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Discussion and References
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Information about Wall thickness
calculation of formed heads under external pressure:
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ASME Section VIII Div 1 paragraphs UG-33,
UG-32, UG-28, UG-29 and UG-30
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Tables and Standards
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ASME Section VIII Div
1 paragraph UG-28, Thickness of Shells and Tubes under External Pressure
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ASME Section VIII Div
1 paragraph UG-29, Stiffening Rings for Cylindrical Shells Under External
Pressure
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ASME Section VIII Div
1 paragraph UG-30, Attachment of Stiffening Rings
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ASME Section VIII Div
1 paragraph UG-32, Formed Heads, and Sections, Pressure on Concave Side
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ASME Section VIII Div
1 paragraph UG-33, Formed Heads, Pressure on Convex Side
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ASME Sec. II D Fig. G, Geometric Chart for
Components Under External or Compressive Loadings (All Materials)
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ASME Sec. II D Fig.
CS, Chart for Determining Shell Thickness of Components Under External
Pressure Developed for Carbon or Low Alloy Steel
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ASME Sec. II D Fig.
HA, Chart for Determining Shell Thickness of Components Under External
Pressure Developed for Austenitic Steel
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ASME Sec. II D Fig.
HT, Chart for Determining Shell Thickness of Components Under External
Pressure Developed for Quenched and Tempered Low Alloy Steel
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ASME Sec. II D Table TM-1 ( Modulus of
Elasticity, E )
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UG-33 Formed Heads, Pressure on Convex Side
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(a)
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The required
thickness for heads due to pressure on the convex side shall be determined as
follows.
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(1) For ellipsoidal and
torispherical heads, the required thickness shall
be the greater of the following:
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(-a) the thickness computed by the procedure given
in UG-32 for heads with pressure on the concave side
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(plus heads) using a design pressure 1.67 times the
design pressure on the convex side, assuming a joint
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efficiency E = 1.00 for all cases; or
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(-b) the thickness as computed by the appropriate
procedure given in (d) or (e) below.
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(c)
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Hemispherical Heads. The required thickness of a hemispherical head having pressure
on the convex side shall be
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determined in the same manner as outlined in
UG-28(d) for determining the thickness for a spherical shell.
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(d)
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Ellipsoidal Heads. The required thickness of an ellipsoidal head having pressure
on the convex side, either seamless or of
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built‐up construction with butt joints, shall not
be less than that determined by the following the same procedure as that
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given for spherical shells in UG-28(d).
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(e)
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Torispherical Heads. The required thickness of a torispherical head having pressure
on the convex side, either seamless
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or of built‐up construction with butt joints, shall
not be less than that determined by the same design procedure as is used for
ellipsoidal heads given in (d) above, using the appropriate value for
Ro.
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for ellipsoidal heads given in (d) above, using the
appropriate value for Ro.
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UG-28, Thickness of Shells and Tubes under External
Pressure
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(d)
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Spherical Shells. The minimum required thickness of
a spherical shell under external pressure, either seamless or of
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built‐up construction with butt joints, shall be
determined by the following procedure:
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Step 1. Assume a value for t and calculate the value of factor A using the following formula:
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A =
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0,125
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Ro/t
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Step 2. Using the value of A calculated in Step 1, enter the applicable material chart in
Subpart 3 of Section II,
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Part D for the material under consideration. Move vertically to an
intersection with the material/temperature line
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for the design temperature (see UG-20). Interpolation may be made
between lines for intermediate temperatures.
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If tabular values in Subpart 3 of Section II, Part D are used, linear
interpolation or any other rational interpolation
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method may be used to determine a B value that lies between two adjacent tabular values for a
specific temperature.
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Such interpolation may also be used to determine a B value at an intermediate temperature that lies between
two
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sets of tabular values, after first determining B values for each set of tabular values. In cases where the
value at A
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falls to the right of the end of the material/temperature line, assume
an intersection with the horizontal projection
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of the upper end of the material/temperatureline. If tabular values
are used,the last (maximum) tabulated value
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shall be used. For values at A falling to the left of the material/temperature line, see Step
5.
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Step 3. From the intersection obtained in Step 2, move horizontally
to the right and read the value of factor B.
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Step 4. Using the value of B obtained in Step 3, calculate the value of the maximum
allowable external working pressure
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Pa using the following equation:
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Pa =
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B
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Ro/t
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Step 5. For values of A falling to the left of the applicable material/temperature
line, the value of Pa
can be calculated using
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the following equation:
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Pa =
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0.0625E
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(Ro/t)2
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If tabulated values are
used, determine B as in Step
2 and apply it to the equation in Step 4.
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Step 6. Compare Pa obtained in Step 4 or Step 5 with P. If Pa
is smaller than P,
select a larger value for t and repeat the
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design procedure until a value for Pa is obtained that is equal to or greater than P.
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(e)
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The external design pressure or maximum allowable
external working pressure shall not be less than the maximum
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expected difference in operating pressure that may
exist between the outside and the inside of the vessel at any time.
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The symbols defined below are used in this
procedure:
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Do = outside diameter of the head
skirt.
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Do/2ho = ratio of the major to the minor
axis of ellipsoidal heads, which equals the outside diameter of the head skirt
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divided by twice the outside height of the head (see Table UG-33.1).
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ho = one‐half of the length of the
outside minor axis of the ellipsoidal head, or the outside height of the ellipsoidal head
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measured from the tangent line (head‐bend line).
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Ko = factor depending on the
ellipsoidal head proportions Do/2ho (see Table UG-33.1).
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Ro = for hemispherical heads, the
outside radius
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= for ellipsoidal heads, the equivalent
outside spherical radius taken as KoDo.
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= for
torispherical heads, the outside radius of the crown portion of the head.
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t =
minimum required thickness of head after forming, in (mm)
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A =
factor determined in step 1 assuming a value for t.
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Using
the value of A calculated in
Step 1, enter the applicable material chart in Subpart 3 of Section II, Part
D for the
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material under consideration. For the case of cylinders having Do/t values less than 10, see (c)(2).
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B =
factor determined from the applicable material chart or table in Subpart 3 of
Section II, Part D (Figures CS, HA,
HT)
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for
maximum design metal temperature [see UG-20(c)]
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E = modulus of elasticity of material at design temperature. For
external pressure design in accordance with this Section,
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the modulus of elasticity to be used
shall be taken from the applicable materials chart in Subpart 3 of Section
II,
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Part D. (Interpolation may be made
made between lines for intermediate temperatures.)
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P = external design pressure [see Note in UG-28 (f)].
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Pa = calculated value of maximum allowable external working
pressure for the assumed
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assumed value of t, [see Note in
UG-28(f)].
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t = minimum required thickness of cylindrical shell or tube, or
spherical shell, in (mm)
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