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Design Calculations,
Section VIII, Division 1
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Pressure Vessel Design
Shall i nclude the requir ements of:
Introduction
Subsection A, General Requirements Subsection B, Methods of
Fabrication
Subsection C, Classes of Materials
Mandatory Appendices
Section II, V, and IX when reference
M ay inclu de:
Code Cases
Nonmandatory Appendices
Other sources which do not conflict with mandatory requirements
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UG-16 General
(b) Minimum thickness of shells and heads is 1/16 in. (1.5 mm) excluding
corrosion allowance (C.A.), after forming & regardless of product form
except:
(1) Heat transfer plates of plate type heat exchangers.
(2) Inner pipe of double pipe heat exchangers and tubes in shell and tube
heat exchangers (where the pipe or tube is NPS 6 [DIN 150] or less.(3) Unfired steam boilers shall be 1/4 in. (6mm) exclusive of corrosion
allowance.
(4) Compressed air, steam or water service vessels of UCS-23 materials
shall be 3/32 in. (2.5mm) excluding corrosion allowance.
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UG-16 General
(c) Mill Under tolerance
Plate material shall not be ordered thinner than the design thickness.
Vessels made of plate furnished with an under tolerance of not more
than the smaller of 0.01 in. (0.25mm) or 6% of the ordered thickness may
be used at the full design pressure for the ordered thickness. When the
material spec, allows a greater under tolerance, the ordered thickness shallbe increased so the material received is within these stated tolerances.
(d) Pipe Under tolerance
If pipe or tube is ordered by its nominal wall thickness, the material
specification manufacturing under tolerance on wall thickness shall be
taken into account (except for nozzle wall reinforcement area
requirements per UG-37).
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After determining the minimum t, the thickness shall be increased
by an amount sufficient to provide the manufacturing under toleranceallowed in the material specification.
UG-16 General
NPS OD SCH 10 SCH 20 SCH
30
SCH
40
SCH
60
SCH
80
SCH
100
SCH
160
6 6.625 - - - 0.280 - 0.432 - 0.718
8 8.625 0.109 0.250 0.277 0.322 0.406 0.500 0.593 0.906
10 10.75 0.134 0.250 0.307 0.365 0.500 0.593 0.718 1.125
The decimal thicknesses listed for the respective pipe sizes represent their nominal or
average wall dimensions and include an allowance of 12.5% under the nominal thickness.
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(e) Corrosion Allowance In Design Formulas All dimensional symbols used in all design formulas throughout
this Division represent dimensions in the corroded condition.
Therefore, material designated for corrosion purposes cannot
contribute to the strength of the vessel. Such material must be
deducted when determining design pressure, and added to the
required thickness to determine design thickness. (Definitions,
Appendix 3)
UG-16 General
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.'.
(b) Special Shapes
Vessels other than cylindrical or spherical and those for which nodesign rules are provided in this Division may be designed under the
conditions set forth in U-2.
U-2(g) This Division of Section VIII does not contain rules to cover
all details of design and construction. Where complete details are not
given, it is intended that the manufacturer, subject to the acceptanceof the Inspector, shall provide details of design and construction
which will be as safe as those provided by the rules of this Division.
UG-19 Special Constructions
(c) No Design Rules
When no design rules are given and the strength of a vessel (or part)
cannot be calculated with a satisfactory assurance of accuracy,Maximum Allowable Working Pressure shall be established in
accordance with the provisions of UG-101. (Proof testing)
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(a) Maximum
Shall not be less than the mean metal temperature under operatingconditions for the part under consideration.
May be determined by computation or measurement from
equipment "in service" under equivalent operating conditions.
UG-20 Design Temperature
(b) Minimum
Is the lowest expected "in service",Determined same as for maximum temperature,
Consideration includes:
Lowest operating temperatures,
Operational upsets,
Auto refrigeration,Atmospheric conditions,
Any other source of cooling.
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(c) Maximum Design temperatures in excess of the maximum temperatures listed
in the tables referenced in UG-23 are not permitted.
In addition, design temperatures for vessels under external pressure
shall not exceed the maximum temperatures given on the external
pressure charts.
UG-20 Design Temperature
(d) The design of zones with different metal temperatures may be
based on their determined temperatures.
(e) Suggested methods for obtaining the operating temperatures of
vessel walls in service are given in Appendix C.
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UG-21 Design Pressure
When determining design pressure, consideration must include thefollowing.
At least the most severe condition if coincident pressure and
temperature expected in normal operation.
The operating and test
conditions including themaximum difference in
pressure between
The inside and outside of the
vessel,
Any two chambers of acombination unit.
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UG-98 Maximum Allowable Working Pressure
(a) It is the maximum permissible pressure at the top of thevessel in its normal operating position.
(b) The MAWP for a vessel is the maximum internal or
external pressure, including static head thereon as
determined by the rules and formulas of this Division,
together with the effect of any combination of loadings
listed in UG-22 which are likely to occur for thedesignated coincident temperature, excluding any metal
specified as corrosion allowance (UG-25).
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UG-22 Loadings
The loadings to be considered in designing a vessel shall include
those from:Internal or external design pressure (UG-21).
Weight of the vessel & normal contents under operating or test
conditions (this includes additional pressure due to the static head of
liquids).
- 1 cubic foot of water at 62F = 62.35 lb.
- 62.35 lb. /1728 cubic inches = 0.0361 lb. / cu. inch
- 0.0361 cu. inches x 12 inches = 0.433 lb./foot (for water)
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The maximum allowable tensile stress values permitted for
different materials are given in Subpart 1 of Section II, Part D.
A listing of these materials are included in Subsection C.
Materials meeting more than one specification and/or grade may
be used provided all requirements for the selected specification and/orgrade are met.
UG-23 Maximum Allowable Stress Values
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(a) the user or his designated agent (see U-2) shall specify
corrosion allowances other than those required by this Division.
Where corrosion allowances are not provided, this fact shall be
indicated in the Data Report.
UG-25 Corrosion
(b) vessels or parts subject to thinning by
CorrosionErosion
Mechanical abrasion
shall have provision made for the desired life of the vessel by a
suitable increase in the thickness over that determined by the design
formulas, or by using some other suitable method of protection. (SeeAppendix E).
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(c) Material for these purposes need not be of the same thickness
for all parts of the vessel if different rates of attack are expected for
the various parts.
(d) No additional thickness need be provided when previous
experience in like service has shown that corrosion does not occur or
is of only a superficial nature.
UG-25 Corrosion
(e) Telltale Holes
May be used to provide some positive indication when the thickness
has been reduced to a dangerous degree.
Shall not be used in vessels which are to contain lethal substances
[seeUW-2(a)], except as permitted by ULW-76 for vent holes inlayered construction.
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(e) Telltale Holes
UG-25 Corrosion
(f) Openings for Drains
Vessels subject to corrosion shall be
supplied with a suitable drain opening at
the lowest point practicable in the vessel;
or a pipe may be used extending inward
from any other location to within 1/4 in.
(6mm) of the lowest point.
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(a) The minimum required thickness of shells under internal
pressure shall not be less than that computed by the following
formulas13 except as permitted in Appendix 32 (local thin areas). In
addition, provision shall be made for any of the loadings listed in UG-
22, when such loadings are expected.
The provided thickness of the shells shall also meet the
requirements of UG-16, except as permitted in Appendix 32.
UG-16(b) requires that minimum thickness be determined after
forming and exclusive of any c.a.
UG-16(c) Mill undertolerance
UG-16(d) Pipe Undertolerance
UG-16(e) Corrosion Allowance in Design Formulas
13 Formulas in terms of outside radius and for thicknesses and pressures beyond the limits
fixed in this paragraph are given in 1-1 to 1-3.
UG-27 Thickness of Shells Under Internal Pressure
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(b) The symbols defined below are used in the formulas of thisparagraph.
t = minimum required thickness
P = internal design pressure
R = inside radius of the shell course under consideration
S = maximum allowable stress value (see UG-23 and the stresslimitations specified in UG-24
E = joint efficiency for, or the efficiency of, appropriate joint in
cylindrical or spherical shells, or the efficiency of ligaments
between openings, whichever is less For welded vessels: UW-12,
for ligaments: UG-53
UG-27 Thickness of Shells Under Internal Pressure
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(c) Cylindrical Shells. The minimum thickness or Maximum
allowable Working Pressure of cylindrical shells shall be the
greater thickness or lesser pressure as given in (1) or (2) below.
UG-27 Thickness of Shells Under Internal Pressure
(c)(l) Circumferential Stress (Longitudinal Joints)
(c)(2) Longitudinal Stress (Circumferential Joints15)
15 These formulas will govern only when the circumferential joint efficiency is less than
one-half the longitudinal joint efficiency, or when the effect of supplemental loadings
(UG-22) are being investigated.
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(c)(l) Circumferential Stress (Longitudinal Joints)
(c)(2) Longitudinal Stress (Circumferential Joints)
UG-27 Thickness of Shells Under Internal Pressure
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Example: Assume P = 150PSI S = 17, 500
R = 24 inches E=1.0
(c)(l) Circumferential stress (Longitudinal Joints)
(c)(2) Longitudinal Stress (CircumferentialJoints)
UG-27 Thickness of Shells Under Internal Pressure
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(a) The required thickness at the thinnest point after forming of
ellipsoidal, torispherical hemispherical, conical and toriconical
heads under pressure on the concave side (plus heads) shall be
computed by the appropriate formulas in this paragraph, except
as permitted in Appendix 32 (Localized Thin Areas).
UG-32 Formed Heads and Sections, Pressureon the Concave Side
(a) In addition, provision shall be made for any of the loadings
listed in UG-22. The provided thickness of the heads shall also
meet the requirements of UG-16, except as permitted in Appendix
32. (b) The thickness of an unstayed ellipsoidal or torispherical
head shall in no case be less than the required thickness of aseamless hemispherical head divided by the efficiency of the head
to shell joint.
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(c) The symbols defined below are used in the formulas of thisparagraph.
t = minimum required thickness of the head after forming
P = internal design pressure
D = inside diameter of the head skirt; or inside length of a major
axis of an ellipsoidal head; or inside diameter of a conical head at thepoint under consideration, measured perpendicular to the longitudinal
axis.
Dt = inside diameter of the conical portion of a toriconical head at
its point of tangency to the knuckle, measured perpendicular to the
axis of the cone. [ = D- 2r(l-cos a)]
UG-32 Formed Heads and Sections, Pressureon the Concave Side
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r = inside knuckle radiusS = maximum allowable stress value in tension as given in the
tables referenced in UG-23, except as limited in UG-24 and (e) below
E = lowest efficiency of any joint in the head; for hemispherical
heads this includes head-to-shell joint; for welded vessels, use the
efficiency specified in UW-12L = inside spherical or crown radius. The value of L for elliptical
heads shall be obtained from Table UG-37
a = one-half of the included (apex) angle of the cone at the center
line of the head (see fig. 1-4)
UG-32 Formed Heads and Sections, Pressureon the Concave Side
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(d) Ellipsoidal Headswith t/L >0.002.The required thickness of a dished
head of semi-ellipsoidal form, in
which half the minor axis (inside
depth of head minus head skirt) equals
one-fourth of the inside diameter of
the head skirt, shall be determined by:
UG-32 Formed Heads and Sections, Pressureon the Concave Side
NOTE: For ellipsoidal heads with t/L< 0.002, the rules of l-4(f)
shall also be met.
An acceptable approximation of a 2:1 ellipsoidal head is one witha knuckle radius of 0.17D and a spherical radius of 0.90D.
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(e)Torispherical Heads with t/L >0.002.The required thickness of a torispherical
head for the case in which the knuckle
radius is 6% of the inside crown radius and
the inside crown radius equals the outside
diameter of the skirt [see (j) below], shall
be determined by:
UG-32 Formed Heads and Sections, Pressureon the Concave Side
Note: For torispherical heads with t/l
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(f) Hemispherical Heads. When the
thickness of a hemispherical head
does not exceed 0.356L, or P does not
exceed 0.665SE, the following
formula shall apply:
UG-32 Formed Heads and Sections, Pressureon the Concave Side
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(g) Conical Heads and Sections
(Without Transition Knuckle).
The required thickness of conical
heads or conical shell sectionsthat have a half apex-angle a not
greater than 30 deg shall be
determined by:
UG-32 Formed Heads and Sections, Pressureon the Concave Side
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(h) Toriconical Heads and Sections
The required thickness of the
knuckle shall be determined by
formula (3)of l-4(d)in which:
UG-32 Formed Heads and Sections, Pressureon the Concave Side
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(i) When an ellipsoidal, torispherical, hemispherical conical ortoriconical head is of a lesser thickness than required by the rules of
this paragraph, it shall be stayed as a flat surface according to the
rules of UG-47 for braced and stayed flat plates.
UG-32 Formed Heads and Sections, Pressureon the Concave Side
(o) If a torispherical, ellipsoidal, or hemispherical head is formedwith a flattened spot or surface, the diameter of the flat spot shall
not exceed that permitted for flat heads as given in Formula (1) in
UG-34, using C = 0.25.
(p) Openings in formed heads under internal pressure shallcomply with the requirements of UG-36 through UG-47.
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(a) The minimum thickness of unstayed flat heads, cover plates and
blind flanges shall conform to the requirements of this paragraph.
Some acceptable types of flat heads and covers are shown in Fig.
UG-34.
In this figure, the dimensions of the component parts and the
dimensions of the welds are exclusive of extra metal required for
corrosion allowance.
UG-34 Unstayed Flat Heads and Covers
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(c) The thickness of flat unstayed heads, covers and blind flangesshall conform to one of the following three requirements.
(c)(l) Circular blind flanges conforming to the standards referenced
in Table U-3, when the blind flange is of the types shown in Fig. UG-
34 sketches (j) and (k).
UG-34 Unstayed Flat Heads and Covers
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(c) Flat unstayed heads, covers and blind flanges shall be
calculated by the following formula:
(c)(2)Circular
(c)(3) square, rectangular, elliptical, obround, segmented orotherwise noncircular
UG-34 Unstayed Flat Heads and Covers
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(c)(2)(a) Openings in Cylindrical or conical shells, or formed
heads shall be reinforced to satisfy the requirements of UG-37
except as given in (3) below.
(c)(2)(b) Openings in flat heads shall be reinforced as required by
UG-39.
UG-36 Openings in Pressure Vessels
(c)(3) Openings in vessels not subject to rapid fluctuation in
pressure do not require reinforcement other than that inherent in theconstruction under the following conditions:
(a) welded, brazed or flued connections with a finished opening
not larger than:
3 1/2 in. (89mm) dia. in vessel shells or heads with a required
minimum thickness of 3/8 in. (10mm) or less 2 3/8 in. (60mm) dia. in vessel shells and heads over a minimum
required thickness of 3/8 in (10mm).
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UG-36(c) exemptions to reinforcement consideration, continued... UG-36(c)(3)(b) threaded, studded or expanded connections in
which the hole cut in the shell or head is not greater than 2 3/8 in.
(60mm) dia.
UG-36 Openings in Pressure Vessels
UG-36(c)(3)(c) no two unreinforced openings, in accordance with
(a) or (b) above, shall have their centers closer to each other than thesum of their diameters
example
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(d) Openings Through Welded Joints
Additional provisions governing openings through welded joints are
given in UW-14.
UW-14 (a) Any type of opening that meets the requirements for
reinforcement given in UG-37 or UG-39 may be located in a welded
joint.
UW-14(b) Single openings meeting the requirements given in UG-36(c)(3) may be located in head-to-shell or Category B or C butt
welded joints, provided the weld meets the RT requirements of UW-51
for a length equal to three times the diameter of the opening with the
center of the hole at midlength.
Defects that are completely removed in cutting the hole shall not beconsidered in judging the acceptability of the weld.
UG-36 Openings in Pressure Vessels
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UW-14(c) In addition to meeting the radiographic requirements of(b) above, when multiple openings meeting UG-36(c)(3) are in line in
head-to-shell or Category B or C butt welded joints, the requirements
of UG-53 (ligaments) shall be met or the openings shall be reinforced
in accordance with UG-37 through UG-42.
UW-14 Openings in or Adjacent to Welds
UW-14(d) Except when the adjacent butt weld satisfies therequirements for radiography in (b) above, the edge of openings in
solid plate meeting the requirements of UG-36(c)(3) shall not be
placed closer than 1/2 in. (13mm) to the edge of a Category A, B, or
C weld for material 1 1/2 in. (38mm) thick or less.
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(b) General. The rules of this paragraph apply to all openings other
than:
Small openings, UG- 36(c)(3)
Openings in flat heads, UG-39
Openings designed as reducer sections, UG-36(e)
Large head openings, UG-36(b)(2)Tube holes with ligaments, UG-53
Reinforcement shall be provided in amount and distribution such
that the area requirements for reinforcement are satisfied for all
planes through the center of the opening and normal to the vessel
surface.
UG-37 Reinforcement Required For Openings inShells and Formed Heads
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Fig. UG-37.1
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Design Review
Design parameters can be reviewed, such as
Code Edition and Addenda
Pressure and Temperature
Materials
Size
Loadings and Service Conditions
Based upon the design parameters, fabricationrequirements can be reviewed such as:
Welding
Nondestructive Examination
Heat Treatment
Impact Testing
Forming and Bending Limitations
Pressure Testing
Data Reports and Stamping
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Based upon a review of design parameters and fabrication
requirements, you are in a better position to determine meaningful
inspection involvements using documents such as:
Calculations
Drawings & Bills of Material
Purchase & Receiving Documents
Process Control DocumentsSpecial Process Procedures (WPS, NDE, HT, etc.)
Design Review
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Design Review Tips
Has the correct construction Code Section been selected
and used?
Is the Code Edition/Addenda correct?
Have the required calculations been prepared?
Do the design documents include criteria as supplemented
by the QC system?
Are design documents reviewed/approved by appropriate
personnel?
Are you reviewing the latest revision to the design/fabrication
document?
If the design work is computer generated, have the computer
program capabilities and results been verified as accurate?