OF THREAD ON PIPE TO MAKE A TIGHT JOINT

I

Nominal Pipe Size

I I

1/8

I I

1/4

I I

3/8

I I

I Dimension [ Nominal I Dimension Pipe A A Size inches inches 1/4

I

3-1/2

3/8

I

4

3/8

I

5

1/2

I

6

3/4

I I I

9/16

I

8

1

I

11/16

I

I I I

1-1/4 1-1/2

I I

11/16

2

I

3/4

I I I

I

2-1/2

I

15/16

I

I I

I I

1-1/16 1-1/8

I I I

1-5/16

I

1-7/16

I

10

I

1

12

I

1-3/4

I

D I M E DN NS IA O NL F SO V L A R OOI T A WT I I T A OP T PH R I EN A N GD I NR G

R O

1/2

}

I

-

I

5

N

DRILLSIZESFORPIPETAPS Nominal Pipe Size 1

b

I

Tap Drill Sizein. / 1

Tap Drill Sizein.

Nominal Pipe Size 1

8 /

23

2

2

-

1/4

7/16

2-1/2

2-9/16

3/8

19/32

3

3-3/16

1/2

23/32

3-1/2

3-11/16

3/4

15/16

4

4-3/16

1

1-5/32

5

5-5/16

1-1/4

1-1/2

6

6-5/16

1-1/2

1-23/32

-

3

/

.

236 BEND ALLOWANCES For 900 Bends in Low-Carbon Steel Metal Thickness (t) in.

Bend Allowance Inches With Inside Radius (r) in. 1/32

1/16

3/32

1/8

1/4

1/2

0.059 0.087

0.066

0.079

0.093

0.146

0.254

0.050 0.062 0.078 0.090 0.125 0.188 0.250 0.313 0.375 0.437 0.500

0.105 0.128 0.146 0.198 0.289 0.382 0.474 0.566 0.658 0.750

0.101 0.118 0.142 0.160 0.211 0.302 0.395 0.488 0.580 0.672 0.764

0.114 0.132 0.155 0.173 0.224 0.316 0.409 0.501 0.593 ~ 0.685 0.777

0.129 0.145 0.169 0.187 0.243 0.329 0.424 0.515 0.607 0.699 0.791

0.168 0.183 0.202 0.217 0.260 0.383 0.476 0.569 0.661 0.752 0.845

0.276 0.290 0.310 0.324 0.367 0.443 0.519 0.676 0.768 0.860 0.952

0.032

r&I

‘1 4

ben~~l~o~~n~e

=a+b+c– w=a+b+c+d– w=a+b+c+d+e– (2 x!end allowance) (3x bend allowance) (4x bend allowance)

Note: w = developed width (length) of blank, t = metal thickness, r = inside radius of bend. EXAMPLE: Carbon steel bar bent at two places. The required length of a 1/4 in. thick bar bent to 90 degrees with 1/4 in inside radius as shown above when the sum of dimensions a, b and c equals 12 inches, is 12 -(2x 0.476)= 11.048 inches MINIMUMRADIUS FOR COLD BENDING: The minimum permissible inside radius of cold bending of metals when bend lines are transverse to direction of the final rolling, varies in terms of the thickness, t from 1-1/2 t up to 6 t depending on thickness and ductility of material. When bend lines are parallel to the direction of the final rolling the above values may have to be approximately doubled.

—

237 LENGTH OF STUD BOLTS FOR FLANGES *

1. Length of the stud bolts do not include the heights of the point. (1.5 times thread pitch) 2. Plus tolerance offlg. thk’s. Sizes 18in. &smaller 0.12in. Sizes 20 in. andlarger O.19 in. 3. Minus tolerance ofstud length Forlengths upto 12’’incl. O.O6in. For lengths over 12“ to 18” incl. 0.12 in. For lengths over 18” 0.25 in. 4. Rounding.offto the next larger 0.25 in. increment. 5. Gasket thickness for raised face, M & F and T & G flanges 0.12 in. For ring type joint see table page 346 and take half of the dimensions shown, since in dimension “A” only half of the gasket thickness is included. *Extracted from American National Standard : ANSI B 16.5 - 1973 Steel Pipe Flanges and Flanged Fittings.

1

238

P

V

D

IN THE PRACTICE THERE A S E RVD E I FRFW EAE RLO EAD N E T TY A I P R E VS S E . UB S RM S E EA TL K DS IR A NHYAWG L I W N WEG T A S S YT SH A M E CT O N H S O I D T E D R ,A C B I BL ES MAA A A VE T NE N Lp OE S DS SH DI L OI T I BO E R A R L O TE R R ESSC OHS ME MM E. N E DE I E T D FH O O L H PL D OR ~N OE N P R A C A T G I EC NAN E A L R CA CL D EL PY T E D .

A. Select the scale so that all HORIZONTALVESSELS 4

f 3nd View

Ref.line

1-

ELEVATION w Saddle MIS~~~~~SEOUS ~

B. Show right-end view if necessary only for clarity because of numerous connections, etc., on heads. In this case lt is not necessary to show on both views the connections etc., in shell.

C. Show the saddles separateGENERAL ly, If showing them on the SP~~EC~~CA-

BLOCK TITLE

1

openings, seams, etc., can be shown without makin the picture overcrowd f or confusing.

end view would overcrowd the picture. On elevatlon show only a simple icture of saddle and ! he centerlines.

D. Locate davit. E. Locate name plate.

L

F. Locate seams, after everyth.mg 1s m place on elevation. The seams have to clear nozzles, lugs and saddles. G. Show on the elevation and end view a simple lcture F etc., of opemngs, internas, lf a se arate detad has to be mat e for these. H. Dimensioning on the elevation drawing. All locatlons shall be. shown with taded chmenslons measured from the reference line. The distance from ref. line ~odbeshown for one saddle The other saddle shaY1. be located showing the dimension between the ;-w$~~ bolt holes of the

END VIEW

I. Two symbolic bolt holes $~aytdy tlgn%~le~~t~ straddling the parallel lines with the principal centerlines of vessel.

239 P

R

E

VS

SE D U SER TES A( EI cL L Io N n G

O

r

i

‘-E* e

n

t Ea

tl i e o vn

a

t Bi

M I S C E L L AD N E EO U TS

b

[

TIIle

G SA c

.

)

A. Select the scale so t a openings, trays, seams, etc., can be shown without making the picture overcrowded or confusing.

VERTICAL VESSELS

+

t

h

B. If the vessel diameter i unproportionally small to na s e the length, draw the width a of the vessel in a l

o

s t ch s a ae p n f e a dr ea ot l la eL c S i f i tc. T i o o r in e h sin nt t v b i ao s ec i n f o r a m at b t c ao n t o e iz

e pI a

Block

D. S

t

ho

r

ln i

r av eo l r s l

a a t i e o no h u we pm , l i oo n h z o lt ne

i oe h sn

t

aw t

E

.

F

.

3

mS

. @

: u

. ---

Em

G. ORIENTATION PLAN

degrees: 00, 900, 1800, 2700 and use it in the same position on all other orientations.

240 —

PRESSURE VESSEL DETAILING (cont.)

Nozzle on Top or ~ottom

00 ~—+ H. It is not necessary to show internals on vessel orientation if their position is clear from detail drawings or otherwise. J. Draw separate orientations for showing different internals, lugs, etc. if there is not space enough to show everything on one.

,

K. For vessels with conical sections, show 2 orientations if necessary, one for the upper section, one for the lower section. L. Two, symbolic bolt holes shown in flanges make clear that the holes are straddling the lines parallel with the principal centerlines of vessel.

~1

M. If there is a sloping tray, ,

1800

(

partition plate, coil, etc., in the vessel,show in the orientation the direction of slope. J

O

(JO

27oo

.

. ●

t

w 1

1800

8 Lowest 0

Point of Plate “D” ORIENTATIONS

2

PREFERRED LOCATIONS Of Vessel Components and Appurtenances

A. Anchor bolts straddle principal centerlines of vessel.

B. Skirt access openings above base minimum to clear anchor lugs, maximum 3’-0”.

c. Skirt vent holes as high as possible. I

I

D. Name plate above manway or liquid level control, or level gauge. If there is no manway, 5’-0” above base.

I

-.

r

H

I

E. Lifting lugs - if the weight of the vessel is uniform, “E” dimension is equal .207 times the overall length of vessel.

F. Manway 3’-0” above top of platform - floor plate.

G. Insulation ring must clear girth seam and shall

1

be cut out to clear nozzles, etc.

H. Insulation ring spacing 8 - 12 feet” (approx. length of metal jacket sheet).

J. Girth seams shall clear trays, nozzles, lugs.

.,

K. Long seams to clear nozzles, lugs, tray downcomers. Do not locate long seams behind downcomers. Seams shall be located so that visual inspection can be made with all internals in place. Longitudinal seams to be staggered

I & %’ +

1

i p 8o

s

s0 i

b

0l

ef .

L. Ladderand platformrelation.

3_u

v .

+

A

M. Davit and hinge to be located as the manway i most accessible, or right hand side. s

N. Ladder rung level with top of platform floor plate. The height of first rung above base varies, . minimum 6“, maximum 1’-6”.

242 COMMON ERRO RS in detailing pressure vessels

Interferences

A.

Openings, seams, lugs, etc. interfere with each other. This can occur: 1. When the location on the elevation and orientation is not checked. The

practiceof not showingopeningsetc. on the elevationin their true position, may increasethe probabilityofthis mistake. 2. The tail dimensionsor the distances between openingson the orientation

do not show interference, but it is disregarded,that the nozzles,lugs etc., havecertain extension. Thusit can take place that: Skirt access opening does not .clear the anchor lugs. Ladder luginterferes with nozzles. . . The reinforcing pads of two nozzles overlap each other. Reinforcing pad covers seam. . Vessel-davit interferes with nozzles. This can be overlooked especially if . the manufacturer does not furnish the vessel-davititself, but the lugs only. f Lugs, open%gs, etc. are on the. vessel seam. on perimeter of the skirt for the required number of ! There is no room 3 . anchor lugs.

a b c d e

Particular care should be taken when ladder, platform, vesseldavit etc., are shown on separate drawings, or more than one orientations are used. B.

Changes. Certain changes are necessary on the drawing which are earned out on the elevation. but not shown on the orientation or reversed. Making changes, it is

c.

advisableto ask the question: “Whatdoesit affect’?” For example: Billof material The changeof materialaffects: Scheduleof openings Generalspecification Legend Orientation The changeof locationaffects: Elevation Locationof internals Locationof other components. ShowingO.D. (outside diameter) instead of I.D.(insidediameter)or reversed.

D.

Dimensionsshownerroneously: l’4Yinsteadof 10” 2~0’insteadof 20’etc.

E.

Overlookingthe requirementof specialmaterial

)

2

1

PRESSURE VESSEL DETAILING (cont.) \

E

M S W

G

.

D P

R

T

E

E P S M

P

E

@ SS R O

U

A

T

R I U

R

E

A X A H A A M O I R G KN &INC N GT

EF

.Y X

. L

I

z o W z u ‘ c S 8 E W

BM P

R

O

I

T

I RL

E

W W W

C I

B E N F

E F

I R W

I

Y

/ D S S

T. QC

EC C N

R FE

H T I I P O P NI GS H ST

L A E

D

SS

F IS EO M

E ( CS E L I

P

E

G U T B

H

ETL

I I N

A

E

R

A x

RA .

O

LSI

W LP T . R E

LT /S R H

I L O

OH E A@ 1 T

ST

FL

H

A

N

K

N

O N

Z

.

G

D I ON A E N C SE M 1 E

Z E

L

CE

KB A

B

O

L

T

I

N

G

c

L

o

I

u

N

p

G

L N0

Y

TA T 0

P

A

S

K

I

E

N

.

A

S

BN

CO D

T

E H

D

. E

I

L

L E

. S

.

A

T 0

K

K

A

D

P

W F

G

N

H

R

S

.

LI Y

A

T

S

E

NW

.

T T

N O

D I O G R A P H I C I TM I N A T I O N A

G L )O N G I T JU E F F I C I .

N

G G B

O.

5

E * a z

T

T

.

T

t I

m

V R

.

.

a

~

. D E

.

E

S RE

S QE

E

L U

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S I

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A S W

P H

P I E L

R P I

P GB

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X N H

. G ST

. d

m

—

5 1

)

●

! I

OPENINGS

PRESSURE VESSEL DETAILING (cont.)

I

Detailingopenings as shownon the oppositepage with data exemplifiedin the scheduleof openings below, eliminatesthe necessity of detailing every single opening on the shop drawing.

Y

I

c-1 A/-f

/lvLET

M-l

/%llvw/ly

2 6 3 3 /8’ 3

c 0G w 0~ w0N

— “- ? -& ~– f- . – — ) 0 ) ( “ ’ I 5 ( 5343 H —. . Y. = 6&” S* 53-49 X 0 H . . 24*X~2“ S/l 5 M

SEnVICE

SIZE

RATING

TYPE

D

29Z” MIN. 8 A “ MlIv.

v // /~

-

yd” M//u..

~/

5 2

~-

M

BORE

yg- Nw.

j 0 7T a

# 0

%

b

c

”/ & “

O R

WE LO SIZE L

1

E

LE OF

GS

/~

r

246

TRANSPORTATION OF VESSELS

Shipping capabilities and limitations.

1.

TRANSPORTATION B TRUCK. The maximum size of loads which maybe carried without special permits a. weight approximately 40.000 Ibs. b. width of load 8 ft., Oin. c. height above road 13 ft., 6 in. (height of truck 4 ft., 6 in. to 5 ft., Oin.) d. length of load 40 ft., Oin. Truck shipments over 12 ft., Oin. width require escort. It increases considerably the costs of transportation.

2.

TRANSPORTATION BY R41LROAD. Maximum dimensions of load which may be carried without special routing. a. width of load 10 ft., Oin. b. height above bed of car 10 ft., Oin. With special routing, loads up to 14 ft., O in. width and 14 ft., O in. height may be handled.

247

P O

S

T S

U ER

F E A F CL

E

S

P U R P O S E T m p ahu o r p ipa eio t ns p t r e ei s nhe of r ga vs a ts sit euo nT r e fp ae r fac eh l e it . a t c o r 1 hr b op sr ei .vtoe ecn n o t o i nc,h nyo tg r aa r ocgfe s tte i vr v nf ese t ouhsa s r s m f ea 2 b r i n .uh ie lb e ics tt r ,io y-v cpt eh er , mo i cop at el pr t m ia ae h st i e r n fi e a t l . T a

p b

ar

am h ib s un u tie sr t s aet tbe s l ef oie fht aa s co i cn toh en i m oi d c na l sf .

s e on tcv i thre oh sn m i eef mne t ap,

a

S U RP RF E PA A CR AE T I O N T p r r ih e mq f uaa si reus yc i ocp t e ej s a is t f r iru loe n o mhm t os bvrci s aed a u l l li s f g r o ea fa os m i ren a e, M t i s lt gdi i ect n br lal .u i hsl t hl - l ehg r osa iei y o, y c r x e ki o w fh oo i s t r cr us mhc s t t uus b r esnat e tl qe h u r e l no hot lpo e l r Io i ate tnmt i go n ih . s i ic na a a t dl at hn ei c te gts tr mh ed tie sp hl tr yop a rv ool ie tt d,et ces tt s hit o hen o e e d v t t e r u or a lh d , l i e oi snpo n eh l cg i ao nmdt pig e l enm s ft s ,et l i i aycs ce al tl l e n c o ui np t r e a r ec dt i c en . I m s p r ot

i i nc b a l c a r ol f ald s ce p lks ht er wy dgi ,ol m i l i iepoml ir ev n nvil i fre o gnl m e e vt l i h dm o es had orci o atsug le l r eeis ea l rt a , lt e s ,m er c,o , v e . de .

E C O CN O N O SM I D E I R CA T I O N S T s e l o hep c a ta s i eoui p n rrn ne f p f baat r cead t t etyi oe noc a h n sn i dnip a p r o o e cb o l n eo mm i c sf . T c a d e x d i s a n o s S T a t t

clu

rt

o p oh i na os i r2 e m n5t oa lf - l t o l t3 s eyc 0 o p %soha ai sr snts rft etu i ct t n t f hgu r v o a u n ht s a q g i iue p an i galaf gpi i p ht Sa yn r p ie et n oxtrm s . c ot t e o t y n tor h o p a pe jn a l s i i et i os n fu p etrrh e fb p saa rnt cae ct e i o on p nohr e p tas d r ae t t f d f ee i rvg e ar ni erat p ye r osi p on o1s trg 1t i n0o F n ex 1 atf o 2mc o p.o l oh er d bi la a s 1bt i tn 0og h i - u it ms1tgt ohe h2t h h es a w r aabh nr i u t nTs f chre i d n oehg u p ~r e f p saa r hcab fbt eoi a o unla a gl t n ai dc n i e ce lndrh o set avit s e ee fsdh s ee

E L E O C P T I SA O YN I S TN FE T M S t ao t h b f ol l pelhe o ss aw a inegg ne gurt e s i v ste d p el e r pse shao c si op nt y te e s i r e s tt n ir me aqq h dtuu eiao pr n eetf a dvi t ai sy r o en ci fro otn v du rTii st dci o e n ash a b t u lh h a b t eaet de fr a v t eekSr e S e t nt o h r neuP c m a te Ciue onr l euts snpi cen ic g li f’ a i r e c oo m m n ne n d a st i o dn s .

C o a s S

ca e eat

n s P

s ti ds e er vi vnha g re o i pr a a aeb ip ll rne ots i b ii lan fed g mv t si r ,s e a t bq t l su e oi ps t ma a a n n cu i f e a c nt u fr et r s . C E O CN D I I A T IL O N S

A B R A S I O N W t ph a m i eh nr t uaen i b nser tsga ig s asit odoht nho t, e oc s oei i dpoah a ntr t i i cf n ue l i m p o F r mt a a n xaot d.i h mb e ucsr l m il oei at na b, ns a i a etnh p g i l ns ic ss ke s alt id t f a cP r t e to r er sa yt am . he u np t hs oc oos w p hph asa r att eei xs mc f re eeh l t l r ec o ne h

and rougheningthe surface. Urethane coatings,epoxies and vinyl paints have very good abrasion resistance. Z rich coating,and phenolicpaints are also good. Oleoresinouspaints may develop m greaterresistanceby incorporationof sand reinforcement.

i u

248

H T EI M P E GR A T H U R E B t e e m lp e o r o5a t0 uw0 r -et so6 0 ba 0g °t f s F aou f ir c o ofon ha optdc h i e o n os gr t r e i a s ta t mi se fAna ct 5t b o 0 r 0yso . a- blast 6v cleaned 0 0e °surface F is desirable.

Recommended Paints: u

to

2 2 3 3 7 8

C

O

R

2 3 4 5 8 0

0F 0F 0F 0F 0F

0 Oil base0 5ppaints limited period 0 0 or phenolic 0 An alkyd vehicle 0 0 modified- alkyds 0 Specially 0 Colored0 5silicones 0 0 zinc coatings 0 Inorganic above 550 F Black or Aluminum silicones 0 F - Aluminum 1 2 silicones 0 0 up to 1600-1800 F Silicone ceramic coatings

R C O H S E I MV IE C

A

L

S

See tables I and V for the selection of paint systems. THE REQUIRED QUANTITY OF PAINT Theoretically, one gallon of paint covers 1600 square feet surface with 1 mil (0.001 inch) thick coat when it is wet. The dry thickness is determined by the solid (non volatile) content of the paint, which can be found in the specification on the label, or in the supplier’s literature. If the content of solids by volume is, for example, 60%, then the maximum dry coverage (spreading rate) theoretically will be 1600x .60-= 960 square feet. THE CONTENT OF SOLIDS OF PAINTS BY VOLUME $% I

%

%

50

1 2 &

3 4

70

70

15 1

6

5 6 8 9

Varnish Paint Aluminum Vinyl Paint White

14

103 104

Black Alkyd Paint Black Phenolic Paint White or Tinted Alkyd Paint,

70

106

Black

37 57 47 - 50

In practice, especially with spray application, the paint never can be utilized at 100 percent. Losses due to overspray, complexity of surface (piping, etc.) may decrease the actual coverage to 40-60$Z0, or even more.

. )

- .

P T

A

I

A I P

s

T

B SA

@

E , TM

1St Coat

2nd Coat

3rd Coat

(:?7)

104 ( I .3) 14

104 (1 104

i Condensation, chemical fumes, brine drippings and Other extremely corrosive conditions are Q present

G S

Paint and Dry Thickness, Mi]s See Table IV

E;=

~ 0: WL+

N

YL I S E TN

~

C

Ps

I

z

c .-o :?=

System Number

N

2

Not

or

Req’d

::h,

&

:;::. ness

104

(1’.;)

5.0 104 (i .3)

(1‘7)

I

3

(1 I

(I I

I (

I

( 1?)

( IC5) 104 (1 .5)

104 (1

(

I ( I .5)

(1

( lc5)

Steel surfaces exposed to the weather, high humidity, infrequent immersion in fresh or salt water or to mild chemical

6

a

or

Not R E

8

5.0

I

(I

Steel s exposed to alternate immersion. high humidity and condensation or to the weather or moderately severe chemical atmospheres or immersed in fresh water Immersion in salt water or in many chemical s c severe weather exposure or chemical atmospheres 4.02

5, 6, 8, or

I , 2, 5, or 6 3, or ( 1.5)

5. or 6 ( I .5)

I 03 (I

5, 6

or 103 *

4

9

G

9

(1G5)

Fresh water immersion, condensation, very severe weather or chemical atmospheres

10

Complete or alternate immersion in salt water, high humidity, condensation, and exposure to the weather

Not Req’d

(lHs)

3 **

( 1!5)

5.5 H

H

H 6.0

6

or 8 6 or 8 6 or 8

404

Condensation, or very severe weather exposure, or chemical atmospheres 4,05 Condensation, severe weather, mild chem]cal atmospheres

9

Not Req’d 3 **

8 4,0

(192)

9

9

(1:5)

F

F

4.5

9

4,0 I

Steel vessels p

t

f

w

s f

w

Dry, non corrosive environment, inside of b t w t

Longtime protection in sheltered or in8.01 accessible places, short term or temporary in corrosive environments p

1

G

G

Corrosive or chemical atmospheres, but should not be used in contact with oils, solvents, or other agents Underground and underwater steeJ struc-

3

(1?)

G

G

G

G

3

n

o

c

ing 1 and 2 or 3

m Req’d

e p

7.0

(1

~

n

a

l

3

K 6.25

I

,/

M (

L

)

(wet)

12 63

63

Not (

)

)

)

d r

w

i

Not R

R u

(1.5)

Not Req‘d

6

tures U c

G (2.0)

G

8

6.03

10.01

(1%

6;r

w

9.0 I

3 6

or for high tempera-

ture *Four coats are recommended in severe exposures

6

0

Req’d (1!-18)

(25)

(8! 5)

35

**The dry film thickness of the wash coat 0.3-0.5 roils.

250 T

A I P

BS A

YL I S( Ec T No G

.-o Uz= Ob

{stem Imber sPcPs

;

Fresh or sea water immersion, tidal and splash zone exposure, condensation, burial in soil and exposure of brine, crude oil, sewageand alkalies, chemical fumes, mists High humidity or marine atmospheric exposures, fresh water immersion. With proper topcoating in brackish and seawater immersion and exposure to chemical acid and

I

I ~,oo

I

6 :;

P

R

e

f

e

r

A I e

n

T

I a 1

b W

l E

T O

d

)

n c nk h i iroils

n

te

;= gbl

1

,Zg Not Req’d

coat

2nd Coat

(’l:)

(’l:)

3rd Coat

&

::!t

;;:-

32

Zinc-rich coatings comprise a number of different commercial types such as: chlorinated rubber, styrene, epoxies, polyesters, vinyls, urethanes, silicones,

Epoxy Paint System

P RB E I T RL E AI T E S PME EC N ,I FT I C A T I C I N S c

t

a T

e

See Table IV

subject to chemical exposure such as acid and alkali.

T

a

E-

:

?J&~

nE , T t Mi n S u

e To e

a iP

TT R I E NA I

ut

G T

M

rn l p

E LN

oe

T

sdS p e e c i f i c N u m

S

S

P C 1-64

Saturation of the surface layer of rusty and scaled steel with wetting oil that is compatible with the priming paint, thus improving the adhesion and performance of the paint system to be applied. 2

C C

P O H o n vt

O S L SP U H AD RT T RF E E A A CT ME ES N ST 2 P es r ut of i rsteel hn gf to insoluble a c e salts e

of phosphoric acid for the purpose of inhibiting corrosion and improving the adhesion and performance of paints to be applied. 3

4

BASIC ZINC CHROMATE-VINYL BUTYRAL WASHCOAT(Wash Primer) Pretreatment which reacts with the metal and at the same time forms a protective vinyl film which contains an inhibitive pigment to help prevent rusting. HOT PHOSPHATE SURFACE TREATMENT Converting the surface of steel to a heavy crystallinelayex of insoluble salts of phosporic acid for the purpose of inhibiting corrosion and improving the adhesion and performance of paints to be applied.

SSPC-PT3-64

SSPC-PT4-64

C-

2— . P T %

e

f

e

A I , r

e

n

c

t T

I a 1

2

3

4

5

6

7

8

10

b S

SB U e T

l O

LC

A

I

N

T

I

N

G

PRL R FE E PA A CRSI A E~ T ~ lI FO I NC A T I O N S

oa

iP

EE

AN N T I

ut

rn l p

oe

e V L

5

N

G

Removalof oil, grease, dirt, soil, salts, and contaminantswith solvents,emulsions,cleaningcompounds,or steam. HANDTOOLCLEANING Removalof loose mill scale,loose rust, and loose paint by hand brushing,hand sanding,hand scraping,hand chippingor other hand impact tools, or by combinationof thesemethods. POWERTOOLCLEANING Removalof loose mill scale,loose rust, and loose paint with power wire brushes, power impact tools, power grinders,power sanders,or by combination of these methods. FLAMECLEANINGOF NEWSTEEL Removal of scale, rust and other detrimental foreign matter by high-velocity oxyacetylene flames,followedby wirebrushing. WHITEMETALBLASTCLEANING Removalof all mill scale,rust, rust-scale,paint or foreignmatter by the use of sand, grit or shot to obtaina gray-wh~te,uniformmetalliccolor surface. COMMERCIAL BLASTCLEANING Removalof mill scale, rust, rust-scale,paint or foreign matter completely except for slight shadows, streaks, or discolorationscaused by rust, stain, mill scale oxides or slight,tight residuesof paint or coating that may remain. BRUSH-OFFBLASTCLEANING Removalof all except tightly adheringresidues of mill scale, rust and paint by the impact of abrasives. (Sand, grit or shot) PICKLING Completeremovalof all mill scale,rust, and rustscale by chemical reaction, or by electrolysis,or by both. The surface shall be free of unreacted or harmfulacid, alkali, or smut. NEAR-WHITE BLASTCLEANING Removalof nearly all mill scale, rust, rust-scale, paint, or foreign matter by the use of abrasives (sand, grit, shot). Very light shadows,veryslight streaks, or slight discolorationscaused by rust stain, millscale oxides, or slight,tight residuesof paint or coatingmay remain.

sd

Se p e c i f i c a t i N u m b

S

1-63

SSPC-SP2-63

SSPC-SP3-63

SSPC-SP443

SSPC-SP5-63

SSPC-SP6-63

SSPC-SP7-63

SSPC-SP8-63

SSPC-SP10453T

I

252 ——

.

P

A

T :e t ~

r

e

1 a 1

2 3 4 5 6 8 9 1

12 13 14 15 16 102 103 104 106 107 .— A B c D E F G H I J K L M N o P

n b

c l

fe Mo e

I

A I

a

N P

t

T

B A

e

r

I W LI

i

Red Lead and Raw Linseed Oil Primer Red Lead, Iron Oxide, Raw Linseed Oil and Alkyd Primer Red Lead, Iron Oxide, and Fractionated Linseed Oil Primer E P Z R A W R

x

tR e L n R de aee Bad aoLd r i m e r D Z i u O nsi xa P it cnh d V e, n L I e Oe ar xa P di ohd dV e, n l u V m Pi i n a un m i y ( hC o i V l o ot P i r eea n dr I O r exZ Ci 1 oh i d r dRo en L nm

N

G NE

a

l

T ,

S

N

u

m

1-64TN0.

1

2-64

2

No.

344TN0.

3

nd di O, n i ws e d e di e d 4 6 44 neak P o r, l na id 5-64T i c i sNo. hn5 6 nean P o r, l na di i c i -s 6 hn 64 8-64 No. 8 n l t i) y n l t9-64 No. 9 , ai O t nca e s, e iw e d

11-64TN0. 11 and Alkyd Primer 12-64 No. 12 Cold Applied Asphalt Mastic (Extra Thick Film) 13-64 No. 13 Red or Brown One-Coat Shop Paint 14454TNo. 14 Red Lead, Iron Oxide & Linseed Oil Primer 15%8TN0. 15 Steel Joist Shop Paint Coal Tar Epoxy-Polyamide Black (or Dark Red) Paint 16-68TN0. 16 Black Alkyd Paint 102%4 No. 102 103-64TNO. 103 Black Phenolic Paint White or Tinted Alkyd Paint, Types I, II, III, IV 10444 No. 104 Black Vinyl Paint 106-64 No. 106 Red Lead, Iron Oxide and Alkyd Intermediate Paint 10744TNO. 107 Paint; Red-Lead Base, Ready-Mixed Type I red lead-raw and bodied linseed oil Type II red lead, iron oxide, mixed pigmentalkyd-linseed oil Type 111red lead alkyd Primer; Paint; Zinc Chromate, alkyd Type Paint; Zinc Yellow-Iron Oxide Base, Ready Mixed, Type II-yellow, alkyd Paint; Outside, White, Vinyl, Alkyd Type Primer; Vinyl-Red Lead Type Vinyl Resin Paint Paint; Antifouling, Vinyl Type Paints; Boottopping, Vinyl-Alkyd, Bright Red Undercoat and Indian Red Finish Coat Enamel, Outside, Gray No. 11 (Vinyl-Alkyd) Enamel, Outside, Gray No. 27 (Vinyl-Alkyd) Compounds; Rust Preventive Coal Tar Enamel and Primers Coal Tar Base Coating Coating, Bituminous Emulsion

TT-P-86C

b

m z l : T N + t < Tt N : ~ U l

: ~ m “ & ~

;Z z.~ TT-P-86C ~z TT-P-86C 32 z~ TT-P-645 ~k MIL-P-15929B ~ j MIL-P-16738B ~ 2 MIL-P-15929B ~ & a II VR-3 Lg MIL-P-15931A I > * !+; MAP44 X’2 MIL-E-1593513 .5 : MIL-E-15936B ~ ~ 52-MA602a ~ .5 MIL-P-15147C j z MIL-C-18480A ~ ~ MIL Are complete weld-details for all welds shown on drawing? ......... c) Are copies of WPS(s) available to shop s u p efor rinstruction? v i s .............................................................. o r E

256

CHECKLIST FOR INSPECTORS(corztinuec/) 1 I QC

7.

Al

d) Isa Welder’sLog and QualificationDirectory kept up-to-dateand available?. . . . . . . . . . . . . . . . . . . . . . . . . . . . e) Are WPS,PQR, & WPQforms correct and signed?...................... f) Are weldersproperlyqualifiedfor thickness,position,pipe diameterand weldingwith no backing(whenrequired)?............... g) Is sub-arcflux,electrodesand shieldinggas(es) used t same as specifiedon applicableWPS?. ........................................... h) Do weld sizes (fillet& butt weld reinforcement) . ............................... complywith drawingand Code requirements? i) Is welder identificationstampedor recordedper QC Manualand./orCode requirements?..........................................

I

Non-DestructiveExamination& Calibration: a) Are SNT-TC-lA cmalificationrecords with currentvisual examinationavail~blefor all RT techniciansused? ....................... . b) Do film reader sheets or checkoff recoid~sbo.wfilm. intemretationby a SNT’-~CLeve1 I or II examiner —. or interpreter?.................................................................................. c) Are the requirednumberof film shots in the proper locationsfor thejoint efficiencyand weldersused (UW-11, 12,& 52)? ........................................................................ d) Is an acceptablePT and/orMT procedureand personnel qualifiedand certifiedin accordancewith Sec. VIII, Appendix6 or 8 available?............................................................. e) Is the PT materialbeing used the sameas specifiedin the PT procedure?......................................................... Do all radiographscomplywith identification, o density,penetrameter,and acceptancerequirements of Sect.VIII and V? ........................................................................ !3) For 1331.1fabrication,is a visual examination procedureand certifiedpersonnelavailable? ................................. , h) Are tested gasesmarkedor identifiedand calibratedas stated in QC Manual? ................................................ i) Isa calibratedgage size per UG-102available for demovessel?.............................................................................. I

I

ABBREVIATIONS: Authorized Inspector AI Maximum Allowable Working Pressure MAWP Maximum Design Metal Temperature MDMT Quality Control $; Radiographic Examination Serial Number s/N Shop Order Slo Welding Procedure Specification Wl?s

257

PART II. GEOMETRY 1.

AND LAYOUT OF PRESSURE VESSELS

GeometricalFormulas........................................................................... 258

2. GeometricalProblemsand Constmction.......""".."""."""-""""".".""""""."..."""""-" 268 3. Solutionof Right Triangles .................................................................. 270 4. OptimumVessel Size ............................................................................ 272 5. Flat RingsMade of Sectors .................................................................. 274 6.

Fustrumof ConcentricCone ................................................................. 276

7.

Fustrumof EccentricCone ................................................................... 278

8.

Bent and Mitered Pipes ........................................................................ 280

9.

Intersections.......................................................................................... 281

10. Drop at the Intersection of Vessel and Nozzle ..................................... 291 11. Table for Locating pointS0n2:l

Ellipsodial Heads ............................ 293

12. Length of Arcs ...................................................................................... 297 13. Circumferences and Areas of Circles ................................................... 300

1

A p p u r4 t ............................................................................ e n a n c .e s

312

258 G E O M E T FR O I C RA M L (

e S

❑ l

’

b

xS Q

U

A% A A = a2 d = 1

b

b

o

R

.~

4

1

=

a

4

a

R E C A A a A d =

T

A N r

G

L e

x

7

1

E = =

a b

~

~

a =$

-

A or- b = — a

o

i

gn n e

eg

)

r

-

r

P A R A L L E L O G R A M A A r e = a A a x = b = A a T = J A b y

A

r a .

A

900

A ,6,

S

2

R I G H T - A TN G R L IE D A c

A

;

, d o 7 a =0

o

L

E e

a = 0

b =

b

A

=

a =

B

l ap ee h cs a

r

.

I

D

ao m t e fp

U

axb A=,

e

=~

N

G a

L

E

~

’

b ‘I/== ~= a2 +b2

A A

CA A

NU T G R T r

LI e

EA E N DG = a

L

E

b

.

h [

A

w

;s : O A

* *

A “

’

\

B A T N UT G RS LI E A E N DG A r e = a b x h = ~

A : ~ s (w : s ; ; ~ : x: s - ’b ’ s

s

L

-

E

c

)

259 E ( S

Q

U

A

Given: Side Area Find:

D

i Side Side

R

oS

ro

A

M

tm e Fu

P

L

E

S

l aP ea h c s a

i

gnn e

eg

)

E

a = 8 inches

A = D i a d g= Area A= Side a = Side a =

R E C T Given: Side F iArea

F

X

~2 =

82 = 1o n a. a= d = 12 0.7071 d = G

‘

6 s i q n 4 . . 1l 4 . 41= 11 4 41i x. 83 n1 1 . = 3/ 61 s 2 2 q2 / . 2 i n4 0 . x 1 7 1 =0 8 . i 7 3 1 1 n 2 = g

i *

N G L E a = 3 in., and b = 4 in. n A = ad x b = : 3 x 4 = 1 s

2 .

. .

n

A

a d g= -o n a = l_ a = A/b = 1 =3i2 b = A/a = 12/3 = 4 in.

q = /

P A R A L L E L O G R A M G i H v e a e= i 8 in g a : t h n s t b =n . 1i h i F iArea n A = adx b = :8 x 12 = 9 s q Height a = A/b = 96/12 = 8 in. Side b = A = 96/8 = /12 in.

R IA NG T G R H LI A T E N DG L E Given: Side a = 6 in., and side b = 8 in. F iArea n A = ad x b = : 6 x 8 = 2 s 2 S c i= d h ~ 6 e+z 8 m S i d e a ‘ ~– 8 = ~1 Side b ‘~c2 – az ‘*102 – 62 =4 1

. ~ n

.

-

i

= 4

,d d -

n 2 f5

.

i

=i

n

.

en e i n 6

2

.

.

a

q

.

= *= 2 – 0 1‘ – =

-

i

n4

.

=2f l 2 =06 6 0 =3 8

i= i2 i

i 0 0

A CA NU T G R T LI EA E N DG L E Given: Side a = 6 in. Side b = 8 in., and side c = 10 in. + 10)= 12 F iArea n A = sd z % (a : + b + c) = %(6+8

Ad s (s- a) x (s-b) x (s-c) =i12 (12-6) X( 12-8) X (12- 10)= 24 sq. in.

OBTUSE ANGLED TRIANGLE Given: Side a = 3 in., b = 4 in., and c = 5 in. Area A = s = % (a + b + c) = % (3 + 4 + 5) = 6 Find: A= # 6(6 -3) X(6-4)X (6-5) =fi = bsq.-in.

4 6

n n~ n~

260 G E O M E TF R O I C RA M L U L A S e xS a o m t e fp l ap ee h c s a i gn n e eg

(

R

IT

A

= A = a 2 =~ l = 0 = 1

A

h [

b h a

a

R GI

A WH N 2 G 4TI LA r

e

e .a .

4 7 4

A

e

A a ~

1 0 1

A m

r

4 7 4

T

u

R

D

A

:

A

@

G

L

E

a h

E

Z

O

b h

I

D

e

=

a

a +

)

O

N

E

A R

A r e = a R aRo c id r c i u mcu=s c irs i b r ef d c l R ao i dn s ic c uri i sr b e cf d l e 2 a0. = 2 5 R . = 93 = 5 r 8. 9 z 4 8 6 z a = 1.155 r 0 a .= 0 8 R. 6 8 6 6 6 R = 1,155 r E G O U C L T AA R G O N

R A a ,(3

N

a = 1.155 h

r

G H U E LX AA R G

A A R R r = R 4 A R 1 r = 1 a = 0

r

=

a 1 h

R

2 i R = r = a = R

@

Eo

2

=

f

HL

( ‘=

w

P

A (c

A

=

x

h = 0.866 a

&

e

5G

a — 2

E Q U I L A TT ER R I A AL 6

E N T

)

r e a = ao c id r c i u mcu=s c irs i b r ef ao i dn s ic c uri i s r b e cf a . = 2 8 R . = 23 = 8 r 8. 2 z 3 a .= 1 3r . 0 =0 7 8 a .= 0 2R. 0 9 7 2 R. = 0 7 r. 6 8 5 2

E

G P UO L L AY R G O = N u o r n e as m = ’ @ = ~go” – a “ =

A *

~

-

J

r

d c l d l e 8 1 z 2 4 8

e 4

e 4

N ib

ed

r

e

261 EXAMPLES (See Formulas on the Facing Page) RIGHT TRIANGLE WITH 2 45° ANGLES Given: Side a = 8 in. 64 Find: Area A=~ a2 =7 82 = ~= 32sq.-in. Side

b = 1.414a

h = 0

=

. a = 70

=

0. x 8 7= 5 01

.i7 6

1 5

n6

8

E Q U I L A TT E R R I A AL N G L E Given: Side a = 8 in. = 0d x .a: = 0 8 x .8 6= 6 8 6i . 6 9 6 n2 8 h F i n 5 95 = h2 . 2 7s4 8 .q 2 .7 4 - 1 = 8 X 6 x =. — Area A = ~a 2 2

T R A P Given: Side F

iArea

Z O I D a = 4 in., b = 8 in., and heidt h = 6 in. ( b h = ( a 4 6 =+ 3 s 8+.-i . ) ) nA = d z : 2

R = a = 1.155 r = 1.155x3.464=4 in.

REGULAR OCTAGON R= 6 in., radius of circumscribed circle Given: Find: Area A = 2.828 R2 = 2.828 x 62 = 101.81 sq.-in. Side a = 0.765 R = 0.765 x 6 = 4.59 in.

REGULAR POLYGON Given: Number of sides n = 5, side a = 9.125 in. Radius of circumscribed circle, R = 7.750

Area

. i 2 n

E

R E G H U E L X AA R G O N Given: Side a = 4k. 5 x .a: = 2.598 x 49 = 4 8 1 w 2 . F iArea n A = 2d r = 0 8 x 4 6= 3.4646in. x .a = 0.866

Find:

.

r=m=-v= 625ino nra 5 X6.25 X9.125 = 142.58 sq.-in. A = ~ = 2.

X

6 q

- 5

i 62

8n

n

.

262

(

d

G E O M E TFR O I C RA M L U e xS a o m t e fp l ap ee h cs a C

I

A

A

R

C

L

r

A S gn n e eg

)

E

C ie r c= u ma f e r e n c e

A= r2 x ~ = rz x 3.1416 z d

L i

n = d

3

x

.

x 4

1

1 x

6

@ L

eo a n f

C A

I

R

ag

S C

a tnr =

UE L CA ra = A e

A

A

< v

C

:

I

R

A

A

A

A

S C

.

1 8

. U E

2 LG

ra o s r

em

2

AM R E

7

c g

n

1 r

2

&

4 9

A e

0f d Icx0a r 8 e 7

R T O R = a=a r A =

‘ r X r x a x 3 a = 1 5 7a a=— r

a

o0h g.

6

0 2A Y

6. N

T

=n

a cg = C l = cea i =ot t nar or f iu r ae

oe sn

ga

l

c = 2r x sin a T

<

Q a —

* +

+

0 D D

0 0

A

A

A

z

E L a — b

.

L

x = u

Q

L

.

I

x

P S E rP = P ee =r i a m e t =a3 . x xa= x1 b 4b 1

a p p r of x oi m f r ap ntmee ut o il . 1 ( a4 + 1b ) 6 { 2 P = 3

x

—

L

A

w

~

E

L o

L pc

I P S E a oo t e ii l n n l g

= R o am . — az - ( 2C x y2 )

m4 Y = c

d

~

(

ti

at i =ct m i nx

ps

e

r 6

ea

t z

s n a oa o

er z

r

e i f j xr

—

w

N = the required number of holes (diam, d) of which total area equals area of circle diam. D.

os

i

2

EXAMPLES (See Formulas on the Facing Page) CIRCLE Radius r = 6 in. A = r2x ~ =

Given:

A =

=

= 12ZX0.7S5Q C = dx = x if a = 60° dx a =

=

CIRCULAR SECTOR Given: Radius T = 6 in., a

= rx

x

a = I

R

S C

xa =

U E

x

= 6x

LG AM R E

Radius r = 6 in., A a = r2 x ~ x —

.

x

x

=

Sq. h.

= =

N a

x

= 18.85

x 6

r

C

=

= = 62 x ~ x ~

= r2 ~ x ~

Area A

=

T = X~

=

A = Chord c = 2r x sin ~ = 2 x 6 x sin ~ = 2 x 6 x 0.7071 = 8.485 in.

E

L

L

I

P

S

E

Half axis, a = 8 in. and b = 3 in. Area A = ~ x a x b = 3.1416 x 8 x 3 = 75.398 in. P = + ) = @ =

E G

L

L i A

) =

I P S E va = 8 ein. x andn b = i 4: in., then s C = ~ = ~ = 2, x = 6 in.

~ = ~

-

~ 2

c -(

E H

+

)

2 (2

2 2x

.

)

. ‘ 6

X m

%i @holes have same areas as a 6 in. diam. pipe? N= (’/d)2 = (6/0.25)2 = 242= 576 holes= Area of 6 in. @pipe= 28,274 in.2 Area of 576 H in. #holes= 28,276 in.2

(

G E O M E TFR O I C RA M L U e xS a o m t e fp l ap ee h cs a

C

o

v=

i–

A S gn n e eg

)

E

l

u

m

e

RI

ES

u

m

~3 1

S I I

Q

P U

V = V

o

— I

B

V = V

b ~

U

L i

RA l

M e

— J

L

:

.;

P

R

;

:* ’

,:

I

S

-

’

:

=

C

&

M

T f : oh : c r ‘b; m ai Ay rpu efaa elpsoa f easl n d iso ho”nere nf=esa dca eu ‘ i h i p e r p e nt de i cs fu ul as r r n f a c o de

m

prrn y .

w C .

v

Y L I Volume . .

;

“‘

. —.

% +

C

q . (—. h

% L

d

3

v

~

-

R

P

I

: 0:

U O SC

’

i s ne du r ri a c f af la

82

x ’

h

E

S = A

o =c r o s

4 = 1

1 6 =. x r x0 h

n ue 4

i r 2

7

c fa a af l 2

d = 1.5708 dc T

UO

M

N

F

E

S = A o =c r o s n ue i r i 0.2618 h ( D2 + Dd + dz ) = a = R–r c.

s =% 1.5708 C( D + d )

I

l

” x: : 7 = d

N

i Volume

v v

h

:

. . x r x1 h

“ S = 3.1416 rc

.

0

;

Volume

F ‘

: O

v

.

;

N D E R o =c ry S = A

c fa a af l ~

265 E ( C Given: F

U Side iV Side

oS

ro

B E a = 8 in. on V =l ad =u 8 : =m 5

ce

a = G

F

X

A

M

tm e Fu

u

P

L

E

l aP ea h c s a

.1

8i

~-

3i

i

gnn e

n2

=

C G F A

R I S M ue A r=nn 1 f s : aq a c. d h -=e 8 iin. n i E vs iVolume n V = hd x A =: 8 x 12 = 96 cu.-in.

Y i

iV o C ry

C G F

A

F G F

L

O i iV

I vr

n

.2 ,

x7 0

2=6 44

; x

2

5

n —

. 72

- 2.

4

.

zc2 57

6 u5 i9

u 1x 22.

c = ~ ‘ 3 1 = 6 {41 ~3i =+ . 4 o C r o S n ue i r S =cf 3a aa f. crl x ce1 = : 4 1 6 = 3 . x 6 x11 43 = 2 1. 5 64s 2 q1 . . 86 - 8 R

9

d

N D E R = e 6 in., nand h : = 12 in. on V =l 3d u . x : rm x1 h =e 43 1. x 6 16x 1 =4 12 1 3c l i S ne du r rSi a=fc 3 afa l .cx d xe1h : = 4 1 6 = 3 . x 1 1x 1 =4 4 15 s 26 q . . 23 - 28

N E v r e= 6 in., n and: h = 12 in. on V =l 1d u . x: rm x0 h =e 4.

)

.

S Q P U RA RI ES M Given: Side a = 8 in., b =6in., and c ‘4 in. F iVolume n V = adx b x c : = 8 x 6 x 4 = 192 cu.-in. v 9b = = n = 1 2 . = 6 i — =1 = 8- i a ! 8 4 b 6 x x c = —1 9 ~ 2 = 4i n c . a 2 x x b 6 P G F

eg

n

.

h- .

i

4n

4= n 1 i7

i

n

UO C S T U O M N F E 32 , n 7 a e D m= n2 e i :t a e d n=r 1 i n h. = 1n 4 , 0i d . . i D vi V =d 0 1= 8 2 2 d ) iVolume n : . h ( 2 + D 6+ d D 0 . x 1 2 0( 6 +. 21 x231 8+ 17 4 =5 2 2 27 c 3u24 17 2= 0 = 8 42 . C ( D5+ d 7 1 0 . X 1 )8 5( Surface S = 1 6 7 s 8 q . .5 -8 i 6 n .

6 .

5

2.7 2 +

266 GEOMETRICAL FORMULAS (See examples on the facing page)

See tables for volume ical, elliptical on page

and

and surface of cylindrical shell, spherflanged and dished heads beginning

267 E (

F

oS

X ro

A

M

m t e Fu

P

L

E

S

l aP ea h c s a

i

gnn e

eg

)

SPHERE Given: Radius r = 6 in. Find: Volume V = 4.1888 r3 = 4.1888 X216 = 904.78 CU.-hi. v= 0.5236 d3 = 0.5236 x 1728= 904.78 cu.-in. or = 4 x 3.1416 x 62 = 452.4 sq.-in. Area A =4Tr2 or A= T d2 = 3.1416 x 122 = 452.4 sq. in. S G

P

F

S G

H ES R E I C G AM L E N T i R v a r e= d6 in.n iand: um = 3s in. iV

on V = l 3 d

= 3

. x 3 1(

A

Ar 2 r

u. x m : m1( 4 =6 1 1 x e

e4 = m @

1

r 6

-4c 6

1u;

2. . ) - 3

z

= r2 Xa 3.1416x=X 6 X 3 =m 1

-

i 7 n

.

1S

3q

..

-1

i 0

P

H E Z R I CO A L N E i R v a r e = d6 in., n i Cl : =u 8 in.,s C2 = 11.625 in., and h = 3 in. 3 X 82 + 3 X 11.6252 + 32 = 248.74 cu. in. Find: Volume V = O.5236X3X ~ 4 ( ) Area

T G F

A = 6

O R i Radius v Re = on V =l iV A A r=

. X 6 X23 = 18

13s

q32

..

- 1

i

0 n

U S 6 in. n and : r = 2 in. 1d u 9 R: m x r. = e 17 9 = 7473.7 3Cu.-in. z 93X 6 X .22 9 3 9eR = . 3 a 4 9 x 6 7x .2 = 844 s7r7 q 8 3 .

.

- .

i

7n

—

268

GEOMETRICAL PROBLEMS AND CONSTRUCTIONS x

AJ

LOCATINGPOINTSON A CIRCLE

z .

.

EXAMPLE = Sin. X= 3 in. ~ind Y == =~ = %= 4 in.

y =x =q~’

& q.

D

L

E

O N F G PF TL C

=

.+

L p

:

~ ~

t

,@ T

‘

e

o

T LO IE N

D

RE

E X A M P L E n I g ndt hi s = ao= i m f 2 ed 4t e e i r t n l T ah i o ct fk :enp1 i e l s as

d i a Lm 2 e t 1 1e5 r 8 FINDTHERAD;USO COF AI R

e ~

q

A HY

x A C

3 L

U

A

: ‘ ~ ~ ~ : ~~ ; ’ : : i n

TO FIND THE CENTER OF A CIRCULAR ARC When the Radius, R, and Chord, C are known, strike an arc from point A and from point B with the given length of the Radius. The intersecting point, O of the two arcs is the center of the circular arc. y .d~

I

o

q

T

P

I

w

y ‘b

p o t a #

FJ J

. A M

z~ D

T t

IC

E NOH NA C O TDI

Ch

REE A C RU

L FA

hC a eh oD i r m n endM ean ,ks i no, dn ro, p r Ao a f o i P rn nB moo t o i s o it a dtC or he t h n i ns nc t ef e erh sc. e tc t ow s i t i nl r atiT t ii snng t heh rhp t s s e co . t i s t l r h aOi i ti n cg f eheo t t hsnc i, t r hesc e r c . ~ C + 41W ; Y=R-A4 = 2

a a tf

r

i r

k

8A4

k

c

F

CONSTRUCTION OF A CIRCULAR ARC The Radius is known, but because of its extreme length it is impossible to draw the arc with a compass. Determine the length of Chord and Dimension M. Draw at the center of the Chord a perpendicular line. Measure on this line Dimension M. a B B lni D As i a e nd c . Connect points

B a m e M an d si mu Dp /e erd rn pe se ni d 4oi cn u l R e p t e p a r th o i t cnt e rgi de uq asr hu e ec s c t o a M w cb a e i yb i a l s 4, te ccll i t eTi te m ho n s e v o o r t t t ir ic a ahet nps g o l rtf ehe ic s n ieht c a u lr a c r .

- .

GEOMETRICAL PROBLEMS AND CONSTRUCTIONS

I

SOLUTION OF RIGHT TRIANGLES R

E

Q

U

NOWNSIDE OR ANGLE

I

R

E

D E

FORMULAS

X

A

M

P

L

E

S

( E N C I R C L E D ) t

@4

a b

b

Sidea s 6 in. b = 12.S67 in. a F A A i n‘n ng ‘ 0 l .d

A ‘ ~ ’ a

= Sidea

tan B = ~

F

b

b

c

A

= 6 in. b = 12.867 in.

A

B i n=

1

= s Side a = 6 in. c a

sin 0.S00

c

B =+

A

c

0

= 30°

a B =y

a

=

C

c

=

Side a = 6 in. c = 12 in.

B

c

= 12 in.

A =~

A =~

A

@

. 8 6 e1 2 l~ d.

= 3 in. b = 4 in. c -

b c

c

2

ng

= Sidea

b

e4

a

= 0

.

O

5 S

a = 3 in. c = 5 in. b =

‘

= 4

A, a

a

A

(

b = a x cot A

b

a

A

a A

AA

b

i

)

c

a

A = 250, side a = 6 in. b = 6 x = 6 x =

a = b x

A n=

?300,

side

g

c =-

A = a = =

A

a

=

=

l6

—6

b = x x

in.

e =

=6

A& @

A b A A

c

A

Angle A = 30°, side b = 12 in. = 12 c i— n

= F

= 13.856

@ AA c

A, C

b

b

c

C

,

a

= c x sin A

b = C X COSA

Angle A = 30°, side c = 12 in. a = x = 12 x 0.500 = 6 in. A = 3o0, side c = 12 in. 30° Find side b = 12 x 12 x 0.866

A

I

= 10.392 in.

d

6

971 A

F

r

uof Es C t C uE E Given:

X

A M

M d

Nm C T P

R OI L

C

N

E

i e ata the mlarge a eend, t D n=e 36 rin.

4.

C of Circles for

t

h A The Bottom

300 6Q0 ~oo 1200 1500

Factor c times mean radius = Chords, Cl C2. . . in. c1 = 9.317“ Cz = 18.000’ C3= 2S.4S2” C4= 31.176“ C5= 34.776* ‘6 =

“Segments

=1

e

At The Top Factor c times mean radius = Chords, Cl C2 etc. S 1,2... ft.-in. s:, 2. . . ft.-in. , in c1 = 6.212“ s; = 4’-0 % S1 = 6’-0 ~ s; = 4’-1 yz C2 = 12.000” Sz = 6’-2 Yle S; = 4’-2 IMG s3 = 6’-4 ~ C3= 16.968” S4 = 6’- 67/lG S: = 4’-4 ‘/fj C4= 20.784“ Ss = 6’-7 I946 S: = 4’-5 Yl(j C5= 23.184“

HZ + & G G’. sl~

t

‘*G=-

=

4’-511/lG

E

272

O

T l T (

et o p

E M F

S

P

a vu eofi a c s l e cso r ad e t w p laathe cminimum i i i n t material, ty theh correct r o a d n i ags mb t hde eh t t a ee o r r m l i n l e ed . p rt h oi al m eftu et nmd i ig aoc th m b f fhe tboa tee f ru o l npn lh r eo od wc iey rT ie l s hi st m1u eirp aet0 e e l s ld0s i hnp os a0eo a i i ds ad as l r ud m s e de

b

F=~

V

, where

CSE

P= c=

Design pressure, psi.

C S = S E = J

o

r a r l o l soi iw oa nn c n e vt or am ea l tp s e u rs si ea e of f i c i n e n t c y

,

. lf i ,

c n o hf t apa e ac tr ra li ht n gnse h g a t ei df nt ee c d tsha d i op t era v tce e e i d sth h o or i z t ovt n l t ar ele l pi hy r e t s nve no ote aE i enh g l u e e f t ir n t e orhms e v cmeto ir eoat n ir v c t a v leen l o yaf ha l d du ) e e f .

The length of vessel = ~

, where V = Volume of vessel, cu. ft. D D = Inside diameter of vessel, ft.

n

EXAMPLE D

Design

P= 100 p F

t

F =

oi

a t a : V = 1s c , fi S0 = 1t , u 0 6p .0 , E s= . 00 , i 0 C. = 0.0 8 p dt hn i i aa m dm l u e e mt nn e rg t d h

100 0

F

c

.X 1 0 6

60 ,

rD = h 5.6 ft., o as

= 0

02

05

i . .0

n1 X

5 ft.rm6 in. t a

Length = 4 x 1,000 3.14 x 5.52

.2 8

-5

. ,i

00

l

y

= 42.1, say 42 ft. 1 in.

* FROM: “ Gulf Publishing Company,

—

Houston.

permission.

273

100,000 80.000 50,000 1 I I I I I I 1 I 1II 40,000 6

I

,

\

20,000 ,

5.000

, ,

I

I0 8 . b.UUUk

1 I I

1

I

I I II

1

I I I I I

1

,

, ,

,

!

[ , , , ! I I I i

,

,

,

,

,

I

I

,000

1

i

I

,

,

,

,

,

, ,

I i 4.000 ..- I 1I1 1[I I I 3.000 2.000 I 1 I

,

f

1

1 I

I

I t.

[

[

1. +[

t

%~ fz~

i

I

w 1+ I 1 I M

i r

1

I

I

1 1 I

1 r , I I

400 300 200 100 80 60 50 40 30 20 10. 1

2

8

4

3

910

VESSELDIAMETER,D FT.

CHART FOR DETERMINING THE OPTIMUM VESSEL SIZE (

f

Sap

fc

e a xi p ln eago ng a t ei o rn )

274 FLAT RINGS MADE OF SECTORS

L

Making flat rings for base, stiffeners etc., by dividing the ring into a number of sectors, less plate will be required.

1

Since the sectors shall be welded to each other, the weMing will be increased by increasing the number of sectors.

ONE PIECE

d Q

The cost of the weMing must be balanced against the savingin plate cost.

o+

The chart on facing page shows the total plate area required when a ring is to be divided into sectors. This area is expressed as a percentage of the square that is needed to cut out the ring in one piece. The figures at the left of this page show the width of the required plate using different number of sectors.

2 SECTORS ER 0,866 D 3 SECTORS

~ u

D z Outsidediameterof riu. d = Insidediameterof ring.

0,707 D

DETERMINATK)N OF THE REQUIRED PLATE SIZE 4 SECTORS

~ m

n

1. Determine D/d and D2 (the area of square plate would be required for the ring made of one piece)

0,500 D

2. R

e n

0

D,

S 3

6 E

C 8

T 3

c r Os

f e d Re

e c r ( ha f o n t tr ae i i v t ni d n Sc t o

3. Determinethe requiredarea of plate 4. Divide the area by the r

* ~

D T R O P M

po aa d t ca rm p i g tn qag h uw e i r t r f h ee d e neg sht du io m ro r s

e qw u o i i r a ls aah t l ot o t ewe ph s t hn f a bt l t eo at hnp i gl n hta e ht S E C T8 O R S 5 A a l l d(o w 1mai n. df acn f e xc l c u b t e t s t i ewa n c ea gt t e e onn dr o t Tp t f e e E QH W U I I R EE D D H l h a LF RA I O T FN E G R S O A S E D C T EO RF S S E x Oa eF m aP p c l ea ei gn n p o

L 13

FLAT RINGS MADE OF SECTORS (cont.) 100 90 % LL 80 o @ ~ 70 u $ 60 & q 50 CA $ do & * 30 CIa + ~ 20 — & 10 ~ o

2

EXAMPLE

w

—

.L. ~

3

4 5 6 NUMBER OF SECTORS

7

l.1

a

Determine the required plate size for a 168 in. O.D., 120 in. I.D. ring made of 6 sectors 1. Did= 1.4; D2 = 28,224 sq. in. 2. From chart (above) the required area of plate is 50% of the area that would be required for the ring made of one piece. 3. Area required 28.224x 0.50= 14,112 sq. in. 4. Divide this area by the required width of plate (facing page). Width = 0.5 X 168 = 84 14,1 12/84 = 167.9 inches, the length of plate. 5. Add allowance for flame cut.

= m a

~

1 169 “

-

.

-

F

r

-

uof Cs O tN Cu E mNC T R I O C G

i

v M M H

D

t t e Rr

R

= D- DI

b—

o T n R i a c

:

m e

iqP hn u le i

ar

e

qP h u

r a ee

tan c1 = +

2 e -

n

E

d i e aa t m la = e e ta n eh rnr d ie aa t m sa e e tm n eh nra eo t if r g u= h s tt u

T

C

e

D DI = H e

N

s

.r 1

R

oa n l

o

a

li

e et d

d

D rl = —1 2’

, c

k

m f

/

P=

x3 T

R

e

qP h u

li

r

ae

+

277 F

r

of u C s O tN Cu E mN C T R IO C

N

E

Made from two or more Plates

t

-

%

G

i

v

e

n

D D, = H n =

M M H N

D

e

b

=

t t e Rr m e D - –

,

:

d i e aa t m la = e e ta n eh rnr d i e aa t m sa e e tm n eh nra eo t if rg =u h s t t uf e u o p m (l b s a ee t cr t e of iqP hn u el i D —

2

r a ee l

d t

tan W = *

-b

I

D

c rl

= ~ +H = D

e

.

Elevation

l’%

2 x Y

b

2

1

/ c

R s DXZ 2 Rxs Rxt exs exc

m X 5

t 7

> +% ~ + 1 2 ~

2 2 +

&

i

. 2 R = i = a = i o

9

6

n n n n s

W o it R d e qP t h u= Rlhi +r 1fa ee d -t L eo t n R eg qP th ui hl i r af ee d t t F r mu h f s at r u e odm me 2 P

Reauired

Plate

:l 2

Y a +Z t

Xe

s

+

:

F

Determination

r

of u Es C t C uE N Cm T R OI C

of the Required

Plate by Layout

N

E

and by Calculation

1. Draw the side view and half of the bottom view of the cone. Divide into equal parts the base and the top circle. Draw arcs from points z’, 3’, 4’, etc. with the center 1’.

c

F t p r 1o 2 oh3i e n m ° °t s at w r c r i Oei k nc t e t S t f a a pr rto aoi 1 no i g ( m 1 ma er t ska pes adu h o t b oc oht i t ct r o cf oe a i n at 2‘en r s er dc 2 # Side view of cone

4 O of the top circle.

A

o C A L C U L A T I O N T f

t

c iu

ro t vhnp a bt ocl uda hrle ace u l t a f O

the

B only (marked

S3)

If the bottom C3 .

circle divided into 12 equal spaces, 2 R x sin 45°

S3

W

=~H2

R hdenoted ethe mean r radius ofe the base

circle. See example. Fig. B

+ C;

970 L

F

r

uof Es C t C uE E

X

A

Nm C T

M

P

R OI L

C

N

E

E

at the large end,

D = 36

in.

C C

C

etc. using

=1

c

c

=

= . . =

S1 = 6’ -0 % = ~ = = =

= . = = =

C~

~ 1, 2 . . . ft.-in.

H2 + D2 = 6$- 8Y2

s;, 2. . .

= = = = =

,

s; = 4’ -0 % s; = 4’ -1 %. = = =

“ “ ‘

6

BENT AND MITERED PIPE

2

I &

C ,

/

k\

./ r [

.—.

\ \

\

‘F } : 17 - ---16 — ‘– ; :b

.

!

-w I

‘Y” h 1

= (

a

1

= (

- a

t i n t e rhp s e i cln t i ena g n p e r p e n t d t i c a u l oa tr xh i o c y l t i ni n d t e hr r is ,ae c t i e o r e l l i p s e . !Cl C O N S T R U O C T T I O N I N HT E IC2 \ \ \ S E C E T L IL NI G P S E D it cv i r ic uh dm of ete r e ne c e c y il ie n np qd a ea utd r r a orn t l a e l a e e m d eia pvn n i toc s i i t h T m a a oh t jxe loi et il h r i sp l o d n i gbs tee at st in w t cn e e h te s e p c oa t t i m nn a nig ti h nsx do t d i ao ht m c e y t l Teehi rn d ef p oo t i e nl c l tbh di s pe a f s et e m bi u nt s c e i h o dth on yr g d c y ls i p bn pad r eco rj a ee c d t i s oh b c o a l cw ua le an t ix or yn es h e t .t i h p l b i e f W l i t eomi d w m b l o as a l t o ui br yp aei a d ny t f l d o ew n - e c s oT m tte , r hs ch i n o t ep a l s t h r a es n qt f h eu ei c l e s a ra h a b nt al c i ea l s k nl c o n s i d e r a t i o n . D E V E L O P M E N T T l e H nih e g t qt t hec u , aih c u m f o et rc e y n l cD hi e n i d v e f e t l i h t i s n i nn a htu s o em m o b e e p q a at u c i rr a c u htmlo f e s r e sn e t c y l hD i n a d er e el r .ea m t h e r d o i a upv e gri cp hse ni d hoi c nu t t l hD i e t nit e l r oe mes i .hn e o e e la a es m c oh be cf ohn t w a c u l Ba c t o i n o n t n e e. c t i hny g p oo t i e ln ec th mb os e n fa et s t at s i t r en t hc le h eo dtd -i o e u t n i n t e r a s em c tb i u on nf a s d c u o t p t a f i t pu n t m g e i oi r t t n p i e n t g c , . E X A M P L E f c a l co uof l length a t i rofo n e l e m e n t s . T c i r c u h m of te r c e nye c el h i n i d i i v 1 ie n d p q e ats du r oa t T a o n ah s g e = c2l e t 2 e i - of d e g r e e s . T a o nt h i ng t e rlhp se e ecl t fi ean t t a o t xh c y i=l oh4 i e ns d f d e g r e e s . c = r x cos 22-1 /2° 1 , c, = r x cos 45° c%= r x sin 22-1 /2° a ,o ~ 0 ) s ° h l h a = l = e 2 2 o 0t a ) scs 4° a. si 40 in 0°t e

‘2== cq 4 c

-

4 a

P

1.~ *G1

When

282

I o e

I

C d q i

a uwm a e a toi nfie nl r t gtse r 9 s l e h c te i o0f n

1

I

—

I

.

I

1

1d

‘/4 O T L D it i e e d p oo o i n t D D c l a D p t o c t

F

O IH IN T E N R S EE C ET I FO N c v i r ci u h md of te er c e ny e c l e hi n np q a a ut d ra a eo rn t ll a e as m d ai vp ic o sT i i i h no nt ne h rt s e . c t ie ln ed th m e st e t e n lfr et m s i i h e r s e c t i o nf .

E V E L O OP M P EA N TT T E R NF s tr lr oa a e i i gl qw h ent tut n ea g i r c u m o f t e rc e yn cl eiDh n itd e v rf es i i t s nn n ea hut o esm m op qb e aee u t c i r c uh m of et r sec ne yc el hi n d a er l t ea hm e r we do n n ai u t v g i c e r p e n t d t i c ul hl a i rD e en t s ee o r es l e o e hn e g al bte ep m chr o e jf hen c c a l c u ( l ae t ixS o b arn . e m e B l p o el o n nt e e c pt i ohnot gn e i l e e nh md s t r o eh curve t c of the h uintersection ee d t

can be developed.

EXAMPLE for calculationof lengthof elements If the circumferenceof cylindersis divided into 16 equalparts a = 22-1/2° c1 = r sin a C’2= r sin 2 a C3 = r c a c4 = r

o

s

-

I o u

I

C n d ei

qa wmu a e a tofi nile n r t gtse r 9 s l e h c te i o0f n

inder into as many equal parts as necessary for the desired accuracy. Draw an element at each division point. Project distances c1, C2 etc. to the circumference of the larger cylinder and draw elements at each points. The intersecting points of the elements of the large and small cylinder determine the curve of intersection.

D E V E L O OP M P EA N TT T E R NF S D a s r t l r of aa e ii lgw q hetn tut n aeg ht c i r c u m o f te rc e yn cl eiDh n itd e v rf es i . h l f t i s c onm yh il a e it rnsl n e d l e a ht r n u o e m p qb a tae u c i r rr ac u fhtm l f e s r e sn o t s c m yh l aDi n afl deer e l r e a. m t h e r d o ia u pv eg ir cp hs e nti dt hoi c nu l a rh l D i e t nt e l r e meo it .hnne el g e ht me he b p r o oj ce a c l t c iu( oly ean t xSi o a nr . me b e Bl c oo nw nt )e e c. pt i ohnyo gn i t e l et h sm t e r on eh ctet sco ut h u ee r d vh i n t e r c s be dc te i v ao e n l o p ne de . T c u r ohv t a h t ui et r oh le al fh e r c y li d i e n t ed b r e t m r l i n e oes dh n g e l ec Cm e e s n p1 t t a s a cdch i,i 2 ns .e gt c a b c e e w t a h ct s l i , . e, or c h, n h g a o t rp a v c rho t t i ls i nc aae hyl r lw g 1

E f D i

c1

der.

X A M P L E c a l c o ou ll a te oi r eon nl ge m t ef hn i t v c i i rd c ui hm no f t eg rc e ny ec le h i1 =n 1 e n p q ata u= 3r oa t 2 sl 0 , = r sin 30° C2 = r cos 300 C3 = r 1 =

t sf . d @ f ee 1r ° 14= @ R

c,

, 2 , +

=

284

I

C w

n

i i n t e roat s e c hxt i nn g e a . b . I I

r —

— ; 1! -

-+

.

,

1’ I I

I

~

;

+

T L O IH IN T E N R S EE C ET I F O D it cv i r i c uh dm of ete r e ne c e b rc ya ol nb i vcn doi h i e r etn a m e a pq a na nu e sr cay e t sl f t i n o t a h ec nc Dud r r ee a dr c a e l a e e m d eia pvn n i toc s i i t T p oo ih in t en r o s t tee c s t i of c o r r e s ep o l n de d i m ne g te e n r t m t l o i ni h t e r sn e c e t ie o fn .

T m l i w m

L

d

.

D D t c n c t t o c B e t

k

f

- –‘

y*-*

-

, I

I

.

\

. -

C

s

E V E L O OP M P E AN TT T E a s r t l r oa e ii l gqw eh n ut n t c i r c u hm o f t e rb e o n rec e ha y al di n i i d nvt e s nri d ad ht e u o em p bq a eat u cr r a f ith l u m f e D r e an rc e e .l a e m h e r d o i a upv e gri cp hse ni d hoi c n t l Di eh t n t e l r eo me i . hn t e l ebh m p r e o n fjo ete cs t a l c u ( l ae t ixS o b an , e m e l p o e c o n nt ee c p t i o hnoty ng i l et sm t e r on eh ct t sco u h u ee r d i n t e rhc s eb cd t e i veoa en l o c u r ohv t a h t ‘u ter oh e c ya il d i e i nt e db r nt em ri n eo e n l egc C m te e s h n 1 t tpf s t a dh n i s a etb ca egn mc t e t ah t l i eo r ca hn o ht g r e t e c ya (l ei il n se vd an e te ri o

E X f c a D c c,

i y

A M P L E l c o ou l l a eo t e i n olr neg vt il

s

n

m t

ci i dr c iu h mn of tge r e n e c e 1i e nn pd q eaa =t 3ur r aot 2

= r sin 30°

C2= r cos 30°

/1 = {

R + C2

12 =~ R2-(r —

1

16 = R

il e

J

+ C1)2

4 R2- (r - C1)2

-

2

285

I

C

B

3 2 1

%

2

/

4

I

3

A

C

T D c m t e D r s b e c e o d o o c l e a o a (

L

O IH IN T E N R S EE C ET I F O N cv i r i c uh dm of eet r e ne c e h y l o i b n v d o ei i r a te n n w h e a p q a annu e rcayf e t sl s s a o d e a hs c ic urD r ee aa drc y . a l ae e m d e ai n vp t i c o s ti h o n c r i o r p a c v l l ww e i s a i en ar , r de Ti l t u2o i s i hc n l ,t n . e o ct tp ii d ol he tn e ar nm e i nn t p oo ih ni t en r ys o te e c ts i o nf l e a m t e c no rnt r esh s p o nd d ie i Pr cr t l o pe hj s ote .te ci st n hte l e vT a i t n i t oe hrnp s . e oc t ii e n gn t p r o aj h e e c l t eow f n erm s e i n e t te rl mo ii inhn t e r ns e ec t e t e l e vh T a st it n or e hne . t c c u r ouv t a h t ui tr oh e l fh i t o b d e n t e b r etm i s no e dh eo a n a ag r e tt r 2chta 3 n f s s cf , e f t pr v olohc i a dl amc e ue l n a w e x e m bp l ei T f lsi e s pod ahw c . a a a r e m 2bc t o3 bf sact , a , i . s ho m o b c wa las c n u l ra yt e Sx ba eem l p oel we ) .

D D t d n c t p t j of

E V E L O O P M P E AN TT T E R a s r t l r oaa l ii eegw hn nq t g u et t c i r c u h m of te r c eo n e yc e h l a d ei i in v t i sn r d d athe u o em pbq a e atu rc r a f tihl u m f e D r e an rc e e .l a e m w h er od aiu vp g i cph os i iheo nn e n dt ti cl u D l i a eh r t n e r eo m e l eo t hn e lg eb th pm e he nr f te e o cb c t a li c tou l l n a e t ir hnny g g 1~, 1 e t ec *.x b( a Se m e l, p e o l

it

w

E X f c a C6 =

r

I

N

A M P L E l c oou l l a eo t e i n olr neg

m t ef

r sin a a R d= h i t

‘,=w=

up

‘tc

s

,a

6

286

I

C

A

S

N

R

>

K

-—.

-

—.

I

A

I

-—.—. 1

.r a “

1

s .

1

-

-

al

.—

a

, I

a-3

\

%

B

R2

,

I

“ Iw

‘E f e

X c l

C a x i g

A a e

M P L E l co uof l length a t i rofo m e n t s .

THE LINE OF INTERSECTION Divide the diameter of the cylinder into equal spaces. The horizontal planes through the division points cut elements from the cylinder and circles from the sphere. The intersections of the elements with the corresponding circles are points on the curvature of intersection. D D c t T m D p l c

E V E L O OP M T E CN TY LH I N D F a s r t lr a ao e i i gwl q h ent t ut n ea g i r c u m o f te rc e ny c ale hdi n i i d nfv ee t s n a hu o p m m a obat e c e ry rl thi s p o aht dc i i pv neh i oag s d i i f eoen bi t ln e o e a hn o d t g r c y ty e l ch hi a e r l t e a h m e r ewd o nianu pvt g i cohs e r p e n td it c ul l a Dri eh t n et r oe me e o t n e gl e bt h m p hr e o n fjo eetb cs t a l c ou t l al t ei oo nh1n 1g e t f h e1 t s2

P i 2 iE l l ip H:p s o e ei nd 1a la T c e p h no o r t th e e i i ra oeh p n p a r m a a s t p he s e l er ityg c r m a aleo h nd w i he 0i q t c ut i d h. aim aso hl t m e 9e h W e t a ph i dw ieh ia. l tpno i 0 h e emi t ti d m i a o h etm he s tt eleh ro iah i n t e r a s ed ce tv i e on l on o t p c m ye d n l th i nc b f i oa t a u d b nenh seomdc rav n i en b

l t c d u i ls xat h X at ene c e l ets 2 , c xi = x ~v + r xesin a n, etc. l s, ; P 2i F i l S i wm t w it kt r ao w d d i

, , . a a Dp n iHg ne s e i c l eap a h on r ~ n h ui ha sci p k nh sl i hie ut i qt s r c s h .

n ehd e da rtt yht e ei r o e ee r ts gi c m u afo ht ahd s

287

T

P

connecting

cylindrical

and rectangular shapes

D E V E L O P M E N T D it c v ii i e hr d np qc e a al ut e d a er l aea e m d w e ai nvn p o i n t .

er a ti c s

F t li e o enhn e g al d b et e m ch e t r i a n go ub l c a at li oc nuT l a t i ro y e l ea m t he y n pr t oho st t e n eu es t r i oa n sideg ofl nwhich e s is e A A A --e a2- t t ’o1 3 n, ct h ’ h s i t i h eo d th i t r ge a snhhe s ti t p i e c e .

A ●

●

A A A-

B t e d e g v e h li o o t p n m l e e n ti h 1 a d t - r r n t i r ah liSg da - wnh S ge w b h S oi ae s t q hs e t u ea aA s s A ai w hdh yn p o oe A t D se dn ue f bo t r ui a n ng o u cl da a t i lyo cn u t Fi t o pi no1 2nh i3 . e n d tt e T l eo 1 h n 2 g3 - e -t em 2h t 3 f , a b t ea t qkt c ue o e t anoh l r o d i v o it st i c o iinht so ra hc f e l p

small enough for the desired accuracy. Strike an arc with 1 as center and the chord of divisions as radius. With A as center and A-2 as radius draw arc at 2. The intersection of these arcs give the point 2. The points 3, 4 etc. in the curve can be Found in”a similar manner. E f

X c c=

a

A M P L E l c oou l l a eot e i norl

r x cos a

n eg

m t ef

d = r x sin a

L E O NE L G E T M HE N TF S I t a db eh so mc r van ci e bn e e n d b f to d e u v e hnl f o et p d m re eno t a s pi tiw ie h oc e ne ns :

one end is square 2. one or both sides of the rectangle are equal to the diameter of the circle 3. the circular and rectangular planes are eccentric 4. the circular and rectangular planes are not parallel

288

T connecting

P cylindrical

1

3

3

4

:

- -

+ 3

3 @

D E V E L O P M E N T D it c v ii i e hr d np qc e a al ut e d a er l aea e m d w e ai nvn p o i n t .

2

2

2

2 1

- -

and rectangular shapes

A

er ti c

F t li e o enhn e g al d b te e m ch t r i a n go ub l c a at li oc nuT l a t i r e l ea m t he y n pr t oho st t e n eu e t r i one a n sideg ofl which e s is A A A--e a2- t t ’o1 3 n, ct h ’ s i t i h eo d th i t r ge a snhhe s ti p i e c e .

B t e d e g v e h li o o t p n m l e e n ti h 1 a d t - r r n t i r ah liSg da - wnh S ge w b h S oi a e s t q hs e t u ea aA s A ai w hd h yn p o oe A t D se dn ue f bo t r ui a n ng o u cl da a t i lyo nc t Fi no1 2nh i3 . e n d t o pi tt e T l eo 1 hn 2 g3 - e -t em 2h t 3 f b t ea t qkt c ue o e t anoh l d i v o it st i c o iinht so ra hc f e

small enough for the desired accuracy. Strike an arc with 1 as center and the chord of divisions as radius. With A as center and A-2 as radius draw arc at 2. The intersection of these arcs give the point 2. The points 3, 4 etc. in the curve can be found in a similar manner. E f

X c

A M P L E l c oou l l a eot e i norl

a

c = r x cos a e

=

~

-

n eg

m t

d = r x sin a +

-d(

a)(

In the above described manner can be found the development for transition pieces when: 1. one end is square 2. one or both sides of the rectangle are equal to the diameter of the circle 3. the circular and rectangular planes are eccentric 4. the circular and rectangular planes are not parallel

b

)2

289

D

C T p m f

c

+

I

o

C =D f

ax m 0 l i b

a

C = D

i

a~

E X I i r

A e

M tq d

C = 100 x sin

ix c

rw

c ch i

e.

No. of

1

0.00000 1.00000 0,86603 0.70711

26 27 28 29

0,12054 0,11609 0.11196 0,10812

51

; 8

0,58779 0.50000 0.43388 0.38268

30 31 32 33

9

0.34202

34

1 1

0 0 0

. . .

1 1

0 @

.

15 16

0.20791 0.19509

40 41

17 18 19 20

0.18375 0.17365 0.16460 0.15643 0,14904 0.14232 0.13617 0.13053 0.12533

:: 44 45 46 47 48 49 50

;; 23 24 25

l e o sa

3 2 2 .

5 c8

3h

lt r e o

ls

6e

.

s

eo c hnn hf go a od dt e r eh on dsn fu iso s mr r penyb sda e cihr t o e o f s w h l e : 1 8 0 m s e t e i r n n uo sm p b a e c r e f s P L E : u ai 1 r iv et ds i d i n 0 dac o meiic e 1 r0t e nhec p rq l 2t a ue ro a 0 t l s 1 8 0 — 1 x s 1 30 1 = i0 x 0 0 ’. 0= n2 0 ° i= 2 .n 0 6 c 26 h 1 2 0

c

5

i e ro r nncq l fut pht e ao h a r f e nd r hci idh r ehe c r u hi r ao f m d e e, t

la f e e at r a c , b eb ut

=t32 e x8 r0 2 . 6=37 8 8 . i 2 60n 6

No. of Spaces

2 3 4

P

M P L E : tq d u aii 2 ri v edt s i di n adc om ieic e 8 er t0 nhesc q r p l t ua e c ao e pf o ta t r c a0 e roh.b s 3 l m8 e 2e : 6 8

i t

E

b m ehe f dt s i h ove aoo ict sd i i ta f tr l i t eo t hnsn c s goo hda e t a l s he wu ntr ideig i ot svtht e Tr el n e o c th ne c . g hC =t hedo

c

E X A I i r e cf 8s T t

I

No.

c

c

c

% 54

0.06153 0.06038 0,05924 0.05814

;: 79

0,04132 0.04079 0,04027 0,03976

0“10453 0.10117 0.09802 0.09506

55 56 57 58

0.05709 0.05607 0.05509 0.05414

80 81 82 83

0.03926 0.03878 0,03830 0.03784

0.09227

59

30 38 35

90 1 01 8 02

0. 20 6 8 7 0 3 86 8 0 2 86

2 33 2 3 2

9 03 204

3. 5.

20 29

76

0,05322 9 05 6 . 7 06 1 . 4 07 8 .

84

0.03739

5 40 60 % 5 10 8 5

88 68

!8 2 08 5. 9 4 0 0.04907 7

0.07846 0.07655

65 66

0,04831 0.04758

0.07473 0.07300 0.07134 0.06976 0.06824 0,06679 0.06540 0.06407 0,06279

67 68 69 70 71 72 73 74 75

0.04687 0,04618 0.04551 0.04487 0.04423 0.04362 0.04302 0.04244 0.04188

)8

89 90 91 92 93 % 96 97 98

1::

20 0 3. 10 1 4. 00 2 6. 4

40 80 50

3 3 3

50 093 8, 0.03529 4

3

0.03490 0.03452 0.03414 0.03377 0.03341 0.03306 0.03272 0,03238 0.03205 0.03173 0

.

0

3

290

m I

SEGMENTSOF CIRCLESFOR R4DIUS= 1

P

Length of arc, height of segment,length of chord, and area of segmentfor anglesfrom 1 to 180 degrees = 1 For other radii, multiply the . values

/ l\

andradi”s

of 1, h and c in the table by the given radius r, and J the values for areas, by r2, the square of the radius.

W

e De[ T . i 4 5 6 -1 8 9 10 11 12 13 14 15 16 17 18 19

h

1

Deg

0 2 9 3 3 0 9 0 2 3 i 0 0 0 0 3 0 0 0 3 3 0 0 3 3 3 0 0 0 o 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 I

7A

0.000o m 0 . 0,ooo1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1

0 0 0 0 0 I 0 0 0 0 0 0 I 0

1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.667

0.715 0.73?

—

0

c

1

0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

;

~ I

1

h

T

m7 62 1,082

63 1.100 64 1.117 65 1.134 66 1,152 67 1.169 68 1.187 69 1.X34 70 [~q~ 71 I.239 7? 1.257 73 1.274 74 1,291 75 I.309 76 1.3?6 77 1.344 78 1.361 79 1.379 80 1.396 81 I.414 82 1.431 83 1.449 84 1.466 85 1.483 86 1 87 1 88 1 89 1 90 1 91 1 92 1 93 1 94 1 95 1 96 1 97 1 98 1 99 1 100 1 1,763 102 1.780 103 1,798 104 1,815 105 1,833 106 1.850 107 1.867 108 1.885 109 1.902 110 1.920 111 1.937 1.955 1.972 I 1.990 I 2.007 2.025 2.042 2.059 2.077 2.094

3-F

I

c

2.11? 2.129 2.147 2.164 2.18? 2.199 2.217 ~,?34 2,:5 ] 2 2 2

I I

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

162 2.827 163 2.845 164 2.862 165 2.880 166 2.897 167 2.915 168 2.932 169 2.950 170 2.967 171 2.984 172 3.002 173 3.019 174 3.037 175 3.054 176 3.072 177 3.089 178 3.107 179 3.124 180 3.142

I

l

ment

A

I 121 122 123 124 I15 126 127 ]28 129

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

; , 1 1 1 1 1 1 1 1 1 1 1

h

Deg

A

1

Area

e

c

0 0 0 0 0 0 0 0 0 0 0 0 0 0 T0

&6~54

0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

I

1

i

[

6

291

Ziii4 I

D

d

A R T I N OT E HR SP E C TT IE O N O S H A NE O L N ZF L Z LD ( D i m e In s ni o cn e hd e s

N M ~

1

1Y2

2

2

%3

NE

I 3

A 4

( %5

0.0625

0.4375

0.0625

0.3750

0.0625

0.3125

0.0625 —. 0.0625

0.3125

0.0625

0.2500 0.3750

0.0625

0.1875 0.3125

0.0625

0.1875

0.2500 0.3750

I

T 6

%8

1.0000

1.8125

0.8125

1.5000

0.6875

1.2.500

0.6250

1.1250

0.1875 0,1875 0.12SC o.1250

E )

+

0.I 25a O.

O.125C 0.12 SC O.125C O.125C 0.062S 0.062 ! 0.062:

0.1250 0.2500

0.062 :

0.1250 0.2500

0.062 !

0.12.50 0.2500

0.062!

0.1250 0.1875

96

0.062 ! 0.0625

0. 12s0

102

0.062 ! 0.0625

0.1875

108

0.062$

0.0625

0.12s0 0.1875

114

0.0625

0.1250 0.1875

120

0.0625 —. 0.062:

0.0625

0.0625 0.1250

126

0.062$

0.0625

0.0625 0.1250

132

0.062$

0.0625

0.0625 0.1250

138

0.0625

0.0625

0.0625 0.1250

144

0.062$

0.0625

0.0625 0.1250

0.1875

292 I

I

I i I

I

I

I

dl

D

A RT O S (

S

h

!

i

e

l

l

a

;

.1

—

D

I N OT E HR SP E C TT IE O N HA NE O LN ZF L Z L D i

N M

m d eI

P I

;

n ns

e

(P A

IN

20

1

ic o hn

s , ) E

82

6

30

!.5000

4.1250

7.000

!.0625

3.1875

4.1250

8.000

[.7500

2.6250

3.3750

9

[

2.3125

2.8750

4.8750 — 4.0000

[

2.0625

2 5000

3.4375

4.6875

[

1.8125

2.2500

3.0625

4.0625

4-

[

1.6875

2.0625

2.7500

3.6250

6.0625

8.0000

1.8750

2.5000

5.3125

6.8125

[.0000

2.3125

4.8125

6.0000

5.0000

).9375

2.1250’

4.3750

5.4375

0.4375

).8750

2.0000

4.0625

4.8125

9.0000

36

).81 25

1.8750

3.7500

4.5625

8.1250

38

).7500

1.7500

3.5000

4.2500

7.3125

40

).7500

1.6875

3.3125

4.0000

6.7500

42

).6875

1.5675 1 1.1875

3.1250

3.7500

6.3125

2.6875

3.1875

5.2500

1.0625

L.0625

+ 0.875

1.0625

5.6250

.

0 D.000o

0

0

0

.1.0000

7.1875 12.0000

I

3.0000

0.7500

0.9375

1.1875

2.3125

2.8125

4.5625

0.6875

0.8125

1.0625

2.1250

2.5000

4.0000

0.6250

0.7500

1.0000

1.8750

2.2500

3.6250

1.4375

1.7500 2.0625

2.4375

0.8125

1.3125

1.5625 1.8750

2.2500

0.7500

1.1875

1.4375 1.7500

2.0625

1.1250

1.3750 1.8750

1.937.5

0.875C

1.2500 1.5000

1.8125

2.375(

0.8750

1.

96

0.3 12! 0.4375

0.500(

0.6875 —— 0.6875

102

0.3 12! 0.37s0

0.500(

0.6250

0.812 :

1.0000

1.1875 1.4375

1.6875

2.250(

108

0.250(

0.3750

0.437$

0.6250

0.750C

0.9375

1.1250 1.3750

1.5625

2. 125C

114

0.250(

0.1875

0.437:

0.5625

0.6875

0.8750

1.0625 1.2500

1.5000

2.000C

120

0.250(

0.1875

0.4375

0.5625

0.6875

0.8125

1.0000 1.1875

1.4375

126

0.250(

0.3125

0.375(

0.5000

0.625C

0.8125

0.9375 1.1250

1.3750

1.8125

132

0.250(

0.3125

0.375C 0.5000

0.625C

0.7500

0.9375 1.1250

1.3125

1.750[

138

0.182! +0.3125

0.375C 0.4375

0.5625

0.7500

0.8750 1.0625

1.2500

1.625C

144

0.1 82!

0.312 :

0.4375

0.5625

0.6875

0.8750 1.0000

1.1875

1.5625

0.3125

E

I

,

293

I

TABLEFOR LOCATINGPOINTS ON2:1 ELLIPSOIDALHEADS t

From these tablesthe dimension y can be found if the diameter, D and dimensionx are known,

~

~Ient ‘ L

3 = 12 Y 2.9580 2 2.8284 3 2.5980 4 2.2360 5 1.6583 0 6 — — D = 14 x Y 1 3.4641

r

I

3.3541 2 3.1622 3 4 2.8722 5 2.4494 6 1.8027 70 D = 16 Y

T

2 3 4 5 6 7 8 —

3.9686 3.8729 3.7081 3.4641 3.1225 2.6457 1.9364 0 ) = 18

z 2 3 4 5 6 7 8 9 10 T T 2 3 4 i 5 6 7 8 9

x 7

T x

1

2 3 4 5 6 7 8 91

2 3 4 5 6 7 8 9 10

Y

4.4721 4.3878 4.2426 4.0311 3.7416 3.3541 2.8284 2.0615 0

I

!

2

i

R=t

n r

e ao h hd

7

=7 0 ?.2284

)

7.0710 Y D = 26 6.8738 4.9749 T Y 6.6332 4.8989 T 6.4807 6.3442 4.7697 6.4226 2 6 4.5825 6.3245 3 5.5901 4.3301 4 6.1846 5.0990 4 5 6 4.5 3.5707 6 5.7662 3.7416 3 7 5.4772 2.6925 2.1794 5.1234 8 0 0 4.6904 9 ~= 32 )= 22 4.1533 10 T Y 3.4641 11 Y 7.9843 2.5 12 7 5.4772 7.9372 0 13 2 5.4083 — 7.8581 3 5.2915 ) = 28 7.7459 4 5.1234 T Y 7.5993 5 4.8989 - Y 6.9821 7.4162 6 4.6097 6.9282 2 7.1937 7 4.2426 6.8374 3 6.9282 8 3.7749 6.7082 4 6.6143 9 3.1622 6.5383 5 2 . 9 1 2 6.245 6.3245 62 5.8094 11 0 6.0621 7 5 12 =24 5.7445 8 4 13 Y 9 5.3619 3.8729 14 5.9791 4.8989 10 2.7838 15 5.9160 4.3301 11 0 16 — 5.8094 3.6055 12 ) = 34 5.6568 13 2.5980 Y Y 5.4543 0 14 — 8.4852 7 5.1961 ) = 30 8.4409 2 4.8734 x Y 8.3666 3 4.4721 7 7.4833 8.2613 4 3.9686 2 7.4330 8.1240 5 3.3166 7.3484 7.9529 2.3979 l L’ l —(

i

5 6 7 8 9 0 ,1 ,2 ,3 ,4 is —

e i

7

7 8 9~ [0 ~ [1 [2 [3 ,4 .5 ,6 ,7 — T T 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 —

ua e

sd

f .

7.7459 7.5 7.2111 6.8738 6.4807 6.0208 5.4772 4.8218 4 2.8722 0 ‘=36 Y 8.9861 8.9442 8.8741 8.7749 8.6458 8.4852 8.2915 8.0622 7.7942 7.4833

-

7

.

6.7082 6.2249 5.6568 4.9749 4.1231 2.9580 0

D =38 x Y 9.4868 2 9.4472 9.3808 T3 41 9.2870 5 9.1651

-J

1

2

294

TABLEFOR LOCATINGPOINTS ON 2: 1 ELLIPSOIDALHEADS(Cont.)

T 7 8 9 10

11 12 13 14 15 16 17 18 19 x

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

=38 9.0138 8.8317 8.6168 8.3666 8.0777 7.7459 7.3654 6.9282 6.4226 5.8309 5.1234 4.2426 3.0413 0 =40 Y 9.9874 9.9498 9.8868 9.7979 9.6824 9.5393 9.3675 9.1651 8.9302 8.6602 8.3516 8 7.5993 7.1414 6.6143 6 5.2678 4.3589 3.1225 0

T =42 x , Y 1 10.4881

8 9 10 1 1 1 1 1 1 1 1 1

20 21 x

T 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20 21 22 23 24

9.7082 9.4868 9.2330 8.9442 8.6168 8.2462 7.8262 7.3484 6.8007 6.1644 5.4083 4.4721 3.2015 0 =48 Y 11.9896 11.9583 11.9059 11.8322 11.7367

11.619 11.4782 11.3137 11.1243 10.9087 10.6654 10.3923 10.0871 9.7467 9.3675 8.9442 8.4705 7.9372 7.3314 6.6332 5.8094 4.7958 3.4278 0 = 54 Y 13.4907 13.4629 13.4164 13.351 13.2665

-L 2 3 4 5 6 7

10.4523 10.3923 10.3078 10.198 10.0623 9.8994

T

1

2 3 4 5

6 7 8 9 10

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

13.1624 13.0384 12.8939 12.72791 12.53992 12.32883 12.09344 11.83225 11.54346 11.225 7 10.87438 10.48819 10.0623 9.5916 9.0691 8.4852 7.8264 7.0710 6.1846 5.0990 3.6400 0 1 =60

x T 2 3 4 5 6 7 8 9 10

1 12 13 14 15 16 17 18 19 20 21 22 23

Y 14.9917 14.9666 14.9248 14.8661 14.7902 14.6969 14.586 14.4568 14.3091 14.1421 13.9553 13.7477 13.5185 13.2665 12.9904 12.6886 12.3592 12 11.1803

10.7121 10.198 9.6306

-7

17.9374 4 17.8885 5 17.8255 6 17.7482 7 17.6564 8 17.5499 9 17.4284 10 17.2916 1 ‘66 11 17.1391 x Y 12 16.9706 1 16.4924 13 16.7854 2 16.4697 14 16.5831 3 16.4317 15 16.3631 4 16.3783 16 16.1245 5 16.3095 17 15.8666 6 16.225 18 15.5885 7 16.1245 19 15.2889 8 16.0078 20 14.9666 9 15.8745 21 14.6202 10 15.7242 22 14.2478 11 15.5563 23 13.8474 12 15.3704 24 13.4164 13 15.1658 25 12.9518 14 14.9416 26 12.4499 15 14.6969 27 11.9059 16 14.4309 28 11.3137 17 14.1421 29 10.6654 9.9498 18 13.8293 30 19 13.4907 31 9.1515 32 8.2462 20 13.1244 7.1937 21 12.7279 33 5.9160 22 12.2984 34 23 1 1 . 35 8 4.2130 3 2 24 11.3248 36 0 10.7703 — =78 ;; 10.1612 Y 27 9.4868 Y 19.4936 28 8.7321 -i29 2 19.4743 7.8740 30 3 19.4422 6.8738 31 4 19.3972 5.6558 32 5 19.3391 4.0311 33 6 19.2678 0 7 19.1833 =7 8 19.0853 Y 9 18.9737 1 17.9931 10 18.8481 17.9722 ~ 2 18.7083

24 25 26 27 28 29 30

9 8.2915 7.4833 6.5383 5.3851 3.8405 0

295 I

TABLEFOR LOCATINGPOINTS ON2:1 ELLIPSOIDALHEADS(Cont.) D=78 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

19.2029 18 18.9737 19 18.7283 20 18.4662 21 18.1865 22 17.8885 23 17.5713 24 17.2337 25 16.8745 26 16.4924 27 16.0857 28 15.6525 29 15.1905 30 14.6969 31 14.1686 32 13.6015 33 12.9904 34 12.3288 35 11.6082 36 10.8167 9.9373 37 8.9442 38 7.7942 39 6.4031 40 4.5552 41 0 42 =90

F

18.554 18.3848 18.2003 18 17.7834 17.5499 17.2988 17.0294 16.7407 16.4317 16.1012 15.748 15.3704 14.9666 14.5344 14.0712 13.5739 13.0384 12.4599 11.8322 11.1467 10.3923 9.5524 8.6023 7.5 6.1644 4.3874 x 0 T 1 =84 2 x Y 3 4 20.994 -i2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

20.9762 20.9464

:

2

7

20.8507 20.7846 20.7063 20.6155 20.5122 20.3961 20.267 20.1246 19.9687 19.799 19.615 19.4165

8 9 10 11 12 13 14 15 16 17 18 19

v

22.4944 22.4778 22.4499 22.4109 2 2

2 2 2 2 2 2 2 2 2 2 2 2 2

2 2

7

T

21.8174 21 21.5812 21 22 21.3307 22 23 21.0654 23 24 20.7846 24 25 20.4878 25 26 20.1742 26 19.8431 27 27 19.4936 28 28 19.1246 29 29 18.735 30 30 18.3235 31 31 17.8885 32 32 17.4284 33 33 16.9411 34 34 16.4241 35 35 15.8745 36 36 15,2889 37 37 14.6629 38 38 13.9911 39 39 13.2665 40 40 12.48 41 41 11.619 42 42 10.6654 43 43 9.5916 44 44 8.3516 45 45 6.8556 46 4.8734 47 x 0 48 7 7 = 108 2 Y Y 3 4 26.9954 -i. 5 3 2 6 3 0 . 72 8 26.9815 6 9 . 6 2 2 9 3 9 . 13 8 26.9583 1 1 7 23.7434 4 26.9258 8 23.6643 5 26.884 9 23.5744 6 26.8328 10 23.4734 7 26.7722 11 23.3613 8 26.7021 12 23.2379 9 26.6224 13 23.103 10 26.533 14 22.9565 11 26.4339 15 22.798 12 26.3249 16 22.6274 13 26.2059 17 22.4444 14 26.0768 18 22.2486 15 25.9374 19 22.0397 16 25.7876 20.1556 19.8997 19.6278 19.3391 19.0329 18.7083 18.3644 18 17.6139 17.2047 16.7705 16.3095 15.8193 15.2971 14.7394 14.1421 13.5 12.8062 12.052 11.225 10.3078 9.2736 8.0777 6.6332 4.7169 0 =96 Y 23.9948 23.9792 23.9531 23.9165

7 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 4

4

50 8 51 52 53 54 -

x

7

2 3 4 5 6 7

25.6271 25.4558 25.2735 25.0799 24.8747 24.6577 24.4285 24.1868 23.9322 23.6643 23.3827 23.0868 22.7761 22.4499 22.1077 21.7486 21.3717 20.9762 20.5609 20.124F 19.666 19.1833 18.6748 18.1384 17.5713 16.9706 16.3325 15.6525 14.9248 14.1421 13.2947 12.3693 11.3468 10.198 8.8741 7.2801 5.1720 0 = 120 Y 29.9958 29.9833 29.9625 29.9333 29.8957 29.8496 29.7951

296 TABLE FOR LOCATING POINTS

r

ON 2:1 ELLIPSOIDALHEADS (Cont.)

T

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 &

❑120 29.7321 29.6606 29.5804 29.4915 29.3939 29.2874 29.1719 29.0474 28.9137 28.7706 28.6182 28.4561 28.2843 28.1025 27.9106 27.7083 27.4955 27.2718 27.037 26.7909 26.533 26.2631 25.9808 25.6856 25.3772 25.0549 24.7184 24.367 24 23.6167 23.2164 22,798 22.3607 21.9032 21.4243 20.9225 20.3961 19.8431 19.2614 18.6481 18 17.3133 16.5831 15.8035 14.9666 14.0624 13.0767

55 56 57 58

10.9896 10.7703 9.3675 7.6811

59

54543

60

0

— D = 132

x

T

2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 ;; 29 30 31 32 33 34 35 36 37 38 39

Y 32.9962 32.9848 32.9659 32.9393 32.9052 32.8634 32.8139 32.7567 32.6917 32.619 32.5384 32.45 32.3535 32.249 32.1364 32.0156 31.8865 31.749 31.603 31.4484 31.285 31.1127 30.9314 30.7409 30.541 30.3315 30.1123 29.8831 29.6437 29.3939 29.1333 28.8617 28.5788 28.2843 27.9777 27.6586 27.3267 26.9815 26.6224

z 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 7 Y T 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

26.2488 25.8602 25.4558 25.035 24.5967 24.1402 23.6643 23.1679 22.6495 22.1077 21.5407 20.9464 20.3224 19.666 18.9737 18.2414 17.4642 16.6358 15.748 14.7902 13.7477 12.5996 11.3137

9.8361 8.0622 5.7227 0 = 144 Y35.9965 35.9861 35.9687 35.9444 35.9131 35.8748 35.8295 35.7771 35.7176 35.6511 35.5774 35.4965 35.4083 35.3129 35.2101 35.0999 34.9821 34.8569

Y

5

34.7239 34.5832 34.4347 34.2783 34.1138 33.9411 33.7602 33.5708 33.3729 33.1662 32.9507 32.7261 32.4923 32.249 31.9961 31.7333 31.4603 31.1769 30.8828 30.5778 30.2614 29.9333 29.5931 29.2404 28.8747 28.4956 28.1025 27.6948 27.2718 26.8328 26.3771 25.9037 25.4116 24.8998 24.367 23.8118

5

2

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 56 57 58 59 60 61 62 63 64 65 J@

22.6274 21.9943 21.3307 20:6337 19.8997 19.1246 18.303 17.4284 16.4924 15.4839 14.3875

L 67 68 69 70 71 72

13.1814

10.2835 8.4261 5.9791 0

N

O

T

T c u r hv a o a e l l i p s h e ei t a i no o s u it i at r e l l i p s T p a r h a l c o ut r o p sp o si i n e l l o i a t n h d o a t t t ha bi a n r o a p p l i c a t l o c a p o i n t g eh o ma r iu c a ln d e t e r m i c u r v ( e i t o h w

s c ha

p

e

c i a 4 ah e a le la

297 LENGTH OF ARCS 1. These tables are for locating points on pipes and shells by measuring the length of arcs. 2. The length of arcs are computed for the most commonly used pipesizes and vessel diameters. 3. The length of arcs for any diameters and any degrees, not shown in the table, can be obtained easily using the values given for diam. 1 or degree 1. 4. All dimensions are in inches. EXAMPLES w

A.

3P

O.D. = 3 N F

/ 2

7 9

4 6

1

Y @

s

3m’

.I =3 O = N ol FW t

) 2

7

d

9

d 4

1

8

p 22%0

D

7 { &

1

f

.

. e 0e eu r cr it n e0 e .r ti e

” d ° oe e ohd m e oh @ 0 ° m e 8i h c 4 f sn 3 : 8

. W t h D0ai c 3 k . lnt / e” s l8hs = ” a ?. 3D 4 . 0 ” oz @ 3c z a l t e e0 d ? ° r l a eo W o3b na f lgm 0t e r ho f ° c

1= 0 i . 0 . @

2 a 6 1 x 23 6 = 08 1

. 8 . 8i.

0 00 7 5

n5 0

. O.D. =3

0 ” N ol oz @ 2c z a 2l t e e? d 4 F t r l a eo o1b an o lgm te r h P’ .0( i )J .pD 2 ” e6 . 1 = 8 03 Y O 0 . x 22 125 i 8 . =6

! 2

? ° h 8

Y

.O = 3 P. V D0 N ol oz @ 6c z a l t T a t b m h e r af st c P 0l c oe n s t @ee r s l T n oi 3h z f z t s 9rl ~ T l eo t hn a 7gh & ’

7 9

I

P

c

(

6 .

2

t V @

8

C

B

ol

0 ” oz @ 3c z a l t e e0 d rt al oebo hn l m g e t e a =7 ’ . i r 8 4 n3 c

9 (

8

W

° f ° c 0 0. 8

n9

298 L

E D

D

i

00

0.

1

0

.

00

1 . 01 0 4.

2 3

w w ~ ~ A m x a 8 $ & a z ~ n

5 6 8

RT

R

E

1

.

800

G

G

.1

0

a ~ z 0 z

5m

E

1 1Y2

: z w & z

a

1

O NA

74.

.86

6801

2 .2

1730

C

E

32.

5015

F

S

S 02

2

033

H

0710

97.

.80 0 27

53 0420

51.

. 1S 20 8

0 382

16

8. 8

31

- ,

L

E D

D

i 1

w N G m & z d 4 g $?

m : u ~

.

30

.4 0.

3930

90.

72 1

E

S

S 52

87 .

F

8

5052.35619 47

03

8 003.14159

0.4688

0.5313

1.0313

2.0625

1.5000

3.0000

3.0938 4.4688

4.1250

0.7500 0.9375 1.1250

1.8750

3.7188 4.5313 5.5000

5.5938 6.7813 8.2500

6.2813 7.0625

9.4375 10.5938 13.0938 15.6250 20.3125 25.3438 30.0313 29.2813 33.0000

7.4688 9.0313 11.0000 12.5625

2 2%

0.7188 0.8750

3 3% 4

1.0625

38 ;:

5 * m +

78

E

:;

66

4

1.2188 1.3750 1.6875 2.0313 2.6250 3.2813 3.9063 3.6563 4.2813 4.8750 5.5000 6.0938 6.7188 7.3438 7.9375 8.5625 9.1563 9.7813

0.8438 1.0000 1.2188 1.4003 1.5625 1.9375 2.3125

1.5625 1.7813 2.1875 2.5938

3.0938 3.7500 4.4375 4.1875

3.3750 4.2188 5.0000 4.7188

4.8750 5.5938

5.5000 6.2813 7.0313 7.8438 8.6563 9.4375

6.2813 6.9688 7.6875 8.3750 9.0625 10.2188 9.7813 11.0000 10.4688 11.7813

10.3750 11.0000 11.5938 12.2188 12.8438 14.6563

11.1563 11.8750 12.5625 13.2500 13.9688 14.6563 16.7500

12.5625 13.3438 14.1250 14.9375 15.7188 16.5000 18.8438

16.5000 18.3125 20.1563 22.0000 23.8125

18.8438 20.9375 23.0313 25.1250 27.2188

21.2188 23.5625 25.9065 28.2813 30.6250

25.6563 2

7

29.3125 3 . 3

5 1

2

9

. 3

3 3

1

3

1

0.3

1

3

3

0.3

4

1.3

9

1.3750

3 3

6

2 .4

3 0 .

2.2500 2.7500 3.1563 3.5313 4.3750 5.2188 6.7813 8.4375 10.0000 9.4375 11.0000 12.5625 14.1250 15.7188 17.2813 18.8438 20.4063 22.0000 23.5625 25.1250 26.7188 28.2813 29.8438 31.4063 33.0000 37.6875 42.4063 47.1250 51.8438 56.5625 61.2500

8.7500 10.4063 13.5625 16.8750 20.0313 18.8438 22.0000 25.1250 28.2813 31.4063 34.5625 37.6875 40.8438

61.2500 65.9688 70.6875

81.6875 87.9688 94.2500 100.5313 106.8125

62.8438 65.9688 75.4063

75.4063 80.1250 84.8125 89.5313 94.2500 98.9688 113.0938

84.8125 94.2500 103.6875 113.0938 122.5313

127.2500 141.3750 155.5000 169.6S63 183.7813

56.5625 59.6875

69.1250 75.4063

113.0938 119.3750 125.6563 131.9375 150.7813 169.6563 188.5000 207.3458 —-..— 226.1875 245.0313

3

.6

05

0 .1

9 03

16 1 . 89 9 0

8 7 3 2 . 7 6 9 53 0

. 6

5 04

.070

2 06

4 .1 3

6 34

18 2 . 71 3 8

5 2 7 2 . 5 8 0 02 6

. 2

5 00 2 . 62 7

3 6 83 . 10 1 31 8

. 7

.570

6 50

8 .1 0

74 5

3 1 .

7 25 6

15

45 .

2065

.389

1 03

2 .1 8

1 56

002 2 . 54 2

0 1 3 . 8 2 3 80 4

. 3

07

40 .

8206

.088

4 47

0 .1 5

8 66

391 3 . 25 6

5 4 53 . 63 4 39 6

. 8

41 .

4927

.588

7 91

8 .1 3

5 17

393 2 . 16 0

3 8 63 . 25 5 58 9

. 3

0 2 0 3 . 0 7 7 07 5

. 0

8 6 0 3 . 6 9 8 35 7 7 5 3 . 6 1 3 3 1 44 . 31 0 84 3 8 5 6 7 3 . 5 2 7 0 5 84 . 13 1 33 5 6 9 3 . 3 3 1 8 9 8 4 . 7 5 2 52 8 5

. 1 . 6

89 61

45 .

0768

.397

1 45

1 2 .0

8 52

085 2 . 08 5

6 .1 8

89

876 2 . 89 9

1

3

8

2 .4

53

40 .

6909

.096

4 88

1

4

0

3.4

36

1. 5

21 20

56 .1

0 8 2 34 2 5 . 30 6

1

4

2

3.4

18

5 .

84 61

.1 35

0 1 6 88 2 3 . 71 3

3

4. 5

6 . 5

46 82

85 .1

1 5 0 36 20 . 22 0

4

0

14.1250 17.4688 20.8125 27.0938 33.7813 40.0625 37.0625 43.9688 50.2500 56.5625 62.8438

50.2500 53.4060

6

5.9688

37.6875 42.4063 47.1250 51.8438 56.5625

43.9688 47.1250

0

7

0.6563

30 32 34 36

1

C

0.4063

8 10 12 12 14 16 18 20 22 24 26 28

1

44.

E

01

59

350

R

H

0.5938

6

1

G

R T

1Y2

A ‘ 48 a LLl g 54 60

s

0

4m

E

G

1

5

z

3 a

O NA

9 0

. 5

. 1

300

C D

I

3A

.

—

A

i Circum.

I

. .

0 0

. . . . . . .

1 1 2 3 4

Area a . .

4 9

. . . . . 5 . 6 .

4 9 9 9 9

. c 0

9 8

0 0 0 0 0 80 8 0

7 6 4 2 0

Circum. 0 6.2832 o 9 1 6.4795 0 8

Q 0

A

0 2 0 3 0 3 1 7 1 8 2% 7 3 2

6.6759 1 6 6.8722 3 5 7.0686 6 2 7.2649 2 0 9 7 7.4613 7 5 7.6576 7.8540 7 2 8.0503 8.2467 9 0 8.4430 2 7 8.6394 6 5 8.8357 2 9 9.0321 0 1 9.2284 9 3

C

Area 1 3.1416 9 7 3.3410 7

7 0 9 2 1 6 5

3 3.5466 7 3.7583 0 3.9761 7 4.20Q0 7 4.4301 1 4.6664 4.9087 8 5.1572 5.4119 9 3 5.6727 5.9396 0 6.2126 1 6.4918 5 6.7771 2

. . . 1 1 1 1 1

7 8 9 . . . . .

. . . . . . . .

8 8 8 0 1 2 3 4

0 0 0 0 1 1 1 1

5 3 1 7 7 7 7 7

4 6 7 9 1 2 5 7

4 5 7 9 8 6 4 0 4 2 9.4248 2 6

1 1 1 1 1 2 2 2

. . . . . . . .

. . . . . . . .

5 6 7 8 9 0 1 2

1 2 2 2 3 3 3 4

7 6 6 6 6 6 5 5

9 2 4 7 0 3 7 0

0 9 7 5 3 1 9 8

3 6 5 8 8 2 2 7

5 6 0 8 0 4 2 4

2 2 2 2 2 2 2 3

. . . . . . . .

. . . . . . . .

3 4 5 6 7 8 9 0

4 4 5 5 6 6 6 7

5 5 5 5 4 4 4 4

4 7 1 5 0 4 9 3

3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6

. . . . . . . . . . . . . . . .

. . . 1 1 1 1 1 1 1 2 2 2 2 2 2

1 3 5 7 9 1 3 5 7 9 1 3 4 6 8 0

6 7 4 3 2 4 0 1 8 3 7 5 1 0 5 10 2 22 3 17 4 20 1— 2 18 1 6 53 78 1 9 63 49 1 3 43 0 10 6 37 7 12 0 37 3 15 3 43 9 18 7 44 6 12 0 43 2 16 4 47 8 11 7 47 5 71 1 35 1 31 4 65 7 01 8 55 4 815.708 1 0 0 6 5 1 415.$04 6 16.101 8 8

9 7 9 4 2 4 12.566 .9 12.962 .8 . 13.364 13.772 .4 14.186 .6 .0 14.607 15.033 .5 .2 15.466 .0 15.904 16.349 .9 16.800 .0 .1 17.257 17.728 .5 18.19u .9 18.665 5. 19.147 3. 2 2 3

. . . . . . . . . . . . .

74 83 93 3 2 2 1 1 1 0 0 0 9 9 9 8

1 2 3 4 6 7 9 0 2 4 5 7 % 9

%

9.6211 9.8175 6 8 10.014 1 0 10.210 8 1 10.407 6 3 10.603 6 5 10.799 8 7 10.996 1 8 11.192 5 0 11.388 11.585 1 2 11.781 9 4 11.977 8 5 12.174 9 7 12.370 1 9

0 1 7 8 4 6 3 5

3 7

I

Circum.

Area

16.297 16.493 16.690 16.886 17.082 17.279 17.475 17.671 17.868 18.064 18.261 18.457 18.653

21.135 21.648 22.166 22.691 23.221 23.758 24.301 24.850 25.406 25.967 26.535 27.109 27.688

18.850 19.242 19.635 20.028 20.420 20.813 21.206 21.598

28.274 29.465 30.680 31.919 33.183 34.472 35.785 37.122

21.991 22.384 22.776 23.169 23.562 23.955 24.347 24.740

5 7 9 1 3 5 7 9 1 3 5 7 9 1 3 5

6 6 5 5 S 4 4 4 3 3 3 2 2 1 1 1

?

x

25.133 25.525 6 25.918 3 26.311 9 26.704 5 27.096 2 27.489 8 27.882

4 1 28.274 7 28.667 4 29.060 0 29.452 6 29.845 3 30.238 9 30.631 5 31.023 —— 2 31,416 31.809 32.201

301

C

A

A r

D

C

o ; % % 3 %

3 3 3 3 3

2‘ 2 3 3 4

% % % % % 3 ~

3 3 3 3 3 3 3 3

41 4 5 5 6 6 6 7

9 9 9 1 1 1 1 1

. . . . . . . .

% % % % ~ % 7

3 3 3 3 3 3 4 4

72 8 8 8 9 9 0 0

1 1 1 1 1 1 1 1

. . . . . . . .

% % % s %

4 4 4 4 4 4 4 4

03 1 1 2 2 2 3 3

1 1 1 1 1 1 1 1

. . . . . . . .

~ x % % ~ ? %

4 4 4 4 4 4 4 4

34 4 4 5 5 5 6 6

1 1 1 1 1 1 1 1

. . . . . . . .

% % % ~ % % 7

4 4 4 4 4 4 4 4

75 7 7 8 8 9 9 9

1 1 1 1 1 1 1 1

. . . . . . . .

%

5 5

06 2 . 0 2 .

1

1

1 ;

1

1

1

i i

r . m C e.i i uD

ac

8 . 8 . 8 . W. 9 .

A

%.. 9~ %. 8 %. 7 77 %A ~. 6 % 55 .. 5 7 91 . 5 9 3 %. 4 0 7 K 1 3 0 1 33 2 0 5 % 6 2 0 9 % 8 A 1 1 3 % 0 08 ~ 1 6 3. 9 1 01 5 9 1 4 ;7 8 2 8 0 7 2 2 ~2 7 2 6 % 5 68 2 0 % 7 5 3 4 ?0 48 — % 3 8 2. 4 3 21 5 3 3 6 % 7 2 4 0 ~0 1 4 4 % 3 1 4 8 ;5 0 4 1 8 9~ 5 5 % 1 9 % 5 9 3. 8 5 32 6 7 5 7 % 9 6 6 1 ~2 6 6 5 ~5 5 6 9 % 7 4 7 3 ~0 34 7 7 x3 3 & 7 — 1 6. 2 7 52 9 1 8 9 g2 0 8 3 x5 0 8 6 % 8 9 9 0 Y 1 8 9 4 % 4 8 9 8 ‘7 78 ~ 0 2 1. 6 0 62 4 5 45 69 83 7. 21

55 55 56 5 58 5 0 52 54 5. 5. 5. 5, 5. 5 . 5. 5. 5. 5. 5. 5. 5. 5 . 5. 6. 6. 6. 6. 6. 6. 6 . 6. 6. 6. 6. 6. 6. 6. 6 . 6. 6. 6. 6. 6. 6. 6. 6 . 6.

C

rA aa c

4 14 2 7 19 2 9 16 2 2 62 2 5 28 2 3 2 8 3 0 307 2 3 30 2 6 64 2 8 84 2 1 14 2 4 45 2 6 75 2 6 2 1 9 2 468 2 5 86 2 7 27 2 0 7 2 3 18 2 5 68 2 8 18 2 9 2 1 7 3 939 2 6 08 2 9 50 2 2 01 2 4 18 2 7 14 3 0 2 3 2 3 2 9 5 270 3 8 34 3 0 3 3 3 41 3 6 49 3 8 48 3 1 57 3 S 3 4 7 7 561 3 9 6 3 2 6 3 5 67 3 7 7 3 0 87 3 3 93 3 8 3 5 0 8 292 3

.1 .0 .4 .3 .6 . 3 .5 .2 2. 7. 4. 3. 5. . 0 7. 6. 8. 2. 9. 8. 9. . 3 .0 .9 0. .4 .0 .9 .0 . 4 .0 .8 .0 .3 .9 .7 .8 . 1 .7 .5 6. 9. 5. 3. 3. . 6 2.

I(

uDr

. mC

~7 5 0 4 X $3 3 ~7 2 0 2 % 33 1 Y 2 4 6. 0 3 82 0 0 3 1 % 3 9 3 5 X7 A 8 4 9 90 7 4 3 % 3 7 4 7 % 7 6 5 1 30 58 % 5 5 4. 4 5 92 8 4 6 3 g1 3 6 7 ?5 2 6 1 98 1 7 5 ?2 1 7 9 % 6 04 7 2 ?9 9 ~ 8 6— 3. 9 8 02 7 8 9 4 ~1 7 9 8 4 6 9 2 ~8 6 0 6 % 2 5 0 0 ~6 4 1 4 % 0 3 ~ 1 8 4. 3 1 22 8 2 2 6 % 2 1 2 0 x6 1 3 4 % 0 0 3 7 Y4 98 3 1 % 8 8 4 5 ~2 8 % 4 9— 6. 7 5 32 0 6 5 7 4 % 5. 5 1 % 8 5 6 5 33 42 6 9 ;7 3 7 3 1 A 3 7 7 ?5 2 % 8 1 0. 1 0 1 1 1 2 2

0 4 8 2 6 0

6. 6. 7. 7. 7. 7. 7 . 7. 7. 7. 7. 7. 7. 7. 7 . 7. 7. 7. 7. 7. 7. 7. 7 . 7. 7. 7. 7. 8. 8. 8. 8 . 8. 8. 8. 8. 8. 8. 0, 8 . 8. 8 8. 8. 8. 8. 8. 8 .

e.i i 1 4 6 9 2 4 7 0 2 5 8 1 3 6 9 1 4 7 9 2 5 8 0 3 6 8 1 4 6 9 2 5 7 0 3 5 8 1 3 6 69 2 4 7 0 2 5

rA aa c

93 3 69 3 80 ’3 0 3 31 4 16 4 1 4 9 323 4 72 4 31 4 53 4 39 4 4 4 49 4 5 4 4 054 4 5 4 16 4 68 4 46 4 71 4 78 4 8 4 5 825 4 80 4 98 5 96 5 04 5 30 5 02 5 1 5 1 16 5 02 5 02 5 20 5 . 31 5 31 5 42 5 4 5 3 457 5 54 5 58 5 60 5/ 62 5 65 5 78 6 7 6 1

.9 0. 2. 8. S . .5 . 8 3. 1. .0 3. .8 .5 .5 . 7 2. .9 8. .0 5 .2 .1 . 3 .7 .4 .3 .5 .9 5 .4 . 6 0. 6. 5. 6 .0 .6 .5 . 6 .0 .5 .4 .5 .8 .4 .3 . 3

ur

.m

8 8 9 9 0 0 1

s 9 2 6 0 4 8

4 8 3 7 2 6 0

O 0 96 8 7 7 A 6E

1 2 2 2 3 3 4 4

2 6 0 4 8 2 6 0

5. 0 4 9 3 8 3 7

5 4 4 38 2 2 1 A 0

5 5 6 6 .7 7 8 8

3 7 1 5

2. 9 7 9 1 84 6 76 1% 4 6 6 1 54 5 48

9 9 0 0 1 51 2 2

s 9 3 7 1

3 3 4 84 5 5 6 6

6 0 4

7 7 8 8

3 7 1

8 2

2 6 0 4

8 2 6 0 93 9 7 0 1 1 5 4

0. 4 5 3 0 2 5 18 0 1 50 0 9 5 88 0. 6 1 66 1 6 2 7 2. 7 3 8

8 7 6

52 4 3 3

2 1 0 08 93 9 8 4 74 0 7

2

2

A

A

~ % % %

C

Area

C

i

615.75 621,26 626.80 632.36 637.94 643.55 649.18 654.84

1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0

R

rArea c

u

m

6 7 7 7 8 8 9 9

8 2 6 9 3 7 1 5

1 0 0 9 8 7 7 6

. . . . . . . .

. 4 125.664 7 126.0s6 0 126.449 126.842 2 127.23s 5 127.627 8 128.020 0 128.413 3 128.805 129.198 129.591 129.983 130.376 130,769 131.161 131.554

660.52 666.23 671.96 677.71 683.49 689.30 695.13 700.98

k

1320.3 1328.3 1336.4 1344.5 1352.7 1360.8 1369.0 1377,2

706.86 712.76 718.69 724.64 730.62 736.62 742.64 748.69 754.77 760.87 766.99 773.14 779.31 785.51 791.73 797.98

1075.2 1082.5 1089.8 1097.1 1104.5 1111.8 1119.2 1126.7

804.25 810.54 816.86 823.21

8

135.088 135.481 135.874 136.267 136.659 137.052 137.445 137.837

119.381 119.773 120.166 120.559

2

9

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122.522 122.915 123.308 123.700 124.093 124.486 124.878 125.271

5

1 8

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139.801 4 . 1 2 140.194 140.586 140.979 141.372 141.764 142.157 142.550 142.942 143.335 143.728 144.121

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147.655 148.048 148.440 148.833 149.226 149.618 150.011 150.404

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4 . 1661.9 4 . 1670.9 5 , 1680.0 5 . 1689.1 6 . 1698.2 6 . 1707.4 6 . 1716.5 7 . 1725.7

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1734.9 1744.2 1753.5 1762.7 1772.1 1781.4 1790.8 1800.1

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6

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2123.7 2133.9 2144.2 2154.5 2164.8 2175.1 2185.4 2195.8

166.504 166.897 167.290 167.683 168.075 168.468 168.861 169.253

2206.2 2216.6 2227.0 2237.5 2248.0 2258.5 2269.1 2279.6

169.646 170.039 170.431 170.824 171.217 171.609 172.002 172.395

2290.2 2300.8 2311.5 2322.1 2332.8 2343.5 23S4.3 236S.0

172.788 173.180 173.573 173.966 174.358 174.751 175.144 175.536

2375.8 2386.6 2397.5 2m8.3 2419.2 243J1.1 2441.1 2452.0

5 1 0 7

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2042.8 2052.8 2062.9 2073.0 2083.1 2093.2 2103.3 2113.5

I

Area

3 163.363 6 163.756 9 164.148 1 164.541 4 164.934 7 165.326 9 165.719 2 166.112

177.893 178.285 178.678 160,221 160.614 161.007 161.399 161.792 162.185 162.577 162.970

C

2463.0 2474.0 2485.0 2496.1 2507.2 7 . 2518.3 2529.4 2540.6 2551.8 2563.0 2574.2 2585.4 2596.7 2608.0 2619.4 2630.7

Area 182.212 182.605 182.998 183.390 183.783 184.176 184.569 184.961

2642.1 2653,5 2664.9 2676.4 2687.8 2699.3 2710.9 2722.4 2734.0 2745.6 2757.2 2768.8 2780.5 2792.2 2803.9 2815.7 2827.4 2839.2 2851.0 2862.9 2874.8 2886.6 2898.6 2910.5

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201.062 201.455 201.847 202.240 202.633 203.025 203.418 203.811

X i % % %

204.204 204.596 204.989 205.382 205.774 206.167 206.5&l 206.952

Circum. 238.761 239.154 239.546 239.939 240.332 240.725 241.117 241.510

% X % % % % 3421.2 3434.2 3447.2 3460.2 3473.2 3486.3 3499.4 3512.5

210.487 210.879 211.272 211.665 212.058 212.450 212.843 213.236

R

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245.044 245.437 245.830 246.222 246.615 247.008 247.400 247.793

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248.M6 248.579 248.971 249.364 249.757 250.149 250.542 250.935

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251.327 251.720 252.113 252.506 252.898 253.291 253.684 254.076

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254.469 254.862 255.254 255.647 256.040 256.433 256.825 257.218

305

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2 .3 .3 .3 .3 .3 .3

Y % % % % % % % % % % % 3 Y

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5808.8 5825.7 5842.6 5859.6 5876.5 5893.5 5910.6 5927.6

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270.177 270.570 270.962 271.355 271.748 272.140 272.533 272.926 273.319 273.711 274.104 274.497 274.889 275.282 275.675 276.067

5944.7 5961.8 5978.9 5996.0 6013.2 6030.4 6047.6 6064.9

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5 4 3 3 2 1 0 0

279.602 02 279.994 65 280.387 38 280.780 90 281.173 63 281.565 26 281.958 88 282.351 51

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Circum. 295.310 295.702 296.09s 296.488 296.881 297.273 297.666 298.059

6939,8 6958.2 6976.7 6995.3 7013.8 7032.4 7051.0 7069.6 ——.

298.451 298.844 299.237 299.629 300.022 300.415 300.807

7088.2 7106.9 7125.6 7144.3 7163.0 7181.8 7200.6

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3

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308.661 309.054 309.447 309.840 310.232 310.625

7581.5 7600.8 7620.1 7639.5 7658.9 7678.3

311.018 311.410 311.803 312.196 312.588 312.981 313.374 313.767

7697.7 7717.1 7736.6 7756.1 7775.6 7795.2 7814.8 7834.4

6082.1 6099.4 1 3 6116.7 6134.1 4 6151.4 6 6168.8 8 6186.2 1 6203.7 3

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x $6 % %

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285.885 45 286.278 18 286.670 71 287.063 43 287.456 16 287.848 89 288.241 52 288.634 14

6361.7 8 6379.4 3 6397.1 8 6414.9 4 6432.6 9 6450.4 5 6468.2 2 6486,0 8 ——— . 6503.9 5 . 6521.8 2 . 6539.7 9 . 6557.6 7 . 6575.5 5 . 6593.5 3 . 6611.5 1 . 6629.6 9

289.027 289.419 289.812 2?0.205 290.597 290.990 291.383 291.775

6647.6 6665.7 6683.8 6701.9 6720.1 6738.2 6756.4 6774.7

292.168 292.561 292.954 293.346 293.739 294.132 294.524 294.917

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12125 0 12150 12174 12199 12223 12248

392.70 393.09 393.49 393.88 394.27 394.66 395.06 395.45

12272 12297 12321 12346 12370 12395 12419 12444

131.

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12469 12494 12518 12543 12568 12593 12618 12643

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12668 12693 12718 12743 12768 12793 12818 12843

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402.13 402.52 402.91 403.30 403.70 404.09 404.48 404.87 405.27 405.66 406.05 406.44 -.~ 407.23 407.62 408.02

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13478 13504 13529 13555 13581 13607 13633 13659

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13685 13711 13737 13763 13789 13815 13841 13867

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13893 13919 13946 13972 13999 14025 14051 14077

420.97 421.37 421.76 422.15 422.55 422.94 423.33 423.72

14103 14130 14156 14183 14209 14236 14262 14288

424.12 424.51 424.90 423.29 425.69 426.08 426.47 426.87

14314 14341 14367 14394 14420 14447 14473 14500

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427.26 427.65 428.04 428.44 428.83 429.22 429.61 430.01

% x % % % % %

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Area 14527 14553 14580 14607 14633 14660 14687 14714

142. ?~ x ?~ ?4 96 3A

143.

430.40

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15175 15203 15230 15258 15285 15313 15340 15367

145.

15394 15422 15449 15477 15504 15532 15559 15587

146.

% % % %

439.82 440.22 440.61 441.00 441.40 441.79 442.18 442.57

15615 15642 15670 15697 15725 15753 15781 15809

147.

% g /8 % % % x

442.97 443.36 443.75 444.14 444.54 444.93 445.32 445.72

140. % % y;

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% % % % % %

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x ~ 3A B

% % 3A N % % %

446.11 446.50 446.89 447.29 447.68 448.07 448.46 448.86

15837 15865 15893 15921 15949 15977 16005 16033

449.25 449.64 450.03 450.43 450.82 451.21 451.61 452.00

16061 16089 16117 16145 16173 16201 16229 16258

452.39 452.78 453.18 453.57 453.% 454.35 454.75 455.14 455.53 455.93 456.32 456.71 457.10 457.50 457.89 458.28

16286 16314 16342 16371 16399 16428 16456 16485 —— 16513 16542 16570 16599 16627 16656 16684 16713

458.67 459.07 459.46

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477.52 477.92 478.31

18146 18175 18205

16856 16885 16914 16943

478.70 479.09 479.49 479.88 480.27

1

460.24 460.64 461.03 461.42 461.82 462.21 462.6Q 462.99 463.39 463.78 464.17 464.56

16972 17000 17029 17058 17087 17116 17145 17174

480.67 481.06 481.45. 481.84 482.24 482.63 4S3.02 483.41

18385 18415’ 18446 18476 18507 18537 18567 18597

459.85 16827

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i8627 18658 18688 18719 18749 1&3779 18809 18839

16Q. >8

502.&5 503.05 503.44 503.83 504.23 504.62 505.01 505.41

20106 20138 20169 20201 20232 20264 20295 20327

166.

486.95 487.34 497.73 488.13 488.52 488.91 489.30 489.70

18869 18900 18930 18%1 18991 19022 19052 19083

161.

505.80 506.19 506.58 506.98 507.37 507.76 508.15 508.55

20358 20390 20421 20453 20484 20516 20548 20580

167.

4S0.09 490.48 490.88 491.27 491.66 492.05 492.45 492.84

19113 19144 19174 19205 19235 19266 19297 19328

162.

508.94 509.33 509.73 510.12 510.51 510.90 511.30 511.69

20612 20644 20675 20707 20739 20771 20803 20835

168.

493.23 493.62 494.02 494.41 494.80 495.20 495.59 495.98

19359 19390 19421 19452 19483 19514 19545 19576

163.

20867 20899 20931 20964 20996 21028 21060 21092

169.

% % % % Y8

512.08 512.47 512.87 513.26 513.65 514.04 514.44 514.83

4%.37 496.77 497.16 497.55 497.94 498.34 498.73 499.12

19607 1%38 19669 19701 19732 19763 19794 19825

164.

21124 21157 21189 21222 21254 21287 21319 21351

170.

% ~ ?$ % % % x

515.22 515.62 516.01 516.40 S16.79 517.19 517.58 517.97

499.51 499.91 500.9 500.69 501.09 501,48 M1.87 S2.26

19856 19887 19919 19950 19982 20013 20044 20075

165.

518.36 518.76 519.15 519.54 519.94 520.33 520.72 521.11

21383 21416 21448 21481 21513 21546 21578 21610

171.

483.81 ! s I 484.20 ;~ 484.59 484.99 38 485.38 % 485.77 % 4S6.16 % 486.56 %

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521.51 521.90 522.29 522.68 523.08 523.47 523.86 524.26

21642 21675 21707 21740 21772 21805 21838 21871

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524.65 525.04 525.43 525.83 526.22 526.61 527.00 527.40

21904 21937 21969 22002 22035 22068 22101 22134

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527.79 528.18 528.57 528.97 529.36 529.75 530.15 530.54

22167 22200 22233 22266 22299 22332 22366 22399

530.93 531.32 531.72 532.11 532.50 532.89 533.29 533.68

22432 22465 22499 22532 22566 22599 22632 22665

534.07 534.47 534.86 535.25 535.64 536.04 536.43 536.82

22698 22731 22765 22798 22832 22865 22899 22932

537.21 537.61 538.00 538.39 538.78 539.18 539.57 539.%

22966 22999 23033 23066 23100 23133 23167 23201

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24885 24920 24955 24990 2%25 25060 25095 25130

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25165 25200 25236 25271 25307 25342 25377 25412

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25447 25482 25518 25553 25589 25624 25660 25695

186.

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578.05 578.45 578.84 579.23 579.63 580.02 580.41 580.80

26590 26626 26663 26699 26736 26772 26808 26844

581.20 581.59 581.98 582.37 582.77 583.16 583.55 583.95

26880 26916 26953 26989 27026 27062 27099 27135

584.34 584.73 585.12 585.52 585.91 586.30 586.59 587.09

27172 27208 27245 27281 27318 27354 27391 27428

587.48 587.87 588.27 588.66 589.05 589.44 589.84 590.23

27465 27501 27538 27574 27611 27648 27685 27722

590.62 591.01 591.41 591.80 592.19 592.58 592.98 593.37

27759 27796 27833 27870 279Q7 27944 27981 28018

593.76 594.16 594.55 594.94 595.33 5U5.73 5%.12 5%.51

28055 28092 28130 28167 28205 28242 28279 28316

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26353 28390 28428 28465 28503 28540 28578 28615

196. % x % ~

600.04 600.44 600.83 601.22 601.62 602.01 602.40 602.79

28652 28689 28727 28764 28802 28839 28877 28915

197.

28953 28990 29028 29065 29103 29141 29179 29217

198.

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603.19 603.58 603.97 604.36 604.76 605.15 605.54 605.94 606.33 606.72 607.11 607.51 607.90 608.29 608.58 609.08

29255 29293 29331 29369 29407 29445 29483 29521

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29559 29597 2%36 2%74 29713 29751 29789 29827

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609.47 609.86 61026 610.65 611.05 611.43 611.83 612.29

195. % % % M % % 7/8

612.61 613.00 613.40 613.79 614.18 614.57 614.97 615.36

29865 29903 29942 29980 30019 30057 30096 30134

201.

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615.75 616.15 616.54 616.93 617.32 617.72 618.11 618.50

30172 30210 30249 30287 30326 30364 30403 30442

202.

30481 30519 30558 305% 30635 30674 30713 30752

203.

Z? % x vu

618.89 619.29 619.68 620.08 620.47 620.86 621.25 621.64 622.04 622.44 622.83 623.22 623.62 624.Oi 624.40 624.79

30791 30830 30869 30908 30947 30986 31025 31064

2W.

% % 3/8 % % x %

625.18 625.58 625.97 626.36 626.76 627.15 627.54 627.94

31103 31142 31181 31220 31263 31299 31338 31377

205.

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628.32 628.72 629.11 629.51 629.S(3 630.29 630.58 631.08

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% ~ ?’4

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Circum.

Area

634.60 635.00 63S.40 635.79 636.18 636.S7 636.97 637.36

32047 32086 32126 32166 32206 32246 32286 32326

637.74 638.15 638.54 638.93 639.32 639.72 640.11 640.50

32366 32405 32445 32485 32525 32565 326435 32645

640.88 641.28 641.67 642.07 642.46 642.85 643.24 643.63

32685 32725 32766 32806 32846 32886 32926 32966

3/8 % % % %

644.03 644.43 644.82 645.21 645.61 ~.~ 646.39 646.78

33006 33046 33087 33127 33168 33208 33249 33289

31416 31455 31495 31534 31574 31613 31653 31692

2@5. % x >s ti % % ~8

647.17 647.57 647.96 648.35 648.75 649.14 649.53 649.93

33329 33369 33410 33450 33491 33531 33572 33613

31731 31770 31810 31849 31889 31928 31%8 32007

207.

650.31 650.71 651.10 651.50 651.89 652.28 652.57 653.07

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SPECIFICATION THICKNESS OF PAD THICKNESS OF WIRE MATERIAL OF WIRE DENSITY lb./Cu. ft. PRESSURE DROP MATERIAL CARBON STEEL BEARING BAR

WIRE MESH

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NAME PLATE Pressure vessels built in aemrdanee with the requirements of the Code maybe stamped withtheofficialsymbol ”U”todenoteTheAmerican SocietyofMechanieal Engineers’ standard. Pressurevessels stamped with the Code-symbolshall bemarkedwith the following: 1. manufacturer’sname;preeededwiththe words:“eertifledby”; maximumallowableworkingpressure,(MAWP)psiat temperature,°F; minimumdesignmetaltemperatureat pressure,psi;(MDMT) manufacturer’sserialnumbeq(S/N) “yearbuilt Abbreviationsmaybe usedasshownin parenthesis. 2. theappropriateabbreviationsindicatingthe typeofccmstruction,sexvice,etc. as tabulated: Wheninspectedbya user’sinspector USER Arcor gaswelded w LethalseMce L Unfiiedsteamboiler UB Directfting DF Fullyradiographedand UW-ll(a) (5)not applied RT 1 JointsA & D fullyradiographed;UW-1l(a) (5)(b) applied RT 2 Spotradiographed RT 3 WhenRT1,RT2or RT3are not applicable RT 4 Postweldheat treated HT Partof the vesselpostweldheat treated PHT Nonstationa~PressureVessels NPV

1.S “UM” y s m b u hb w to asv hl i el e x hs efl e iesm dn nrpse[ pet Ule eCo cs- d t oli mo( nd k )e ] 2 F v em os o 8sa fa 9e n 5 ld, sr iYs % ntt cuYe oe n, k ea 0 mhedil ms0e slap fln, sa d ett aeheh fti s bco ke r nsey e l s l sr Mi n p n a a[ p r a .oema tf r h e ;ie rec C kr s U lne ee 1dos Ls e5n slTd . ( - e c 1 ) — C

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ACCESSOPENINGS PIPE OPENING

The shape of openings may be circular o any other shapes. Circular openings are used most frequently with pipe o bent plate sleeves. The projection of t thickness of h sleeve equals fireproofing minimum 2 inches. The projection of sleeves shall be increased when necessary for reinunder k certain i load- r forcing the s ing conditions. D

&u O Y S

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321

PART III. MEASURES

AND WEIGHTS

1. Table ofProperties ofPipes, Tubes. . . . . . . . . . . . . . . . . . . . . . . . . . . 322 2. Dimensions............................................................................................ 334 of Heads, Flanges, Long Welding Necks, Welding Fittings, ScrewedCouplings. 3. Weight..----ti ----------------------------------------of Shells and Heads, Pipes and Fittings, Flanges, Openings, Packingand Insulation,Plates, CircularPlates, Bolts.

374

5, Area ofSurfaces ofShells and Heads. . . . . . . . . . . . . . . . . . . . . . . . . . 425 6. ConversionTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 DecimalsofanInch, Decimalsofa FooCMetricSystem,Inches to Millimeters,Millimetersto Inches, Square Feetto Square Meters, Square Meters to Square Feet, Pounds to Kilograms, Kilograms to Pounds, U.S. Gallon to Liters, Liters to U.S. Gallons,PoundsperSquareInches to KilogramperCentimeter, KilogramperCentimetertoPounds perSquareInch,Degreesto Radius,Minutesand Secondsto Decimalsofa Degree,Centi-

322

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side diam. in.

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7 .106 9 .106 5 .106

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341

FLANGES FLANGE FACING FINISH In pressure vessel construction only gasket seats of flanges, studded openings, etc. require special finish beyond that afforded by turning, grinding or milling.

The surface finish for flange facing shall have certain roughness regulated by Standard ANSI B16.5. The roughness is repetitive deviationfrom the nominal surfacehavirigspecifieddepth and width. Raised faced flange shall have serrated finish having 24 to 40 groovesper inch. The

cutting tool shall have an approximate0.06 in. or larger radius resulting 500 microinchapproximateroughness/ANSI B16.5, 6.3.4. 1./ The side wall surface of gasket groove of ring joint flange shall not exceed 63 microinchroughness. /ANSI B16.5-6.3.4.3./ Other finishes may be furnished by agreement between user and manufacturer. The finish of contact faces shall be judged by visual comparison with Standard ANSI B46-1 . The center part of blind flanges need not to be finished within a diameter which equals or less than the bore minus one inch of the joining flange. /ANSI B 16.5-6.3.3/ Surface symbol used to designate roughness ~ is placed either on the line indicating the surface or on a leader pointing to the surface as shown below. The numbers: 500 and 63 indicate the height of roughness; letter “c” the direction of surface pattern: “concentric-serrated”.

&“’cED

1 J CONCENTRIC SERRATED FINISH

SYMBOL USED IN PAST PRACTICE

342

r

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