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

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2010 SECTION VIII, DIVISION 2

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Figure 4.3.3 – Torispherical Head of Uniform Thickness

0.8 D Max.

Figure 4.3.4 – Torispherical Head of Different Thickness of Dome and Knuckle

Figure 4.3.5 – Ellipsoidal Head

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t/2

weld

Reduced girth

must be on O.D.

t max.

Figure 4.3.6 – Local Thin Band in a Cylindrical Shell

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Section Considered

(a) Stresses Within A

Cylindrical Shell

Section Considered

(b) Stresses Within A

Spherical Shell

Conical Shell

Figure 4.3.7 – Shells Subjected to Supplemental Loadings

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(a) Cone without a Knuckle at Large and

without a Flare at the Small End

(b) Cone with a Knuckle at Large and

without a Flare at the Small End

with a Flare at the Small End

(d) Cone with a Knuckle at Large and

with a Flare at the Small End

Figure 4.3.8 – Conical Transition Details

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3030

2.0 R

cos

1.4 R

cos

(a) Large End of Cone

(b) Small End of Cone

(d) Small End of Cone with Flare

3030

Figure 4.3.9 – Reinforcement Requirements for Conical Transition Junction

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TL-1

TL-2

TL-4

TL-3

Figure 4.3.10 – Parameters for Knuckle and Flare Design

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4.4 Design of Shells Under External Pressure and Allowable Compressive Stresses

4.4.1 Scope

4.4.1.1 Paragraph 4.4 provides rules for determining the required wall thickness of cylindrical, conical,

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

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

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

included in paragraphs 4.4.5 to 4.4.9. The effects of supplemental loads that result in combined loadings

shall be evaluated in a separate analysis performed in accordance with the methods in paragraph 4.4.12.

4.4.1.3 Rules are also provided for the design of cylindrical-to-conical shell transition junctions in

paragraphs 4.4.13 and 4.4.14. To facilitate the use of these rules, it is recommended that the shell wall

thickness and stiffener configuration, as applicable, first be designed using the rules in paragraphs 4.4.5

through 4.4.9. After an initial design is determined, this design should then be checked and modified as

required using the rules of paragraphs 4.4.13 and 4.4.14.

4.4.1.4 The equations in this paragraph are applicable for

2000

≤

. If 2000

Dt> , then the

design shall be in accordance with Part 5. In developing the equations in the paragraph, the shell section is

assumed to be axisymmetric with uniform thickness for unstiffened cylinders and formed heads. Stiffened

cylinders and cones are also assumed to be of uniform thickness between stiffeners. Where nozzles with

reinforcing plates or locally thickened shell sections exist, the thinnest uniform thickness in the applicable

unstiffened or stiffened shell section shall be used for the calculation of the allowable compressive stress.

4.4.1.5 Special consideration shall be given to ends of components (shell sections) or areas of load

application where stress distribution may be in the inelastic range and localized stresses may exceed those

predicted by linear theory.

4.4.1.6 When the localized stresses extend over a distance equal to one-half the length of the buckling

mode (approximately

1.2

Dt), the localized stresses shall be considered as a uniform stress for the design

of the shell section.

4.4.1.7 The buckling strength formulations presented in this paragraph are based upon linear structural

stability theory which is modified by reduction factors which account for the effects of imperfections, boundary

conditions, non-linearity of material properties and residual stresses. The reduction factors are determined

from approximate lower bound values of test data of shells with initial imperfections representative of the

tolerance limits specified in this paragraph.

4.4.2 Design Factors

The allowable stresses are determined by applying a design factor,

FS , to the predicted buckling stresses.

The required values of

are 2.0 when the buckling stress is elastic and 1.667 when the predicted buckling

stress equals the minimum specified yield strength at the design temperature. A linear variation shall be used

between these limits. The equations for

FS are given below where

F is the predicted buckling stress that

is determined by setting

1.0FS =

in the allowable stress equations. For combinations of design loads and

earthquake loading or wind loading (see paragraph 4.1.5.3), the allowable stress for

bha

F or

F in Equations

(4.4.106), (4.4.107), (4.4.108), (4.4.111), (4.4.112) and (4.4.113) may be increased by a factor of 1.2.

2.0 0.55

ic y

FS for F S=≤ (4.4.1)

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2.407 0.741 0.55

yicy

FS for S F S

⎛⎞

=− <<

⎜⎟

⎝⎠

(4.4.2)

1.667

ic y

FS for F S== (4.4.3)

4.4.3 Material Properties

4.4.3.1 The equations for the allowable compressive stress are based on carbon and low alloy steel plate

materials as given in Part 3. The maximum temperature limit permitted for these materials is defined in Table

4.4.1. For materials other than carbon or low alloy steel, a modification to the allowable stress is required.

The procedure for modification of the allowable stress is to calculate the allowable compressive stress based

on carbon and low alloy steel plate materials, and then make the following adjustments as described below.

a) Determine the tangent modulus,

E , from paragraph 3.D.5 based on a stress equal to

F . For Axial

Compression the allowable stress is adjusted as follows:

FS E

(4.4.4)

ba xa

FF= (4.4.5)

b) Determine the tangent modulus,

E , from paragraph 3.D.5 based on a stress equal to

F . For External

Pressure the allowable stress is adjusted as follows:

he t

FS E

(4.4.6)

c) Determine the tangent modulus,

E , from paragraph 3.D.5 based on a stress equal to

F . For Shear

the allowable stress is adjusted as follows:

ve t

FS E

(4.4.7)

4.4.3.2 The equations for the allowable compressive stress may be used in the time-independent region

for the material of construction as provided in Table 4.4.1. If the component as designed is in the time-

dependent region (i.e. creep is significant), the effects of time-dependent behavior shall be considered.

4.4.4 Shell Tolerances

4.4.4.1 Permissible Out-Of-Roundness Of Cylindrical, Conical, and Spherical Shells – The shell of a

completed vessel subject to external pressure shall meet the following requirements at any cross section.

a) The out-of-roundness requirements in paragraph 4.3.2.1 shall be satisfied.

b) The maximum plus or minus deviation from a true circle,

e , measured from a segmental circular

template having the design inside or outside radius (depending on where the measurements are taken)

and a chord length,

L , should not exceed the following value:

[

]

min , 2

eet= (4.4.8)

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where

1.069

0.0165 3.25 0.2 0.0242

c c

et validforteR

⎛⎞

=+ ≤≤

⎜⎟

⎝⎠

(4.4.9)

2sin

⎡⎤

⎢⎥

⎣⎦

(4.4.10)

21.41

n valid for n

tL t

⎛⎞

=⋅ ≤≤

⎜⎟

⎝⎠

(4.4.11)

0.54

min 2.28 , 2.80

⎡⎤

⎛⎞

⎢⎥

⎜⎟

⎝⎠

⎢⎥

⎣⎦

(4.4.12)

0.044

min 0.38 , 0.485

⎡⎤

⎛⎞

⎢⎥

⎜⎟

⎝⎠

⎢⎥

⎣⎦

(4.4.13)

c) The value of thickness,

t , used in the above equations shall be determined as follows:

1) For vessels with butt joints,

t is the nominal plate thickness less the corrosion allowance.

2) For vessels with lap joints,

t is the nominal plate thickness and the permissible deviation is et

3) Where the shell at any cross section is made from plates of different thicknesses

t is the nominal

plate thickness of the thinnest plate less the corrosion allowance.

d) For cones and conical sections,

t shall be determined using paragraph 4.4.4.1.c except that t shall be

replaced by

t .

e) Measurements for out–of-tolerances shall be taken on the surface of the base metal and not on welds or

other raised parts of the component.

f) The dimensions of a completed vessel may be brought within the requirements of this paragraph by any

process that will not impair the strength of the material.

g) Sharp bends and flats spots shall not be permitted unless provision is made for them in the design or

they satisfy the tolerances in paragraphs 4.4.4.2 and 4.4.4.4.

h) Vessels fabricated of pipe may have permissible variations in the outside diameter in accordance with

those permitted under the specification covering its manufacture.

4.4.4.2 Cylindrical and Conical Shells Subject To Uniform Axial Compression and Axial Compression

Due to a Bending Moment – the tolerance requirements in paragraph 4.3.2.1 shall be satisfied. In addition,

the local inward deviation from a straight line,

e , measured along a meridian over gauge length,

L , shall not

exceed the maximum permissible deviation,

e , given below:

0.002

eR= (4.4.14)

and,

2010 SECTION VIII, DIVISION 2

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min 4 ,

L R t L for cylindrical shells

⎡⎤

⎣⎦

(4.4.15)

[] []

min 4 ,

cos cos

mc c

Rt L

L for conical shells

αα

⎡⎤

⎢⎥

⎣⎦

(4.4.16)

L t across circumferential welds= (4.4.17)

4.4.4.3 Cylindrical and Conical Shells Subject To External Pressure And Uniform Axial Compression and

Axial Compression Due to a Bending Moment – all of the tolerance requirements in paragraphs 4.4.4.1 and

4.4.4.2 shall be satisfied.

4.4.4.4 Spherical Shells and Formed Heads – the tolerance requirements in paragraph 4.3.2.2 shall be

satisfied. In addition, the maximum local deviation from true circular form,

e , for spherical shells and any

spherical portion of a formed head shall not exceed the shell thickness. Measurements to determine the

maximum local deviation shall be made with a template with a chord length,

L , given by the following

equation.

3.72

LRt= (4.4.18)

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

paragraph 4.14.

4.4.5 Cylindrical Shell

4.4.5.1 Required Thickness – The required thickness of a cylindrical shell subjected to external pressure

loading shall be determined using the following procedure.

a) STEP 1 – Assume an initial thickness,

t , and unsupported length, L (see Figures 4.4.1 and 4.4.2).

b) STEP 2 – Calculate the predicted elastic buckling stress,

F .

1.6

CEt

(4.4.19)

(4.4.20)

0.94

0.55 2

CforM

⎛⎞

=≥

⎜⎟

⎝⎠

(4.4.21)

0.94

1.058

1.12 13 2

hx x

CM forM

−

⎛⎞

=<<

⎜⎟

⎝⎠

(4.4.22)

0.92

1.5 13

0.579

CforM

=<≤

−

(4.4.23)

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