ASME Sec VIII - Division 1 - App 1

Mandatory Appendices

A02 MANDATORY APPENDICES

Appendix 1 Supplementary Design Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313Appendix 2 Rules for Bolted Flange Connections With Ring Type Gaskets . . . . . . . . . . . . . . . . . . 329Appendix 3 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350Appendix 4 Rounded Indications Charts Acceptance Standard for Radiographically

Determined Rounded Indications in Welds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353Appendix 5 Flanged and Flued or Flanged Only Expansion Joints . . . . . . . . . . . . . . . . . . . . . . . . . . 360.1Appendix 6 Methods for Magnetic Particle Examination (MT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361Appendix 7 Examination of Steel Castings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363Appendix 8 Methods for Liquid Penetrant Examination (PT). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366Appendix 9 Jacketed Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368Appendix 10 Quality Control System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377Appendix 11 Capacity Conversions for Safety Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380Appendix 12 Ultrasonic Examination of Welds (UT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384Appendix 13 Vessels of Noncircular Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385Appendix 14 Integral Flat Heads With a Large, Single, Circular, Centrally Located

Opening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431Appendix 16 Submittal of Technical Inquiries to the Boiler and Pressure Vessel

Committee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438Appendix 17 Dimpled or Embossed Assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440Appendix 18 Adhesive Attachment of Nameplates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452Appendix 19 Electrically Heated or Gas Fired Jacketed Steam Kettles . . . . . . . . . . . . . . . . . . . . . . . . 453Appendix 20 Hubs of Tubesheets and Flat Heads Machined From Plate . . . . . . . . . . . . . . . . . . . . . . 454Appendix 21 Jacketed Vessels Constructed of Work-Hardened Nickel. . . . . . . . . . . . . . . . . . . . . . . . . 455Appendix 22 Integrally Forged Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456Appendix 23 External Pressure Design of Copper, Copper Alloy, and Titanium Alloy

Condenser and Heat Exchanger Tubes With Integral Fins . . . . . . . . . . . . . . . . . . . . . 458Appendix 24 Design Rules for Clamp Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460Appendix 25 Acceptance of Testing Laboratories and Authorized Observers for Capacity

Certification of Pressure Relief Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467Appendix 26 Pressure Vessel and Heat Exchanger Expansion Joints . . . . . . . . . . . . . . . . . . . . . . . . . . 469Appendix 27 Alternative Requirements for Glass-Lined Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481Appendix 28 Alternative Corner Weld Joint Detail for Box Headers for Air-Cooled Heat

Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483Appendix 29 Requirements for Steel Bars of Special Section for Helically Wound

Interlocking Strip Layered Pressure Vessels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486Appendix 30 Rules for Drilled Holes Not Penetrating Through Vessel Wall . . . . . . . . . . . . . . . . . . . 489Appendix 31 Rules for Cr–Mo Steels With Additional Requirements for Welding and Heat

Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491Appendix 32 Local Thin Areas in Cylindrical Shells and in Spherical Segments of Shells . . . . . . 493.1

312

APPENDIX 1SUPPLEMENTARY DESIGN FORMULAS

1-1 THICKNESS OF CYLINDRICALAND SPHERICAL SHELLS

(a) The following formulas, in terms of the outsideradius, are equivalent to and may be used instead ofthose given in UG-27(c) and (d).

(1) For cylindrical shells (circumferential stress),

t pPRo

SE + 0.4Por P p

SEtR o − 0.4t

(1)

whereR op outside radius of the shell course under consid-

eration, in. (mm)(2) For spherical shells,

t pPR o

2SE + 0.8Por P p

2SEtR o − 0.8t

(2)

Other symbols are as defined in UG-27.

1-2 THICK CYLINDRICAL SHELLS

(a)(1) Circumferential Stress (Longitudinal Joints).When the thickness of the cylindrical shell under internaldesign pressure exceeds one-half of the inside radius,or when P exceeds 0.385SE, the following formulasshall apply:

When P is known and t is desired,

t p R (Z1⁄2 − 1) p R o

(Z1⁄2 −1)

Z1⁄2

(1)

where

Z pSE + PSE − P

Where t is known and P is desired,

P p SE �Z − 1Z + 1� (2)

313

where

Z p �R + tR �

2

p �Ro

R �2

p � R o

Ro − t�2

(2) Longitudinal Stress (Circumferential Joints).When the thickness of the cylindrical shell under internaldesign pressure exceeds one-half of the inside radius,or when P exceeds 1.25SE, the following formulasshall apply:


t p R (Z1⁄2 − 1) p Ro �Z

1⁄2 −1

Z1⁄2

� (3)

where

Z p � PSE

+ 1�When t is known and P is desired,

P p SE (Z − 1) (4)

where

Z p �R + tR �

2

p �Ro

R �2

p � R o

Ro − t�2

Symbols are as defined in UG-27 and 1-1.

1-3 THICK SPHERICAL SHELLS

When the thickness of the shell of a wholly sphericalvessel or of a hemispherical head under internal designpressure exceeds 0.356R, or when P exceeds 0.665SE,the following formulas shall apply:

1-3 2001 SECTION VIII — DIVISION 1 1-4

FIG. 1-4 PRINCIPAL DIMENSIONS OF TYPICAL HEADS


t p R (Y1⁄3 − 1) p R o �Y

1⁄3 −1

Y1⁄3

� (1)

where

Y p2(SE + P)2SE − P

When t is known and P is desired,

P p 2SE �Y − 1Y + 2� (2)

314

where

Y p �R + tR �

3

p � R o

R o − t�3

Symbols are as defined in UG-27 and 1-1.

1-4 FORMULAS FOR THE DESIGN OFFORMED HEADS UNDERINTERNAL PRESSURE

(a) The formulas of this paragraph provide for thedesign of formed heads of proportions other thanthose given in UG-32, in terms of inside and outsidediameter.

The formulas in 1-4(c) and (d) given below shallbe used for t/L ≥ 0.002. For t/L < 0.002, the rules of1-4(f) shall also be met.

(b) The symbols defined below are used in theformulas of this paragraph (see Fig. 1-4):

tpminimum required thickness of head after form-ing, in. (mm)

Pp internal design pressure (see UG-21), psi (kPa)

A03

1-4 APPENDIX 1 — MANDATORY 1-4

TABLE 1-4.1VALUES OF FACTOR K

(Use Nearest Value of D/2h; Interpolation Unnecessary)

D/2h 3.0 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2.0K 1.83 1.73 1.64 1.55 1.46 1.37 1.29 1.21 1.14 1.07 1.00

D/2h 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 . . .K 0.93 0.87 0.81 0.76 0.71 0.66 0.61 0.57 0.53 0.50 . . .

Dp inside diameter of the head skirt; or inside lengthof the major axis of an ellipsoidal head; or insidediameter of a cone head at the point under con-sideration measured perpendicular to the longi-tudinal axis, in. (mm)

Dop outside diameter of the head skirt; or outsidelength of the major axis of an ellipsoidal head;or outside diameter of a cone head at the pointunder consideration measured perpendicular tothe longitudinal axis, in. (mm)

Spmaximum allowable working stress, as given inSubsection C, psi (kPa), except as limited byfootnote 1 to 1-4(c) and (d), UG-24, UG-32(e),and UW-12.

Ep lowest efficiency of any Category A joint inthe head (for hemispherical heads this includeshead-to-shell joint). For welded vessels, use theefficiency specified in UW-12.

rp inside knuckle radius, in. (mm)Lp inside spherical or crown radius for torispherical

and hemispherical heads, in. (mm)Lp K1 D for ellipsoidal heads in which K1 is ob-

tained from Table UG-37, in. (mm)Lop outside spherical or crown radius, in. (mm)

L / rp ratio of the inside crown radius to the insideknuckle radius, used in Table 1-4.2

Mp a factor in the formulas for torispherical headsdepending on the head proportion L / r

hp one-half of the length of the minor axis of theellipsoidal head, or the inside depth of the ellip-soidal head measured from the tangent line(head-bend line), in. (mm)

Kp a factor in the formulas for ellipsoidal headsdepending on the head proportion D / 2h

D / 2hp ratio of the major to the minor axis ofellipsoidal heads, which equals the insidediameter of the skirt of the head divided bytwice the inside height of the head, and isused in Table 1-4.1

�p one-half of the included (apex) angle of the coneat the center line of the head

ETpmodulus of elasticity at maximum design tem-

315

perature, psi. The value of ET shall be takenfrom applicable Table TM, Section II, Part D

Syp yield strength at maximum design temperature,psi. The value of Sy shall be taken from applica-tion Table Y, Section II, Part D

(c) Ellipsoidal Heads1

t pPDK

2SE − 0.2Por P p

2SEtKD + 0.2t

(1)

t pPDo K

2SE + 2P (K − 0.1)

or

P p2SEt

KD o − 2t (K − 0.1)(2)

where

K p16 �2 + � D

2h�2

�

Numerical values of the factor K are given in Table1-4.1.

Example 1.2 Determine the required thickness t ofa seamless ellipsoidal head, exclusive of provision forcorrosion for the following conditions:

D p 40 in; h p 9 in; P p 200 psi; S p 13,750psi; E p 1.00.

011 Ellipsoidal heads designed under K > 1.0 and all torispherical headsmade of materials having a specified minimum tensile strengthexceeding 70,000 psi (482 MPa) shall be designed using a value ofS equal to 20,000 psi (137.2 MPa) at room temperature and reducedin proportion to the reduction in maximum allowable stress valuesat temperature for the material as shown in the appropriate table(see UG-23).2 This calculation is intended only to illustrate the use of the formulaherein. Other paragraphs in this Division may have to be satisfiedto permit use of the full tabular stress value.


D2hp

4018p 2.22

From Table 1-4.1, K p 1.14. Substituting in Eq. (1),

t p200 � 40 � 1.14

[2 � 13,750 � (1.00) − (0.2 � 200)]p 0.33 in.

Example 2.2 Determine the maximum allowableworking pressure P of a seamless ellipsoidal head forthe following conditions:

D p 30 in.; h p 7.5 in.; total thickness p 1⁄2 in.with no allowance for corrosion; maximum operatingtemperature p 800°F; E p 1.00.

From the appropriate table given in Subpart 1 ofSection II, Part D, S p 10,200 psi.

D2hp

3015p 2.0

From Table 1-4.1, K p 1.0. Substituting in Eq. (1),

P p2 � 10,200 � 1.0 � 0.5[1 � 30 + (0.2 � 0.5)]

p 339 psi

(d) Torispherical Heads1

t pPLM

2SE − 0.2Por P p

2SEtLM + 0.2t

(3)

t pPL o M

2SE + P (M − 0.2)

or

P p2SEt

ML o − t (M − 0.2)(4)

where

M p 1⁄4 �3 + � Lr �

316

Numerical values of the factor M are given in Table1-4.2.

Example 1.2Determine the required thickness t, exclu-sive of allowance for corrosion, of a torispherical headfor the following conditions:

D p 40 in.; L p 40 in.; r p 4 in.; P p 200 psi;S p 13,750 psi; E p 1.00 (seamless head).

Lrp

404p 10

and from Table 1-4.2, M p 1.54. Substituting in Eq.(3),

t p200 � 40 � 1.54

[2 � 13,750 � (1.00) − (0.2 � 200)]p 0.45 in.

Example 2.2Determine the maximum allowable work-ing pressure P of a torispherical head for the followingconditions:

D p 30 in.; L p 24 in.; r p 2.00 in.; E p 1.00(seamless head); total thickness p 0.5 in. with noallowance for corrosion; material conforms to SA-515Grade 70; maximum operating temperature p 900°F.

From the appropriate table given in Subpart 1 ofSection II, Part D, S p 6500 psi.

Lrp

242.00

p 12.0

From Table 1-4.2, M p 1.62. Substituting in Eq. (3),

P p2 � 6500 � 1.0 � 0.524 � 1.62 + 0.2 � 0.5

p 167 psi

(e) Conical Heads

t pPD

2 cos � (SE − 0.6P)

or

P p2SEt cos �

D + 1.2t cos �(5)

t pPD o

2 cos � (SE + 0.4P)

A03

A03


TABLE 1-4.2VALUES OF FACTOR M

(Use Nearest Value of L/r; Interpolation Unnecessary)

L/r 1.0 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50M 1.00 1.03 1.06 1.08 1.10 1.13 1.15 1.17 1.18 1.20 1.22

L/r 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0M 1.25 1.28 1.31 1.34 1.36 1.39 1.41 1.44 1.46 1.48 1.50

L/r 9.5 10.00 10.5 11.0 11.5 12.0 13.0 14.0 15.0 16.0 162⁄31

M 1.52 1.54 1.56 1.58 1.60 1.62 1.65 1.69 1.72 1.75 1.77

NOTE:(1) Maximum ratio allowed by UG-32(j) when L equals the outside diameter of the skirt of the head.

TABLE 1-4.3 MAXIMUM METAL TEMPERATURE

Table in WhichMaterial is Listed Temperature, °F

UCS-23 700UNF-23.1 300UNF-23.2 150UNF-23.3 900UNF-23.4 600UNF-23.5 600UHA-23 800UHT-23 700

or

P p2SEt cos �

D o − 0.8t cos �(6)

(f) Design of Heads With t/L < 0.002. The followingrules shall be used when the maximum design tempera-ture is less than or equal to th temperature limitgiven in Table 1-4.3. See U-2(g) for maximum designtemperature exceeding the temperature limit given inTable 1-4.3

(1) Torispherical Heads With t/L < 0.002. Theminimum required thickness of a torispherical headhaving 0.0005 ≤ t/L < 0002 shall be lager of thethickness calculated by the formulas in UG-32(e), 1-4(d), or by the formulas given below.

(a) Calculate a coefficient, C1.

C1 p 9.31r/D − 0.086, for r/D ≤ 0.08C1 p 0.692r/D + 0.605, for r/D > 0.08

(b) Calculate the elastic buckling stess, Se.

317

TABLE 1-4.4 VALUES OF KNUCKLE RADIUS, “r ”

D/2h r/D

3.0 0.102.8 0.112.6 0.122.4 0.132.2 0.152.0 0.171.8 0.201.6 0.241.4 0.291.2 0.371.0 0.50

GENERAL NOTE: Interpolation permitted for intermediate values

Se p C1ET (t/r)

(c) Calculate a coefficient, C2.

C2 p 1.25, for r/D ≤ 0.08

C2 p 1.46 − 2.6r/D, for r/D > 0.08

(d) Calculate values of constants a, b, �, and �.

a p 0.5D − r

b p L − r

� p arc cos (a/b), radians

� p ��LT��r

(e) Calculate values of c and Re.If � is less than �, then

A03

A02


c p a�cos (� − �)

If � is equal to or greater than �, then

c p a

Re p c + r

(f) Calculate the value of internal pressure ex-pected to produce elastic buckling, Pe.

Pe pSyt

C2Re �0.5Re�r� − 1

(g) Calculate the value of internal pressure ex-pected to result in yield stress at the point of maximumstress, Py.

Py pSyt

C2Re �0.5Re�r� − 1

(h) Calculate the value of internal pressure ex-pected to result result in knuckle failure, Pek.

Pek p 0.6Pe, for Pe/Py ≤ 1.0

Pek p 0.408Py + 0.192Pe, for 1.0 < Pe/Py ≤ 8.29

Pek p 2.0Py, for Pe/Py > 8.29

(i) Calculate the value Pek/1.5. If Pek/1.5 isequal to or greater than the required internal designpressure P, then the design is complete. If Pek/1.5 isless than the required internal design pressure P, thenincrease the thickness and repeat the calculations.

(2) Design of Ellipsoidal Heads With t/L < 0.002.The minimum required thickness of an ellipsoidal headhaving 0.0005 ≤ t/L < 0.002 shall be larger of thethicknesses calculated by the formulas in UG-32(d), 1-4(c), or by the formulas in 1-4(f)(1). In using 1-4(f)(1)formulas, the value of L is to be obtained from TableUG-37 and the value of r is to be obtained from Table1-4.4.

1-5 RULES FOR CONICAL REDUCERSECTIONS AND CONICAL HEADSUNDER INTERNAL PRESSURE

(a) The formulas of (d) and (e) below provide forthe design of reinforcement, if needed, at the cone-to-cylinder junctions for conical reducer sections and

317.1

conical heads where all the elements have a commonaxis and the half-apex angle � ≤ 30 deg. Subparagraph(g) below provides for special analysis in the designof cone-to-cylinder intersections with or without rein-forcing rings where � is greater than 30 deg.

In the design of reinforcement for a cone-to-cylinderjuncture, the requirements of UG-41 shall be met.

(b) NomenclatureArLp required area of reinforcement at large end of

cone, in.2 (mm2)Arsp required area of reinforcement at small end of

cone, in.2 (mm2)AeLp effective area of reinforcement at large end in-

tersection, in.2 (mm2)Aesp effective area of reinforcement at small end in-

tersection, in.2 (mm2)Espmodulus of elasticity of cylinder material, psi

(kPa)Ecpmodulus of elasticity of cone material, psi (kPa)Erpmodulus of elasticity of reinforcing ring mate-

rial, psi (kPa)

NOTE: The modulus of elasticity shall be taken from the applicableTable TM in Section II, Part D. When a material is not listed inthe TM tables, the requirements of U-2(g) shall be applied.

E1p efficiency of longitudinal joint in cylinder. Forcompression (such as at large end of cone),E1 p 1.0 for butt welds.

E2p efficiency of longitudinal joint in cone. For com-pression, E2 p 1.0 for butt welds.

f1p axial load at large end due to wind, dead load,etc., excluding pressure, lb /in. (kN/m)

f2p axial load at small end due to wind, dead load,etc., excluding pressure, lb /in. (kN/m)

Pp internal design pressure (see UG-21), psi (kPa)QLp algebraical sum of PRL /2 and f1, lb /in. (kN/m)Qsp algebraical sum of PRs /2 and f2, lb /in. (kN/m)Rsp inside radius of small cylinder at small end of

cone, in. (mm)RLp inside radius of large cylinder at large end of

cone, in. (mm)Ssp allowable stress of cylinder material at design

temperature, psi (kPa)Scp allowable stress of cone material at design tem-

perature, psi (kPa)Srp allowable stress of reinforcing ring material at

design temperature, psi (kPa)tpminimum required thickness of cylinder at

cone-to-cylinder junction, in. (mm)tcp nominal thickness of cone at cone-to-cylinder

junction, in. (mm)trpminimum required thickness of cone at cone-

to-cylinder junction, in. (mm)


317.2

tsp nominal thickness of cylinder at cone-to-cylin-der junction, in. (mm)

�p half-apex angle of cone or conical section, deg.�p angle indicating need for reinforcement at cone-to-

cylinder junction having a half-apex angle � ≤ 30deg. When � ≥ �, no reinforcement is required at thejunction (see Tables 1-5.1 and 1-5.2), deg.

yp cone-to-cylinder factorp SsEs for reinforcing ring on shellp ScEc for reinforcing ring on cone


TABLE 1-5.1VALUES OF � FOR JUNCTIONS AT THE LARGE

CYLINDER FOR � ≤ 30 deg.

P/SsE1 0.001 0.002 0.003 0.004 0.005�, deg. 11 15 18 21 23

P/SsE1 0.006 0.007 0.008 0.0091 . . .�, deg. 25 27 28.5 30 . . .

NOTE:(1) � p 30 deg. for greater values of P/SsE1.

TABLE 1-5.2VALUES OF � FOR JUNCTIONS AT THE SMALL

CYLINDER FOR � ≤ 30 deg.

P/SsE1 0.002 0.005 0.010 0.02�, deg. 4 6 9 12.5

P/SsE1 0.04 0.08 0.10 0.1251

�, deg. 17.5 24 27 30

NOTE:(1) � p 30 deg. for greater values of P/SsE1.

(c) For a cone-to-cylinder junction, the followingvalues shall be determined at large end and again atthe small end in order that both the large end and thesmall end can be examined:

Determine P/SsE1 and then determine � at the largeend and at the small end, as appropriate, from Tables1-5.1 and 1-5.2.

Determine k:kp 1 when additional area of reinforcement is not

requiredp y /Sr Er when a stiffening ring is required, but

k is not less than 1.0(d) Reinforcement shall be provided at the junction

of the cone with the large cylinder for conical headsand reducers without knuckles when the value of �obtained from Table 1-5.1, using the appropriate ratioP /SsE1, is less than �. Interpolation may be made inthe Table.

The required area of reinforcement shall be at leastequal to that indicated by the following formula whenQL is in tension:

ArL pkQLRL

SsE1 �1 −�

�� tan � (1)**

At the large end of the cone-to-cylinder juncture,the PRL /2 term is in tension. When f1 is in compression

** For some of the terms of the above equation(s), it may benecessary to convert millimeters to meters to obtain a rational resultin SI units.

318

and the quantity is larger than the PRL /2 term, thedesign shall be in accordance with U-2(g). The calcu-lated localized stresses at the discontinuity shall notexceed the stress values specified in 1-5(g)(1) and (2).

The effective area of reinforcement can be determinedin accordance with the following formula:

AeL p (ts − t) � RLts + (tc − tr) � RLtc /cos � (2)

Any additional area of reinforcement which is required

shall be situated within a distance of � RL ts from thejunction of the reducer and the cylinder. The centroidof the added area shall be within a distance of 0.25

� � RL ts from the junction.(e) Reinforcement shall be provided at the junction

of the conical shell of a reducer without a flare andthe small cylinder when the value of � obtained fromTable 1-5.2, using the appropriate ratio P/SsE1, is lessthan �.

The required area of reinforcement shall be at leastequal to that indicated by the following formula whenQs is in tension:

Ars pkQsRs

SsE1 �1 −�

�� tan � (3)**

At the small end of the cone-to-cylinder juncture,the PRs /2 term is in tension. When f2 is in compressionand the quantity is larger than the PRs /2 term, thedesign shall be in accordance with U-2(g). The calcu-lated localized stresses at the discontinuity shall notexceed the stress values specified in 1-5(g)(1) and (2).


Aes p 0.78� Rsts[(ts − t) + (tc − tr) /cos �] (4)

Any additional area of reinforcement which is required

shall be situated within a distance of � Rs ts from thejunction, and the centroid of the added area shall be

within a distance of 0.25 � Rs ts from the junction.( f ) Reducers not described in UG-36(e)(5), such as

those made up of two or more conical frustums havingdifferent slopes, may be designed in accordance with (g).

(g) When the half-apex angle � is greater than 30deg. (0.52 rad), cone-to-cylinder junctions without aknuckle may be used, with or without reinforcing rings,if the design is based on special analysis, such asthe beam-on-elastic-foundation analysis of Timoshenko,Hetenyi, or Watts and Lang. See U-2(g). When suchan analysis is made, the calculated localized stresses

A02

A02

A02


FIG. 1-6 SPHERICALLY DISHED COVERS WITH BOLTING FLANGES

at the discontinuity shall not exceed the followingvalues.

(1) (Membrane hoop stress) + (average discontinu-ity hoop stress) shall not be greater than 1.5S, wherethe “average discontinuity hoop stress” is the averagehoop stress across the wall thickness due to the disconti-nuity at the junction, disregarding the effect of Poisson’sratio times the longitudinal stress at the surfaces.

(2) (Membrane longitudinal stress) + (discontinuitylongitudinal stress due to bending) shall not be greaterthan SPS [see UG-23(e)].

The angle joint (see 3-2) between the cone andcylinder shall be designed equivalent to a double butt-welded joint, and because of the high bending stress,there shall be no weak zones around the angle joint.The thickness of the cylinder may have to be increasedto limit the difference in thickness so that the anglejoint has a smooth contour.

1-6 SPHERICALLY DISHED COVERS(BOLTED HEADS)

(a) Circular spherical dished heads with boltingflanges, both concave and convex to the pressure andconforming to the several types illustrated in Fig. 1-6,

319

shall be designed in accordance with the formulaswhich follow.

(b) The symbols used in the formulas of this para-graph are defined as follows:

tpminimum required thickness of head plate afterforming, in. (mm)

Lp inside spherical or crown radius, in. (mm)rp inside knuckle radius, in. (mm)Pp internal pressure (see UG-21) for the pressure

on concave side, and external pressure for thepressure on convex side [see UG-28(f)], psi(kPa)

Spmaximum allowable stress value, psi (kPa) (seeUG-23)

Tp flange thickness, in. (mm)Mop the total moment, in.-lb (kNWm), determined as

in 2-6 for heads concave to pressure and 2-11for heads convex to pressure; except that forheads of the type shown in Fig. 1-6 sketch (d),HD and hD shall be as defined below, and anadditional moment Hr hr (which may add or sub-tract) shall be included whereHrp radial component of the membrane load

in the spherical segment, lb (kN), actingat the intersection of the inside of the


flange ring with the center line of thedished cover thickness

pHD cot �1

hrp lever arm of force Hr about centroid offlange ring, in. (mm)

HDpaxial component of the membrane load inthe spherical segment, lb (kN), acting atthe inside of the flange ring

p0.785 B 2 PhDp radial distance from the bolt circle to the

inside of the flange ring, in. (mm)�1pangle formed by the tangent to the center

line of the dished cover thickness at itspoint of intersection with the flange ring,and a line perpendicular to the axis of thedished cover

parc sin � B2L + t�

NOTE: Since Hr hr in some cases will subtract from the total moment,the moment in the flange ring when the internal pressure is zeromay be the determining loading for flange design.

Ap outside diameter of flange, in. (mm)Bp inside diameter of flange, in. (mm)Cp bolt circle, diameter, in. (mm)

(c) It is important to note that the actual value ofthe total moment Mo may calculate to be either plusor minus for both the heads concave to pressure andthe heads convex to pressure. However, for use in allof the formulas which follow, the absolute values forboth P and Mo are used.

(d) Heads of the type shown in Fig. 1-6 sketch (a):

(1) the thickness of the head t shall be determinedby the appropriate formula in UG-32 for pressureon concave side, and UG-33(a)(1) for pressure onconvex side;

(2) the head radius L or the knuckle radius r shallcomply with the limitations given in UG-32;

(3) the flange shall comply at least with the require-ments of Fig. 2-4 and shall be designed in accordancewith the provisions of 2-1 through 2-7 for pressure onconcave side, and 2-11 for pressure on convex side.(Within the range of flange standards listed in TableU-3, the flange and drillings may conform to thestandards, and the thickness specified therein shall beconsidered as a minimum requirement.)

(e) Heads of the type shown in Fig. 1-6 sketch (b)(no joint efficiency factor is required):

320

(1) head thickness(a) for pressure on concave side,

t p5PL6S

(1)

(b) for pressure on convex side, the head thick-ness shall be determined based on UG-33(c) using theoutside radius of the spherical head segment;

(2) flange thickness for ring gasket

T p�Mo

SB �A + BA − B� (2)**

(3) flange thickness for full face gasket

T p 0.6 � PS �B (A + B)(C − B )

A − B � (3)

NOTE: The radial components of the membrane load in the sphericalsegment are assumed to be resisted by its flange.

(Within the range of flange standards listed in TableU-3, the flange and drillings may conform to thestandards, and the thickness specified therein shall beconsidered as a minimum requirement.)

( f ) Heads of the type shown in Fig. 1-6 sketch (c)(no joint efficiency factor is required):


t p5PL6S

(4)


(2) flange thickness for ring gasket for heads withround bolting holes

T p Q + � 1.875Mo (C + B)SB (7C − 5B )

(5)**

where

Q pPL4S � C + B

7C − 5B� **



(3) flange thickness for ring gasket for heads withbolting holes slotted through the edge of the head

T p Q + � 1.875Mo (C + B)SB(3C − B)

(6)**

where

Q pPL4S � C + B

3C − B�(4) flange thickness for full-face gasket for heads

with round bolting holes

T p Q + � Q2 +3BQ (C − B)

L(7)

where

Q pPL4S � C + B

7C − 5B�(5) flange thickness for full-face gasket for heads

with bolting holes slotted through the edge of the head

T p Q + � Q2 +3BQ (C − B)

L(8)

where

Q pPL4S � C + B

3C − B�(6) the required flange thickness shall be T as

calculated in (2), (3), (4), or (5) above, but in no caseless than the value of t calculated in (1) above.

(g) Heads of the type shown in Fig. 1-6 sketch (d)(no joint efficiency factor is required):


t p5PL6S

(9)



321

(2) flange thickness

T p F + � F 2 + J (10)

where

F pPB � 4L2 − B2

8S (A − B)

and

J p �M o

SB � �A + BA − B�

(h) These formulas are approximate in that they donot take into account continuity between the flangering and the dished head. A more exact method ofanalysis which takes this into account may be used ifit meets the requirements of U-2.

1-7 LARGE OPENINGS INCYLINDRICAL SHELLS

1-7(a) Openings exceeding the dimensional limitsgiven in UG-36(b)(1) shall be provided with reinforce-ment that complies with the following rules. Two-thirds of the required reinforcement shall be within thefollowing limits:

1-7(a)(1) parallel to vessel wall: the larger ofthree-fourths times the limit in UG-40(b)(1), or equalto the limit in UG-40(b)(2);

1-7(a)(2) normal to vessel wall: the smaller of thelimit in UG-40(c)(1), or in UG-40(c)(2).

1-7(b) Openings for radial nozzles that exceed thelimits in UG-36(b)(1)

1-7(b)(1) and which also are within the rangedefined by the following limits shall meet the require-ments in (b)(2), (3), and (4) below:

(a) vessel diameters greater than 60 in. (mm)I.D.;

(b) nozzle diameters which exceed 40 in. (mm)

I.D. and also exceed 3.4 � Rt; the terms R and t aredefined in Figs. 1-7-1 and 1-7-2;

(c) the ratio Rn /R does not exceed 0.7; fornozzle openings with Rn /R exceeding 0.7, refer to (c)below and/or U-2(g).

A02


FIG. 1-7-1

The rules are limited to radial nozzles in cylindricalshells that do not have internal projections, and do notinclude any analysis for stresses resulting from exter-nally applied mechanical loads. For such cases U-2(g)shall apply.

1-7(b)(2) The membrane stress Sm as calculatedby Eq. (1) or (2) below shall not exceed S, as definedin UG-37 for the applicable materials at design condi-tions. The maximum combined membrane stress Sm

and bending stress Sb shall not exceed 1.5S at designconditions. Sb shall be calculated by Eq. (5) below.

1-7(b)(3) Evaluation of combined stresses frominternal pressure and external loads shall be made inaccordance with U-2(g).

1-7(b)(4) For membrane stress calculations, usethe limits defined in Fig. 1-7-1, and comply with thestrength of reinforcement requirements of UG-41. Forbending stress calculation, the greater of the limitsdefined in Fig. 1-7-1 or Fig. 1-7-2 may be used. Thestrength reduction ratio requirements of UG-41 neednot be applied, provided that the allowable stress ratioof the material in the nozzle neck, nozzle forging,

322

reinforcing plate, and/or nozzle flange divided by theshell material allowable stress is at least 0.80.

NOTE: The bending stress Sb calculated by Eq. (5) is valid andapplicable only at the nozzle neck-shell junction. It is a primarybending stress because it is a measure of the stiffness required tomaintain equilibrium at the longitudinal axis junction of the nozzle-shell intersection due to the bending moment calculated by Eq. (3).

Case A (See Fig. 1-7-1)

Sm p P �R(Rn + tn + �Rmt) + Rn(t + te + �Rnmtn)As � (1)

Case B (See Fig. 1-7-1)

Sm p P �R(Rn + tn + �Rmt) + Rn(t + �Rnmtn)As � (2)


FIG. 1-7-2

Cases A and B (See Fig. 1-7-1 or Fig. 1-7-2)

M p �R3n

6+ R Rne� P (3)**

a p e +t /2 (4)

Sb pMaI

(5)**

1-7(b)(5) Nomenclature. Symbols used in Figs.1-7-1 and 1-7-2 are as defined in UG-37(a) and asfollows:

Asp shaded (cross-hatched) area in Fig. 1-7-1, CaseA or Case B, in.2 (mm2)


323

Ipmoment of inertia of the larger of the shadedareas in Fig. 1-7-1 or Fig. 1-7-2 about neutralaxis, in.4 (mm4)

ap distance between neutral axis of the shaded areain Fig. 1-7-1 or Fig. 1-7-2 and the inside ofvessel wall, in. (mm)

Rmpmean radius of shell, in. (mm)Rnmpmean radius of nozzle neck, in. (mm)

ep distance between neutral axis of the shaded areaand midwall of the shell, in. (mm)

Smpmembrane stress calculated by Eq. (1) or (2),psi (kPa)

Sbp bending stress at the intersection of inside ofthe nozzle neck and inside of the vessel shellalong the vessel shell longitudinal axis, psi (kPa)

Syp yield strength of the material at test temperature,see Table Y-1 in Subpart 1 of Section II, PartD, psi (kPa)

1-7(c) It is recommended that special considerationbe given to the fabrication details used and inspection

A02


employed on large openings; reinforcement often may beadvantageously obtained by use of heavier shell plate for avessel course or inserted locally around the opening; weldsmay be ground to concave contour and the inside corners ofthe opening rounded to a generous radius to reduce stressconcentrations. When radiographic examination of welds isnot practicable, liquid penetrant examination may be usedwith nonmagnetic materials and either liquid penetrant ormagnetic particle inspection with ferromagnetic materials.Ifmagneticparticle inspection isemployed, theprodmethodis preferred. The degree to which such measures should beused depends on the particular application and the severityof the intended service. Appropriate proof testing may beadvisable in extreme cases of large openings approachingfull vessel diameter, openings of unusual shape, etc.

1-8 RULES FOR REINFORCEMENT OFCONE-TO-CYLINDER JUNCTIONUNDER EXTERNAL PRESSURE

(a) The formulas of (b) and (c) below provide forthe design of reinforcement, if needed, at the cone-to-cylinder junctions for reducer sections and conical headswhere all the elements have a common axis and thehalf-apex angle � ≤ 60 deg. Subparagraph (e) belowprovides for special analysis in the design of cone-to-cylinder intersections with or without reinforcing ringswhere � is greater than 60 deg.

In the design of reinforcement for a cone-to-cylinderjuncture, the requirements of UG-41 shall be met.

The nomenclature given below is used in the formulasof the following subparagraphs:

Ap factor determined from Fig. G and used to enterthe applicable material chart in Subpart 3 ofSection II, Part D

AeLp effective area of reinforcement at large end in-tersection, in.2 (mm2)

Aesp effective area of reinforcement at small end in-tersection, in.2 (mm2)

ArLp required area of reinforcement at large end ofcone, in.2 (mm2)

Arsp required area of reinforcement at small end ofcone, in.2 (mm2)

Asp cross-sectional area of the stiffening ring, sq in.(mm2)

ATp equivalent area of cylinder, cone, and stiffeningring, sq in. (mm2), where

ATLpLL ts

2+

Lc tc2

+ As for large end

ATSpLs ts2

+Lc tc

2+ As for small end

324

Bp factor determined from the applicable materialchart in Subpart 3 of Section II, Part D formaximum design metal temperature, psi (kPa)[see UG-20(c)]

DLp outside diameter of large end of conical sectionunder consideration, in. (mm)

Dop outside diameter of cylindrical shell, in. (mm).(In conical shell calculations, the value of Ds

and DL should be used in calculations in placeof Do depending on whether the small end Ds ,or large end DL , is being examined.)

Dsp outside diameter at small end of conical sectionunder consideration, in. (mm)

E1p efficiency of longitudinal joint in cylinder. Forcompression (such as at small end of cone),E1 p 1.0 for butt welds.

E2p efficiency of longitudinal joint in cone. For com-pression, E2 p 1.0 for butt welds.

Ecpmodulus of elasticity of cone material, psi (kPa)Erpmodulus of elasticity of stiffening ring material,

psi (kPa)Espmodulus of elasticity of shell material, psi (kPa)Exp Ec , Er , or Es

NOTE: The modulus of elasticity shall be taken from the applicableTable TM in Section II, Part D. When a material is not listed inthe TM tables, the requirements of U-2(g) shall be applied.

f1p axial load at large end due to wind, dead load,etc., excluding pressure, lb / in. (kN/m)

f2p axial load at small end due to wind, dead load,etc., excluding pressure, lb / in. (kN/m)

Ip available moment of inertia of the stiffeningring cross section about its neutral axis parallelto the axis of the shell, in.4 (mm4)

I ′p available moment of inertia of combined shell-cone or ring-shell-cone cross section about itsneutral axis parallel to the axis of the shell, in.4

(mm4). The nominal shell thickness ts shall beused, and the width of the shell which is takenas contributing to the moment of inertia of thecombined section shall not be greater than 1.10

� Dts and shall be taken as lying one-half oneach side of the cone-to-cylinder junction or ofthe centroid of the ring. Portions of the shellplate shall not be considered as contributingarea to more than one stiffening ring.

CAUTIONARY NOTE: Stiffening rings may be subject to lateralbuckling. This should be considered in addition to the requirementsfor Is and I ′s [see U-2(g)].

Isp required moment of inertia of the stiffening ringcross section about its neutral axis parallel tothe axis of the shell, in.4 (mm4)

I ′sp required moment of inertia of the combined


shell-cone or ring-shell-cone cross section aboutits neutral axis parallel to the axis of the shell,in.4 (mm4)

If the stiffeners should be so located that the maximumpermissible effective shell sections overlap on eitheror both sides of a stiffener, the effective shell sectionfor that stiffener shall be shortened by one-half of eachoverlap.

kp 1 when additional area of reinforcement is notrequired

p y/SrEr when a stiffening ring is required, butkis not less than 1.0

Lp axial length of cone, in. (mm)Lcp length of cone between stiffening rings mea-

sured along surface of cone, in. (mm). For coneswithout intermediate stiffeners,

Lc p ! L2 + (RL − Rs)2

LLp design length of a vessel section, in. (mm), takenas the largest of the following:

(1) the center-to-center distance betweenthe cone-to-large-shell junction and an adjacentstiffening ring on the large shell;

(2) the distance between the cone-to-large-shell junction and one-third the depth of headon the other end of the large shell if no otherstiffening rings are used.

Lsp design length of a vessel section, in. (mm), takenas the largest of the following:

(1) the center-to-center distance betweenthe cone-to-small-shell junction and adjacentstiffening ring on the small shell;

(2) the distance between the cone-to-small-shell junction and one-third the depth of headon the other end of the small shell if no otherstiffening rings are used.

Pp external design pressure, psi (kPa)QLp algebraical sum ofPRL /2 andf1, lb /in. (kN/m)Qsp algebraical sum ofPRs/2 andf2, lb /in. (kN/m)RLp outside radius of large cylinder, in. (mm)Rsp outside radius of small cylinder, in. (mm)Scp allowable stress of cone material at design tem-

perature, psi (kPa)Sr p allowable stress of stiffening ring material at

design temperature, psi (kPa)Ssp allowable stress of cylinder material at design

temperature, psi (kPa)tp minimum required thickness of cylinder at

cone-to-cylinder junction [see UG-28(c)], in.(mm)

325

TABLE 1-8.1VALUES OF D FOR JUNCTIONS AT THE LARGE

CYLINDER FOR a ≤ 60 deg.

P/SsE1 0 0.002 0.005 0.010 0.02D, deg. 0 5 7 10 15

P/SsE1 0.04 0.08 0.10 0.125 0.15D, deg. 21 29 33 37 40

P/SsE1 0.20 0.25 0.30 0.35 Note (1)D, deg. 47 52 57 60

NOTE:(1) D p 60 deg. for greater values of P/SE.

tcp nominal thickness of cone at cone-to-cylinderjunction, in. (mm)

tr p minimum required thickness of cone at cone-to-cylinder junction, in. (mm)

tsp nominal thickness of cylinder at cone-to-cylin-der junction, in. (mm)

yp cone-to-cylinder factorp SsEs for stiffening ring on shellp ScEc for stiffening ring on cone

ap one-half the included (apex) angle of the coneat the center line of the head

Dp value to indicate need for reinforcement at cone-to-cylinder intersection having a half-apexanglea ≤ 60 deg. WhenD ≥ a, no reinforcementis required at the junction (see Table 1-8.1).

(b) Reinforcement shall be provided at the junctionof the cone with the large cylinder for conical headsand reducers without knuckles when the value ofDobtained from Table 1-8.1 using the appropriate ratioP/SsE1 is less thana. Interpolation may be made inthe Table.

The required area of reinforcement shall be at leastequal to that indicated by the following formula whenQL is in compression:

ArL pkQLRL tan a

SsE131 − 1⁄4 1PRL − QL

QL 2 D

a4 (1)**

At the large end of the cone-to-cylinder juncture,the PRL /2 term is in compression. Whenf1 is in tensionand the quantity is larger than thePRL /2 term, thedesign shall be in accordance with U-2(g). The calcu-lated localized stresses at the discontinuity shall notexceed the stress values specified in 1-5(g)(1) and (2).




AeL p 0.55! DLts(ts + tc /cosa) (2)

Any additional area of stiffening which is required

shall be situated within a distance of! RLts from thejunction of the reducer and the cylinder. The centroidof the added area shall be within a distance of 0.25

× ! RLts from the junction.When the cone-to-cylinder or knuckle-to-cylinder

juncture is a line of support, the moment of inertiafor a stiffening ring at the large end shall be determinedby the following procedure.

Step 1.Assuming that the shell has been designedand DL, LL , and t are known, select a member to beused for the stiffening ring and determine cross-sectionalareaATL. Then calculate factorB using the followingformula. If FL is a negative number, the design shallbe in accordance with U-2(g):

B p 3⁄4 1FLDL

ATL 2 **

where

FL p PM + f1 tan a **

M p−RL tan a

2+

LL

2+

RL2 − Rs

2

3RL tan a**

Step 2.Enter the right-hand side of the applicablematerial chart in Subpart 3 of Section II, Part D forthe material under consideration at the value ofBdetermined by Step 1. If different materials are usedfor the shell and stiffening ring, use the material chartresulting in the larger value ofA in Step 4 below.

Step 3.Move horizontally to the left to thematerial / temperature line for the design metal tempera-ture. For values ofB falling below the left end of thematerial / temperature line, see Step 5 below.

Step 4.Move vertically to the bottom of the chartand read the value ofA.

Step 5.For value of B falling below the left endof the material / temperature line for the design tempera-ture, the value ofA can be calculated using the formulaA p 2B / Ex. For value of B above the material /


326

temperature line for the design temperature, the designshall be either per U-2(g) or by changing the cone orcylinder configuration, stiffening ring location on theshell, and/or reducing the axial compressive force toreduce theB value to below or at the material/tempera-ture line for the design temperature. For values ofBhaving multiple values ofA, such as whenB falls ona horizontal portion of the curve, the smallest valueof A shall be used.

Step 6.Compute the value of the required momentof inertia from the formulas forIs or I′s. For thecircumferential stiffening ring only,

Is pADL

2ATL

14.0

For the shell-cone or ring-shell-cone section,

I ′s pADL

2ATL

10.9

Step 7.Determine the available moment of inertiaof the ring onlyI or the shell-cone or ring-shell-coneI ′.

Step 8.When the ring only is used,

I ≥ Is

and when the shell-cone or ring-shell-cone is used,

I ′ ≥ I ′s

If the equation is not satisfied, a new section witha larger moment of inertia must be selected, and thecalculation shall be done again until the equation ismet.

The requirements of UG-29(b), (c), (d), (e), and (f )and UG-30 are to be met in attaching stiffening ringsto the shell.

(c) Reinforcement shall be provided at the junctionof the conical shell of a reducer without a flare andthe small cylinder. The required area of reinforcementshall be at least equal to that indicated by the followingformula whenQs is in compression:

Ars pkQsRs tan a

SsE1(3)**

At the small end of the cone-to-cylinder juncture,the PRs/2 term is in compression. Whenf2 is in tensionand the quantity is larger than thePRs/2 term, thedesign shall be in accordance with U-2(g). The calcu-


lated localized stresses at the discontinuity shall notexceed the stress values specified in 1-5(g)(1) and (2).

The effective area of reinforcement can determinedin accordance with the following formula:

Aes p 0.55� Dsts[(ts − t) + (tc − tr) /cos �] (4)

Any additional area of stiffener which is required

shall be situated within a distance of � Rs ts from thejunction, and the centroid of the added area shall be

within a distance of 0.25 � Rs ts from the junction.When the cone-to-cylinder or knuckle-to-cylinder

juncture is a line of support, the moment of inertiafor a stiffening ring at the small end shall be determinedby the following procedure.

Step 1. Assuming that the shell has been designedand Ds, Ls, and t are known, select a member to beused for the stiffening ring and determine cross-sectionalarea ATS. Then calculate factor B using the followingformula. If Fs is a negative number, the design shallbe in accordance with U-2(g):

B p 3⁄4 �Fs Ds

ATS �where

Fs p PN + f2 tan �

N pRs tan �

2+

Ls

2+

RL2 − Rs

2

6Rs tan �**

Step 2. Enter the right-hand side of theapplicablematerial chart in Subpart 3 of Section II, Part D forthe material under consideration at the value of Bdetermined by Step 1. If different materials are usedfor the shell and stiffening ring, use the material chartresulting in the larger value of A in Step 4 below.

Step 3. Move horizontally to the left to thematerial / temperature line for the design metal tempera-ture. For values of B falling below the left end of thematerial / temperature line, see Step 5 below.

Step 4. Move vertically to the bottom of the chartand read the value of A.

Step 5. For values of B falling below the left endof the material / temperature line for the design tempera-ture, the value of A can be calculated using the formula


327

A p 2B / Ex . For value of B above the material /temperature line for the design temperature, the designshall be either per U-2(g) or by changing the cone orcylinder configuration, stiffening ring location on theshell, and/or reducing the axial compressive force toreduce the B value to below or at the material /temperature line for the design temperature. For valuesof B having multiple values of A, such as when Bfalls on a horizontal portion of the curve, the smallestvalue of A shall be used.

Step 6. Compute the value of the required momentof inertia from the formulas for Is or I ′s .

For the circumferential stiffening ring only,

Is pADs

2 ATS

14.0

For the shell-cone or ring-shell-cone section,

I ′s pADs

2 ATS

10.9

Step 7. Determine the available moment of inertiaof the ring only I or the shell-cone or ring-shell-coneI ′.

Step 8. When the ring only is used,

I ≥ Is

and when the shell-cone or ring-shell-cone is used:

I ′ ≥ I ′s

If the equation is not satisfied, a new section witha larger moment of inertia must be selected, and thecalculation shall be done again until the equation is met.

The requirements of UG-29(b), (c), (d), (e), and (f )and UG-30 are to be met in attaching stiffening ringsto the shell.

(d) Reducers not described in UG-36(e)(5), such asthose made up of two or more conical frustums havingdifferent slopes, may be designed in accordance with (e).

(e) When the half-apex angle � is greater than 60deg. (1.1 rad), cone-to-cylinder junctions without aknuckle may be used, with or without reinforcing rings,if the design is based on special analysis, such asthe beam-on-elastic-foundation analysis of Timoshenko,Hetenyi, or Watts and Lang. See U-2(g). The effectof shell and cone buckling on the required area andmoment of inertia at the joint is to be taken intoconsideration in the analysis. When such an analysis

A02


328

A02

A02

is made, the calculated localized stresses at the disconti-nuity shall not exceed the following values.

(1) (Membrane hoop stress) + (average discontinu-ity hoop stress) shall not be greater than 1.5S.

(2) (Membrane longitudinal stress) + (discontinuitylongitudinal stress due to bending) shall not be greaterthan SPS [see UG-23(e)], where the “average discontinu-ity hoop stress” is the average hoop stress across thewall thickness due to the discontinuity at the junction,disregarding the effect of Poisson’s ratio times thelongitudinal stress at the surfaces.

Documents

ASME Sec VIII - Division 1 - App 1