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Discussion and References
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Information about Wall thickness
calculation of shell and tubes under external pressure:
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ASME Section VIII Div 1 paragraphs UG-28,
UG-29 and UG-30
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ASME B31.3 Process Piping, paragraph
304.1.3
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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 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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Cylinders having Do/t
values ≥ 10
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Step 1. Assume a value for t and determine the ratios L/Do and Do/t.
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Step 2. Enter Figure G in Subpart 3 of Section II, Part D at the value of L/Do
determined in Step 1.
For
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values of L/Do greater than 50, enter the chart at a value of L/Do =
50. For values of L/Do less
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than 0.05, enter the chart at a value of L/Do = 0.05.
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Step
3. Move horizontally to the line for the value of
Do /t determined in Step 1. Interpolation may be
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made for intermediate values of
Do/t; extrapolation is not permitted. From this point of
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intersection move vertically
downward to determine the value of factor A.
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Step
4. Using the value of A calculated in Step 3, enter the applicable material chart in Subpart 3 of
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Section II, Part D for the
material under consideration. (See figures CS for Carbon
and Low Alloy
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Steel and
HT for Ferritic Steels with Properties Enhanced by Heat Treatment). Move vertically to
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an intersection with the
material/temperature line for the design temperature (see UG-20).
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Interpolation may be made
between lines for intermediate temperatures. If tabular values in
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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
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specific temperature. Such
interpolation may also be used to determine a B value at an
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intermediate temperature that
lies between two sets of tabular values, after first determining
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B values for each set of tabular values.
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In cases where the value of A falls to the right of the end of
the material/temperature line,
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assume an intersection with the
horizontal projection of the upper end of the material/
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temperature line. If tabular
values are used, the last (maximum) tabulated value shall be used.
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For values of A falling to the left of the
material/temperature line, see Step 7.
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Step 5. From the intersection obtained in Step
4, move horizontally to the right and read the
value of
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factor B.
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Step 6. Using this value of B, 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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4B
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3(Do/t)
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Step 7. For values of A falling to the left of the applicable
material/temperature line, the value of Pa can be
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calculated using the following
equation:
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Pa =
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2AE
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3(Do/t)
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If tabular values
are used, determine B as in Step 4 and apply it to the
equation in Step 6.
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Step 8. Compare the calculated value of Pa obtained in Step 6 or Step 7 with P. If Pa is smaller than P,
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select a larger value for t and
repeat the design procedure until a value of Pa is obtained that is
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equal to or greater than P.
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The symbols defined below are used in this
procedure:
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A
= factor determined from Figure G in Subpart 3 of Section II, Part D and used
to enter the
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applicable material chart in Subpart 3 of Section II, Part D. For the
case of cylinders having
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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,
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Part
D (Figures CS, HA, HT) for maximum
design metal temperature [see UG-20(c)]
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Do
= outside diameter of cylindrical shell course or tube.
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E = modulus of elasticity of material at design temperature. For
external pressure design in
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accordance with this Section, the
modulus of elasticity to be used shall be taken from the
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applicable materials chart in Subpart
3 of Section II, Part D. (Interpolation may be made
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made between lines for intermediate
temperatures.)
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L = the running
centerline length between any two sections stiffened in accordance with
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UG-29. in. (mm).
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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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Cylinders having Do/t
values < 10
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Step 1. Using the same procedure as given in UG-28(c)(1), obtain the
value of B. For values
of Do/t less than 4,
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the value of factor A
can be calculated using the following formula:
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A =
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1,1
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(Do/t)2
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For values of A greater than 0.10, use a value of
0.10.
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Step 2. Using the value of B obtained in Step 1, calculate a value Pa1 using the following formula:
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Pa1 =
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[
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2,167
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-0,0833
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]
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B
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(Do/t)
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Step 3. Calculate a value Pa2 using the following formula:
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Pa2 =
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2S
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[
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1 -
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1
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]
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(Do/t)
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(Do/t)
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where S is the
lesser of two times the maximum allowable stress value in tension at design
metal temperature, from the applicable table referenced in UG-23, or 0.9
times the yield strength of the material at design temperature. Values of
yield strength are obtained from the applicable external pressure chart as
follows:
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(a) For a given
temperature curve, determine the B value that corresponds to the right hand
side termination point of the curve.
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(b) The yield
strength is twice the B value obtained in (a) above.
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Step 4. The smaller of the values of Pa1 calculated in Step 2, or Pa2 calculated in Step 3 shall be used
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for the maximum allowable external working
pressure Pa. Compare Pa with P. If Pa is smaller than P,
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select a larger value for t and repeat the design
procedure until a value for Pa is obtained that is equal to
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or greater than P.
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The symbols defined below are used in this
procedure:
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A
= factor determined from Figure G in Subpart 3 of Section II, Part D and used
to enter the
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applicable material chart in Subpart 3 of Section II, Part D. For the
case of cylinders having
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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,
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Part
D (Figures CS, HA, HT) for maximum
design metal temperature [see UG-20(c)]
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Do
= outside diameter of cylindrical shell course or tube.
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E = modulus of elasticity of material at design temperature. For
external pressure design in
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accordance with this Section, the
modulus of elasticity to be used shall be taken from the
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applicable materials chart in Subpart
3 of Section II, Part D. (Interpolation may be made
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made between lines for intermediate
temperatures.)
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L = the running
centerline length between any two sections stiffened in accordance with
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UG-29. in. (mm).
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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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