ASME Section VIII div 2 2010. ASME Boiler and Pressure Vessel Code. Alternative Rules

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2010 SECTION VIII, DIVISION 2

4-45

Note: see paragraph 4.2.5.6.e for limitations

Figure 4.2.3 – Some Acceptable Methods of Attaching Stiffening Rings

2010 SECTION VIII, DIVISION 2

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Notes:

1. All welds are continuous

is the minimum thickness of the weld metal from the root to the face of the weld

3. Attachment weld size:

ct≥

Figure 4.2.4 – Some Acceptable Skirt Weld Details

Double

Welded

Forging

(a)

(b)

(c)

(d) (e)

(f)

Obtained

by Weld

Overlay

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2010 SECTION VIII, DIVISION 2

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4.3 Design Rules For Shells Under Internal Pressure

4.3.1 Scope

4.3.1.1 Paragraph 4.3 provides rules for determining the required wall thickness of cylindrical, conical,

spherical, torispherical, and ellipsoidal shells and heads subject to internal pressure. In this context, internal

pressure is defined as pressure acting on the concave side of the shell.

4.3.1.2 The effects of supplemental loads are not included in design equations for shells and heads

included in paragraphs 4.3.3 to 4.3.7. Supplemental loads shall be defined in the User’s Design Specification

and their effects that result in combined loadings shall be evaluated in a separate analysis performed in

accordance with the methods in paragraph 4.3.10.

4.3.1.3 Rules are provided for the design of cylindrical-to-conical shell transition junctions in paragraphs

4.3.11 and 4.3.12. To facilitate the use of these rules, the shell wall thickness and stiffener configuration, as

applicable, shall be designed using the rules in paragraphs 4.3.3 through 4.3.7. After an initial design is

determined, this design should then be checked and modified as required using the rules of paragraphs

4.3.12 and 4.3.13.

4.3.2 Shell Tolerances

4.3.2.1 The shell of a completed vessel shall satisfy the following requirements.

a) The difference between the maximum and minimum inside diameters at any cross section shall not

exceed 1% of the nominal diameter at the cross section under consideration. The diameters may be

measured on the inside or outside of the vessel. If measured on the outside, the diameters shall be

corrected for the plate thickness at the cross section under consideration.

b) When the cross section passes through an opening or within one inside diameter of the opening

measured from the center of the opening, the permissible difference in inside diameters given above

may be increased by 2% of the inside diameter of the opening. When the cross section passes through

any other location normal to the axis of the vessel, including head-to-shell junctions, the difference in

diameters shall not exceed 1%..

4.3.2.2 Tolerances for formed heads shall satisfy the following requirements.

a) The inner surface of torispherical, toriconical, hemispherical, or ellipsoidal heads shall not deviate

outside of the specified shape by more than 1.25% of

D nor inside the specified shape by more than

0.625% of

D , where D is the nominal inside diameter of the vessel shell at the point of attachment.

Such deviations shall be measured perpendicular to the specified shape and shall not be abrupt. The

knuckle radius shall not be less than that specified

b) Measurements for determining the deviations specified in paragraph 4.3.2.2.a shall be taken from the

surface of the base metal and not from welds.

c) When the straight flange of any unstayed formed head is machined to make a lap joint connection to a

shell, the thickness shall not be reduced to less than 90% of that required for a blank head or the

thickness of the shell at the point of attachment. When so machined, the transition from the machined

thickness to the original thickness of the head shall not be abrupt but shall be tapered for a distance of at

least three times the difference between the thicknesses.

4.3.2.3 Shells that do not meet the tolerance requirements of this paragraph may be evaluated using

paragraph 4.14.

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4.3.3 Cylindrical Shells

4.3.3.1 Required Thickness – The minimum required thickness of a cylindrical shell subjected to internal

pressure shall be determined using the following equation.

exp 1

⎛⎞

⎡⎤

=−

⎜⎟

⎢⎥

⎣⎦

⎝⎠

(4.3.1)

4.3.3.2 Combined Loadings – cylindrical shells subject to internal pressure and other loadings shall

satisfy the requirements of paragraph 4.3.10.

4.3.4 Conical Shells

4.3.4.1 Required Thickness – the minimum required thickness of a conical shell (see Figure 4.3.1)

subjected to internal pressure shall be determined using the following equation.

[]

exp 1

2cos

⎛⎞

⎡⎤

=−

⎜⎟

⎢⎥

⎣⎦

⎝⎠

(4.3.2)

4.3.4.2 Offset Transitions – the cylinders for an offset cone shall have parallel centerlines that are offset

from each other by a distance no greater than the difference of their minimum radii, as shown in Figure 4.3.2.

Configurations that do not satisfy this requirement shall be evaluated per Part 5. The offset cone shall be

designed as a concentric cone using the angle,

, as defined in Equation (4.3.3).

[

]

max ,

αα

= (4.3.3)

4.3.4.3 Combined Loadings – conical shells subject to external pressure and other loadings shall satisfy

the requirements of paragraph 4.3.10.

4.3.5 Spherical Shells and Hemispherical Heads

4.3.5.1 The minimum required thickness of spherical shells and hemispherical heads shall be determined

using the following equation:

0.5

exp 1

⎛⎞

⎡⎤

=−

⎜⎟

⎢⎥

⎣⎦

⎝⎠

(4.3.4)

4.3.5.2 Combined Loadings – spherical shells and hemispherical heads subject to internal pressure and

other loadings shall satisfy the requirements of paragraph 4.3.10.

4.3.6 Torispherical Heads

4.3.6.1 Torispherical Heads With The Same Crown and Knuckle Thicknesses – the minimum required

thickness of a torispherical head (see Figure 4.3.3) subjected to internal pressure shall be calculated using

the following procedure.

a) STEP 1 – Determine the inside diameter,

D , and assume values for the crown radius, L , the knuckle

radius,

r , and the wall thickness t .

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2010 SECTION VIII, DIVISION 2

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b) STEP 2 – Compute the head

LD, rD, and Lt ratios and determine if the following equations are

satisfied. If the equations are satisfied, then proceed to Step 3; otherwise, the head shall be designed in

accordance with Part 5.

0.7 1.0

≤≤ (4.3.5)

0.06

≥ (4.3.6)

20 2000

≤≤

(4.3.7)

c) STEP 3 – Calculate the following geometric constants:

0.5

arccos ,

radians

−

⎡⎤

⎢⎥

−

⎣⎦

(4.3.8)

radians

= (4.3.9)

[]

0.5

cos

th th th

th th

Rrfor

βφ

−

=+ <

−

(4.3.10)

0.5

th th th

RD for

=≥ (4.3.11)

d) STEP 4 – Compute the coefficients

C and

C using the following equations.

9.31 0.086 0.08

Cfor

⎛⎞

=− ≤

⎜⎟

⎝⎠

(4.3.12)

0.692 0.605 0.08

Cfor

⎛⎞

=+ >

⎜⎟

⎝⎠

(4.3.13)

1.25 0.08

Cfor

=≤

(4.3.14)

1.46 2.6 0.08

Cfor

⎛⎞

=− >

⎜⎟

⎝⎠

(4.3.15)

e) STEP 5 – Calculate the value of internal pressure expected to produce elastic buckling of the knuckle.

eth

CE t

CR r

⎛⎞

−

⎜⎟

⎝⎠

(4.3.16)

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f) STEP 6 – Calculate the value of internal pressure that will result in a maximum stress in the knuckle

equal to the material yield strength.

⎛⎞

−

⎜⎟

⎝⎠

(4.3.17)

If the allowable stress at the design temperature is governed by time-independent properties, then

C is

the material yield strength at the design temperature, or

3 y

. If the allowable stress at the design

temperature is governed by time-dependent properties, then

C is determined as follows.

1) If the allowable stress is established based on 90% yield criterion, then

C is the material allowable

stress at the design temperature multiplied by 1.1, or

1.1CS

2) If the allowable stress is established based on 67% yield criterion, then

C is the material allowable

stress at the design temperature multiplied by 1.5, or

1.5CS

g) STEP 7 – Calculate the value of internal pressure expected to result in a buckling failure of the knuckle.

0.6 1.0

ck eth

PP forG=≤ (4.3.18)

0.77508 0.20354 0.019274G

1.0

1 0.19014 0.089534 0.0093965

ck y

PPforG

GG G

⎛⎞

−+

⎜⎟

+− +

⎝⎠

(4.3.19)

where

eth

(4.3.20)

h) STEP 8 – Calculate the allowable pressure based on a buckling failure of the knuckle.

1.5

P =

(4.3.21)

i) STEP 9 – Calculate the allowable pressure based on rupture of the crown.

0.5

(4.3.22)

j) STEP 10 – Calculate the maximum allowable internal pressure.

[

]

min ,

aakac

PPP=

(4.3.23)

k) STEP 11 – If the allowable internal pressure computed from STEP 10 is greater than or equal to the

design pressure, then the design is complete. If the allowable internal pressure computed from STEP 10

is less than the design pressure, then increase the head thickness and repeat Steps 2 through 10. This

process is continued until an acceptable design is achieved.

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2010 SECTION VIII, DIVISION 2

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4.3.6.2 Torispherical Heads With Different Crown and Knuckle Thicknesses – a torispherical head

formed from several welded components as shown in Figure 4.3.4 may have a smaller thickness in the

spherical crown than in the knuckle region. The transition in thickness shall be located on the inside surface

of the thicker part, and shall have a taper not exceeding 1:3.

a) The minimum required thickness of the spherical dome of the head shall be determined in accordance

with paragraph 4.3.5.

b) The minimum required thickness of the knuckle region of the head shall be determined in accordance

with paragraph 4.3.6.1.b.

4.3.6.3 Combined Loadings – torispherical heads subject to internal pressure and other loadings shall

satisfy the requirements of paragraph 4.3.10. In this calculation, the torispherical head shall be approximated

as an equivalent spherical shell with a radius equal to

L .

4.3.7 Ellipsoidal Heads

4.3.7.1 Required Thickness – The minimum required thickness of an ellipsoidal head (see Figure 4.3.5)

subjected to internal pressure shall be calculated using the equations in paragraph 4.3.6 with the following

substitutions for

and

0.5

0.08rD

⎛⎞

=−

⎜⎟

⎝⎠

(4.3.24)

()

0.44 0.02LD k=+ (4.3.25)

where

(4.3.26)

The rules in this paragraph are applicable for elliptical heads that satisfy Equation (4.3.27). Elliptical heads

that do not satisfy this equation shall be designed using Part 5.

1.7 2.2k≤≤ (4.3.27)

4.3.7.2 Combined Loadings – ellipsoidal heads subject to internal pressure and other loadings shall

satisfy the requirements of paragraph 4.3.10. In this calculation, the ellipsoidal head shall be approximated as

an equivalent spherical shell with a radius equal to

4.3.8 Local Thin Areas

4.3.8.1 Local Thin Areas

Rules for the evaluation of Local Thin Areas are covered in paragraph 4.14.

4.3.8.2 Local Thin Band in Cylindrical Shells

A complete local circumferential band of reduced thickness at a weld joint in a cylindrical shell as shown in

Figure 4.3.6 is permitted providing all of the following requirements are met.

a) The design of the local reduced thickness band is evaluated by limit load or elastic plastic analysis in

accordance with Part 5. All other applicable requirements of Part 5 for stress analysis and fatigue

analysis shall be satisfied.

b) The cylinder geometry shall satisfy

Rt≥ .

2010 SECTION VIII, DIVISION 2

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c) The thickness of the reduced shell region shall not be less than two-thirds of the cylinder required

thickness determined in accordance with paragraph 4.3.3.

d) The reduced thickness region shall be on the outside of the vessel shell with a minimum taper transition

of 3:1 in the base metal. The transition between the base metal and weld shall be designed to minimize

stress concentrations.

e) The total longitudinal length of each local thin region shall not exceed

t (see Figure 4.3.6).

f) The minimum longitudinal distance from the thicker edge of the taper to an adjacent structural

discontinuity shall be the greater of

2.5

t or the distance required to assure that overlapping of

areas where the primary membrane stress intensity exceeds

1.1S does not occur.

4.3.9 Drilled Holes Not Penetrating Through the Vessel Wall

4.3.9.1 Design requirements for partially drilled holes that do not penetrate completely through the vessel

wall are provided in this paragraph. These rules are not applicable for studded connections or telltale holes.

4.3.9.2 Partially drilled radial holes in cylindrical and spherical shells may be used provided the following

requirements are satisfied.

a) The drilled hole diameter is less than or equal to 50 mm (2 in.).

b) The shell inside diameter to thickness ratio is greater than or equal to 10.

c) The centerline distance between any two partially drilled holes or between a partially drilled hole and an

unreinforced opening shall satisfy the requirements of paragraph 4.5.13.

d) Partially drilled holes shall not be placed within the limits of reinforcement of a reinforced opening.

e) The outside edge of the hole shall be chamfered. For flat bottom holes, the inside bottom corner of the

hole shall have a minimum radius,

r of the following:

min , 6 (0.25 .)

rmmin

⎡⎤

⎢⎥

⎣⎦

(4.3.28)

f) The minimum acceptable remaining wall thickness,

t at the location of a partially drilled hole shall be

determined as follows:

[

]

max,6(0.25.)

rw rw

ttmmin≥ (4.3.29)

where,

0.5

1.2261727 1.9842895 2.236553 ln

ddd

DDD

⎛⎞

⎛⎞ ⎛⎞ ⎡⎤

=− + −

⎜⎟

⎜⎟ ⎜⎟

⎢

⎥

⎜⎟

⎝⎠ ⎝⎠ ⎣⎦

⎝⎠

(4.3.30)

g) The calculated average shear stress, as determined below shall not exceed

0.8S .

= (4.3.31)

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2010 SECTION VIII, DIVISION 2

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4.3.10 Combined Loadings and Allowable Stresses

4.3.10.1 General - The rules of this paragraph shall be used to determine the thickness requirements for

cylindrical, spherical, and conical shells subjected to internal pressure plus supplemental loads of applied net

section axial force, bending moment, and torsional moment, as shown in Figure 4.3.7. These rules are

applicable if the requirements shown below are satisfied. If all of these requirements are not satisfied, the

shell section shall be designed per Part 5.

a) The rules are applicable for regions of shells that are

2.5

t from any major structural discontinuity.

b) These rules do not take into account the action of shear forces, since these loads generally can be

disregarded.

c) The ratio of the shell inside radius to thickness is greater than 3.0.

4.3.10.2 The following procedure shall be used to design cylindrical, spherical, and conical shells

subjected to internal pressure plus supplemental loads of applied net section axial force, bending moment,

and torsional moment is shown below.

a) STEP 1 – Calculate the membrane stress.

1) For cylindrical shells:

⎡⎤

⋅

⎢⎥

⎣⎦

(4.3.32)

()

[]

()

22 44

32 cos

PD F

ED D

DD DD

ππ

⎛⎞

⎜⎟

=++

⎜⎟

−

−−

⎝⎠

(4.3.33)

()

−

(4.3.34)

2) For spherical shells:

2ln

⎡⎤

⋅

⎢⎥

⎣⎦

(4.3.35)

()

[]

()

[]

222 443

32 cos

sin sin

2ln

DD DD

φπ φ

⎛⎞

⎜⎟

=+ +

⎡⎤

⎜⎟

−−

⋅

⎜⎟

⎢⎥

⎣⎦

⎝⎠

(4.3.36)

()

[

]

[]

()

[]

44 442

cos

32 16

sin

oto

MD M D

DD DD

τθ

πφ

−−

(4.3.37)

2010 SECTION VIII, DIVISION 2

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3) For conical shells:

[]

ln 1 cos 1

⎡⎤

⎛⎞

⋅− +

⎜⎟

⎢⎥

⎝⎠

⎣⎦

(4.3.38)

()

[]

()

[]

()

[]

22 22 44

32 cos

cos cos cos

ooo

PD F

DD DD DD

παπα

⎛⎞

⎜⎟

=++

⎜⎟

−−−

⎝⎠

(4.3.39)

()

[] []

()

44 44

32 16

tan sin

oto

MD M D

DD DD

ταθ

ππ

−−

(4.3.40)

b) STEP 2 – Calculate the principal stresses.

()

0.5 4

msm msm

θθ

σσ σσ τ

⎛⎞

=++−+

⎜⎟

⎝⎠

(4.3.41)

()

0.5 4

msm msm

θθ

σσ σσ τ

⎛⎞

=+−−+

⎜⎟

⎝⎠

(4.3.42)

0.5P

=− (4.3.43)

c) STEP 3 – At any point on the shell, the following limit shall be satisfied.

()()()

0.5

222

12 23 31

σσ σσ σσ

⎡⎤

−+−+− ≤

⎣⎦

(4.3.44)

d) STEP 4 – For cylindrical and conical shells, if the meridional stress

is compressive, then Equation

(4.3.45) shall be satisfied where

F is evaluated using paragraph 4.4.12.2 with

0.15

. For

spherical shells, the allowable compressive stress criteria in paragraph 4.4.12.4 shall be satisfied. Note

that the controlling condition for this case may be the combined loadings without internal pressure.

mxa

≤ (4.3.45)

4.3.11 Cylindrical-To-Conical Shell Transition Junctions Without a Knuckle

4.3.11.1 The following rules are applicable for the design of conical transitions or circular cross-sections

that do not have a knuckle at the large end or flare at the small end under loadings of internal pressure and

applied net section axial force and bending moment. Acceptable conical transition details are shown in

Figure 4.3.8. Design rules for a knuckle at the large end or flare at the small end are provided in paragraph

4.3.12.

4.3.11.2 Design rules are provided for the cylinder-to-cone junction details shown in Figure 4.3.9. Details

with a stiffening ring at the cylinder-to-cone junction, or other details that differ from the ones shown in this

figure shall be designed in accordance with Part 5.

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